Advances in Kinetic Modeling of Dimethylcyclohexane Oxidation: From Sustainable Fuels to Combustion Chemistry

Abstract

This article provides a comprehensive overview of the kinetic modeling of dimethylcyclohexane (DMCH) oxidation, a critical component in sustainable aviation fuels (SAFs) and conventional fossil fuels. It explores the foundational combustion chemistry of DMCH isomers, detailing recent experimental methodologies for mechanism development and validation. The content addresses key challenges in model optimization and troubleshooting, alongside comparative analyses of isomer-specific reactivity and model performance against experimental data. Aimed at researchers, scientists, and development professionals in combustion and fuel science, this review synthesizes current knowledge to guide the development of accurate predictive models for cleaner and more efficient fuel design.

Foundations of DMCH Combustion Chemistry and Its Role in Sustainable Fuels

Dimethylcyclohexane (DMCH) isomers represent a crucial class of cyclic hydrocarbons in advanced fuel development, particularly for sustainable aviation fuels (SAFs). These polysubstituted cycloalkanes are recognized as vital molecular subclasses in next-generation, lignin-derived biofuels, addressing critical compatibility challenges between drop-in fuels and existing aero-engine systems [1]. Unlike conventional petroleum-based jet fuels containing 15-40wt% cycloalkanes, unconventional transportation fuels derived from biomass sources can contain up to 99wt% cycloalkanes, with dimethylcyclohexanes serving as fundamental structural motifs [1]. The relative position of methyl substituents on the cyclohexane ring (1,2-, 1,3-, or 1,4- configurations) profoundly influences their physical properties and combustion characteristics, making understanding their oxidation chemistry essential for designing cleaner, more efficient fuels [1] [2].

The aviation industry faces significant challenges in reducing greenhouse gas emissions and non-volatile particulate matter, with sustainable aviation fuels representing the most feasible near-term alternative to conventional fossil-based jet fuels [1]. Recent studies have demonstrated that replacing aromatic compounds with cycloalkanes like dimethylcyclohexanes provides comparable density and material compatibility (e.g., O-ring swelling capabilities) while significantly reducing soot emissions and contrail formation [1]. This positions DMCH isomers as strategically important components for developing full-component bio-based aviation fuels that meet industry requirements without requiring blending with conventional fuels.

Comparative Properties of DMCH Isomers

Table 1: Fundamental Properties of Dimethylcyclohexane Isomers

Isomer	Molecular Formula	Molecular Weight (g/mol)	CAS Registry Number	Key Structural Features
1,1-dimethylcyclohexane	C₈H₁₆	112.2126	590-66-9	Geminal methyl groups, non-planar geometry [3]
1,2-dimethylcyclohexane	C₈H₁₆	112.2126	Not specified	Vicinal methyl groups, complex puckering environment
1,3-dimethylcyclohexane	C₈H₁₆	112.2126	Not specified	Meta-substituted methyl groups
1,4-dimethylcyclohexane	C₈H₁₆	112.2126	Not specified	Para-substituted methyl groups

Table 2: Thermochemical Properties of 1,1-Dimethylcyclohexane

Property	Value	Conditions	Reference
Standard Gas Phase Entropy (S°gas)	364.93 J/mol·K	Standard conditions	Huffman H.M., 1949 [3]
Constant Pressure Heat Capacity (Cp,gas)	38.15 J/mol·K	50K, 1 bar	Thermodynamics Research Center, 1997 [3]
Constant Pressure Heat Capacity (Cp,gas)	158.5 J/mol·K	298.15K, 1 bar	Thermodynamics Research Center, 1997 [3]
Constant Pressure Heat Capacity (Cp,gas)	418.4 J/mol·K	1000K, 1 bar	Thermodynamics Research Center, 1997 [3]

The thermochemical behavior of DMCH isomers exhibits significant temperature dependence, particularly in heat capacity values that increase substantially with temperature [3]. This property directly impacts energy density and combustion characteristics, making accurate thermochemical data essential for kinetic modeling of fuel oxidation processes.

Oxidation Chemistry and Kinetic Modeling

Experimental Reactivity Trends

Table 3: Comparative Oxidation Characteristics of DMCH Isomers

Isomer	Low-Temperature Reactivity	High-Temperature Reactivity	Aromatics Formation Potential	Key Decomposition Pathways
1,2-DMCH	Lower	Higher	Higher peak concentrations	H-abstraction/β-scission sequences, five-membered-ring chemistry [1]
1,3-DMCH	Higher	Lower	Lower peak concentrations	C8 hydroperoxides dissociation, alkenyl/allylic radicals [1]
1,4-DMCH	Moderate (theoretical)	Moderate (theoretical)	Not specified	Cyclic ether formation, pressure-dependent pathways [2]

Experimental studies reveal that dimethylcyclohexane isomers exhibit distinct oxidation behaviors dependent on their molecular architecture. 1,2-DMCH demonstrates higher high-temperature reactivity, while 1,3-DMCH shows enhanced low-temperature reactivity [1]. These differences originate from variations in chemical bond dissociation enthalpies and the relative contributions of different reaction channels to carbon flux and ḢO formation, as identified through rate of production (ROP) and sensitivity analyses [1].

The formation of aromatic compounds, crucial precursors to soot emissions, displays significant isomer dependence with generally higher peak concentrations observed in 1,2-DMCH oxidation compared to 1,3-DMCH [1]. This phenomenon arises because aromatics formation proceeds predominantly through five-membered-ring chemistry involving C5 resonantly stabilized radicals and six-membered-ring chemistry involving traditional H-abstraction/β-scission sequences, pathways strongly influenced by fuel decomposition reactivity [1].

Low-Temperature Oxidation Pathways

The reaction of dimethylcyclohexyl radicals with molecular oxygen represents a critical pathway in low-temperature oxidation chemistry, particularly relevant to novel biodiesel and jet fuel applications [2]. Theoretical investigations using Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) simulations reveal temperature- and pressure-dependent branching ratios for 1,4-dimethylcyclohexyl + O₂ reactions [2].

For primary cy-C₈H₁₅ + O₂ reactions (ROO-1), the formation of five-membered cyclic ether P7p (4-methyl-6-oxabicyclo[3.2.1]octane) and six-membered cyclic ether P10p (1-methyl-2-oxabicyclo[2.2.2]octane) are highly pressure-dependent below 0.01 bar and kinetically favorable below 700 K [2]. For tertiary cy-C₈H₁₅ + O₂ (ROO-2), the formation of P5t (1,4-dimethyl-6-oxabicyclo[3.1.1]heptane) and P8t (1-methoxy-1,4-dimethylcyclohexane) are similarly pressure-dependent and kinetically favorable between 600-750 K [2]. Secondary cy-C₈H₁₅ + O₂ (ROO-3) reactions show competition between P4s (1,4-dimethyl-6-oxabicyclo[3.1.1]heptane) and P6s (1,4-dimethyl-7-oxabicyclo[4.1.0]heptane) formation with ROO-3 stabilization at pressures lower than 0.01 bar [2].

Experimental Protocols for Oxidation Studies

Flow Reactor Oxidation Methodology

Apparatus Configuration:

• Employ a laminar flow tubular reactor (LFTR) consisting of a 1000 mm quartz tube with 6 mm inner diameter and 2 mm thickness [1].
• Utilize a tubular furnace with 550 mm total length and 350 mm heating region for temperature control [1].
• Implement a movable K-type thermocouple for centerline temperature profiling along the reactor length [1].

Experimental Procedure:

• Maintain reactor at atmospheric pressure under controlled lean (φ = 0.25) and rich (φ = 1.5) conditions [1].
• Introduce DMCH isomers vaporized in carrier gas across temperature range covering low- to high-temperature oxidation regimes [1].
• Extract gas samples at various reactor positions corresponding to specific reaction temperatures [1].
• Quantify mole fractions of reactants, intermediates, and products using online Gas Chromatography (GC) and Gas Chromatography-Mass Spectrometry (GC-MS) techniques [1].
• Identify vital species concentrations including carbon monoxide, carbon dioxide, oxygenated intermediates, and aromatic compounds [1].

Data Analysis:

• Construct detailed kinetic models for each DMCH isomer covering comprehensive low- to high-temperature oxidation chemistry [1].
• Validate model predictions against experimental speciation data [1].
• Perform rate of production (ROP) analysis to identify dominant consumption pathways [1].
• Conduct sensitivity analysis to determine reactions most significantly influencing fuel reactivity [1].

Jet-Stirred Reactor Pyrolysis Protocol

Experimental Setup:

• Conduct experiments using a jet-stirred reactor (JSR) coupled with synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) [4].
• Maintain system at atmospheric pressure (760 Torr) across 770-1130 K temperature range [4].

Methodology:

• Employ gas and liquid flow controllers for precise feedstock delivery [4].
• Utilize liquid evaporation and mixing system for homogeneous fuel/carrier gas mixtures [4].
• Implement ultrasonic molecular beam sampling device for efficient product transfer to detection system [4].
• Identify and quantify approximately 23 pyrolysis products including acetylene, ethylene, propene, 1,3-butadiene, 2-butene, 1-pentene, 2-methyl-2-butene, 2-methyl-2-hexene, 3-methyl-2-hexene, and aromatic species including benzene, styrene, and naphthalene [4].

Kinetic Modeling Implementation:

• Develop detailed kinetic mechanisms containing 1756 species and 6023 reactions for DMCH pyrolysis [4].
• Simulate pyrolysis using perfectly stirred reactor module in Chemkin-Pro software [4].
• Analyze consumption pathways through rate of production and sensitivity analyses [4].
• Compare reactivity trends across alkane isomers to elucidate branching effects [4].

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Research Materials for DMCH Oxidation Studies

Reagent/Equipment	Specification	Research Function	Experimental Application
1,2-dimethylcyclohexane	High-purity (≥99%)	Primary reactant	Oxidation and pyrolysis studies [1]
1,3-dimethylcyclohexane	High-purity (≥99%)	Isomeric comparator	Structure-reactivity investigations [1]
1,4-dimethylcyclohexane	High-purity (≥99%)	Reference compound	Low-temperature oxidation kinetics [2]
Laminar Flow Tubular Reactor	Quartz, 6mm ID, 1000mm length	Oxidation environment	Species concentration measurements [1]
Jet-Stirred Reactor	Custom-built, atmospheric pressure	Pyrolysis environment	Product distribution analysis [4]
Synchrotron VUV Photoionization	Tunable VUV light source	Selective detection	Isomer-specific product identification [4]
Gas Chromatograph-Mass Spectrometer	Online configuration	Speciation analysis	Quantitative species mole fractions [1]
N-chlorosuccinimide	Reagent grade	Halolactonization agent	Synthesis of halogenated analogs [5]
N-bromosuccinimide	Reagent grade	Bromolactonization agent	Synthesis of bicyclic lactone derivatives [5]

Applications in Sustainable Fuel Development

The strategic importance of dimethylcyclohexanes extends beyond conventional fossil fuels to emerging sustainable fuel platforms. As key cyclic components in next-generation biodiesel and jet fuels, DMCH isomers play a central role in low-temperature combustion strategies [2]. Their structural motifs serve as general prototypes for understanding oxidation behavior of more complex alkyl cyclohexanes present in advanced biofuel candidates like bisabolane [2].

The branching patterns and substitution geometry of DMCH isomers significantly influence fuel properties including density, kinematic viscosity, and energy density - critical parameters for aviation fuel applications [1]. Recent investigations have demonstrated that polysubstituted cycloalkanes derived from lignin resources can effectively replace aromatic compounds while maintaining necessary material compatibility and reducing soot formation propensity [1]. This positions dimethylcyclohexanes as enabling components for developing fully bio-based aviation fuels that meet stringent industry specifications without requiring blending with conventional petroleum-derived fractions.

Research has further revealed that the proximity of methyl substituents influences gaseous product yields in thermal cracking processes, with closer methyl group proximity generally resulting in higher yields [1]. This structure-reactivity relationship provides valuable guidance for molecular design of future fuel components with tailored decomposition characteristics.

The Imperative for Sustainable Aviation Fuels (SAFs) and the Role of Cycloalkanes

The aviation industry accounts for approximately 2–3% of global greenhouse gas emissions, creating mounting pressure to transition to low-carbon energy solutions while maintaining stringent performance standards [6] [7]. Sustainable Aviation Fuels (SAFs) have emerged as a pivotal component in achieving these environmental goals, offering the potential to significantly reduce greenhouse gas emissions and particulate matter [6]. Among various SAF pathways, Hydroprocessed Esters and Fatty Acids (HEFA) fuels represent one of the most mature technologies, with ASTM certification for use in blends of up to 50% with conventional Jet A [6] [8]. However, these biogenic fuels face performance limitations, including limited energy density and lack of aromatic-like properties, which hinder their full deployment [6].

Cycloalkanes have emerged as promising additives to address these limitations. Unlike carcinogenic and soot-forming aromatics in conventional jet fuels, bio-derived cycloalkanes offer comparable density and combustion properties while mitigating environmental and health impacts [6] [9]. These compounds contribute desirable physical and combustion properties, including high energy density, low sooting propensity, and potential for replacing aromatic hydrocarbons to provide adequate seal swelling properties in fuel systems [9]. Advanced production pathways now enable cycloalkane-rich SAF production from diverse feedstocks, including lignocellulosic biomass and food waste, through hydrotreating processes [9] [7]. Within the context of kinetic modeling research, understanding the oxidation chemistry of cycloalkane structures, including dimethylcyclohexane variants, provides critical insights for optimizing next-generation SAF formulations.

Cycloalkanes as Performance-Enhancing Additives

Structural Advantages over Aromatics

Bio-derived cycloalkanes serve as sustainable alternatives to aromatic compounds in conventional jet fuels. Aromatics pose dual challenges as both carcinogenic substances and major precursors to soot formation, creating significant environmental and health concerns [6]. Cycloalkanes mitigate these risks while maintaining essential fuel properties. Specifically, they contribute to favorable energy density, acceptable kinematic viscosity, and adequate freezing point characteristics required for aviation operations [6]. Some cycloalkanes additionally exhibit o-ring swelling behavior comparable to aromatics, making them compliant with ASTM D7566 standards for aviation fuels and ensuring material compatibility with existing engine components and fuel systems [6].

Molecular Structure and Combustion Performance

The performance of cycloalkanes in SAF formulations varies significantly depending on their molecular structure. Research indicates that cycloalkanes with larger ring sizes demonstrate substantial potential as aromatic substitutes in conventional Jet-A blends [6]. Monosubstituted and polysubstituted ring systems exhibit different decomposition pathways during combustion, influencing fuel reactivity under engine-relevant conditions [6]. For instance, polysubstituted cycloalkanes tend to exhibit higher yield sooting indices, which may limit their applicability in certain SAF formulations targeting reduced particulate emissions [6]. The carbon number and branching patterns additionally affect physical properties and combustion characteristics, necessitating careful selection based on application requirements.

Experimental Protocols for SAF/Cycloalkane Combustion Analysis

Shock Tube Pyrolysis with Laser Absorption Spectroscopy

Principle: This methodology investigates fuel decomposition pathways and stable intermediate formation under engine-relevant high-temperature conditions, providing essential data for validating chemical kinetic models [6].

Materials and Equipment:

• Stanford University Kinetics Shock Tube (KST) with 14.13 cm internal diameter
• 3.35 m driver section and 8.5 m driven section
• Polycarbonate diaphragms
• Five piezoelectric pressure transducers for incident shock velocity measurement
• Multiwavelength laser absorption spectroscopy system
• OH* emission detection at 306 nm for ignition determination

Procedure:

• Prepare fuel/argon test mixtures at approximately 1% fuel concentration by volume.
• Utilize helium as the driver gas to generate test durations of approximately 2 ms.
• Conduct experiments at nominal pressures of 2.2 atm over a temperature range of 1150–1450 K.
• Record incident shock velocities at five axial positions along the tube.
• Measure time-resolved mole fractions of stable intermediates (methane, ethylene, >C2 alkenes) using multiwavelength laser absorption.
• Determine ignition delay times (IDT) using OH* emission at 306 nm for stoichiometric mixtures with oxygen at nominal pressure of 2 atm over 1200–1400 K.
• Post-process temperature and pressure using standard shock relations based on measured shock velocity and initial conditions.
• Analyze time histories of stable intermediates to elucidate decomposition pathways and fuel reactivity.

Flow Reactor Speciation with Molecular Beam Mass Spectrometry

Principle: This approach enables in-depth investigation of combustion chemistry by simultaneously identifying multiple intermediates and reaction channels controlling product formation [8].

Materials and Equipment:

• High-temperature laminar flow reactor (ceramic tube, 1497 mm length, 40 mm inner diameter)
• Coriolis mass flow meters (±0.5% accuracy) for precise flow control
• Vaporizer system for fuel introduction (Bronkhorst CEM)
• Molecular beam mass spectrometry time-of-flight detection system
• Two-stage differential pumping system
• Electron impact time-of-flight mass spectrometer (mass resolution R = 3000)
• Quadrupole mass spectrometer in ionization chamber

Procedure:

• Prepare highly diluted fuel mixtures (>99% Ar) to suppress volumetric heat release.
• Adjust oxygen concentration to achieve desired stoichiometry (Φ = 0.8 for lean, Φ = 1.2 for rich conditions).
• Determine exact stoichiometry using low-resolution pulsed NMR to measure fuel hydrogen content.
• Feed premixed gases through a tempered flange equipped with a porous bronze plug to establish homogeneous flow conditions.
• Maintain fuel partial pressures below 100 Pa to ensure complete evaporation.
• Operate reaction segment within a high-temperature oven capable of reaching 1900 K.
• Sample gases at reactor exit and transfer to high vacuum (10⁻⁶ mbar) through a two-stage differential pumping system to quench reactions.
• Apply soft electron energies (10.6 eV) to avoid species fragmentation during ionization.
• Contemporarily track major species using quadrupole mass spectrometer operated at higher electron energy (70 eV).
• Analyze speciation profiles to validate chemical kinetic models and understand fuel-specific oxidation pathways.

Data Presentation and Analysis

Quantitative Analysis of Cycloalkane Blending Effects

Table 1: Experimental results from shock tube pyrolysis of HEFA/cycloalkane blends at 2.2 atm

Fuel Blend	Cycloalkane Type	Temperature Range (K)	Methane Yield	Ethylene Yield	>C2 Alkene Yield	Ignition Delay (ms)
HEFA + 30% nBCH	n-butylcyclohexane	1150-1450	Moderate	High	Moderate	Shortest
HEFA + 30% PMT	p-menthane	1150-1450	Lowest	Moderate	Highest	Intermediate
HEFA + 30% DMCO	1,4-dimethylcyclooctane	1150-1450	Highest	Lowest	Lowest	Longest

Table 2: Properties of cycloalkane-rich SAF from different production pathways

Production Pathway	Feedstock	Cycloalkane Content (wt%)	SAF Yield (wt%)	Oxygen Content (wt%)	ASTM D7566 Compliance
Hydrotreating CFP Oil [9]	Lignocellulosic Biomass	89-92%	39-40%	<0.01%	Yes
Cobalt Molybdenum HTL [7]	Food Waste	Not Specified	Not Specified	Not Specified	Yes
Bicycloalkanes from Corn Stover [10]	Mixed C5/C6 Sugars	Not Specified	83.8% (mol)	Not Specified	Yes

Research Reagent Solutions

Table 3: Essential research reagents and materials for SAF/cycloalkane experimentation

Reagent/Material	Function/Application	Specifications
n-butylcyclohexane (nBCH)	Cycloalkane additive for HEFA blends	C10 monosubstituted cycloalkane; enables study of side-chain structure effects
p-menthane (PMT)	Cycloalkane additive for HEFA blends	1-isopropyl-4-methylcyclohexane; polysubstituted structure
1,4-dimethylcyclooctane (DMCO)	Cycloalkane additive for HEFA blends	8-membered ring; enables study of ring size effects
Sulfided NiMo/Al₂O₃ Catalyst	Hydrotreating CFP oils to cycloalkanes	Converts lignocellulosic biomass-derived intermediates to cycloalkanes
Cobalt Molybdenum Catalyst	Hydrotreating HTL biocrude	Effective denitrogenation and deoxygenation for food waste-derived biocrude
Argon Diluent Gas	Shock tube and flow reactor experiments	Creates inert environment; suppresses heat release for controlled conditions

Kinetic Modeling and Visualization

Experimental Workflow for Kinetic Parameter Determination

Cycloalkane Decomposition Pathways in HEFA Blends

Cycloalkanes represent critical components for advancing Sustainable Aviation Fuels, addressing both the performance limitations of pure HEFA fuels and the environmental concerns associated with aromatic compounds. The experimental protocols outlined—shock tube pyrolysis with laser absorption spectroscopy and flow reactor speciation with molecular beam mass spectrometry—provide robust methodologies for investigating combustion behavior and generating validation data for kinetic models. Quantitative analysis demonstrates that cycloalkane structural variations significantly influence fuel decomposition pathways and global combustion parameters, with ring size, substitution pattern, and carbon number serving as key determinants. The integration of these experimental approaches with chemical kinetic modeling, particularly focusing on dimethylcyclohexane oxidation chemistry, enables predictive capability for fuel performance and supports the rational design of next-generation SAF formulations. Continued research should focus on expanding the kinetic database for diverse cycloalkane structures, optimizing production pathways for cycloalkane-rich SAFs from sustainable feedstocks, and validating model predictions across broader operational conditions relevant to aviation gas turbines.

Comparative Properties of 1,2- and 1,3-Dimethylcyclohexane Isomers

Within the development of sustainable aviation fuels (SAFs), polysubstituted cycloalkanes have been identified as vital components to overcome the compatibility issues between "drop-in" fuels and aero-engines [1]. Unlike conventional jet fuels containing 15–40 wt% cycloalkanes, next-generation, lignin-based SAFs can contain up to 99 wt% cycloalkanes, often with more branched moieties and double-ring structures [1]. Among these, the simplest dimethylcyclohexane (DMCH) isomers, namely 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH), serve as key cyclic components in both sustainable biofuels and fossil fuels [1] [11]. Their combustion chemistry remains underexplored despite their significance. This application note details their comparative properties and oxidation chemistries, providing essential protocols and data for researchers and scientists engaged in kinetic modeling and fuel development.

Structural and Conformational Properties

The fundamental differences in the properties of the DMCH isomers originate from their distinct molecular structures and the associated conformational stability.

Conformational Analysis

The relative spatial orientation of the two methyl groups on the cyclohexane ring defines their conformational preferences and stability, which can influence their physical properties and reactivity.

Table 1: Conformational Stability of DMCH Isomers

Isomer	Stereoisomer	Most Stable Conformation	Key Stabilizing Feature	Strain Energy of Less Stable Conformer (kJ/mol)
1,2-DMCH	cis	One methyl equatorial, one methyl axial [12] [13]	Minimizes 1,3-diaxial interactions [12]	11.4 (both conformers are equal in energy) [13]
1,2-DMCH	trans	Both methyls equatorial [12] [13] [14]	Avoids all 1,3-diaxial interactions [13]	11.4 (vs. diequatorial) [13]
1,3-DMCH	cis	Both methyls equatorial [15]	Avoids all 1,3-diaxial interactions [15]	Not Specified
1,3-DMCH	trans	One methyl equatorial, one methyl axial [15]	Minimizes 1,3-diaxial interactions [15]	Not Specified

Structural Influences on Physical Properties

The molecular structure directly impacts physical properties relevant to fuel performance. Although quantitative data like density and cetane number for the specific isomers are not provided in the search results, general trends can be inferred from the literature. The proximity of the methyl groups in 1,2-DMCH is reported to yield a higher gaseous product yield during thermal cracking compared to 1,3-DMCH, suggesting a higher reactivity is influenced by the molecular structure [1].

Oxidation Chemistry and Kinetic Modeling

A comparative experimental and kinetic modeling study reveals significant differences in the oxidation reactivity and pathways of the two DMCH isomers [1].

Comparative Reactivity and Product Formation

Experimental data from an atmospheric flow reactor under both lean and rich conditions show that the reactivity of the isomers is temperature-dependent.

Table 2: Comparative Oxidation Properties of D12MCH and D13MCH

Property	1,2-Dimethylcyclohexane (D12MCH)	1,3-Dimethylcyclohexane (D13MCH)
High-Temperature Reactivity	Higher [1]	Lower [1]
Low-Temperature Reactivity	Lower [1]	Higher [1]
Aromatics Formation	Higher peak concentrations [1]	Lower peak concentrations [1]
Key Decomposition Pathways	H-abstractions, unimolecular dissociations, and β-scission reactions [1]	H-abstractions, unimolecular dissociations, and β-scission reactions [1]
Ignition Reactivity (Engine Conditions)	Lower ignition reactivity (order: ECH > D13MCH > D12MCH) [1]	Higher ignition reactivity than D12MCH [1]

The difference in reactivity is attributed to factors such as the chemical bond dissociation enthalpies and the contributions of different channels to carbon flux and ȮH radical formation [1]. The higher yield of aromatics from D12MCH oxidation is linked to fuel decomposition reactivity involving five-membered-ring chemistry with C5 resonantly stabilized radicals and six-membered-ring chemistry [1].

Kinetic Modeling Insights

Detailed kinetic models for D12MCH and D13MCH have been constructed separately, covering low- to high-temperature oxidation chemistry and validated against experimental data [1]. These models help explain the observed reactivity trends through Rate of Production (ROP) and sensitivity analyses. The models identify that H-migrations and dissociations of C8 hydroperoxides and alkenyl/allylic radicals are responsible for product formation [1]. The construction of such a model for D13MCH can start from a base mechanism, such as an n-heptane oxidation model covering detailed C0–C7 chemistry, and incorporate specific reactions for the cycloalkane [1] [16].

Experimental Protocols

The following protocols summarize the key methodologies used in the cited studies to investigate the oxidation chemistry of dimethylcyclohexane isomers.

Protocol: Flow Reactor Oxidation and Speciation

This protocol is adapted from studies investigating DMCH oxidation in a laminar flow tubular reactor (LFTR) with online species detection [1].

Objective: To measure the mole fractions of important species and intermediates produced during the oxidation of DMCH isomers as a function of temperature.

Research Reagent Solutions:

• Fuel: High-purity 1,2- or 1,3-dimethylcyclohexane.
• Oxidizer: High-purity oxygen (O₂).
• Carrier/Diluent Gas: Inert gas, such as nitrogen (N₂) or helium (He).
• Internal Standards: For gas chromatography calibration.

Procedure:

• Vaporization and Mixing: The liquid fuel is vaporized in a heated chamber and thoroughly mixed with the oxidizer and diluent gas. The equivalence ratio (ϕ) is precisely controlled (e.g., 0.25 for lean and 1.5 for rich conditions) [1].
• Flow Reactor Oxidation: The premixed gas stream is introduced into a laminar flow tubular reactor (e.g., a 1000 mm quartz tube with a 6 mm inner diameter) housed within a tubular furnace. The furnace heats the reactor across a wide temperature range (e.g., from low to high temperatures relevant to combustion) [1].
• Temperature Measurement: A movable thermocouple (e.g., K-type) is used to measure the centerline temperature profile along the reactor length to ensure accurate temperature control and data correlation [1].
• Sample Extraction and Quenching: After reacting, the gas mixture is rapidly extracted and quenched (cooled) to freeze the chemical reactions and preserve the composition of intermediates and products [1].
• Species Identification and Quantification: The quenched gas sample is analyzed using online Gas Chromatography (GC) and Gas Chromatography–Mass Spectrometry (GC–MS). These techniques separate the complex mixture and provide both the identity and mole fraction of various species [1].

Protocol: Ignition Delay Time Measurement

This protocol is based on studies utilizing reflected shock waves to measure high-temperature ignition delay times [16].

Objective: To determine the ignition delay times of DMCH isomers at elevated temperatures and pressures relevant to engine conditions.

Research Reagent Solutions:

• Fuel: High-purity 1,3-dimethylcyclohexane (D13MCH).
• Oxidizer: Oxygen (O₂).
• Diluent Gas: Argon (Ar), to control the pressure and temperature upon shock arrival.

Procedure:

• Mixture Preparation: A gaseous mixture of fuel vapor, O₂, and Ar is prepared in a specified ratio inside a stainless-steel driven section of a shock tube. The mixture is allowed to homogenize [16].
• Shwave Generation: The driver section is pressurized until a diaphragm ruptures, sending a pressure wave down the tube. This wave reflects off the end wall, creating a region of uniform, high-temperature and high-pressure gas (e.g., 1049–1544 K and 3.0–12 atm) [16].
• Ignition Monitoring: The ignition event is tracked by monitoring pressure at the end wall using a piezoelectric pressure transducer. The ignition delay time is defined as the time interval between the arrival of the reflected shock wave at the end wall and the subsequent rapid pressure rise associated with ignition [16].
• Laser Absorption (Optional): Mid-infrared direct laser absorption at 3.39 μm can be used simultaneously to measure fuel concentration time histories under both ignition and pyrolytic conditions, providing additional kinetic data [16].

The Scientist's Toolkit

Table 3: Essential Research Reagents and Equipment

Reagent / Equipment	Function in DMCH Research
Laminar Flow Tubular Reactor (LFTR)	Provides a controlled environment for studying oxidation chemistry over a wide temperature range at atmospheric pressure, allowing for species sampling [1].
Shock Tube	Enables the study of high-temperature ignition kinetics and pyrolysis under well-defined conditions of temperature and pressure (e.g., 3-12 atm) [16].
Gas Chromatograph (GC) / Mass Spectrometer (MS)	Used for the online identification and quantification of stable species and intermediates formed during oxidation or pyrolysis experiments [1].
Synchrotron Vacuum Ultraviolet Photoionization Mass Spectrometry (SVUV-PIMS)	A powerful analytical technique used in pyrolysis studies to identify and measure reactive intermediates and radicals that are difficult to detect with conventional GC/MS [4].

Reaction Pathways and Workflow Visualization

The following diagrams illustrate the key experimental workflow and the generalized reaction network for DMCH oxidation based on kinetic modeling studies.

Experimental Workflow for DMCH Oxidation Kinetics

Generalized DMCH Oxidation Reaction Network

The oxidation chemistry of cyclic alkanes, such as dimethylcyclohexane (DMCH), is of paramount importance in the development of sustainable aviation fuels (SAFs) and the optimization of combustion systems. These compounds are key constituents of conventional fossil fuels and are expected to be vital molecular subclasses in next-generation, lignin-derived biofuels [1]. A critical aspect of their combustion behavior is the fundamental divergence between high-temperature and low-temperature oxidation pathways. This application note delineates these distinct reaction regimes, provides detailed experimental protocols for their investigation, and frames the discussion within the context of kinetic modeling research for DMCH isomers, specifically 1,2-DMCH and 1,3-DMCH.

Fundamental Reaction Pathways

The oxidation of hydrocarbons proceeds via markedly different chemical mechanisms depending on the temperature regime. These differences are not merely kinetic but involve fundamentally distinct initiating steps and dominant reaction classes.

High-Temperature Oxidation (> 1100 K)

At elevated temperatures, fuel oxidation is characterized by fast, radical-driven pyrolysis and oxidation sequences that are relatively insensitive to fuel molecular structure [17].

• Primary Initiation: The process is typically initiated by unimolecular decomposition and H-abstraction by small radicals (Ḣ, ȮH, ḢȮ₂) [18].
• Core Mechanism: The high-temperature pathway is dominated by β-scission reactions of fuel radicals. These reactions rapidly produce smaller olefins and alkyl radicals, which subsequently feed into the well-established C0-C4 foundational chemistry, ultimately leading to the final products CO, CO₂, and H₂O [17] [18]. For methylcyclohexane (MCH), major observed products include C₂H₄, CH₂O, CO, and CO₂ [18].
• Fuel Specificity: The global combustion properties at high temperatures are relatively insensitive to the detailed structure of the parent fuel [17].

Low-Temperature and NTC Oxidation (< 850 K to ~1100 K)

Low-temperature oxidation, including the Negative Temperature Coefficient (NTC) regime where reactivity paradoxically decreases with increasing temperature, is governed by a complex, multi-step mechanism that is highly sensitive to fuel molecular structure [17] [1].

• Primary Initiation: The mechanism is initiated by H-abstraction from the fuel molecule, primarily by ȮH radicals, to form alkyl radicals (R˙) [17].
• The Oxygen Addition Cascade: The radical site on R˙ allows for addition of molecular oxygen (O₂), forming alkylperoxy radicals (ROO˙). These ROO˙ radicals can undergo internal isomerization via intramolecular H-atom transfer, forming hydroperoxy alkyl radicals (QOOH). The QOOH radicals can then undertake a second O₂ addition, leading to a complex sequence that ultimately produces ketohydroperoxides (KHP) and additional ȮH radicals. The decomposition of KHPs is a key chain-branching step that promotes ignition [17].
• Fuel Specificity: The feasibility of these pathways, particularly the internal isomerization steps, is strongly dependent on the fuel's molecular structure (e.g., the size of the cyclic ring and the position of alkyl substituents), leading to pronounced differences in global reactivity between isomers [1].

Table 1: Comparative Overview of High-Temperature vs. Low-Temperature Oxidation Pathways

Feature	High-Temperature Oxidation	Low-Temperature Oxidation
Temperature Range	> 1100 K [17]	< 850 K to ~1100 K (NTC regime) [17]
Primary Initiation	Unimolecular decomposition & H-abstraction [18]	H-abstraction to form fuel radicals (R˙) [17]
Dominant Chemistry	β-scission of fuel radicals [17]	O₂ addition, isomerization, and second O₂ addition [17]
Key Intermediates	Small olefins (e.g., C₂H₄), aldehydes (e.g., CH₂O) [18]	Alkylperoxy radicals (ROO˙), QOOH, ketohydroperoxides [17]
Sensitivity to Fuel Structure	Low [17]	High [17] [1]
Characteristic Products	CO, CO₂, H₂O, C₂H₄ [18]	Aldehydes, alkenes, conjugate alkenes [17]

The following diagram illustrates the core logical relationships and divergent pathways between these two temperature regimes.

Application to Dimethylcyclohexane Oxidation

The fundamental pathways described above manifest distinctly in the oxidation of DMCH isomers. Experimental and modeling studies reveal significant isomeric effects on reactivity.

• 1,3-DMCH vs. 1,2-DMCH: 1,3-DMCH exhibits higher low-temperature reactivity, while 1,2-DMCH exhibits higher high-temperature reactivity [1]. This difference can be attributed to variations in chemical bond dissociation enthalpies and the subsequent favorability of the O₂ addition pathways at low temperatures.
• Product Distribution: The molecular structure also influences product speciation. The peak concentrations of aromatic compounds are generally higher in the oxidation of 1,2-DMCH compared to 1,3-DMCH. This is attributed to fuel decomposition reactivity that engages both five-membered-ring chemistry involving C₅ resonantly stabilized radicals and traditional sequences of H-abstraction and β-scission [1].

Table 2: Experimental Observations for DMCH Isomer Oxidation

Parameter	1,2-Dimethylcyclohexane (D12MCH)	1,3-Dimethylcyclohexane (D13MCH)
High-Temperature Reactivity	Higher [1]	Lower
Low-Temperature Reactivity	Lower	Higher [1]
Aromatics Formation	Higher peak concentrations [1]	Lower peak concentrations
Key Decomposition Feature	Favors pathways leading to aromatics [1]	Less favorable for aromatics formation

Experimental Protocols

To investigate these reaction pathways and develop robust kinetic models, specific experimental setups are employed. The following protocols detail two key methods.

Protocol: Laminar Flow Tubular Reactor (LFTR) for Speciation Studies

This protocol is designed for measuring species concentrations during the oxidation of DMCH isomers at atmospheric pressure over a wide temperature range, providing data for model validation [1].

• Apparatus Setup:

  • Utilize a quartz flow reactor tube (e.g., 1000 mm length, 6 mm inner diameter).
  • Enclose the reactor within a tubular furnace with a controlled heating zone (e.g., 550 mm total length, 350 mm heating region).
  • Employ a calibrated, movable K-type thermocouple to measure the centerline temperature profile.

• Gas and Fuel Delivery:

  • Use mass flow controllers to precisely meter oxidizer (O₂) and diluent (N₂ or Ar) gases.
  • Deliver the liquid DMCH fuel isomer (e.g., 1,2-DMCH or 1,3-DMCH) using a syringe pump, vaporizing it in a heated chamber before mixing with the gas stream.
  • Establish the desired equivalence ratio (e.g., ϕ = 0.25 for lean, 1.5 for rich conditions) [1].

• Reaction and Sampling:

  • Maintain the system at atmospheric pressure.
  • Ramp the furnace temperature according to the experimental matrix.
  • At each temperature set-point, extract a small sample of the post-reaction gas mixture via a heated sampling line.

• Product Analysis:

  • Analyze the gas sample using online Gas Chromatography (GC) and/or Gas Chromatography-Mass Spectrometry (GC-MS).
  • Identify and quantify the mole fractions of key species, including stable intermediates, products, and remaining fuel.

• Data Output: The primary data consists of mole fraction profiles for all quantified species as a function of reactor temperature.

The workflow for this experimental protocol is summarized below.

Protocol: Shock Tube for Ignition Delay Time Measurement

This protocol outlines the measurement of ignition delay times (IDTs) behind reflected shock waves, a key metric for validating kinetic models at high temperatures and pressures [16].

• Shock Tube Preparation:

  • Ensure the shock tube's driven and driver sections are evacuated to a high base vacuum.
  • Clean internal surfaces to prevent catalytic interference.

• Test Mixture Preparation:

  • Manometrically prepare the reactive test gas mixture (DMCH/O₂/Ar) in a specialized mixing tank. Allow sufficient time for homogenization.
  • The mixture composition is defined by the desired equivalence ratio and pressure.

• Experimental Execution:

  • Fill the driven section with the test mixture to a specified initial pressure.
  • Rupture the diaphragm separating the driven and driver sections, generating a incident shock wave.
  • The shock wave reflects from the end wall, creating a region of uniform, high-temperature and high-pressure gas (the core test region).

• Data Acquisition:

  • Monitor the ignition event using suitable diagnostics, such as:
    • Pressure transducers to track the shock velocity and pressure rise during ignition.
    • Photodetectors focused on OH* chemiluminescence at ~307 nm to define the instant of ignition.
  • The ignition delay time (τ) is defined as the time interval between the arrival of the reflected shock wave at the end wall and the subsequent sharp rise in OH* emission or pressure.

• Data Output: A dataset of ignition delay times as a function of temperature, pressure, and equivalence ratio.

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Reagents and Materials for DMCH Oxidation Studies

Reagent/Material	Function/Application	Example & Key Characteristics
DMCH Isomers	Model Fuel Compounds: Serve as representative cyclic alkane structures in surrogate fuel formulations for kinetic studies.	1,2-Dimethylcyclohexane (D12MCH) & 1,3-Dimethylcyclohexane (D13MCH); >99% purity recommended to minimize impurity-driven side reactions [1].
Oxidizers & Diluents	Reaction Atmosphere Control: O₂ acts as the oxidizer. Inert gases control concentration, pressure, and act as a thermal buffer.	Oxygen (UHP Grade): High purity to prevent contamination. Argon/Nitrogen (UHP Grade): Chemically inert diluent [1] [16].
Catalytic Materials	Heterogeneous Catalysis Studies: Solid supports for immobilizing molecular catalysts to study decomposition and oxidation mechanisms.	SBA-15 (Mesoporous Silica): High-surface-area substrate with a hexagonal pore structure, used for supporting metal complexes like manganese porphyrins [19].
Chemical Oxidants	Model Oxidants: Used in lieu of O₂ for studying specific catalytic oxidation cycles under controlled conditions.	Iodosylbenzene (PhIO): A common single-oxygen-atom transfer reagent in mechanistic studies of metal-complex catalysis [19].
Internal Standards	Analytical Quantification: Added in known quantities to analytical samples to enable accurate quantification via GC/MS.	Deuterated Analogs: e.g., d₁₄-toluene or other stable, non-interfering compounds with well-resolved GC/MS signals.

Kinetic Modeling Guidance

Integrating experimental data into a robust kinetic model is essential for predictive capability. The LT-HyChem (Low-Temperature Hybrid Chemistry) approach provides a physics-based framework for real fuels [17].

• Model Formulation: The LT-HyChem approach describes real fuel combustion by combining an experimentally constrained, lumped model for the initial fuel-specific reactions with a detailed foundational model for the oxidation of smaller hydrocarbon fragments. The key is the accurate treatment of the rate-determining steps in the low-temperature chain-branching pathway [17].
• Parameterization: A small set of shock tube and flow reactor experiments (e.g., measuring IDTs and species time histories) are used to determine the stoichiometric and kinetic parameters for the lumped, fuel-specific reactions [17].
• Validation: The model must be validated against a separate set of experimental data, such as speciation profiles from a flow reactor or ignition delays from a rapid compression machine, not used in the parameterization process [17] [1].

Exploring the Negative-Temperature-Coefficient (NTC) Behavior in DMCH Oxidation

The oxidation chemistry of dimethylcyclohexane (DMCH) isomers presents a complex system where molecular structure significantly influences reactivity, including pronounced Negative-Temperature-Coefficient (NTC) behavior. This application note explores the intricate low-temperature oxidation pathways of 1,2- and 1,3-dimethylcyclohexane (D12MCH and D13MCH), key cyclic components in sustainable aviation fuels (SAFs). Through comparative experimental analysis and detailed kinetic modeling, we demonstrate how the relative positioning of methyl substituents on the cyclohexane ring dictates fundamental reaction kinetics, hydrocarbon growth processes, and aromatic formation tendencies. The insights gained provide critical understanding for designing next-generation bio-based aviation fuels with optimized combustion characteristics and reduced emission profiles.

Within the context of kinetic modeling research for sustainable aviation fuels, understanding the oxidation chemistry of polyalkylated cycloalkanes is paramount. These compounds, particularly dimethylcyclohexane isomers, represent vital molecular subclasses in lignin-derived sustainable aviation fuels (SAFs) that can overcome compatibility issues between drop-in fuels and aero-engines [1]. Compared to conventional monoalkylated cycloalkanes in jet fuels, the combustion chemistry of novel polyalkylated cycloalkanes remains insufficiently explored, especially regarding their distinctive NTC behavior – a phenomenon where oxidation reactivity decreases with increasing temperature within a specific temperature range [1].

The negative temperature coefficient phenomenon presents significant challenges in combustion prediction and control, making its understanding in potential fuel components particularly valuable. Recent investigations have revealed that polysubstituted cycloalkanes exhibit different low-temperature reactivities depending on their specific isomeric structures, with important implications for their autoignition characteristics in practical combustion systems [1]. This application note synthesizes recent experimental and kinetic modeling findings to elucidate the NTC behavior in DMCH isomers, providing researchers with comprehensive protocols and analytical frameworks for investigating cyclic hydrocarbon oxidation.

Comparative Reactivity of DMCH Isomers

Experimental data reveals significant differences in the oxidation behavior of DMCH isomers across temperature regimes, particularly in the context of NTC behavior.

Experimental Reactivity Trends

Table 1: Comparative Oxidation Characteristics of DMCH Isomers

Parameter	1,2-DMCH	1,3-DMCH	Experimental Conditions
High-Temperature Reactivity	Higher	Lower	Flow reactor, 550-850 K, lean & rich conditions [1]
Low-Temperature Reactivity	Lower	Higher	Flow reactor, 550-850 K, lean & rich conditions [1]
Ignition Delay Times	Information limited	Longer than ethylcyclohexane	Shock tube, 1049-1544 K, 3-12 atm [16]
Aromatic Formation	Higher peak concentrations	Lower peak concentrations	GC-MS detection [1]
Primary Decomposition	Closer methyl groups enhance gaseous products	More staggered methyl arrangement	Bond dissociation energetics [1]

The observed reactivity inversion between temperature regimes underscores the profound influence of molecular geometry on reaction pathway dominance. D13MCH exhibits higher low-temperature reactivity, whereas D12MCH demonstrates superior high-temperature oxidation characteristics [1]. This divergence stems fundamentally from differences in chemical bond dissociation enthalpies and the relative contributions of various channels to carbon flux and ȮH radical formation [1].

Quantitative Species Formation Data

Table 2: Key Intermediate Species Concentration Ranges in DMCH Oxidation

Species Category	Specific Compounds	Concentration Range (ppm)	Notable Isomer Differences
C8 Hydroperoxides	Varied structural isomers	5-85 (temperature-dependent)	D13MCH pathways favored at low T [1]
Alkenyl/Allylic Radicals	C8H15•, C8H13•	10-120 (temperature-dependent)	D12MCH pathways favored at high T [1]
Aromatic Compounds	Benzene, alkylbenzenes	15-95 (peak concentrations)	Significantly higher in D12MCH oxidation [1]
Oxygenated Intermediates	Ketohydroperoxides, cyclic ethers	8-65 (temperature-dependent)	Critical for low-temperature chain branching [1]

Chemical Kinetics of NTC Behavior in DMCH Systems

The NTC phenomenon in hydrocarbon oxidation manifests as a temporary decrease in global reactivity as temperature increases, creating challenging ignition characteristics in practical combustion systems. For DMCH isomers, this behavior is governed by competing reaction pathways whose relative dominance shifts with temperature.

Fundamental NTC Mechanisms

The negative temperature coefficient behavior arises from a delicate balance between chain-branching and chain-propagation reactions. At lower temperatures, the oxidation process favors chain-branching through complex sequence involving O₂ addition to fuel-derived radicals, internal H-atom transfer (isomerization), and second O₂ addition forming ketohydroperoxides that decompose to reactive radicals [1] [20]. As temperature increases within the NTC regime, decomposition of intermediate alkyl radicals via β-scission to form more stable olefins and resonance-stabilized radicals begins to dominate over the second O₂ addition, effectively reducing the overall reactivity [1].

For DMCH isomers, the specific molecular architecture dictates the accessibility of various transition states in the isomerization steps and the stability of the resulting radicals, thereby modulating the temperature range and intensity of NTC behavior [1]. H-migrations and dissociations of C8 hydroperoxides and alkenyl/allylic radicals are particularly important in controlling product formation and overall reactivity trends [1].

Isomer-Specific Reaction Pathways

The divergent NTC characteristics of D12MCH and D13MCH originate from their distinct decomposition pathways and radical stabilization capabilities. D13MCH, with its more distributed methyl groups, facilitates certain H-atom transfer reactions that enhance low-temperature chain branching, while D12MCH's adjacent methyl groups create favorable geometries for high-temperature decomposition channels [1].

Rate of production (ROP) and sensitivity analyses indicate that the relative contribution of different channels to carbon flux and ȮH radical formation explains the reactivity differences between isomers [1]. Specifically, the proximity of methyl groups in D12MCH enables more favorable ring-strain configurations that accelerate high-temperature decomposition, while the spatial arrangement in D13MCH stabilizes key intermediates in the low-temperature oxidation sequence.

Experimental Protocols for DMCH Oxidation Studies

This section provides detailed methodologies for investigating NTC behavior in DMCH isomers, enabling researchers to obtain reproducible, high-quality kinetic data.

Flow Reactor Oxidation Experiments

Apparatus Configuration:

• Utilize an atmospheric laminar flow reactor consisting of a 1000 mm quartz tube with 6 mm inner diameter and 2 mm thickness [1]
• Employ a tubular furnace with 550 mm total length containing a 350 mm heated region [1]
• Implement a movable K-type thermocouple to measure centerline temperature profiles along the reactor axis [1]
• Maintain precise temperature control through three independent heating zones with PID controllers [1]

Experimental Procedure:

• Fuel Vaporization System: Introduce liquid DMCH isomers using a syringe pump into a vaporizer maintained at 473 K [1]
• Gas Flow Control: Employ mass flow controllers for precise metering of oxidizer (O₂) and diluent (N₂ or He) streams [1]
• Reaction Quenching: Rapidly cool gas samples at reactor exit to quench chemical reactions [1]
• Species Identification: Analyze products using online gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) [1]
• Quantification: Determine mole fractions of reactants, intermediates, and products through calibrated detector responses [1]

Critical Parameters:

• Temperature range: 550-850 K (covering low-temperature, NTC, and high-temperature regimes) [1]
• Equivalence ratios: 0.25 (lean) and 1.5 (rich) to examine oxygen dependence [1]
• Pressure: Atmospheric pressure (1 atm) [1]
• Residence time: Controlled through total gas flow rate [1]

Ignition Delay Time Measurements

For high-temperature kinetic validation, shock tube experiments provide essential ignition delay data:

Shock Tube Methodology:

• Conduct experiments behind reflected shock waves [16]
• Cover temperature range of 1049-1544 K at pressures of 3.0-12 atm [16]
• Monitor ignition events using pressure transducers and optical diagnostics [16]
• Measure fuel concentration time histories via mid-infrared direct laser absorption at 3.39 μm [16]

Kinetic Modeling Approach

Constructing accurate chemical kinetic models for DMCH oxidation requires a systematic approach that captures the essential chemistry across temperature regimes.

Model Development Framework

Base Mechanism Selection:

• Begin with established n-heptane oxidation model providing detailed C0–C7 chemistry [1]
• Incorporate methylcyclohexane (MCH) submechanism as foundational cycloalkane chemistry [1]
• Extend with DMCH-specific reaction classes and rate parameters [1]

Critical Reaction Classes:

• H-Abstraction Reactions: Account for site-specific H-atom removal from different carbon positions (tertiary vs. secondary) considering substituent effects [1]
• Unimolecular Decomposition: Include ring-opening pathways and β-scission reactions of fuel-derived radicals [1]
• Isomerization Processes: Model internal H-atom transfer reactions in peroxy radicals, particularly those governing NTC behavior [1]
• Oxidation Pathways: Implement O₂ addition sequences forming peroxy radicals and subsequent ketohydroperoxide chemistry [1]

Model Validation and Analysis

Validation Targets:

• Species concentration profiles from flow reactor experiments across temperature range [1]
• Ignition delay times from shock tube measurements [16]
• Pyrolysis product distributions under inert conditions [16]

Analytical Techniques:

• Rate of Production (ROP) Analysis: Quantify contributions of individual reactions to species formation/consumption [1]
• Sensitivity Analysis: Identify reactions with greatest influence on global observables (ignition delay, fuel consumption) [1]
• Reaction Pathway Analysis: Trace dominant consumption routes and their temperature dependence [1]

The Researcher's Toolkit

Table 3: Essential Research Reagents and Materials for DMCH Oxidation Studies

Reagent/Material	Specifications	Function/Application
1,2-Dimethylcyclohexane	High purity (>99%), stereoisomer mixture	Primary fuel isomer for structure-reactivity studies [1]
1,3-Dimethylcyclohexane	High purity (>99%), stereoisomer mixture	Comparative fuel isomer with different methyl group positioning [1]
Ultra-high Purity Oxygen	99.999% purity, hydrocarbon-free	Oxidizer for controlled oxidation experiments [1]
Inert Diluent Gases	N₂ or He, 99.999% purity	Dilution medium for controlling reactant concentrations and residence times [1]
Calibration Gas Standards	Certified hydrocarbon mixtures at known concentrations	Quantitative species calibration for GC and GC-MS systems [1]
Internal Standard Compounds	Deuterated cycloalkanes or stable hydrocarbons	Reference compounds for quantitative analysis [1]

Implications for Sustainable Aviation Fuel Development

The distinct NTC behaviors and oxidation characteristics of DMCH isomers present important considerations for sustainable aviation fuel formulation and optimization.

The experimental observation that D12MCH produces significantly higher concentrations of aromatic compounds compared to D13MCH has substantial implications for soot formation and emission characteristics in practical engines [1]. This finding is particularly relevant for fuel designers seeking to minimize particulate matter emissions while maintaining material compatibility through adequate aromatic content.

Furthermore, the established relationship between methyl group positioning and low-temperature reactivity provides molecular-level design criteria for synthesizing bio-based cycloalkanes with tailored ignition characteristics. The higher low-temperature reactivity of D13MCH suggests potential applications in fuels requiring improved cold-start performance, while the superior high-temperature characteristics of D12MCH may benefit high-efficiency combustion systems [1].

The exploration of NTC behavior in DMCH oxidation chemistry reveals intricate structure-reactivity relationships governed by molecular geometry. Through integrated experimental and kinetic modeling approaches, researchers can elucidate the fundamental chemical processes controlling ignition and oxidation across temperature regimes. The protocols and methodologies outlined in this application note provide a foundation for systematic investigation of cyclic hydrocarbon combustion, supporting the continued development of sustainable aviation fuels with optimized performance and environmental characteristics. Future work should expand to include tri-methylated cyclohexane isomers and their synergistic effects in multi-component fuel blends to more accurately represent real fuel behavior.

Methodologies for Kinetic Model Development and Practical Application

The development of accurate chemical kinetic models for fuel oxidation, such as for dimethylcyclohexane, relies on experimental data obtained from well-designed apparatus that can replicate relevant temperature and pressure conditions. Flow reactors, shock tubes, and rapid compression machines constitute three complementary classes of experimental devices that provide fundamental combustion data across different regimes. These facilities enable researchers to investigate phenomena ranging from low-temperature oxidation chemistry to high-temperature ignition characteristics, providing validation targets for kinetic mechanism development. This article presents detailed application notes and protocols for these techniques within the context of dimethylcyclohexane oxidation research, providing structured quantitative comparisons and standardized methodologies for researchers in the field.

Apparatus-Specific Application Notes

Rapid Compression Machines (RCMs)

2.1.1 Principle and Applications Rapid Compression Machines (RCMs) simulate a single compression stroke of an internal combustion engine under idealized conditions, free from complications such as cycle-to-cycle variations, residual gas effects, and complex swirl bowl geometry [21]. They are primarily employed to measure ignition delay times as a function of temperature, pressure, and fuel/oxygen/diluent ratio, particularly in the low-to-intermediate temperature range (600–1100 K) where reactivity may be too slow for shock tube investigations [21]. This capability makes RCMs exceptionally suitable for studying fuel-specific effects during low-temperature combustion, including phenomena such as two-stage ignition and the negative temperature coefficient (NTC) region where ignition delay times temporarily increase with rising temperature [21]. The experimental durations in RCMs are typically longer than those available in shock tubes, making them ideal for investigating autoignition chemistry at elevated pressures under conditions relevant to advanced engine concepts like HCCI (Homogeneous Charge Compression Ignition) [21] [22].

2.1.2 Critical Design Features Modern RCMs are pneumatically driven and hydraulically actuated to achieve rapid compression and vibration-free piston stopping [23]. A crucial design element is the implementation of creviced pistons, which suppress the boundary layer from becoming entrained into the reaction chamber via a roll-up vortex, thereby preserving a homogeneous core of reaction mixture essential for meaningful kinetic measurements [21] [23]. The compression process should be sufficiently rapid (approximately 20-30 ms) and achieve high compression ratios (up to 21:1 as demonstrated in some designs) to attain target conditions of up to 50 bar and temperatures exceeding 1000 K [21] [23]. Advanced RCMs may incorporate optical access for visualization techniques like Schlieren imaging and chemiluminescence, as well as rapid sampling systems connected to gas chromatographs for species concentration analysis during ignition delay [21] [24].

Table 1: Representative RCM Design and Operational Parameters

Parameter	Specification Range	Contextual Notes
Compression Time	~20-30 ms	Fast compression minimizes heat loss during process [21]
Bore x Stroke	50 x 250 mm [24]	Larger dimensions promote more uniform core region [23]
Compression Ratio	9:1 to 32:1 [24]	Variable ratio enables wide condition mapping [23]
Achievable Pressure	Up to 160 bar [24]	Design reactor pressure may be higher (e.g., 1000 bar) [24]
Temperature Range	600–1100 K [21]	Covers low-to-intermediate temperature chemistry [21]
Measurement Regime	4–200 ms [24]	Suitable for longer ignition delays than shock tubes [21]

Shock Tubes

2.2.1 Principle and Applications Shock tubes create homogenous high-pressure and elevated-temperature conditions almost instantaneously behind a reflected shock wave, making them ideal for studying high-temperature ignition phenomena [21] [25]. They are particularly valuable for measuring ignition delay times at temperatures typically ranging from 1168 K to 2115 K, as demonstrated in recent studies on ammonia/methyl hexanoate mixtures [25]. The uniform conditions behind the reflected shock wave typically persist for less than 10 ms, though recent advancements have extended this duration to approximately 50 ms for certain applications [21]. Shock tubes provide nearly adiabatic and constant volume conditions after shock reflection, enabling the study of fundamental chemical kinetics without wall effects and fluid dynamic complications present in other devices.

2.2.2 Operational Considerations A heated shock tube is essential for studying low-vapor-pressure fuels and mixtures to prevent condensation [25]. Ignition delay time determination relies on precise pressure measurements using piezoelectric transducers installed at multiple locations along the driven section, with ignition typically identified by a rapid pressure rise or OH* chemiluminescence [25]. The facility requires careful characterization of incident and reflected shock properties to accurately determine temperature and pressure conditions behind the reflected shock wave using established shock relations.

Table 2: Representative Shock Tube Operational Parameters for Kinetic Studies

Parameter	Specification Range	Contextual Notes
Temperature Range	1168–2115 K [25]	Focus on high-temperature ignition chemistry
Pressure Range	1.4–30 atm [25]	Wide pressure capability relevant to engine conditions
Test Duration	<10 ms (typically) [21]	Extended to ~50 ms with modified driver [21]
Ignition Detection	Pressure rise, OH* chemiluminescence	Multiple methods ensure accurate ignition determination
Heating Requirement	Essential for low-vapor-pressure fuels	Prevents condensation of fuel mixtures [25]

Flow Reactors

2.3.1 Principle and Applications Flow reactors, particularly jet-stirred reactors (JSRs), provide continuous, well-mixed reaction environments ideal for studying low-temperature oxidation chemistry and generating detailed species concentration profiles [22] [26]. They operate at steady-state conditions with precise temperature control, enabling investigation of complex oxidation pathways and intermediate species formation [22]. The jet-stirred reactor used in 1,3,5-trimethylcyclohexane oxidation studies typically consists of a fused silica sphere with a volume of 107 cm³, fused with a quartz sampling nozzle for species analysis [22]. These systems are particularly valuable for identifying reactive intermediates such as hydroperoxides, cyclic ethers, and other oxygenated species that are crucial for understanding low-temperature oxidation mechanisms [22].

2.3.2 Operational Characteristics Flow reactor experiments are typically conducted at atmospheric pressure with temperatures ranging from 875 K to 1425 K, covering the low-to-intermediate temperature regime [22] [26]. The system maintains a total gas flow rate of 1000 mL·min⁻¹ (STP), resulting in gas residence times of approximately 190 ms at 1000 K [26]. Species quantification is achieved using analytical techniques such as synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) or gas chromatography, enabling detection of reactants, stable products, and reactive intermediates [22].

Experimental Protocols

Rapid Compression Machine Protocol for Ignition Delay Measurements

3.1.1 Preparation Phase

• Reaction Mixture Preparation: Prepare fuel-oxidizer-diluent mixtures in a mixing tank using partial pressure manometry, allowing sufficient time for homogenization (typically 12-24 hours) [21]. For dimethylcyclohexane studies, prepare mixtures at varying equivalence ratios (φ = 0.5-2.0) relevant to engine conditions.
• RCM Pre-Experimental Checks: Verify pneumatic and hydraulic systems for proper operation. Ensure the creviced piston is clean and undamaged. Check that the reaction chamber is leak-tight at test pressures.
• Instrumentation Calibration: Calibrate pressure transducers (e.g., piezoelectric sensors) and thermocouples using traceable standards. Confirm data acquisition system synchronization.

3.1.2 Experimental Procedure

• Evacuate the reaction chamber to below 10⁻³ mbar to remove residual gases.
• Fill the reaction chamber with the prepared test mixture to the desired initial pressure.
• Activate the pneumatic drive system to initiate rapid compression.
• Record pressure-time history throughout compression and post-compression period at high frequency (≥100 kHz).
• Determine ignition delay time (τ) as the temporal interval from the end of compression (identified by peak pressure) to the onset of ignition (identified by rapid pressure rise or maximum pressure rise rate) [21].
• Repeat experiments multiple times (typically 3-5 repetitions) under identical conditions to ensure reproducibility.

3.1.3 Data Interpretation

• Adiabatic Core Assumption: The temperature at the end of compression (T_C) is calculated using adiabatic compression relations, accounting for heat loss during compression [21].
• Computational Simulation: Simulate RCM experiments using chemical kinetic modeling software with a well-stirred reactor approximation, incorporating facility-specific heat loss characteristics determined from non-reactive experiments [21].

Shock Tube Protocol for High-Temperature Ignition Studies

3.2.1 Preparation Phase

• Shock Tube Cleaning: Thoroughly clean the driven section to remove contaminants from previous experiments. Passivate internal surfaces if necessary to minimize wall effects.
• Mixture Preparation: Prepare test mixtures manometrically in a specialized mixing vessel. For low-vapor-pressure components, heat the mixing vessel to ensure complete vaporization.
• Diaphragm Selection: Install appropriate diaphragm material (typically metal) with scored cross pattern to achieve desired burst pressure.

3.2.2 Experimental Procedure

• Evacuate both driver and driven sections to below 10⁻⁴ mbar.
• Fill the driven section with test mixture to desired initial pressure.
• Pressurize the driver section with helium or helium-nitrogen mixtures until diaphragm rupture occurs.
• Measure incident shock velocity using multiple pressure transducers; extrapolate to end-wall to calculate reflected shock conditions using standard shock relations.
• Record pressure history and OH* chemiluminescence (if available) at the end-wall location.
• Define ignition delay time as the interval between the arrival of the reflected shock wave at the end-wall and the onset of ignition, identified by rapid pressure rise or OH* emission [25].

3.2.3 Post-Experiment Analysis

• Validate test conditions by comparing measured incident shock velocity with calculated values.
• Perform uncertainty analysis accounting for uncertainties in initial temperature, pressure, and mixture composition.

Flow Reactor Protocol for Low-Temperature Oxidation Studies

3.3.1 System Preparation

• Reactor Conditioning: Pre-heat the jet-stirred reactor to desired temperature under inert gas flow to establish stable thermal conditions.
• Calibration: Calibrate mass flow controllers for all gaseous feeds using primary standards. For liquid fuels like dimethylcyclohexane, use a precision liquid syringe pump with vaporization system.
• Analytical Instrument Calibration: Calibrate GC-MS/FID or SVUV-PIMS systems using certified standard mixtures for quantitative species quantification [22].

3.3.2 Experimental Procedure

• Establish isothermal conditions at the target temperature (500-1100 K) under inert flow.
• Introduce pre-vaporized fuel/oxidizer/diluent mixture at predetermined flow rates to achieve desired residence time.
• Allow the system to stabilize for at least three residence times before collecting data.
• Extract samples from the reactor outlet for analysis using SVUV-PIMS or GC-MS/FID at each temperature point [22].
• Systematically vary temperature in increments (typically 25-50 K) to map species profiles across the low-temperature oxidation regime, including the NTC region if present.

3.3.3 Data Processing

• Convert raw signal intensities to mole fractions using calibration factors and carbon balance.
• Validate data consistency through elemental (C, H, O) conservation checks.
• Compare experimental species profiles with predictions from detailed kinetic models.

Research Reagent Solutions and Essential Materials

Table 3: Essential Research Reagents and Materials for Combustion Kinetics Experiments

Reagent/Material	Function/Application	Technical Specifications
High-Purity Fuel Samples	Primary reactant for oxidation studies	e.g., Dimethylcyclohexane isomers (≥99.5% purity) [22]
Oxidizers	Oxidation partner in reaction mixtures	Oxygen (≥99.995% purity) [22]
Diluent Gases	Thermal ballast and pressure control	Argon or Nitrogen (≥99.998% purity) [22] [26]
Certified Standard Mixtures	Analytical instrument calibration	Known concentrations of relevant species in balance gas
CRES Pistons	Creviced piston for RCM studies	Machined with specific crevice designs to suppress vortex [21]
Diaphragm Materials	Shock tube operation	Scored metal foils of precise thickness
SVUV Light Source	Species detection in flow reactors	Synchrotron radiation for soft photoionization [22]
Calibration Gases	Species quantification	CO, CO₂, CH₄, C₂H₄, C₂H₂, H₂, etc. (certified concentrations)

Complementary Data Integration for Kinetic Model Development

The three experimental techniques provide complementary data for comprehensive kinetic model development. RCMs deliver ignition delay times at engine-relevant low-to-intermediate temperatures, shock tubes provide high-temperature ignition data under nearly ideal conditions, and flow reactors generate detailed species concentration profiles that reveal specific reaction pathways [21] [22] [25]. For dimethylcyclohexane oxidation mechanism development, this multi-faceted experimental approach allows researchers to:

• Identify and quantify low-temperature oxidation intermediates such as cyclic ethers, hydroperoxides, and carbonyl compounds [22]
• Characterize NTC behavior where ignition delay times increase with temperature [21]
• Validate model predictions across wide temperature ranges (600-2100 K) and pressures (1-50 atm) [21] [25]
• Elucidate specific reaction pathways through intermediate species identification [22]

This integrated experimental approach, combining RCMs, shock tubes, and flow reactors, provides the comprehensive dataset necessary to develop and validate accurate chemical kinetic models for dimethylcyclohexane oxidation, ultimately supporting the optimization of advanced combustion systems utilizing cycloalkane-rich fuels.

Within the broader context of kinetic modeling research for dimethylcyclohexane (DMCH) oxidation chemistry, speciation analysis provides the critical experimental foundation for model development and validation. Speciation analysis, the identification and quantification of reactive intermediates and stable products, is indispensable for elucidating complex reaction networks in hydrocarbon oxidation [1]. The molecular structure of dimethylcyclohexane isomers—specifically the relative positions of methyl substituents on the cyclohexane ring—profoundly influences their low-temperature and high-temperature oxidation reactivity, subsequently dictating the distribution of oxidation products [1]. This application note details standardized protocols for conducting speciation analysis during DMCH oxidation, enabling researchers to generate consistent, high-quality data for refining chemical kinetic models of sustainable biofuel components.

Experimental Setup and Workflow for Speciation Analysis

The following section outlines the core experimental system and procedural workflow for obtaining speciation data during DMCH oxidation.

Flow Reactor System Configuration

Oxidation experiments for speciation analysis are optimally conducted using a laminar flow tubular reactor (LFTR) operating at atmospheric pressure [1].

• Reactor Core: The system centers on a quartz tube (typically 1000 mm in length with a 6 mm inner diameter) heated by a controllable tubular furnace providing a uniform temperature zone.
• Fuel/Oxidizer Delivery: Vaporized DMCH isomer is precisely metered and mixed with a molecular oxygen/inert gas stream (e.g., N₂ or He) prior to entering the heated reactor section. The equivalence ratio (φ) is adjusted by varying the O₂ to fuel ratio, with lean (φ=0.25) and rich (φ=1.5) conditions recommended for comprehensive model validation [1].
• Temperature Profiling: An axial temperature profile is recorded using a movable K-type thermocouple to define the precise thermal environment experienced by the reacting mixture.

Analytical Instrumentation and Methodology

Post-reactor analysis employs coupled gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) for detailed species identification and quantification [1].

• Online Gas Chromatography (GC): Effluent from the flow reactor is directly sampled and injected into a GC system equipped with a flame ionization detector (FID) for quantifying hydrocarbon species and a thermal conductivity detector (TCD) for permanent gases (e.g., CO, CO₂, O₂).
• Gas Chromatography-Mass Spectrometry (GC-MS): This technique is crucial for the definitive identification of unknown intermediates and products, particularly isomers with similar retention times. Electron impact ionization facilitates spectral library matching.
• Calibration Protocol: Quantitative analysis requires prior calibration using standard gas mixtures of known concentration for permanent gases and authentic liquid standards for hydrocarbon species to establish response factors.

Comprehensive Speciation Analysis Workflow

The diagram below illustrates the integrated experimental pathway from sample preparation to data acquisition for kinetic model validation.

Key Research Reagents and Materials

The table below catalogues essential reagents, materials, and analytical standards required for conducting DMCH oxidation and speciation analysis experiments.

Table 1: Essential Research Reagents and Materials for DMCH Oxidation Studies

Category	Item / Reagent	Specification / Purity	Primary Function in Protocol
Fuel Isomers	1,2-Dimethylcyclohexane (D12MCH)	High Purity (e.g., ≥99%)	Primary reactant for studying molecular structure effects on oxidation pathways [1].
	1,3-Dimethylcyclohexane (D13MCH)	High Purity (e.g., ≥99%)	Primary reactant; exhibits different low-temperature reactivity vs. D12MCH [1].
Oxidizers & Gases	Molecular Oxygen (O₂)	Ultra-high purity	Oxidizing agent in fuel/O₂/inert gas mixture [1].
	Nitrogen (N₂) or Helium (He)	Ultra-high purity, dry	Diluent gas for controlling reactant concentration and residence time [1].
Analytical Standards	Carbon Monoxide (CO) / Carbon Dioxide (CO₂)	Certified standard mixture	Calibration of GC-TCD for permanent gas quantification [1].
	Hydrocarbon Mixture	Custom mixture of C1-C9 alkanes, alkenes, oxygenates	Calibration of GC-FID response factors for accurate species quantification [1].
Catalytic Systems	Metalloporphyrin Complexes (e.g., Fe, Mn)	Synthetic catalysts	Biomimetic catalysts for selective C–H bond oxidation studies [27].
	Polyoxometallates	Defined structure	Bulky oxidants for probing steric effects in C–H oxidation [28].

Data Presentation and Interpretation

This section summarizes characteristic speciation data and provides guidance for its interpretation in the context of kinetic modeling.

Characteristic Speciation Data from DMCH Oxidation

Experimental data reveals distinct product distributions for D12MCH and D13MCH, highlighting the influence of molecular structure. The following table compiles key quantitative observations from flow reactor studies.

Table 2: Comparative Speciation Data for DMCH Isomer Oxidation

Parameter	1,2-Dimethylcyclohexane (D12MCH)	1,3-Dimethylcyclohexane (D13MCH)	Experimental Conditions
High-Temp Reactivity	Higher	Lower	Flow reactor, lean/rich, 1 atm [1]
Low-Temp Reactivity	Lower	Higher	Flow reactor, lean/rich, 1 atm [1]
Aromatics Formation	Higher peak concentrations	Lower peak concentrations	Attributed to five-membered-ring chemistry and β-scission sequences [1]
Major Product Pathways	H-migrations and dissociations of C₈ hydroperoxides and alkenyl/allylic radicals [1]	H-migrations and dissociations of C₈ hydroperoxides and alkenyl/allylic radicals [1]	Determined via Rate of Production (ROP) analysis
Key Oxidized Intermediates	Cyclic alcohols, ketones, cyclic ethers	Cyclic alcohols, ketones, cyclic ethers	Identified via GC-MS [1]

Interpreting Selectivity and Reaction Mechanisms

Speciation data provides insights into the fundamental oxidation mechanism.

• cis/trans-1,2-Dimethylcyclohexane as a Stereochemical Probe: The ratio of cis and trans tertiary alcohols produced from the oxidation of cis- or trans-1,2-dimethylcyclohexane reveals the lifetime of the radical intermediate. A cis:trans ratio close to 1.2 suggests a long-lived free radical that epimerizes before the "oxygen rebound" step. In contrast, high stereospecificity (retention of configuration) indicates a metal-based oxidant with an extremely fast rebound step, as demonstrated with the Os(VIII) catalyst [27] [29].
• Adamantane Oxidation for Electronic Effects: The regioselectivity of adamantane oxidation (3°/2° ratio, corrected for statistical prevalence) indicates the nature of the oxidant. A low 3°/2° ratio (<6) is characteristic of a free-radical mechanism, while a high ratio (>13-15) strongly suggests a metal-based oxidant [27].

Troubleshooting and Technical Notes

• Low Product Yields: Ensure the vaporization system is properly heated to prevent fuel condensation. Verify the integrity of calibration curves for quantitative species.
• Poor Chromatographic Resolution: Optimize GC temperature ramp programs for complex mixtures. Regularly maintain and condition chromatography columns.
• Model Discrepancies: Pay particular attention to the accurate quantification of unsaturated species (alkenes) and oxygenates, as these are critical for validating key fuel-specific pathways predicted by kinetic models, such as those involving resonantly stabilized radicals [1].

The application of robust speciation analysis protocols, as detailed in this document, is fundamental for advancing the understanding of dimethylcyclohexane oxidation chemistry. The precise identification and quantification of intermediates and products provide the necessary experimental constraints for developing and refining detailed kinetic models. These models are vital for optimizing the performance of next-generation sustainable aviation fuels containing polyalkylated cycloalkanes, ultimately contributing to reduced greenhouse gas emissions from the aviation sector [1].

Hierarchical Mechanism Construction and the Role of Core Chemistry (C0-C7)

The combustion of sustainable aviation fuels (SAFs) derived from biomass is a critical area of modern research. A significant subclass of components in these next-generation fuels is polyalkylated cycloalkanes, which are vital for overcoming the compatibility issues between drop-in fuels and aero-engines [1]. Among these, the simplest dialkylated cycloalkanes, the dimethylcyclohexane (DMCH) isomers, serve as fundamental model compounds for understanding the oxidation chemistry of more complex cyclic structures found in real fuels [1]. Constructing accurate, predictive chemical kinetic models for these fuels is paramount for the development of efficient and clean combustion technologies. The most robust and successful methodology for developing such detailed kinetic models is the hierarchical approach, wherein a well-validated core mechanism describing the chemistry of small species (C0-C7) forms the foundation upon which the fuel-specific reactions are built. This application note details the protocol for constructing a hierarchical kinetic model for DMCH oxidation, leveraging the established core chemistry of smaller hydrocarbons, and is framed within a broader thesis on dimethylcyclohexane oxidation chemistry research.

The Hierarchical Construction Methodology

The hierarchical approach to mechanism development is based on the principle of chemical similarity and the systematic validation of sub-mechanisms against experimental data at each level of complexity. The construction of a model for a target fuel, such as 1,2-DMCH or 1,3-DMCH, begins with a core mechanism that has been rigorously tested for its constituent fragments.

The C0-C7 Core Chemistry Foundation

The core mechanism forms the indispensable backbone of any detailed combustion model. It describes the oxidation chemistry of small molecules, including hydrogen, carbon monoxide, formaldehyde, and C1-C7 hydrocarbons.

• Role and Importance: The core mechanism governs the overall reactivity, heat release, and final product distribution (e.g., CO, CO₂) across a wide range of temperatures and pressures. It includes the critical H₂/O₂ reactions, carbon monoxide oxidation, and the peroxide chemistry that drives low-temperature ignition and negative temperature coefficient (NTC) behavior. For cycloalkanes, the core must also include validated sub-mechanisms for key intermediate fragments like C2-C4 alkenes, butadiene, and cyclopentene, which are produced during ring-opening [30] [1].
• Construction and Validation: The core mechanism is not developed in isolation. It is typically assembled and refined by integrating well-established sub-mechanisms from the literature, which have been validated against fundamental experimental targets such as:
  • Laminar burning velocities for small hydrocarbon/air flames.
  • Ignition delay times measured in shock tubes and rapid compression machines.
  • Species concentration profiles from jet-stirred reactors (JSR) and flow reactors.

Table 1: Key Experimental Targets for Validating C0-C7 Core Chemistry

Validation Target	Apparatus	Example Conditions	Key Measured Data
High-Temperature Ignition	Shock Tube	T > 1000 K, P = 1-50 atm	Ignition Delay Time [30]
Low-Temperature Ignition & NTC	Rapid Compression Machine (RCM)	T = 500-850 K, P = 7-40 bar	Ignition Delay Time [30]
Species Profiling (Oxidation)	Jet-Stirred Reactor (JSR)	T = 500-1100 K, P ~ 1-10 atm	Mole fractions of reactants, intermediates, and products [30]
Species Profiling (Pyrolysis)	Flow Reactor / Shock Tube	T > 950 K, P ~ 40 mbar - 4 atm	Fuel decay and product mole fractions [30] [16]
Laminar Burning Velocity	Flat Flame Burner	T = 298-398 K, P = 1 atm	Flame speed [30]

Building the Fuel-Specific Dimethylcyclohexane Mechanism

Once a reliable core is established, the fuel-specific reactions for the DMCH isomers are added. This process involves defining the primary reaction classes that govern fuel consumption.

Diagram 1: Hierarchical kinetic model construction and validation workflow.

Step 1: H-Abstraction Reactions The initiation step for fuel consumption is predominantly H-abstraction by small radicals (˙OH, HȮ₂, Ḣ, ĊH₃) from the DMCH molecule. This generates a variety of dimethylcyclohexyl radicals. The protocol involves:

• Identifying Abstraction Sites: The fuel structure dictates the types of C-H bonds. For DMCH isomers, this includes secondary C-H bonds on the ring and primary C-H bonds on the methyl substituents. The bond dissociation energies (BDEs) can differ slightly between isomers due to 1,3-diaxial interactions or other steric effects, influencing the site-specific abstraction rates [1] [15].
• Assigning Rate Rules: Rate constants for H-abstraction are typically assigned based on analogous reactions for cyclohexane and methylcyclohexane, using the principle of analogy. For example, the rate for abstracting an H-atom from a methyl group in DMCH can be derived from methylcyclohexane, adjusted for the number of equivalent H-atoms [1].

Step 2: alkyl Radical Reactions The fate of the resulting dimethylcyclohexyl radicals is highly temperature-dependent.

• At High Temperatures (> 850 K): The radicals primarily undergo β-scission to decompose into smaller alkenes and other radicals. For instance, a radical site on the ring can lead to ring-opening, producing dienes or alkene radicals like 1,3-butadiene and ethene, which are already part of the core mechanism [1] [16].
• At Low Temperatures (< 850 K): The alkyl radicals rapidly add to molecular oxygen (O₂) to form peroxy radicals (RȮ₂), initiating the low-temperature oxidation chain that is critical for auto-ignition.

Step 3: Peroxy Radical Chemistry (Low-Temperature Pathways) The peroxy radicals undergo isomerization via intramolecular H-shift from a different carbon atom in the molecule, forming hydroperoxyalkyl radicals (Q̇OOH). These isomerization reactions are central to the low-temperature reactivity and exhibit strong stereochemical dependence in cyclic systems due to ring strain and transition state geometry [30] [1].

• Isomerization: The Q̇OOH radicals can undergo further O₂ addition, internal isomerization, and decomposition.
• Cyclic Ether Formation: One key pathway is the decomposition of the hydroperoxyalkyl radical to form cyclic ethers and a hydroxyl (ȮH) radical. For cyclohexane, typical products include 1,2-epoxycyclohexane and 1,4-epoxycyclohexane [30].
• Ketohydroperoxide Formation: Alternatively, the Q̇OOH radical can decompose to form a carbonyl (ketone or aldehyde) and a new radical, or undergo a second O₂ addition, leading to the formation of ketohydroperoxides (KHP). The decomposition of KHPs yields highly reactive ȮH radicals, creating a chain-branching sequence that promotes ignition.

Table 2: Major Reaction Classes in DMCH Oxidation Mechanism

Reaction Class	Representative Reaction	Temperature Regime	Significance
H-Abstraction	DMCH + ȮH → DMCH-yl + H₂O	All Temperatures	Primary fuel consumption path; determines radical pool.
β-Scission	DMCH-yl → C₂H₄ + C₆H₁₁-yl	High-Temperature (> 850 K)	Major ring-opening and decomposition pathway.
O₂ Addition	DMCH-yl + O₂ → DMCH-ylȮ₂	Low-Temperature (< 850 K)	Initiates low-temperature oxidation chain.
Isomerization	DMCH-ylȮ₂ → DMCH-(ȮOH)-yl	Low-Temperature	Key step governing fuel reactivity and NTC behavior.
Cyclic Ether + ȮH	DMCH-(ȮOH)-yl → Cyclic Ether + ȮH	Low-Temperature	A termination path for peroxy radicals; forms stable intermediates.
Ketohydroperoxide Formation	DMCH-(ȮOH)-yl + O₂ → OOQ̇OOH → KHP + ȮH	Low-Temperature	Chain-branching path leading to ignition.

Experimental Protocols for Model Validation

A hierarchical model must be validated against a suite of experimental data to ensure predictive accuracy across different combustion regimes. The following protocols outline key experiments for DMCH validation.

Jet-Stirred Reactor (JSR) Speciation

Objective: To measure quantitative species concentration profiles (reactants, intermediates, and products) over a wide temperature range (500-1100 K) to validate both low- and high-temperature reaction pathways [30] [1].

Detailed Protocol:

• Apparatus Setup: Utilize a spherical fused-silica JSR housed in a regulated temperature furnace. The reactor should be equipped with multiple nozzles to ensure perfect mixing of the reactants.
• Reaction Mixture Preparation: Prepare highly diluted mixtures of DMCH and oxygen in an inert gas (e.g., nitrogen or helium). Standard equivalence ratios (ϕ) of 0.5 (lean), 1.0 (stoichiometric), and 2.0 (rich) should be used. A typical fuel mole fraction is 0.00667 [30].
• Experimental Conditions:
  • Pressure: 1.07 bar (atmospheric).
  • Residence Time: 2 seconds.
  • Temperature Ramp: Conduct experiments from 500 K to 1100 K in increments (e.g., 50 K).
• Product Analysis:
  • Use online Gas Chromatography (GC) with Flame Ionization Detection (FID) and Mass Spectrometry (MS) for species identification and quantification.
  • Calibrate the GC-MS/FID with standard gas mixtures for absolute mole fraction determination.
  • Expected intermediates include cyclic ethers, alkenes (e.g., cyclohexene), carbonyls (e.g., cyclohexanone), and aromatic compounds (e.g., benzene) [30] [1].
• Data Comparison: Simulate the JSR experiment using the detailed kinetic model in a perfectly stirred reactor module (e.g., in CHEMKIN-PRO). Compare the simulated and experimental mole fractions of all major and intermediate species to identify discrepancies in the model.

Ignition Delay Time Measurement in Shock Tube & RCM

Objective: To measure the time interval between fuel/air mixture compression and auto-ignition at elevated temperatures and pressures, providing a global validation target for model reactivity [30] [16].

Detailed Protocol:

• Apparatus Setup:
  • Shock Tube: For high-temperature data (T > 1000 K). The test mixture is heated and compressed by a reflected shock wave.
  • Rapid Compression Machine (RCM): For low-to-intermediate temperature data (T = 600-900 K), including the Negative Temperature Coefficient (NTC) region. The mixture is compressed rapidly by a piston.
• Mixture Preparation: Prepare DMCH/oxidizer mixtures in a stainless-steel vessel. The oxidizer is typically synthetic air (21% O₂, 79% N₂ or Ar). Mixtures should be prepared manometrically.
• Ignition Detection: Monitor pressure time-history at the end-wall. Ignition delay time (τ_ign) is defined as the time from the end of compression (RCM) or the arrival of the reflected shock wave (Shock Tube) to the point of maximum pressure rise.
• Varied Conditions:
  • Temperature & Pressure: For Shock Tubes: 1049–1544 K, 3–12 atm [16]. For RCM: 600-900 K, compressed pressures of 7-40 bar [30].
  • Equivalence Ratio: ϕ = 0.5, 1.0, 2.0.
• Data Comparison: Simulate the ignition delay times using the model in a closed homogeneous batch reactor module, matching the pressure and temperature history of the experiment. Compare simulated and experimental τ_ign to validate the model's predictive capability for global reactivity.

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Research Reagents and Materials for DMCH Combustion Studies

Reagent/Material	Function/Application	Example & Notes
DMCH Isomers (High Purity)	Fuel surrogate for kinetic studies and model validation.	1,2-DMCH (cis-/trans- mix) & 1,3-DMCH; >99% purity to minimize impurities impact [1] [31].
Oxidizer Gases	Provide oxygen for oxidation experiments.	Ultra-high purity O₂, synthetic air (N₂/O₂), and inert dilution gases (N₂, Ar) [30] [1].
Calibration Gas Standards	Quantitative analysis of reaction products via GC.	Certified mixtures of expected intermediates (e.g., cyclohexene, cyclohexanone, benzene, C2-C6 alkenes/alkanes) [30].
Catalytic Reactor Materials	For surface passivation to minimize wall reactions.	Quartz or silica reactors; Fused Silica Jet-Stirred Reactors (JSR) are standard for homogeneous chemistry studies [30].
Chromatography Columns	Separation and analysis of complex product mixtures.	Capillary GC columns (e.g., DB-5, HP-PONA) for separating hydrocarbons and oxygenates [30] [1].

Key Insights from Modeling DMCH Isomers

Applying this hierarchical protocol reveals significant isomeric effects in DMCH oxidation. Reaction path and sensitivity analyses performed on validated models show that:

• 1,2-DMCH vs. 1,3-DMCH Reactivity: D13MCH exhibits higher low-temperature reactivity, while D12MCH is more reactive at high temperatures [1]. This can be explained by differences in BDEs and the relative ease of forming specific radical isomers that favor low-temperature chain-branching pathways in D13MCH.
• Aromatic Formation: The peak concentrations of aromatic compounds are generally higher in the oxidation of D12MCH compared to D13MCH [1]. This is attributed to fuel-specific decomposition pathways; D12MCH decomposition more readily produces precursors like 1,3-butadiene and resonantly stabilized radicals (e.g., C5 cyclopentadienyl) that are key to forming benzene via six-membered-ring and five-membered-ring chemistry.

Diagram 2: Divergent dominant reaction pathways for DMCH isomers, explaining their different reactivity.

Automated Kinetic Model Generation with Tools like EXGAS and RMG

Automated kinetic model generation represents a transformative approach in reaction kinetics, enabling researchers to construct detailed chemical mechanisms with unprecedented speed and comprehensiveness. Within the context of dimethylcyclohexane (DMCH) oxidation chemistry, these tools provide essential capabilities for mapping complex reaction pathways relevant to sustainable aviation fuel development. The Reaction Mechanism Generator (RMG) and EXGAS systems stand as pioneering platforms in this domain, employing fundamental chemical principles to automatically generate elementary reaction steps and associated kinetic parameters [32] [33]. This application note details protocols for leveraging these computational tools to elucidate the oxidation mechanisms of 1,2- and 1,3-dimethylcyclohexane isomers, compounds of significant interest for next-generation bio-derived fuels [34].

The pressing need for accurate kinetic models of polyalkylated cycloalkanes stems from their emerging role in addressing material compatibility challenges in sustainable aviation fuels (SAFs). Unlike conventional petroleum-derived fuels containing 15-40wt% cycloalkanes, biomass-derived fuels can contain up to 99wt% cycloalkanes, often with more branched moieties and complex ring structures [34]. Automated mechanism generation provides the necessary computational framework to rapidly explore the combustion behavior of these complex molecules, significantly accelerating fuel development cycles.

Available Software Tools for Automated Kinetic Model Generation

Table 1: Overview of Automated Kinetic Model Generation Software

Software Tool	Primary Application Domain	Key Features	Development Source
RMG	General chemical reaction mechanism generation	Automatic construction of elementary reaction steps; database-driven kinetics; handles both acyclic and cyclic compounds	William H. Green Research Group (MIT); Richard H. West Research Group (Northeastern University) [32]
EXGAS	Gas-phase oxidation of gasoline components (alkanes, ethers)	Comprehensive mechanism generation; canonical treelike molecule description; validated mechanisms	Academic research group [33]
KUCRS	Combustion kinetic modeling for hydrocarbon oxidation	Automated generator with utilities for chemical kinetic model construction	A. Miyoshi tools [35]

The selection of an appropriate automated mechanism generation tool depends heavily on the specific chemical systems under investigation and the desired level of mechanism detail. RMG has evolved through multiple versions, with the latest stable release (3.2.0) incorporating significant advances in automatic mechanism generation [32] [36]. The software employs a referenced canonical treelike description of molecules and free radicals, enabling it to handle both acyclic and cyclic compounds like dimethylcyclohexane isomers [33]. RMG's comprehensive database includes thermodynamics, transport, and kinetics data critical for accurate mechanism generation [32].

The EXGAS system specializes in gas-phase oxidation mechanisms for components relevant to gasoline, particularly alkanes and ethers. Its programming architecture ensures generated mechanisms are comprehensive enough for direct use in simulation codes [33]. For combustion-specific applications, KUCRS provides automated generation utilities tailored to hydrocarbon oxidation systems [35].

Complementary tools facilitate various aspects of kinetic model development. GPOP serves as a Gaussian post-processor for rate coefficient calculation based on transition-state theory and thermodynamics, while SSUMES implements RRKM theory for steady-state dissociation/isomerization and chemically activated reactions [35]. These specialized utilities provide critical rate parameter estimation capabilities that enhance the mechanism generation process.

Application to Dimethylcyclohexane Oxidation Chemistry

The application of automated mechanism generation to dimethylcyclohexane oxidation addresses significant gaps in understanding the combustion behavior of polysubstituted cycloalkanes. Recent experimental investigations reveal distinct reactivity patterns between DMCH isomers, with 1,2-dimethylcyclohexane (D12MCH) exhibiting higher high-temperature reactivity, while 1,3-dimethylcyclohexane (D13MCH) demonstrates higher low-temperature reactivity [34]. These differences stem from variations in chemical bond dissociation enthalpies and the contributions of different channels to carbon flux and ȮH formation, factors that automated mechanism generation can systematically explore.

Automated tools like RMG enable construction of detailed kinetic models that capture the nuanced decomposition pathways of these cyclic compounds. For DMCH isomers, key reaction classes include H-migrations and dissociations of C8 hydroperoxides and alkenyl/allylic radicals, which govern product formation distributions [34]. The models also elucidate molecular structure effects on aromatics formation, where D12MCH oxidation produces generally higher peak concentrations of aromatic compounds compared to D13MCH oxidation, a consequence of five-membered-ring chemistry involving C5 resonantly stabilized radicals and six-membered-ring chemistry involving traditional H-abstraction/β-scission sequences [34].

Table 2: Experimental Observations for Dimethylcyclohexane Isomer Oxidation

Parameter	1,2-Dimethylcyclohexane (D12MCH)	1,3-Dimethylcyclohexane (D13MCH)
High-Temperature Reactivity	Higher	Lower
Low-Temperature Reactivity	Lower	Higher
Aromatics Formation	Higher peak concentrations	Lower peak concentrations
Dominant Pathways	Traditional H-abstraction/β-scission	Five-membered-ring chemistry with C5 radicals
Key Intermediate Chemistry	C8 hydroperoxides and alkenyl/allylic radicals	C8 hydroperoxides and alkenyl/allylic radicals

The capability to automatically generate these complex reaction networks significantly accelerates mechanism development for polyalkylated cycloalkanes. As research extends to more complex tri-alkylated cycloalkanes like 1,2,4-trimethylcyclohexane (T124MCH) and 1,3,5-trimethylcyclohexane (T135MCH), which undergo even more complex thermal decomposition and oxidation pathways, automated tools become increasingly essential for comprehensive mechanism development [34].

Experimental Protocols for Mechanism Generation and Validation

Protocol for RMG-Based Mechanism Generation for DMCH Isomers

Workflow for DMCH Mechanism Generation

Step 1: Problem Definition and Scope

• Define temperature range: 500-1500 K for comprehensive low-to-high-temperature oxidation chemistry
• Set pressure conditions: 1 atm for flow reactor simulations
• Specify equivalence ratios: φ = 0.25 (lean) and 1.5 (rich) to cover relevant combustion environments [34]
• Identify key validation targets: species concentration profiles and global reactivity metrics

Step 2: Molecular Structure Input

• Prepare SMILES representations or molecular structure files for D12MCH and D13MCH
• Account for conformational isomers, particularly for 1,3-dimethylcyclohexane which exhibits distinct steric considerations
• Define initial core chemistry including relevant reaction families: H-abstraction, β-scission, intramolecular H-migration, radical recombination

Step 3: RMG Parameter Configuration

• Set tolerance for mechanism termination (typically 0.01-0.05) to balance mechanism size and comprehensiveness
• Configure thermodynamics and kinetics estimation methods
• Specify maximum depth for reaction pathway exploration
• Enable pressure-dependent rate analysis for critical reaction channels

Step 4: Mechanism Execution and Expansion

• Execute RMG to generate core mechanism
• Monitor mechanism growth and intervene if necessary to maintain computational tractability
• Iteratively expand mechanism using rate-based algorithm until tolerance criteria are met
• Export complete mechanism in standard formats (CHEMKIN format) for simulation

Step 5: Model Validation Against Experimental Data

• Simulate laminar flow tubular reactor conditions: atmospheric pressure, temperature range 500-1100 K [34]
• Compare predicted and measured species mole fractions for key intermediates: alkenes, carbon monoxide, carbon dioxide, aromatic precursors
• Validate against experimental observation of D12MCH's higher high-temperature reactivity and D13MCH's enhanced low-temperature reactivity [34]
• Perform sensitivity analysis to identify rate-limiting steps

Step 6: Model Refinement

• Adjust critical rate parameters within uncertainty bounds based on validation results
• Incorporate theoretical kinetics calculations for key elementary steps if significant discrepancies persist
• Verify mechanism performance across all experimental conditions before finalizing

Protocol for Experimental Data Collection for Model Validation

Apparatus Setup:

• Utilize laminar flow tubular reactor (LFTR) with 1000 mm quartz tube (6 mm inner diameter) [34]
• Employ tubular furnace with 550 mm total length (350 mm heating region)
• Implement movable K-type thermocouple for centerline temperature profiling
• Establish fuel/O2/N2 mixture delivery system with precise flow control

Experimental Procedure:

• Prepare fuel mixtures with specified equivalence ratios (φ = 0.25 and 1.5) in nitrogen diluent
• Establish stable flow conditions with residence times appropriate for oxidation kinetics (typically 0.5-2 seconds)
• Heat reactor to desired initial temperature (500 K) and introduce reaction mixture
• Gradually increase temperature in increments while maintaining stable flow conditions
• At each temperature set point, extract gas samples for analysis after reaching steady state

Analytical Methods:

• Employ online Gas Chromatography (GC) and Gas Chromatography-Mass Spectrometry (GC-MS) for species identification and quantification [34]
• Calibrate instruments with standard mixtures for accurate mole fraction determination
• Measure concentration profiles for reactants, stable intermediates, and products across temperature range
• Focus special attention on aromatic compound formation (benzene, toluene) due to their importance in soot precursor chemistry

Data Processing:

• Convert chromatographic peak areas to mole fractions using calibration factors
• Normalize carbon mass balance to verify data quality
• Compile species concentration versus temperature profiles for model validation

Essential Research Reagent Solutions

Table 3: Key Research Materials and Computational Tools for DMCH Oxidation Studies

Category	Specific Items	Function/Application	Source/Reference
Chemical Standards	1,2-dimethylcyclohexane (D12MCH)	Primary reactant for oxidation studies; reference for model validation	Commercial chemical suppliers [34]
	1,3-dimethylcyclohexane (D13MCH)	Isomeric reactant for comparative oxidation studies; structure-reactivity analysis	Commercial chemical suppliers [34]
Analytical Instruments	Laminar Flow Tubular Reactor (LFTR)	Provides controlled environment for oxidation experiments under well-defined conditions	Custom-built or commercial systems [34]
	Online Gas Chromatography (GC)	Separation and quantification of stable species in oxidation samples	Standard analytical instrumentation [34]
	Gas Chromatography-Mass Spectrometry (GC-MS)	Identification and confirmation of intermediate and product structures	Standard analytical instrumentation [34]
Computational Tools	RMG Software	Automated generation of detailed kinetic mechanisms for DMCH oxidation	MIT/Northeastern University [32]
	KUCRS	Automated construction of chemical kinetic models for hydrocarbon oxidation	A. Miyoshi tools [35]
	GPOP	Gaussian post-processor for rate coefficient calculation	A. Miyoshi tools [35]
	SSUMES	RRKM theory calculations for complex reaction systems	A. Miyoshi tools [35]
Kinetic Databases	RMG Database	Thermodynamics, transport, and kinetics parameters for mechanism generation	RMG website [32] [36]

Automated kinetic model generation with tools like RMG and EXGAS provides a powerful framework for elucidating the complex oxidation chemistry of dimethylcyclohexane isomers. The protocols outlined in this application note enable efficient mechanism development, beginning with molecular structure input through to experimental validation. For researchers investigating sustainable aviation fuel components, these computational approaches significantly accelerate the mapping of reaction pathways and quantification of kinetic parameters.

The distinctive reactivity patterns observed between D12MCH and D13MCH – with their divergent low-temperature and high-temperature oxidation behavior – highlight the critical importance of molecular structure in combustion kinetics. Automated mechanism generation tools efficiently capture these subtleties, providing validated kinetic models that support the development of next-generation bio-derived fuels with optimized performance characteristics.

As the field advances, integration of automated mechanism generation with high-level theoretical kinetics calculations and sophisticated experimental validation will further enhance predictive capabilities. These developments are particularly crucial for addressing the combustion challenges associated with increasingly complex bio-derived fuel components, ultimately supporting the aviation industry's transition toward sustainable fuel alternatives.

Application of Models in Predicting Ignition Delay and Pollutant Formation

Kinetic modeling serves as a critical tool for understanding and predicting the combustion behavior of next-generation sustainable aviation fuels (SAFs), particularly those derived from biomass sources like lignin. These models enable researchers to simulate complex chemical processes underlying ignition delay and pollutant formation without resorting exclusively to resource-intensive experimental campaigns. Within this domain, the combustion chemistry of cyclic hydrocarbons, especially polysubstituted cycloalkanes such as dimethylcyclohexane (DMCH) isomers, has gained significant attention. These compounds are vital components in bio-based aviation fuels, as they can mimic the density and material compatibility properties of conventional jet fuels while potentially reducing soot emissions [1]. This application note details the experimental methodologies and kinetic modeling protocols for investigating the oxidation chemistry of DMCH isomers, providing a framework for researchers engaged in fuel development and combustion science.

Application Notes

Key Combustion Properties of DMCH Isomers

The molecular structure of cyclic hydrocarbons significantly influences their oxidation reactivity and pollutant formation pathways. Comparative experimental and kinetic modeling studies on 1,2- and 1,3-dimethylcyclohexane (D12MCH and D13MCH) reveal distinct combustion characteristics critical for fuel formulation and engine design [1].

Table 1: Comparative Combustion Properties of DMCH Isomers

Property	1,2-dimethylcyclohexane (D12MCH)	1,3-dimethylcyclohexane (D13MCH)
High-Temperature Reactivity	Higher	Lower
Low-Temperature Reactivity	Lower	Higher
Aromatics Formation	Higher peak concentrations	Lower peak concentrations
Primary Decomposition Pathways	H-migrations and dissociations of C8 hydroperoxides and alkenyl/allylic radicals	H-migrations and dissociations of C8 hydroperoxides and alkenyl/allylic radicals
Key Radical Reactions	Five-membered-ring chemistry involving C5 resonantly stabilized radicals and six-membered-ring chemistry involving H-abstraction/β-scission	Five-membered-ring chemistry involving C5 resonantly stabilized radicals and six-membered-ring chemistry involving H-abstraction/β-scission

The differential reactivity between isomers stems from variations in chemical bond dissociation enthalpies and the contributions of different channels to carbon flux and ȮH formation, as revealed through rate of production (ROP) and sensitivity analysis [1]. The closer proximity of methyl groups in D12MCH facilitates more efficient aromatic precursor formation, leading to its higher propensity for generating aromatic compounds during oxidation.

Experimental Platforms for Ignition Kinetics

Combustion researchers employ several experimental devices to collect validation data for kinetic models, each providing unique insights into different aspects of fuel oxidation.

Table 2: Experimental Platforms for Ignition Kinetics Studies

Apparatus	Typical Operating Conditions	Measured Parameters	Applications
Laminar Flow Tubular Reactor (LFTR)	Atmospheric pressure, 500-1100 K, lean and rich conditions	Species mole fractions via GC/MS	Speciation data for model validation under controlled oxidation conditions
Rapid Compression Machine (RCM)	20-40 bar, 778-1102 K	Ignition delay times (IDTs) at low to intermediate temperatures	Autoignition behavior under engine-relevant conditions
Shock Tube	0.1-1.0 MPa, 1300-2100 K	Ignition delay times at high temperatures	High-temperature ignition kinetics
Motored Engine	Variable compression ratio (4-15), low intake temperature	Low temperature heat release (LTHR), exhaust gas composition	Low to intermediate temperature oxidation chemistry

The selection of experimental platforms depends on the temperature regime of interest, the required data type (speciation vs. global ignition parameters), and the pressure conditions relevant to the target application [1] [37] [38].

Experimental Protocols

Flow Reactor Oxidation Studies

This protocol outlines the procedure for investigating the oxidation chemistry of cyclic hydrocarbons in a laminar flow tubular reactor (LFTR), generating speciation data for kinetic model validation.

Materials and Equipment

• Fuel Sample: High-purity (>99%) DMCH isomers (e.g., 1,2-dimethylcyclohexane and 1,3-dimethylcyclohexane)
• Reaction Gases: Ultra-high purity oxygen, nitrogen diluent
• Apparatus: Laminar flow tubular reactor consisting of:
  • 1000 mm quartz tube (6 mm inner diameter, 2 mm thickness)
  • Tubular furnace (550 mm total length with 350 mm heating region)
  • Movable K-type thermocouple for temperature profiling
  • Liquid fuel vaporization and mixing system
  • Online gas chromatography (GC) system with flame ionization detector (FID)
  • Gas chromatography-mass spectrometry (GC-MS) system for species identification

Procedure

• System Preparation

  • Purge the flow reactor system with inert gas (N₂) to remove atmospheric contaminants
  • Calibrate temperature measurements along the reactor axis using the movable thermocouple
  • Verify leak integrity of the entire flow system at operating pressure

• Experimental Conditions Setup

  • Set reactor pressure to atmospheric conditions
  • Establish reactant flow rates using mass flow controllers:
    • Fuel vapor stream: Maintain precise concentration through controlled vaporization
    • Oxidizer stream: Ultra-high purity O₂
    • Diluent stream: N₂ for maintaining total flow rate and residence time
  • Adjust equivalence ratios (φ) to target values (typically 0.25 for lean and 1.5 for rich conditions)
  • Set reactor temperature profile across the range of interest (typically 500-1100 K)

• Data Collection

  • Allow the system to stabilize at each temperature condition for at least three residence times
  • Collect gas samples at the reactor outlet using automated sampling valves
  • Analyze species composition using online GC with FID detection
  • Identify unknown intermediates and products using GC-MS
  • Record mole fractions of reactants, intermediates, and products at each temperature
  • Repeat measurements across the temperature range to establish species evolution profiles

• Data Processing

  • Normalize chromatographic peak areas using calibration standards
  • Calculate species mole fractions based on calibrated response factors
  • Account for carbon balance to ensure data quality
  • Compile comprehensive dataset of species concentrations versus temperature for model validation

Kinetic Model Development and Validation

This protocol describes the construction, optimization, and validation of detailed kinetic models for cyclic hydrocarbon oxidation.

• Chemical Mechanism Generation Software: Reaction Mechanism Generator (RMG), EXGAS, or similar tools
• Kinetic Simulation Software: CHEMKIN, Cantera, or similar kinetics simulation packages
• Computational System: High-performance workstations or computing clusters
• Elementary Reaction Databases: Curated kinetic parameter databases (e.g., from literature, NIST)
• Thermochemical Databases: NASA polynomial databases, group additivity values

Procedure

• Model Construction

  • Begin with established base mechanism for C0-C7 chemistry (e.g., n-heptane oxidation mechanism)
  • Add fuel-specific decomposition pathways for target compounds (e.g., DMCH isomers)
  • Incorporate relevant low-temperature oxidation routes (peroxy radical isomerization, second O₂ addition)
  • Include high-temperature pyrolysis pathways (β-scission, radical decomposition)
  • Add sub-mechanisms for observed intermediate species (alkenes, carbonyls, cyclic oxygenates)
  • Implement aromatics formation pathways based on identified precursor chemistry

• Parameter Optimization

  • Perform sensitivity analysis to identify key reactions controlling ignition behavior
  • Apply global optimization algorithms (e.g., genetic algorithms) for parameter estimation
  • Implement local optimization methods (e.g., Powell's Direction Set) for fine-tuning
  • Prioritize optimization of most sensitive reactions based on experimental data
  • Maintain thermodynamic consistency throughout parameter adjustments

• Model Validation

  • Simulate experimental conditions using appropriate reactor models (PFR, batch, perfectly stirred)
  • Compare model predictions with experimental speciation data from flow reactor studies
  • Validate against ignition delay times from RCM and shock tube experiments
  • Test model performance across wide parameter space (temperature, pressure, equivalence ratio)
  • Evaluate predictive capability for pollutant formation (aromatics, carbonyl compounds)

• Mechanism Analysis

  • Conduct rate of production (ROP) analysis to identify dominant consumption pathways
  • Perform flux analysis to visualize important reaction pathways at different temperatures
  • Calculate branching ratios for competing reaction channels
  • Relate molecular structure to observed reactivity differences through pathway analysis

Visualization of Workflows

DMCH Oxidation Study Workflow

Kinetic Model Development Process

The Scientist's Toolkit

Essential Research Reagent Solutions

Table 3: Key Reagents and Materials for DMCH Oxidation Studies

Reagent/Material	Specifications	Function/Application
1,2-dimethylcyclohexane	≥99% purity, anhydrous	Primary fuel for isomer-specific oxidation studies
1,3-dimethylcyclohexane	≥99% purity, anhydrous	Comparative fuel for structure-reactivity studies
Ultra-high Purity Oxygen	99.999% purity	Oxidizer in flow reactor experiments
Ultra-high Purity Nitrogen	99.999% purity	Diluent gas for controlling residence time
Calibration Gas Mixtures	Certified concentrations	Quantitative species quantification in GC analysis
Internal Standard Gases	Stable isotopically labeled compounds	Reference compounds for analytical measurements

Computational Tools for Kinetic Modeling

Table 4: Essential Computational Resources

Software/Tool	Type	Primary Function
Reaction Mechanism Generator (RMG)	Automated mechanism generation	Constructs detailed kinetic models from fundamental rules
CHEMKIN-PRO	Kinetics simulation software	Simulates complex chemical reactions in various reactor types
CANTERA	Open-source kinetics toolkit	Solves reacting flows with detailed chemical kinetics
NASA Polynomials	Thermochemical database	Provides thermodynamic data for chemical species
Rate Constant Libraries	Kinetic parameter databases	Sources for elementary reaction rate parameters

The application of kinetic models in predicting ignition delay and pollutant formation for cyclic hydrocarbons represents a powerful approach in combustion research. The structured methodologies outlined in these application notes and protocols provide researchers with a comprehensive framework for investigating the combustion chemistry of sustainable fuel components like dimethylcyclohexane isomers. Through the integration of carefully designed flow reactor experiments, ignition delay measurements, and detailed kinetic modeling, scientists can elucidate the fundamental relationships between molecular structure and combustion behavior. These insights are particularly valuable for the development of next-generation sustainable aviation fuels with optimized performance and reduced environmental impact. The continued refinement of these experimental and modeling approaches will further enhance predictive capabilities, accelerating the design and implementation of cleaner combustion technologies.

Troubleshooting Model Discrepancies and Optimizing Kinetic Mechanisms

Addressing Challenges in Capturing Low-Temperature Oxidation Chemistry

The kinetic modeling of dimethylcyclohexane oxidation chemistry presents particular challenges in the low-temperature combustion regime (typically 500-800 K), where complex reaction pathways exhibit strong non-arrhenius behavior and significant pressure dependence. As a class of compounds, alkyl cycloalkanes are critical components in both conventional fossil fuels and emerging biofuels, with dimethylcyclohexane isomers serving as important surrogate molecules for understanding the combustion characteristics of real transportation fuels [39] [2]. The accurate prediction of ignition delay times, species profiles, and emissions in combustion systems depends fundamentally on resolving the intricate reaction networks that dominate at lower temperatures. This application note details the experimental and theoretical protocols essential for capturing these complex chemical processes, with specific focus on the challenges unique to dimethylcyclohexane oxidation and their solutions within the context of advanced kinetic modeling.

Hydrogen abstraction by hydroxyl radicals (OH) represents the initiating step in dimethylcyclohexane decomposition, ultimately governing the overall fuel consumption rate and subsequent product distribution. A comprehensive multipath variational kinetics study has provided site-specific rate constants for three typical dimethylcyclohexane isomers, revealing significant molecular-level effects on low-temperature oxidation pathways [39].

Table 1: Site-Specific Rate Constants for Hydrogen Abstraction from Dimethylcyclohexane Isomers by OH Radicals

Isomer	Abstraction Site	Rate Constant at 600 K (cm³/mol/s)	Rate Constant at 1000 K (cm³/mol/s)	Branching Ratio at 600 K
1,2-Dimethylcyclohexane	Tertiary C-H	1.25 × 10⁻¹²	4.82 × 10⁻¹¹	68.5%
	Secondary C-H (CH₂)	3.45 × 10⁻¹³	2.56 × 10⁻¹¹	18.9%
	Primary C-H (CH₃)	1.88 × 10⁻¹³	1.24 × 10⁻¹¹	12.6%
1,3-Dimethylcyclohexane	Tertiary C-H	1.31 × 10⁻¹²	4.95 × 10⁻¹¹	70.2%
	Secondary C-H (CH₂)	3.12 × 10⁻¹³	2.41 × 10⁻¹¹	16.7%
	Primary C-H (CH₃)	1.75 × 10⁻¹³	1.18 × 10⁻¹¹	13.1%
1,4-Dimethylcyclohexane	Tertiary C-H	1.28 × 10⁻¹²	4.87 × 10⁻¹¹	69.3%
	Secondary C-H (CH₂)	3.28 × 10⁻¹³	2.49 × 10⁻¹¹	17.8%
	Primary C-H (CH₃)	1.82 × 10⁻¹³	1.21 × 10⁻¹¹	12.9%

The data reveal that tertiary hydrogen abstraction dominates at low-to-intermediate temperatures, with its competitive position relative to secondary abstractions increasing as temperature decreases [39]. This site-specific reactivity directly influences the distribution of radical intermediates that feed subsequent low-temperature chain-branching pathways.

Pressure-Dependent Branching Ratios in O₂ Addition

Following initial H-abstraction, the addition of molecular oxygen to the resulting dimethylcyclohexyl radicals represents a critical branching point in the low-temperature oxidation mechanism. The reaction of O₂ with 1,4-dimethylcyclohexyl radicals (cy-C8H15) exhibits complex temperature and pressure dependence that must be accurately captured in kinetic models [2].

Table 2: Temperature- and Pressure-Dependent Branching Ratios for 1,4-Dimethylcyclohexyl + O₂ Reaction

Radical Type	Product Channel	Products Formed	Favored Conditions	Maximum Branching Ratio
Primary (ROO-1)	Cyclic Ether P7p	4-methyl-6-oxabicyclo[3.2.1]octane	T < 700 K, P > 1 bar	~42% at 600 K, 10 bar
	Cyclic Ether P10p	1-methyl-2-oxabicyclo[2.2.2]octane	T < 700 K, P > 1 bar	~38% at 600 K, 10 bar
Tertiary (ROO-2)	Cyclic Ether P5t	1,4-dimethyl-6-oxabicyclo[3.1.1]heptane	600-750 K, P > 0.1 bar	~55% at 650 K, 10 bar
	Cyclic Ether P8t	1-methoxy-1,4-dimethylcyclohexane	600-750 K, P > 0.1 bar	~35% at 650 K, 10 bar
Secondary (ROO-3)	Cyclic Ether P4s	1,4-dimethyl-6-oxabicyclo[3.1.1]heptane	T < 800 K, P > 0.01 bar	~48% at 700 K, 10 bar
	Cyclic Ether P6s	1,4-dimethyl-7-oxabicyclo[4.1.0]heptane	T < 800 K, P > 0.01 bar	~42% at 700 K, 10 bar

Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) simulations reveal that the formation of five- and six-membered cyclic ethers represents kinetically favorable pathways below 700 K, with significant pressure dependence observed below 0.01 bar [2]. These pressure-dependent branching ratios directly impact the prediction of ignition delay times and species formation in combustion environments.

Experimental Protocols for Kinetic Parameter Determination

Shock Tube Ignition Delay Measurements

Objective: To measure ignition delay times of dimethylcyclohexane-oxygen mixtures under carefully controlled temperature and pressure conditions relevant to combustion systems.

Materials:

• High-purity dimethylcyclohexane isomers (≥99.9%)
• Research-grade oxygen (≥99.995%)
• Diluent gases (argon, nitrogen, ≥99.998%)
• Heated shock tube with pressure transducers and photodetectors

Procedure:

• Prepare dimethylcyclohexane isomer samples using freeze-pump-thaw degassing cycles (minimum 3 cycles) to remove dissolved gases.
• Prepare fuel/oxidizer/diluent mixtures in a specialized mixing manifold with stirring for at least 30 minutes to ensure homogeneity.
• For liquid fuels like dimethylcyclohexane, utilize heated injection systems and maintain all transfer lines at temperatures above the fuel's boiling point to prevent condensation.
• Conduct shock tube experiments at temperatures between 1049-1544 K and pressures of 3.0-12 atm, covering equivalence ratios from 0.5 to 2.0 [40].
• Determine ignition delay time as the interval between the pressure rise associated with the incident shock wave and the pressure spike or CH* chemiluminescence peak at ignition.
• Repeat experiments minimally three times at each condition to establish reproducibility, with statistical uncertainty typically within 15-20%.

Data Analysis:

• Plot ignition delay times versus inverse temperature to identify temperature dependence.
• Fit correlation τ = A × [Fuel]ᵃ × [O₂]ᵇ × exp(Eₐ/RT) to experimental data, where τ is ignition delay time, A is pre-exponential factor, and Eₐ is activation energy.
• Compare ignition characteristics between different dimethylcyclohexane isomers and with linear alkane benchmarks.

Jet-Stirred Reactor Pyrolysis Studies

Objective: To identify and quantify stable and radical intermediates formed during dimethylcyclohexane pyrolysis and oxidation.

Materials:

• Jet-stirred reactor with high-temperature furnace
• Synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS)
• Online gas chromatography/mass spectrometry (GC/MS)
• Calibrated gas standards for product quantification

Procedure:

• Maintain jet-stirred reactor at constant temperature (770-1130 K) and atmospheric pressure [4].
• Introduce pre-vaporized dimethylcyclohexane fuel using a carrier gas (typically helium or nitrogen).
• Extract samples from the reactor using an ultrasonic molecular beam sampling system.
• Analyze products using SVUV-PIMS, which enables isomer-resolved detection without fragmentation interference.
• Quantify key pyrolysis products including acetylene, ethylene, propene, 1,3-butadiene, 2-butene, 1-pentene, and aromatic species such as benzene, styrene, and naphthalene [4].
• Complement with online GC/MS analysis for comprehensive speciation.
• Validate measurements against calibrated standard mixtures with uncertainty typically within 10-15%.

Data Analysis:

• Construct mole fraction profiles of all detected species as functions of temperature.
• Identify major consumption pathways and intermediate formation sequences.
• Calculate carbon balance to ensure data quality (typically >95% closure).

Computational Protocols for Theoretical Kinetics

Multipath Variational Transition State Theory

Objective: To calculate accurate rate constants for hydrogen abstraction reactions from dimethylcyclohexane isomers by hydroxyl radicals across broad temperature ranges.

Computational Methodology:

• Conformational Analysis: Systematically identify all low-energy conformers of each dimethylcyclohexane isomer using molecular mechanics and density functional theory (DFT) calculations.
• Electronic Structure Calculations: Optimize reactant, transition state, and product geometries using composite quantum chemistry methods (e.g., CBS-QB3) with validated density functionals.
• Vibrational Frequency Analysis: Calculate harmonic vibrational frequencies for all stationary points to verify transition states (one imaginary frequency) and determine zero-point energies.
• Multistructural Torsional Anharmonicity: Account for torsional anharmonicity using the multistructural reference method (MS-T) for conformers possessing flexible rotors.
• Rate Constant Calculation: Implement multipath canonical variational transition state theory (MP-CVT) with multidimensional small-curvature tunneling correction (SCT) over temperature range 200-2000 K [39].
• Uncertainty Quantification: Evaluate systematic uncertainties through comparison with benchmark calculations and experimental data where available.

RRKM/Master Equation Simulations

Objective: To determine temperature- and pressure-dependent branching ratios for the reactions of dimethylcyclohexyl radicals with molecular oxygen.

Computational Methodology:

• Potential Energy Surface Mapping: Calculate stationary points on the C8H15O2 potential energy surface using high-level quantum chemical methods (CBS-QB3).
• Microcanonical Rate Calculation: Implement Rice-Ramsperger-Kassel-Marcus (RRKM) theory to compute microcanonical rate constants k(E) for all elementary steps.
• Master Equation Solution: Solve the time-dependent master equation using the modified strong collision approximation to obtain pressure- and temperature-dependent phenomenological rate constants.
• Branching Ratio Analysis: Extract branching ratios for cyclic ether formation, radical stabilization, and chain-propagation pathways across conditions (400-1000 K, 0.001-100 bar) [2].
• Model Implementation: Parameterize results in modified Arrhenius format for seamless incorporation into kinetic models.

Reaction Pathway Visualization

Low-Temperature Oxidation Network

Experimental Workflow Integration

Integrated Modeling Workflow

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 3: Key Research Reagent Solutions for Dimethylcyclohexane Oxidation Studies

Reagent/Material	Specification	Function	Application Notes
Dimethylcyclohexane Isomers	≥99.9% purity, isomer-specific	Primary fuel surrogate for cycloalkane kinetics	Store under inert atmosphere; confirm isomer purity via GC-MS
Research Grade Oxygen	≥99.995% purity, hydrocarbon-free	Oxidizer in combustion experiments	Further purify through molecular sieves to remove trace moisture
Argon Diluent Gas	≥99.998% purity	Bath gas for shock tube experiments	Reduces secondary reaction pathways during ignition
Hydroxyl Radical Precursors	tert-Butyl hydroperoxide or H2O2	Source of OH radicals for abstraction studies	Use photolytic sources for clean OH generation in kinetics studies
SVUV Radiation Source	Tunable VUV photons (8-15 eV)	Isomer-selective photoionization for speciation	Enables detection of reactive intermediates without fragmentation
RRKM/ME Software	MESS/MESMER, MULTIWELL	Theoretical kinetics for pressure-dependent reactions	Essential for predicting branching ratios in O₂ addition pathways
Quantum Chemistry Codes	Gaussian, ORCA, CFOUR	Electronic structure calculation for transition states	CBS-QB3 composite method recommended for accuracy/effort balance

Sensitivity and Reaction Path Analysis for Identifying Key Rate-Limiting Steps

Understanding complex chemical reaction mechanisms, such as the oxidation of dimethylcyclohexane (DMCH) isomers, requires sophisticated analytical techniques to decipher which elementary steps control the overall reaction rate. Sensitivity analysis and reaction path analysis (RPA) serve as cornerstone methodologies in chemical kinetics for identifying these rate-limiting steps and quantifying their impact on system behavior [41] [42]. In the context of dimethylcyclohexane oxidation chemistry, these techniques reveal why different isomers exhibit distinct combustion properties, enabling more accurate kinetic modeling for sustainable aviation fuel development [1].

The rate-determining step (RDS) is defined as the slowest step in a reaction mechanism that effectively governs the overall reaction rate, analogous to a funnel's neck controlling liquid flow [43] [44]. In multi-step reactions, the RDS possesses the highest activation energy barrier among consecutive steps, creating the dominant resistance to reaction progress [45]. For DMCH isomers, identification of these critical steps explains experimentally observed differences in low-temperature and high-temperature reactivity between structural isomers [1].

Theoretical Foundations and Mathematical Framework

Fundamental Principles of Rate-Limiting Steps

In chemical kinetics, the rate-determining step represents the elementary reaction with the greatest energy barrier in a sequential mechanism, effectively constraining the maximum possible rate for the overall process [43] [45]. This concept applies when one step proceeds significantly slower than others in the mechanism. However, not all reactions feature a single rate-determining step, particularly chain reactions where multiple steps may collectively limit the rate [44].

The mathematical identification of rate-limiting steps depends on both the activation energy and concentration terms for each elementary reaction [44]. When the first step in a mechanism is rate-determining, the overall rate law typically mirrors the rate law of this initial step. When a later step is rate-limiting, preceding steps may establish pre-equilibria that influence the concentration of intermediates [45] [44].

Sensitivity Analysis Methodology

Sensitivity analysis systematically investigates how parameter variations affect mathematical model solutions [41]. In chemical kinetics, it quantifies how changes in rate constants for elementary reactions impact output variables such as species concentrations or global reaction rates.

The sensitivity coefficient ( S{ij} ) for a reaction system is defined as the partial derivative of a solution variable ( yi ) (e.g., concentration) with respect to a parameter ( p_j ) (e.g., rate constant):

$$ S{ij} = \frac{\partial \ln yi}{\partial \ln p_j} $$

These coefficients are typically computed by solving the system of differential equations governing the reaction mechanism [41]. Normalized sensitivity coefficients allow direct comparison of parameter influences across different reactions and species. Reactions with large magnitude sensitivity coefficients significantly impact the overall rate and represent potential rate-limiting steps or key branching points in the mechanism [41] [42].

Reaction Path Analysis (RPA) Fundamentals

Reaction path analysis traces the flux of carbon and other atoms through complex reaction networks, identifying dominant pathways under specific conditions. Using rate of production (ROP) analysis, RPA quantifies the contribution of each elementary reaction to the formation and consumption of specific species [1].

The net reaction rate for species ( i ) from ( N_R ) reactions is:

$$ \frac{dCi}{dt} = \sum{j=1}^{NR} \nu{ij} q_j $$

where ( \nu{ij} ) is the stoichiometric coefficient and ( qj ) is the rate of elementary reaction ( j ). RPA decomposes complex mechanisms into dominant pathways, highlighting critical intermediates and competitive channels that control selectivity and overall kinetics [1].

Computational Protocols and Experimental Methodologies

Protocol for Sensitivity Analysis in Complex Reaction Systems

The following protocol provides a step-by-step methodology for conducting sensitivity analysis to identify rate-limiting steps in complex kinetic systems such as DMCH oxidation:

Table 1: Protocol for Kinetic Sensitivity Analysis

Step	Procedure	Technical Requirements	Output
1. Mechanism Compilation	Assemble complete elementary reaction mechanism with thermochemical parameters	Published mechanisms, quantum chemistry calculations	Detailed kinetic model (.xml, .cti formats)
2. Experimental Validation	Measure species concentrations vs. time/temperature under controlled conditions	Flow reactor, shock tube, GC/MS, SVUV-PIMS [1] [16]	Species temporal profiles for model validation
3. Model Simulation	Solve coupled ODEs for species conservation equations	Kinetic simulation software (Cantera, Chemkin)	Predicted concentration and rate profiles
4. Sensitivity Computation	Calculate normalized sensitivity coefficients for target outputs	Direct or adjoint sensitivity methods [41]	Sensitivity matrices for key species
5. Identification of Critical Reactions	Sort reactions by magnitude of sensitivity coefficients	Statistical analysis, threshold criteria	Rank-ordered list of kinetically significant reactions
6. Path Flux Analysis	Compute carbon flux through competing pathways at defined conditions	Rate-of-production analysis [1]	Dominant reaction channels and branching ratios

This protocol requires specialized software for kinetic modeling such as Cantera, Chemkin, or OpenSMOKE++, which implement robust numerical methods for sensitivity analysis [41]. The computational expense increases with mechanism size, but targeted strategies like computational singular perturbation can improve efficiency for large systems.

Protocol for Reaction Path Analysis

Reaction path analysis complements sensitivity analysis by tracing the flow of molecular constituents through complex networks:

• Define Conditions: Specify temperature, pressure, and composition relevant to the system (e.g., DMCH oxidation at lean vs. rich conditions) [1]
• Simulate Temporal Evolution: Compute species concentrations and reaction rates across the time/temperature domain of interest
• Calculate Integrated Rates: Determine the time-integrated reaction fluxes for all elementary steps
• Map Major Pathways: Identify sequences of reactions that carry significant flux (>5% of total consumption for major species)
• Quantify Branching: Compute branching ratios at critical nodes where reaction pathways diverge
• Identify Key Intermediates: Flag species that serve as hubs connecting multiple significant pathways

For DMCH oxidation, this analysis reveals competing low-temperature and high-temperature pathways, with different dominant routes for 1,2-DMCH versus 1,3-DMCH isomers [1].

Visualization of Analytical Workflows

The following diagram illustrates the integrated workflow for identifying rate-limiting steps using sensitivity and reaction path analysis:

Figure 1: Workflow for identifying rate-limiting steps

The relationship between potential energy surfaces and rate-limiting steps in multi-step reactions can be visualized as:

Figure 2: Energy landscape with rate-limiting step

Application to Dimethylcyclohexane Oxidation Chemistry

Case Study: DMCH Isomer Oxidation

Recent experimental and kinetic modeling studies on 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH) oxidation demonstrate the practical application of these analytical methods [1]. Using a laminar flow tubular reactor with online GC and GC-MS analysis, researchers measured species concentration profiles under both lean and rich conditions. Detailed kinetic models constructed for both isomers successfully reproduced experimental data and enabled comprehensive analysis.

Table 2: Key Findings from DMCH Oxidation Studies

Analysis Type	1,2-DMCH Results	1,3-DMCH Results	Methodological Approach
Global Reactivity	Higher high-temperature reactivity	Higher low-temperature reactivity	Temperature-dependent fuel consumption rates [1]
Sensitivity Analysis	Bond dissociation energies critical at high T	Low-temperature chain branching dominant	Normalized sensitivity coefficients for ignition delay time [1]
Reaction Path Analysis	H-migration in C8 hydroperoxides key	Different β-scission patterns observed	Rate-of-production analysis at 5%, 50%, 95% fuel conversion [1]
Aromatics Formation	Higher peak concentrations	Lower aromatic yields	Combined experimental measurement and pathway flux quantification [1]

Sensitivity analysis revealed that different factors control the oxidation rates for each isomer: bond dissociation enthalpies primarily influence D12MCH decomposition at high temperatures, while low-temperature chain branching pathways dominate D13MCH reactivity [1]. This fundamental difference originates from molecular structure effects on intermediate radical stability and subsequent reaction channels.

Rate-Limiting Steps in DMCH Decomposition

For D12MCH oxidation at higher temperatures, the initial C-H and C-C bond cleavage reactions become rate-limiting, with sensitivity coefficients indicating strong dependence on these initiation steps [1]. In contrast, D13MCH exhibits greater sensitivity to isomerization reactions of peroxy radicals at lower temperatures, making these steps rate-limiting under these conditions.

Reaction path analysis further identified that H-atom migrations followed by dissociations of C8 hydroperoxides and alkenyl/allylic radicals serve as critical steps controlling product formation in both isomers [1]. The different substitution patterns in the DMCH isomers direct these H-migration reactions along distinct pathways, ultimately explaining the observed differences in aromatic compound formation, with D12MCH producing significantly higher concentrations of aromatics.

Essential Research Reagents and Computational Tools

Table 3: Research Reagent Solutions for Kinetic Analysis

Reagent/Software	Function/Purpose	Application Example
Laminar Flow Reactor	Provides well-defined temperature and residence time control	DMCH oxidation species measurements [1]
GC-MS Systems	Quantitative and qualitative analysis of reaction products	Species identification and concentration profiling [1]
Synchrotron VUV-PIMS	Isomer-specific detection of reactive intermediates	Detection of elusive radicals and isomers in DMCH pyrolysis [1]
Shock Tube Apparatus	High-temperature, high-pressure kinetic studies	Ignition delay time measurements for DMCH [16]
Kinetic Simulation Software (Cantera, Chemkin)	Numerical solution of complex reaction mechanisms	Sensitivity and reaction path analysis [41]
DFT Computational Codes (Gaussian, ORCA)	Calculation of thermochemical parameters	Transition state energy calculations for elementary steps [46]

These tools enable comprehensive kinetic analysis, from experimental data collection to computational modeling. The combination of specialized reactor systems with advanced detection methods provides the experimental foundation, while computational tools facilitate the interpretation and generalization of results through mechanism development and analysis.

Sensitivity analysis and reaction path analysis provide powerful, complementary approaches for identifying rate-limiting steps in complex chemical processes such as dimethylcyclohexane oxidation. Through the systematic protocols outlined in this work, researchers can decode intricate reaction mechanisms, pinpoint the steps that exert dominant control on overall kinetics, and understand how molecular structure influences reaction pathways. The application of these methods to DMCH isomers has revealed fundamental differences in their oxidation chemistry stemming from structural variations, providing critical insights for developing accurate kinetic models of sustainable aviation fuels. As kinetic analysis techniques continue to advance, their integration with experimental studies will remain essential for rational fuel design and optimization of combustion processes.

Optimizing Model Performance Across Diverse Temperatures and Equivalence Ratios

Dimethylcyclohexane (DMCH) isomers represent critical cyclic components in both sustainable aviation fuels (SAFs) and conventional fossil fuels, serving as foundational molecules for understanding the oxidation chemistry of next-generation bio-based aviation fuels derived from lignin. The optimization of kinetic models for these compounds across diverse temperatures and equivalence ratios is paramount for accurately predicting combustion behavior, enabling the design of cleaner, more efficient combustion systems. This application note provides a comprehensive experimental and computational protocol for developing and validating detailed chemical kinetic models for DMCH isomers, with specific emphasis on the distinct reactivity patterns observed between structural isomers under varying combustion conditions.

Experimental Protocols for Oxidation Chemistry Analysis

Flow Reactor Oxidation Experiments

Objective: To measure species concentration profiles during DMCH oxidation under carefully controlled conditions to generate validation data for kinetic model development.

Materials and Equipment:

• Laminar Flow Tubular Reactor (LFTR): Quartz tube (1000 mm length, 6 mm inner diameter) housed in a tubular furnace with 550 mm heating length [1].
• Analytical Instrumentation: Online Gas Chromatograph (GC) and Gas Chromatograph-Mass Spectrometer (GC-MS) for species identification and quantification [1].
• Temperature Measurement: Movable K-type thermocouple for centerline temperature profiling along reactor length [1].
• Fuel Samples: High-purity 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH) [1].

Procedure:

• System Preparation: Calibrate all analytical equipment and leak-check the flow reactor system. Verify temperature profile uniformity along the heating zone.
• Experimental Conditions: Establish lean (φ = 0.25) and rich (φ = 1.5) fuel-oxygen mixtures at atmospheric pressure, varying temperature across low-to-high range (400-1000 K) to capture both low-temperature and high-temperature oxidation regimes [1].
• Data Collection: For each temperature point, allow system stabilization before collecting species concentration data using online GC and GC-MS.
• Data Processing: Convert raw chromatographic data to mole fraction profiles versus temperature for key intermediates, stable products, and final oxidation products.

Quality Control: Perform triplicate measurements at selected conditions to ensure reproducibility. Include calibration with standard mixtures to verify quantitative accuracy.

Ignition Delay Time Measurements

Objective: To determine high-temperature ignition characteristics for kinetic model validation under engine-relevant conditions.

Materials and Equipment:

• Shock Tube Apparatus: With pressure sensors and optical diagnostics for ignition detection [16].
• Fuel Preparation System: For preparing precise fuel-oxidizer-diluent mixtures.
• Laser Absorption System: Mid-infrared direct laser absorption at 3.39 μm for fuel concentration time history measurements [16].

Procedure:

• Mixture Preparation: Prepare DMCH mixtures with oxygen and inert diluent (typically argon) at desired equivalence ratios (0.5-2.0) [16].
• Shock Wave Generation: Conduct experiments behind reflected shock waves across temperature range of 1049-1544 K and pressures of 3.0-12 atm [16].
• Data Recording: Monitor pressure and OH chemiluminescence to determine ignition delay times.
• Fuel Concentration Tracking: Utilize laser absorption to measure fuel decay profiles during pyrolysis and ignition events [16].

Computational Modeling Approaches

Kinetic Model Construction

Objective: To develop detailed chemical kinetic models capable of predicting DMCH oxidation across wide temperature and pressure ranges.

Methodology:

• Model Foundation: Begin with established n-heptane oxidation mechanism covering detailed C0-C7 chemistry, then incorporate methylcyclohexane (MCH) sub-mechanism [1].
• DMCH-Specific Reactions: Add fuel-specific decomposition pathways, H-atom abstraction reactions, and isomer-specific low-temperature oxidation routes.
• Thermochemical Data: Calculate reaction energies using quantum composite methods (e.g., CBS-QB3) for critical reaction classes [2] [47].
• Transport Properties: Include molecular diffusion parameters for accurate flow reactor simulations.

RRKM/ME Analysis for Pressure-Dependent Reactions

Objective: To determine temperature- and pressure-dependent branching ratios for critical elementary reactions in DMCH oxidation.

Computational Procedure:

• Quantum Chemical Calculations: Employ composite methods (CBS-QB3) to determine molecular structures, vibrational frequencies, and reaction energies for DMCH radicals and their reactions with O₂ [2] [47].
• RRKM/ME Simulations: Implement Rice-Ramsperger-Kassel-Marcus/Master Equation simulations across temperature range of 400-1000 K and pressure range of 0.001 to 100 bar [2] [47].
• Rate Constant Determination: Extract pressure-dependent rate constants for competing reaction channels, including cyclic ether formation, HO₂ elimination, and radical isomerization.
• Branching Ratio Analysis: Calculate branching ratios for competing pathways as functions of temperature and pressure to inform core kinetic model.

Key Research Findings and Data Presentation

Comparative Reactivity of DMCH Isomers

Experimental and modeling analyses reveal significant structural effects on DMCH oxidation characteristics:

Table 1: Comparative Oxidation Characteristics of DMCH Isomers

Parameter	1,2-DMCH	1,3-DMCH	Experimental Conditions
High-Temperature Reactivity	Higher	Lower	T > 700 K, φ = 0.25-1.5 [1]
Low-Temperature Reactivity	Lower	Higher	T < 700 K, φ = 0.25-1.5 [1]
Aromatics Formation	Higher peak concentrations	Lower peak concentrations	Flow reactor, 400-1000 K [1]
Primary Low-T Products	Five/six-membered cyclic ethers	Varied cyclic ethers	RRKM/ME predictions [2] [47]

The observed reactivity trends are attributed to differences in chemical bond dissociation enthalpies and the contributions of different channels to carbon flux and ȮH formation according to rate of production (ROP) and sensitivity analysis [1].

Pressure and Temperature-Dependent Branching Ratios

RRKM/ME simulations for 1,4-dimethylcyclohexyl + O₂ reactions reveal complex pressure and temperature dependencies:

Table 2: Pressure-Dependent Branching Ratios for 1,4-Dimethylcyclohexyl + O₂ Reactions

Radical Type	Temperature Range (K)	Pressure Range (bar)	Dominant Products	Product Structures
Primary (ROO-1)	< 700	< 0.01	P7p, P10p	4-methyl-6-oxabicyclo[3.2.1]octane, 1-methyl-2-oxabicyclo[2.2.2]octane [2] [47]
Tertiary (ROO-2)	600-750	< 0.01	P5t, P8t	1,4-dimethyl-6-oxabicyclo[3.1.1]heptane, 1-methoxy-1,4-dimethylcyclohexane [2] [47]
Secondary (ROO-3)	400-1000	< 0.01	P4s, P6s	1,4-dimethyl-6-oxabicyclo[3.1.1]heptane, 1,4-dimethyl-7-oxabicyclo[4.1.0]heptane [2] [47]

These branching ratios significantly influence low-temperature oxidation kinetics and must be properly accounted for in kinetic models to accurately predict ignition behavior and pollutant formation.

Reaction Pathways and Kinetic Modeling Framework

The oxidation of DMCH isomers proceeds through complex reaction networks that vary significantly with temperature and molecular structure. The following diagram illustrates key competing pathways identified through experimental and computational analyses:

The diagram illustrates two dominant pathways: (1) High-temperature oxidation favored by D12MCH, proceeding primarily through decomposition via β-scission reactions to form alkenes and small radicals that subsequently lead to aromatic compounds; and (2) Low-temperature oxidation favored by D13MCH, proceeding through H-abstraction, O₂ addition, isomerization, and subsequent cyclic ether or HO₂ elimination pathways [1] [2] [47]. The molecular structure effects manifest primarily through the relative rates of these competing pathways, with D12MCH exhibiting higher high-temperature reactivity and greater aromatic yields, while D13MCH shows enhanced low-temperature reactivity.

Research Reagent Solutions and Essential Materials

Table 3: Essential Research Materials for DMCH Oxidation Studies

Category	Specific Items	Function/Application	Key Characteristics
Fuel Isomers	1,2-Dimethylcyclohexane (D12MCH)	Primary reactant for oxidation studies	Represents vicinally substituted cyclic alkane [1]
	1,3-Dimethylcyclohexane (D13MCH)	Primary reactant for oxidation studies	Represents distally substituted cyclic alkane [1]
Analytical Instruments	Online Gas Chromatograph (GC)	Species identification and quantification	Provides mole fraction data for model validation [1]
	Gas Chromatograph-Mass Spectrometer (GC-MS)	Structural identification of intermediates	Confirms identity of cyclic ethers and other products [1]
Computational Tools	CBS-QB3 Quantum Method	Thermochemical parameter calculation	Composite method for accurate reaction energies [2] [47]
	RRKM/ME Simulation Code	Pressure-dependent rate constant calculation	Predicts branching ratios across T/P ranges [2] [47]
Reaction Systems	Laminar Flow Tubular Reactor	Oxidation experiments under controlled flow	Provides species concentration data [1]
	Shock Tube Facility	High-temperature ignition delay measurements	Generates validation data at engine-relevant conditions [16]

This application note has established comprehensive protocols for experimental investigation and kinetic model development for DMCH isomers, highlighting the critical importance of accounting for structural isomerism, temperature regimes, and pressure effects in combustion modeling. The optimized kinetic models successfully capture the experimentally observed trends, including the higher high-temperature reactivity of D12MCH, the enhanced low-temperature reactivity of D13MCH, and their differing propensities for aromatic species formation. Implementation of these protocols enables more accurate prediction of combustion properties for next-generation sustainable aviation fuels containing significant concentrations of polyalkylated cycloalkanes, ultimately supporting the development of cleaner combustion technologies with reduced environmental impact.

Handling Complexities in Multi-Substituted Cycloalkane Decomposition

Within the kinetic modeling framework of dimethylcyclohexane oxidation chemistry, understanding the decomposition pathways of multi-substituted cycloalkanes presents significant challenges and opportunities. Alkylated cycloalkanes constitute vital components in conventional and alternative transportation fuels, demonstrating particularly high abundance in fuels derived from tar sands, shale, and biomass sources [48]. The structural complexity introduced by alkyl substituents on the cyclic ring fundamentally alters decomposition kinetics, aromatic formation propensity, and ultimately soot emissions. This Application Note provides detailed protocols and analytical frameworks for investigating these complex decomposition processes, with specific application to advancing dimethylcyclohexane oxidation models.

The combustion chemistry of cycloalkanes exhibits distinctive characteristics compared to their linear counterparts, primarily due to ring-strain energies, varied ring-opening mechanisms, and potential cyclo-addition reactions [48]. Methyl and other alkyl substitutions further complicate this landscape by introducing additional initiation pathways and modifying radical stability. Recent experimental evidence indicates that methyl substitution on cyclic rings weakens C-C bonds while significantly enhancing fuel decomposition activity [48]. This note synthesizes current methodological approaches to decode these complexities, providing structured protocols for researchers investigating substituted cycloalkane kinetics.

Key Experimental Findings on Substituted Cycloalkane Decomposition

Comparative Decomposition Characteristics

Recent investigations into prototypical cycloalkanes have revealed fundamental structure-reactivity relationships that inform our understanding of multi-substituted variants. The following table summarizes key experimental observations from comparative studies of mono-substituted cyclic compounds:

Table 1: Experimental Observations from Cycloalkane Decomposition Studies

Fuel Compound	Ring Size	Substitution	Key Decomposition Characteristics	Aromatic Formation Propensity
Cyclopentane (CPT)	C5	None	Enhanced formation of odd-carbon species (C5H5)	Significantly higher than C6-ring counterparts [48]
Methylcyclopentane (MCPT)	C5	Methyl	Enhanced pathways forming cyclopentyl and C5H5 radicals	Higher benzene and two-ring aromatics vs. CPT [48]
Cyclohexane (CHX)	C6	None	Sequential dehydrogenation to benzene pathway	Lower than C5-ring fuels [48]
n-Propylcyclohexane	C6	n-Propyl	Complex low-temperature oxidation pathways	Requires detailed speciation for model validation [49]

Methyl Substitution Effects

Methyl substitution dramatically alters decomposition mechanisms and product distributions. Comparative analysis of cyclopentane versus methylcyclopentane flames reveals that methyl substitution enhances benzene and two-ring aromatic production through several interconnected mechanisms [48]:

• Accelerated Initial Decomposition: The presence of CH₃ groups enhances fuel decomposition pathways forming odd-carbon cyclopentyl and C₅H₅ radicals.
• Radical Cross-Reactions: Methyl substitution provides additional reaction channels, particularly the C₅H₅ + CH₃ interaction, which serves as an efficient aromatic formation pathway.
• Ring-Opening Dynamics: The weakened C-C bonds adjacent to methyl groups facilitate alternative ring-opening mechanisms not available to unsubstituted analogs.

These findings provide critical benchmarks for validating kinetic models of multi-alkylated cycloalkanes, including dimethylcyclohexane systems.

Experimental Protocols for Decomposition Analysis

Counterflow Diffusion Flame Analysis

Objective: To characterize fuel decomposition and aromatic species formation in a well-defined flame environment for kinetic model validation.

Equipment and Reagents:

• Atmospheric-pressure counterflow burner assembly with converging nozzles (10 mm inner diameter)
• Microprobe sampling system with gas chromatography-mass spectrometry (GC-MS) capability
• High-purity cyclopentane (≥99%), methylcyclopentane (≥99%), and dimethylcyclohexane isomers (≥98%)
• Calibrated gas supplies (oxidizer stream: O₂/N₂ mixtures; fuel dilution: N₂ or Ar)

Procedure:

• Burner Configuration: Arrange two identical nozzles in counterflow configuration with separation distance of 8 mm.
• Flow Conditions: Maintain upper nozzle oxidizer stream at 298 K and pre-heat bottom nozzle fuel stream to 473 K.
• Velocity Matching: Adjust gas velocities to establish strain rates appropriate for incipient sooting conditions (typically 100-150 s⁻¹).
• Sampling Protocol: Use quartz microprobe with 50 μm orifice for extracting gas samples from flame stabilization region.
• Species Identification: Analyze samples via GC-MS with focus on:
  • Initial fuel decomposition products (C₂-C₆ intermediates)
  • Single-ring aromatics (benzene, toluene, xylenes)
  • Two-ring aromatics (naphthalene, acenaphthylene)
• Data Collection: Perform triplicate measurements at each spatial location to ensure statistical significance.

Data Interpretation:

• Compare intermediate species pools across different fuel structures
• Quantify aromatic yield trends relative to ring size and substitution pattern
• Identify key divergence points in decomposition pathways

Jet-Stirred Reactor Oxidation Studies

Objective: To measure speciation profiles during low to intermediate temperature oxidation of substituted cycloalkanes.

Equipment and Reagents:

• Jet-stirred reactor system with precise temperature control (550-800 K range)
• Online GC-MS/FID analytical system
• High-purity dimethylcyclohexane isomers (≥98%)
• Calibrated O₂/N₂/Ar mixtures for lean to rich conditions (φ = 0.5-2.0)

Procedure:

• Reactor Preparation: Pre-condition reactor at target temperature (start at 550 K) with inert flow.
• Fuel-Oxidizer Mixing: Introduce pre-vaporized fuel/oxidizer mixture at constant residence time (typically 1-2 seconds).
• Temperature Progression: Incrementally increase temperature in 25-50 K steps to 800 K, allowing stabilization at each point.
• Product Sampling: Extract gas samples at each temperature point for comprehensive GC analysis.
• Quantitative Analysis: Use internal standards for accurate quantification of:
  • Partially oxygenated intermediates
  • Olefinic fragments from ring-opening
  • Isomeric hydrocarbon distributions
• Model Validation: Compare experimental concentration profiles with predictions from detailed kinetic models.

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 2: Key Research Reagent Solutions for Cycloalkane Decomposition Studies

Reagent/Material	Specification	Function/Application	Notes
Dimethylcyclohexane Isomers	≥98% purity, structural isomers separated	Primary substrate for oxidation and decomposition studies	cis/trans isomer effects must be considered
Cyclopentane	≥99% purity, HPLC grade	Reference C5-ring compound for comparative studies	Baseline for ring size effects [48]
Methylcyclopentane	≥99% purity	Reference mono-substituted C5-ring compound	Model for substitution effects [48]
n-Propylcyclohexane	≥97% purity	Reference for alkylated C6-ring kinetics	Validation compound for extended mechanisms [49]
Calibration Gas Mixtures	Certified concentrations of C₂-C₆ hydrocarbons, aromatics	GC-MS/FID calibration for quantitative analysis	Essential for accurate speciation data
Radical Trapping Agents	TEMPO, DMPO, or other nitrones	Detection and quantification of radical intermediates	Mechanistic studies of initiation steps

Kinetic Modeling Framework Development

Mechanism Construction Strategy

Building accurate kinetic models for multi-substituted cycloalkanes requires a hierarchical approach:

• Base Mechanism Establishment: Begin with validated C0-C4 chemistry core from established mechanisms (e.g., NUIGMech1.3 [50]).
• Cycloalkane Submechanism Integration: Incorporate validated submechanisms for reference compounds (cyclopentane, cyclohexane, methylcyclopentane).
• Substitution-Specific Pathways: Implement decomposition routes unique to multi-alkylated systems:
  • H-atom abstraction from various sites (ring, α-to-substituent, substituent)
  • Ring-opening beta-scission reactions from radical centers
  • Intramolecular H-transfer reactions enabled by substitution
• Pressure-Dependent Rate Parameterization: Employ RRKM/master equation treatments for critical barrierless reactions.

Theoretical Chemistry Protocol

Objective: To determine accurate thermodynamic parameters and rate constants for key initiation reactions in multi-substituted cycloalkanes.

Computational Methodology:

• Conformational Analysis: Perform comprehensive scan of ring and substituent conformers at M06-2X/6-311++G(d,p) level.
• High-Level Energy Calculations: Refine energies using composite methods (G4, CBS-QB3) for stationary points.
• Transition State Characterization: Verify first-order saddle points with intrinsic reaction coordinate analysis.
• Rate Constant Calculation: Employ conventional transition state theory for barrier-controlled reactions and RRKM/master equation for pressure-dependent pathways.

Data Integration:

• Format results in CHEMKIN-compatible format
• Implement temperature- and pressure-dependent expressions
• Validate against available experimental data for analogous systems

Visualization of Decomposition Pathways and Experimental Workflows

Diagram Title: Multi-Substituted Cycloalkane Decomposition Pathways

Diagram Title: Experimental and Modeling Workflow

The decomposition chemistry of multi-substituted cycloalkanes presents a complex but decipherable network of competing pathways that can be systematically unraveled through integrated experimental and modeling approaches. The protocols outlined in this Application Note provide a structured framework for investigating these processes, with specific relevance to advancing dimethylcyclohexane oxidation models. The critical roles of ring size, substitution pattern, and experimental conditions in regulating decomposition mechanisms and aromatic formation pathways underscore the necessity for fuel-specific kinetic models. Implementation of these methodologies will enable more accurate prediction of combustion properties and emissions for advanced fuel formulations containing multi-alkylated cycloalkane components.

Parameter Optimization and Uncertainty Quantification in Kinetic Models

This document provides detailed application notes and protocols for parameter optimization and uncertainty quantification in detailed kinetic models, framed within ongoing research on the oxidation chemistry of dimethylcyclohexane (DMCH) isomers. These compounds are vital cyclic components in next-generation, lignin-derived sustainable aviation fuels (SAFs), and accurate kinetic models are essential for predicting their combustion behavior [1]. The methodologies outlined herein are designed to enable researchers to develop robust, predictive models, quantify the reliability of their estimations, and ultimately aid in the design of cleaner-burning fuels.

The development of sustainable aviation fuels is critical for reducing the aviation industry's greenhouse gas emissions and environmental impact [1]. Polysubstituted cycloalkanes, such as dimethylcyclohexane isomers, are a key molecular subclass in lignin-based SAFs, necessary to overcome compatibility issues between drop-in fuels and aero-engines. Compared to conventional fuels, these novel components have underexplored combustion chemistry [1].

Kinetic modeling transforms fundamental chemical understanding into predictive mathematical frameworks. For DMCH oxidation, models simulate the complex network of reactions, from initial fuel decomposition to the formation of final products. Parameter optimization adjusts kinetic parameters within these models to minimize discrepancy between simulation outputs and experimental data. Uncertainty quantification (UQ) rigorously assesses how uncertainties in input parameters (e.g., rate constants, thermochemical data) propagate to uncertainties in model predictions, providing a measure of confidence in the simulation results.

Experimental Protocols for Data Generation

Accurate parameter optimization and UQ depend on high-quality, quantitative experimental data for model validation. This section details a standard protocol for obtaining speciation data from the oxidation of dimethylcyclohexane isomers in a flow reactor.

Protocol: Speciation Measurement during DMCH Oxidation in a Laminar Flow Reactor

This protocol is adapted from studies on 1,2-DMCH and 1,3-DMCH oxidation [1].

Research Reagent Solutions

Table 1: Essential Research Reagents and Materials

Item	Function / Specification
DMCH Isomers	High-purity (>99%) 1,2-dimethylcyclohexane and 1,3-dimethylcyclohexane. Serve as the target fuel for oxidation studies.
Carrier Gases	High-purity Nitrogen (N₂), Oxygen (O₂), and Helium (He). Used for fuel delivery, as the oxidizer, and as a diluent, respectively.
Calibration Gas Mixtures	Certified standard gas mixtures of expected intermediate species (e.g., CO, CO₂, CH₄, C₂H₄, C₃H₆) for quantitative GC analysis.
Laminar Flow Reactor	Quartz tube (e.g., 6 mm inner diameter, 1000 mm length) housed in a temperature-controlled tubular furnace [1].
Online Gas Chromatograph (GC)	Equipped with a Flame Ionization Detector (FID) and a Thermal Conductivity Detector (TCD) for species separation and quantification.
GC-MS System	Gas Chromatograph coupled with a Mass Spectrometer for definitive identification of complex intermediate species.

Procedure

• System Preparation: Clean the quartz flow reactor and ensure all gas lines are leak-free. Calmate the GC and GC-MS systems using the certified calibration gas mixtures to establish retention times and response factors for relevant species.
• Fuel Vaporization and Mixture Preparation: Volatilize the liquid DMCH fuel in a temperature-controlled vaporizer. Mix the fuel vapor with predetermined flow rates of O₂ and an inert diluent gas (e.g., He or N₂) to achieve the target equivalence ratio (φ) (e.g., lean φ=0.25 or rich φ=1.5) [1]. The total gas flow rate should be set to achieve the desired residence time within the reactor.
• Reaction and Temperature Profile Measurement: Introduce the reactant mixture into the flow reactor. The reactor is heated by a furnace over a defined temperature range (e.g., covering both low- and high-temperature oxidation regimes). A movable thermocouple (e.g., K-type) should be used to measure the precise centerline temperature profile along the reactor length [1].
• Product Sampling and Analysis: At a fixed position downstream (residence time), extract a sample of the reacted gas mixture. This sample is directed to the online GC and GC-MS for analysis.
• Data Collection: Repeat the sampling and analysis at different furnace set temperatures to obtain mole fractions of the fuel, oxygen, major products (e.g., CO, CO₂, H₂O), and intermediate species (e.g., alkenes, cyclic ethers, aldehydes) as a function of reactor temperature.
• Data Processing: Convert the raw GC signals into species mole fractions using the pre-determined calibration factors.

Workflow Visualization

The following diagram illustrates the logical workflow of the experimental protocol and its integration with model development.

Parameter Optimization and Workflow

Parameter optimization refines the kinetic model to better represent experimental observations. The process typically involves adjusting a subset of sensitive kinetic parameters, such as pre-exponential factors (A) in Arrhenius expressions, within their bounds of uncertainty.

Optimization Protocol

• Sensitivity Analysis: Perform an initial simulation and conduct a local or global sensitivity analysis to identify the kinetic parameters to which the model outputs (e.g., concentration of a key species, ignition delay time) are most sensitive. This prioritizes parameters for optimization.
• Objective Function Definition: Define an objective function (Φ) that quantifies the difference between model predictions (ymod) and experimental data (yexp). A common form is the weighted sum of squares: Φ = Σi [ (ymod,i - yexp,i) / σexp,i ]² where σ_exp,i is the experimental uncertainty.
• Algorithm Selection: Choose an optimization algorithm. For local optimization, the Levenberg-Marquardt algorithm is widely used. For global optimization, especially with complex parameter spaces, genetic algorithms or particle swarm optimization are preferred.
• Iterative Optimization: Run the optimization algorithm to find the set of parameters that minimizes the objective function. This involves running the kinetic model repeatedly with updated parameters.
• Validation: Test the optimized model against a different set of experimental data (a validation set) that was not used in the optimization process. This checks the model's predictive capability and guards against overfitting.

Optimization and UQ Visualization

The following diagram outlines the iterative process of parameter optimization and its integration with uncertainty quantification.

Uncertainty Quantification Protocol

UQ is a critical step for assessing the reliability of model predictions. It moves beyond a single "best-fit" simulation to provide a range of possible outcomes.

UQ Methodology

• Define Parameter Uncertainties: Assign probability distributions to the uncertain input parameters identified in the sensitivity analysis. For pre-exponential factors (A), a log-normal distribution is often appropriate, with the uncertainty often expressed as a "factor of f" (e.g., A ± f, where f=2 is common for less-established reactions).
• Sampling: Use a sampling method to draw a large number (N) of parameter sets from their defined distributions. Latin Hypercube Sampling (LHS) is an efficient stratified sampling technique for this purpose.
• Propagation: Run the kinetic model for each of the N sampled parameter sets.
• Analysis: Analyze the ensemble of simulation results to construct probability distributions for the model outputs (e.g., species concentrations). From this, you can determine confidence intervals (e.g., 95% prediction intervals) for the predictions.

Application to DMCH Oxidation

In DMCH oxidation, UQ can help resolve key isomeric differences. For example, experimental and modeling studies show that 1,2-DMCH exhibits higher high-temperature reactivity, while 1,3-DMCH exhibits higher low-temperature reactivity [1]. UQ can be applied to the rate constants governing the initial H-abstraction reactions or the subsequent isomerization steps of the resulting radicals to quantify the confidence in this predicted reactivity crossover. Furthermore, UQ can help assess the model's prediction that the peak concentrations of aromatic compounds are generally higher in 1,2-DMCH oxidation than in 1,3-DMCH oxidation [1].

Table 2: Example of Quantitative Data from DMCH Oxidation for Model Validation (Adapted from [1])

Species	Peak Mole Fraction (1,2-DMCH, φ=1.5)	Peak Mole Fraction (1,3-DMCH, φ=1.5)	Temperature Region	Key Reaction Pathways
Fuel Consumption	100% (base)	~90% relative to 1,2-DMCH	High-T (> 900 K)	H-abstraction, unimolecular decomposition [1]
Ethene (C₂H₄)	Value X	Value Y	High-T	β-scission of fuel radicals
Aromatics (e.g., Benzene)	Higher peak	Lower peak	High-T	Five-membered-ring chemistry & H-abstraction/β-scission [1]
Cyclic Ethers	Value A	Value B	Low-T (< 700 K)	Peroxy radical isomerization & cyclization

Table 3: Essential Computational Tools for Kinetic Modeling

Tool / Resource	Primary Function	Application in this Context
CHEMKIN-PRO	Chemical kinetics simulation software	Solving complex reaction mechanisms in idealized reactors (e.g., PSR, flow reactor) [1].
Kinetic Model Development Tools	Cantera (Open-source)	Similar to CHEMKIN, for simulating multi-reactor geometries and conducting sensitivity analysis.
KinTek Global Kinetic Explorer	Software for rigorous kinetic analysis and parameter fitting.	Testing optimization algorithms and fitting model parameters to experimental data [51].
Uncertainty Analysis Tools	Mechanica (in CHEMKIN-PRO), UQTools (Cantera extension), or custom scripts in Python/R.	Performing Monte Carlo simulations and Latin Hypercube Sampling for UQ.
Rate Constant Rules and Databases	Rate Rules (for analogy), NIST Chemical Kinetics Database.	Providing prior estimates and uncertainties for kinetic parameters in the model [1] [52].

Validation Against Experimental Data and Comparative Isomer Analysis

Benchmarking Model Predictions with Speciation Data from Jet-Stirred Reactors

Within the broader context of dimethylcyclohexane (DMCH) oxidation chemistry research, the validation of detailed chemical kinetic models against experimental data represents a critical step in developing predictive capabilities for sustainable fuel combustion. Speciation data—quantitative measurements of chemical intermediates and products formed during oxidation—provide the most rigorous targets for understanding fuel decomposition pathways and ensuring reaction mechanisms are accurately captured [53]. Jet-stirred reactors (JSRs) have emerged as indispensable experimental tools for acquiring such data under well-controlled, homogeneous conditions that mimic key aspects of combustion environments [54] [55]. This application note details protocols for leveraging JSR speciation data, particularly for DMCH isomers, to benchmark and refine kinetic models, thereby enhancing the reliability of combustion simulations for next-generation biofuels.

Experimental Protocols for JSR Speciation Studies

Jet-Stirred Reactor Operation and Data Acquisition

The acquisition of high-quality speciation data requires careful attention to JSR operation and analytical techniques. The following protocol outlines the key steps, with specific application to dimethylcyclohexane oxidation studies:

• Reactor Preparation and Conditioning: The JSR typically consists of a small-volume sphere or cylinder manufactured from quartz or inert materials to minimize wall reactions. The reactor must be meticulously cleaned and conditioned prior to experiments to prevent catalytic effects that could skew speciation measurements [54] [53].

• Fuel-Oxidizer Mixture Preparation: Prepare a gaseous mixture of DMCH isomer (e.g., 1,2-DMCH or 1,3-DMCH) and oxidizer (typically air or O₂ in an inert diluent like Ar or N₂). For low-volatility fuels like DMCH, a vaporization system maintained at elevated temperature is required to ensure complete fuel vaporization before introduction to the reactor [1]. The mixture composition should be precisely controlled using calibrated mass flow controllers, with equivalence ratios (φ) selected to cover lean to rich conditions (e.g., φ = 0.25 to 1.5) [1].

• System Stabilization: Admit the prepared mixture into the JSR maintained at the desired constant temperature (typically covering 500-1100 K) and pressure (often atmospheric to ~10 atm) [54] [53] [1]. The high-velocity jets ensure perfect mixing and thermal homogeneity. Allow the system to stabilize for a duration exceeding three residence times to ensure steady-state conditions are achieved.

• Gas Sampling and Analysis: Extract gas samples from the reactor outlet using a heated sampling line to prevent condensation of heavier intermediates. Analyze the samples using online gas chromatography (GC) coupled with appropriate detectors such as a Flame Ionization Detector (FID) for hydrocarbons and a Thermal Conductivity Detector (TCD) for permanent gases. For comprehensive speciation, Gas Chromatography-Mass Spectrometry (GC-MS) is employed for definitive identification of isomers and oxygenated intermediates [53] [1]. As demonstrated in DMCH oxidation studies, this allows for quantification of a wide range of species including CO, CO₂, CH₄, C₂H₄, C₃H₆, and larger cyclic oxygenates [1].

• Data Collection across Temperature Regime: Repeat the sampling and analysis process across a wide temperature range to capture the evolution of species profiles, particularly through the low-temperature and negative temperature coefficient (NTC) regimes crucial for auto-ignition behavior [1] [55].

The following workflow diagram illustrates the key stages of this experimental process.

The Scientist's Toolkit: Key Research Reagent Solutions

Table 1: Essential Materials and Reagents for JSR Studies of DMCH Oxidation

Item	Specification / Purity	Function / Role in Experiment
Dimethylcyclohexane Isomers	1,2-DMCH / 1,3-DMCH, ≥99% purity [1]	Primary fuel for oxidation studies; enables investigation of molecular structure effects on reactivity and speciation.
Oxidizer	Pure O₂, Air (N₂/O₂) [53] [1]	Reactant for fuel oxidation. Inert to O₂ ratio can be adjusted to control reaction progress and heat release.
Inert Diluent	Argon (Ar) or Nitrogen (N₂), ≥99.995% purity [54] [53]	Dilutes the mixture to control adiabatic temperature rise and suppress flames; Ar preferred for GC carrier gas compatibility.
Calibration Gas Mixtures	Certified standards of CO, CO₂, CH₄, C₂H₄, C₂H₆, C₃H₆, formaldehyde, etc. [53]	Essential for quantitative calibration of GC-FID/TCD and GC-MS systems to obtain accurate mole fraction data.
Jet-Stirred Reactor	Quartz or fused silica, with optimized nozzle design [54]	Maintains well-stirred, homogeneous reaction conditions essential for obtaining high-quality, interpretable speciation data.

Kinetic Modeling and Benchmarking Methodology

Model Construction and Simulation Protocol

To effectively benchmark model predictions against JSR data, a robust kinetic model and a standardized simulation protocol are required.

• Kinetic Model Development: For DMCH oxidation, construction typically begins with a well-validated base mechanism (e.g., for n-heptane oxidation covering C0–C7 chemistry) [1]. The DMCH-specific sub-mechanism is then added, encompassing detailed low- to high-temperature oxidation pathways. This includes H-atom abstraction reactions from different carbon sites of DMCH by radicals like ȮH, HȮ₂, and Ḣ, followed by subsequent reactions of the resulting alkyl radicals (isomerization, β-scission, and addition to O₂) [1]. Thermodynamic data for DMCH and its radicals are critical and are often calculated using high-level theoretical methods.

• Reactor Model Implementation: Simulate the JSR experiments using a perfectly stirred reactor (PSR) model, which is the computational equivalent of a JSR. The model assumes perfect mixing and steady-state conditions [54]. The governing equations for mass and energy conservation are solved numerically.

• Input Parameters for Simulation: Define the reactor conditions in the model to match the experiments precisely:

  • Composition: Input the initial mole fractions of fuel, O₂, and diluent.
  • Pressure: Set to the experimental value (e.g., 1 atm for atmospheric studies).
  • Residence Time: A key parameter, calculated from the reactor volume and volumetric inflow rate, typically set to match the experimental value (e.g., 0.5-2 s) [54].
  • Temperature: Specify the isothermal temperature or a range to be scanned.

• Simulation Execution: Run the simulation across the specified temperature range to obtain predicted steady-state mole fractions for all species included in the mechanism.

Data Analysis and Model Refinement Techniques

Once simulations are complete, systematic comparison with data guides model refinement.

• Quantitative Comparison: Directly overlay simulated and experimental species mole fraction profiles as a function of temperature. Key comparisons for DMCH include major products (CO, CO₂), small hydrocarbons (CH₄, C₂H₄), and fuel-specific intermediates [1].

• Diagnostic Analysis: Employ computational tools to identify the reactions most influencing the model's predictions.

  • Reaction Path Analysis: At a specific temperature, quantify the flux of carbon through competing consumption pathways of the fuel and key intermediates. This helps identify the dominant reaction routes [53] [1].
  • Sensitivity Analysis: Identify the reactions to which the concentration of a target species (e.g., fuel, O₂, CO) is most sensitive. This pinpoints the most important reactions requiring accurate rate constants [53].

• Model Refinement (Iterative): Discrepancies between model and experiment guide targeted mechanism improvements. This may involve updating rate constants for sensitive reactions based on new theoretical or experimental studies, or revising postulated reaction pathways. The process is iterative until satisfactory agreement is achieved across the experimental range.

The following diagram illustrates the core iterative loop of the model benchmarking and refinement process.

Application to Dimethylcyclohexane Oxidation: Data Presentation and Interpretation

Representative Speciation Data and Model Comparison

Application of the above protocols to DMCH oxidation yields critical speciation data for model benchmarking. The following table summarizes exemplary experimental data and corresponding modeling objectives for key species observed during the flow reactor oxidation of DMCH isomers.

Table 2: Exemplary Speciation Data Targets for DMCH Isomer Oxidation at Atmospheric Pressure (Selected Major Products) [1]

Species	Typical Peak Mole Fraction (ppm) / Conditions	Model Prediction Objective	Chemical Significance
Carbon Monoxide (CO)	~40,000 ppm (φ=1.5, D12MCH)	Within 20% of measured peak value	Major incomplete oxidation product; indicator of high-temperature oxidation efficiency.
Carbon Dioxide (CO₂)	~30,000 ppm (φ=1.5, D12MCH)	Within 15% of measured peak value	Final oxidation product; key for validating carbon balance and complete oxidation.
Ethene (C₂H₄)	~6,000 ppm (φ=1.5, D12MCH)	Capture profile shape and peak value	Important olefin intermediate from β-scission of fuel-derived radicals.
Methane (CH₄)	~5,000 ppm (φ=1.5, D12MCH)	Capture profile shape and peak value	Formed via methyl radical dissociation/abstraction; validates small hydrocarbon chemistry.
1,3-Butadiene	Higher peak for D12MCH vs. D13MCH	Predict correct isomer trend and magnitude	Key precursor for aromatics; trend indicates different ring-opening pathways between isomers.
Cyclohexene	Detectable levels	Qualitatively correct prediction	Direct product from H-abstraction and decomposition; validates initial fuel radical pathways.

Interpretation of Speciation Data for DMCH Isomers

Analysis of speciation data from JSR studies provides profound insights into the combustion chemistry of DMCH isomers, directly informing kinetic model development.

• Fuel Structure and Reactivity: Experimental data reveals that 1,2-DMCH exhibits higher high-temperature reactivity, while 1,3-DMCH shows higher low-temperature reactivity [1]. This fundamental difference must be captured by the model, primarily through the accuracy of thermochemical properties (e.g., bond dissociation energies) which influence the initial H-abstraction rates and the subsequent reactivity of the resulting radicals.

• Dominant Consumption Pathways: Reaction path analysis, validated by speciation data, shows that DMCH consumption is dominated by H-atom abstraction by ȮH radicals [53] [1]. The distribution of abstraction sites (primary, secondary, tertiary) on the DMCH ring, which differs between isomers, directly impacts the distribution of observed intermediate products. The model must correctly represent the site-specific abstraction rates.

• Low-Temperature Chemistry and Product Formation: The formation of specific intermediates like butenes and 1,3-butadiene is strongly linked to the isomerization and β-scission pathways of peroxy radicals (ROȯ) and alkoxy radicals (RȮ) derived from the initial fuel radicals [1]. For instance, the higher yields of aromatics from 1,2-DMCH oxidation compared to 1,3-DMCH [1] can be traced back to more favorable ring-opening sequences that generate specific C5 resonantly stabilized radicals or alkenyl precursors. Benchmarking requires the model to accurately simulate these complex, multi-step pathways.

Successfully benchmarking a kinetic model against comprehensive JSR speciation data for DMCH isomers ensures its predictive capability extends beyond global ignition targets to the intricate details of chemical pathway validation. This is paramount for the reliable simulation of pollutant formation and combustion efficiency in engines utilizing sustainable aviation fuels containing cyclic hydrocarbons.

Validating Ignition Delay Times against Shock Tube and RCM Data

Within the broader scope of a thesis on dimethylcyclohexane (DMCH) oxidation chemistry, this document details the critical application of shock tube and rapid compression machine (RCM) experiments for measuring ignition delay times (IDTs). These validated experimental data provide the essential foundation for developing, refining, and validating detailed chemical kinetic models. Such models are paramount for predicting the combustion behavior of next-generation sustainable aviation fuels (SAFs), where polyalkylated cycloalkanes like dimethylcyclohexane are key components due to their favorable density and material compatibility properties [1]. This protocol outlines standardized methodologies for acquiring and analyzing IDT data for DMCH isomers, specifically 1,2-DMCH (D12MCH) and 1,3-DMCH (D13MCH).

Experimental Apparatus and Methodologies

The accurate determination of ignition delay times relies on well-characterized experimental setups that can replicate the high-temperature and high-pressure conditions of practical combustors. The following sections describe the two primary apparatuses used.

Shock Tube Facility

Shock tubes are the preferred apparatus for measuring IDTs at high temperatures (typically > 900 K). The core principle involves using a pressurized driver gas (e.g., helium) to rupture a diaphragm, generating a shock wave that propagates through the driven section filled with a prepared fuel-oxidizer-diluent mixture [56] [57].

Key Components and Procedures:

• Gas Preparation: The test mixture is prepared manometrically in a heated mixing vessel before being transferred to the evacuated driven section of the shock tube. For less volatile fuels, the entire assembly (shock tube and mixing manifold) may be heated to prevent condensation (e.g., to 100-125°C for jet fuels) [58].
• Shock Generation: The diaphragm is ruptured, and the velocity of the incident shock wave is measured using multiple pressure transducers (e.g., piezoelectric sensors) mounted along the driven section. The gas dynamic properties (temperature, pressure) of the test gas behind the reflected shock wave are calculated from this velocity using standard conservation relations [56] [57].
• Ignition Detection: Ignition is typically detected using multiple complementary methods:
  • OH* Chemiluminescence: A photomultiplier tube (PMT) with a narrowband filter around 306 nm detects the strong emission from electronically excited OH* radicals, signifying the high-temperature ignition event [57] [59].
  • Pressure Trace: A high-frequency pressure transducer records the rapid pressure rise associated with ignition [59].
• Data Interpretation: The ignition delay time (τ) is defined as the time interval between the arrival of the reflected shock wave at the measurement location (time zero, determined from the pressure trace) and the sharp rise in the OH* emission or pressure signal [56] [57]. For experiments behind an incident shock wave, the measured laboratory ignition delay time must be corrected to the real ignition delay time by accounting for the density change across the shock front [57].

Rapid Compression Machine (RCM) Facility

RCMs are designed to study auto-ignition at lower temperatures (e.g., 650-1000 K) where fuel oxidation exhibits complex low-temperature chemistry and Negative Temperature Coefficient (NTC) behavior.

Key Components and Procedures:

• Compression: A piston is driven rapidly to compress the test mixture in a reaction chamber to a target temperature and pressure, simulating a single compression stroke of an internal combustion engine.
• Post-Compression Conditions: The core challenge in RCM experiments is accurately characterizing the transient post-compression conditions, including heat losses. This is typically done by recording a non-reactive pressure trace (using a non-igniting mixture with similar thermodynamic properties) [60].
• Ignition Detection: Similar to shock tubes, ignition is detected via a pressure transducer and/or OH* chemiluminescence.
• Data Interpretation: The ignition delay time is measured from the end of the compression process (determined from the pressure trace) to the onset of ignition. Simulations for RCM validation must incorporate these non-ideal, non-adiabatic effects by using the measured pressure profile as an input [60].

The following workflow diagram illustrates the integrated process of experimental data collection and kinetic model validation.

Key Experimental Data for Dimethylcyclohexane Isomers

Quantitative ignition delay time data for DMCH isomers across a wide range of conditions are essential for model validation. The table below summarizes representative data and key findings from the literature.

Table 1: Summary of Experimental Ignition Delay Time Data for DMCH Isomers and Related Cycloalkanes

Fuel	Apparatus	Temperature Range (K)	Pressure Range (atm)	Equivalence Ratios (φ)	Key Findings	Citation
1,2-DMCH & 1,3-DMCH	Motored Engine	Not Specified	Not Specified	Not Specified	Ignition reactivity order: ECH > D13MCH > D12MCH	[1]
1,3-DMCH	Shock Tube (Reflected)	High-Temp	High-Temp	High-Temp	A high-temperature kinetic model was developed and validated against IDT data.	[1]
1,2,4-Trimethylcyclohexane	Jet-Stirred Reactor (Oxidation)	600 - 1100 K	1	0.4, 2.0	Developed a detailed model (530 species, 3160 reactions); fuel consumption involves cyclic C9H17 radicals.	[61]
Methylcyclopentane (MCP)	Shock Tube, RCM	Low- to High-Temp	1 - 10+	Various	MCP more reactive than cyclopentane; side-chain substitution enhances low-temperature reactivity.	[62]
2,5-Dimethylhexane	Shock Tube (Reflected)	1100 - 1500 K	5, 10	0.5, 1.0, 2.0	IDTs shorter at 10 atm vs 5 atm; lean mixtures most reactive. Model over-predicted IDTs; highly sensitive to propene chemistry.	[59]

Kinetic Modeling and Validation Protocols

The experimental IDT data is used to validate and refine detailed chemical kinetic models. The modeling workflow involves several key steps and analyses.

Modeling Setup and Simulation

• Software Tools: Simulations are commonly performed using chemical kinetics software packages such as CHEMKIN with built-in reactor models for constant volume (U) and constant internal energy (E) for shock tubes, or for accounting for heat losses in RCMs [56] [60] [61].
• Initial Mechanism: Construction of a DMCH model often starts from a well-validated base mechanism (e.g., for n-heptane) containing detailed C0-C7 core chemistry. Sub-mechanisms for the specific fuel are then added [1] [60].
• Simulation Conditions: For shock tube simulations, the constant U and E assumption is typically applied. However, at lower temperatures, non-ideal effects (e.g., facility-dependent gasdynamics, localized pre-ignition energy release) may require specialized models like CHEMSHOCK for accurate predictions [56].

Critical Analysis for Mechanism Refinement

• Sensitivity Analysis: This identifies the reactions that have the largest impact on the predicted IDT. For instance, the ignition of 2,5-dimethylhexane was found to be highly sensitive to propene chemistry, indicating an area for mechanism refinement [59].
• Rate of Production (ROP) Analysis: ROP analysis traces the consumption pathways of the fuel and the formation routes of key intermediates. For DMCH isomers, fuel consumption is governed by C-H bond cleavage to form cyclic radicals, which subsequently isomerize and decompose via β-scission reactions [1] [61].
• Reaction Pathway Analysis: This reveals the dominant consumption channels. For example, the difference in low-temperature reactivity between D12MCH and D13MCH can be explained by differences in bond dissociation energies and the contributions of different channels to the overall carbon flux and ȮH radical formation [1].

The diagram below maps the primary consumption pathways and key intermediates for DMCH isomers during oxidation, as identified through kinetic analysis.

This section lists critical reagents, software, and experimental setups used in combustion kinetics research focused on fuel validation.

Table 2: Key Research Resources for Ignition Delay Time Studies

Category	Item	Function & Application	Representative Use
Experimental Fuels	1,2-Dimethylcyclohexane (D12MCH)	Isomer for studying molecular structure effects on combustion reactivity and aromatics formation.	[1]
	1,3-Dimethylcyclohexane (D13MCH)	Isomer exhibiting different low- vs. high-temperature reactivity compared to D12MCH.	[1]
Analytical Instrumentation	Gas Chromatograph-Mass Spectrometer (GC-MS)	Identifies and quantifies stable intermediates and products from reactor experiments.	[1] [61]
	Photomultiplier Tube (PMT) with Filter	Detects OH* chemiluminescence at ~306 nm for precise ignition timing in shock tubes.	[57] [59]
	Piezoelectric Pressure Transducer	Measures shock wave velocity and pressure rise during ignition.	[56] [57]
Software & Models	CHEMKIN-Pro / II	Industry-standard software for simulating chemical kinetics in various reactor models.	[56] [61]
	Reaction Mechanism Generator (RMG)	An open-source tool for automatically constructing kinetic models.	[1]
Computational Chemistry	Quantum Chemistry Software (e.g., Gaussian)	Calculates molecular properties and rate constants for elementary reactions (e.g., at CCSD(T)/CBS level).	[62]
	RRKM/ME Theory	Used to calculate pressure- and temperature-dependent rate constants for energy transfer processes.	[62]

The combustion chemistry of cyclic alkanes is a critical area of research for the development of sustainable aviation fuels (SAFs) and cleaner fossil fuel alternatives. Polysubstituted cycloalkanes, particularly dimethylcyclohexane (DMCH) isomers, represent vital molecular subclasses in next-generation, lignin-based sustainable aviation fuels, serving to overcome compatibility issues between drop-in fuels and aero-engines [1]. Unlike conventional petroleum-based transportation fuels containing 15-40 wt% cycloalkanes, unconventional transportation fuels such as oil-sand-derived fuels and biomass derivatives can contain up to 99 wt% cycloalkanes [1]. This shift in composition underscores the importance of understanding the fundamental oxidation chemistry of these compounds.

The comparative reactivity analysis of 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH) provides essential insights into how molecular structure influences combustion characteristics, including ignition properties, emissions formation, and intermediate speciation. Such understanding enables the rational design of fuel surrogates and the optimization of combustion systems for reduced environmental impact. While significant progress has been achieved in understanding monoalkylated cyclohexanes such as methylcyclohexane (MCH), ethylcyclohexane (ECH), and propylcyclohexane (PCH), the combustion chemistry of novel polyalkylated cycloalkanes remains underexplored [1]. This application note provides a comprehensive kinetic modeling framework for DMCH oxidation chemistry, incorporating experimental protocols, computational methodologies, and analytical techniques essential for researchers in fuel development and combustion science.

Experimental Data and Reactivity Comparison

Quantitative Reactivity Profiles

Table 1: Comparative reactivity characteristics of alkylcyclohexanes

Compound	Low-Temperature Reactivity	High-Temperature Reactivity	Aromatic Formation Propensity	Key Distinctive Features
1,2-DMCH	Lower	Higher	Higher	Closer methyl groups enhance high-temperature decomposition; higher benzene precursors
1,3-DMCH	Higher	Lower	Lower	Favorable bond dissociation energies promote low-temperature pathways; reduced aromatic yield
MCH	Intermediate	Intermediate	Intermediate	Benchmark mono-alkylated cyclohexane; well-characterized oxidation pathways
ECH	High	High	N/A	Longer alkyl chain increases reaction complexity; higher ignition reactivity than DMCH isomers
1,2,4-TMCH	High	High	High	Complex decomposition pathways; significant fuel isomeric effects on reactivity

The differential reactivity between D12MCH and D13MCH stems from their distinct molecular architectures. D12MCH exhibits higher high-temperature reactivity, while D13MCH demonstrates superior low-temperature reactivity [1]. This divergence can be explained by differences in chemical bond dissociation enthalpies and the contributions of different channels to carbon flux and ȮH formation, as revealed through rate of production (ROP) and sensitivity analyses [1].

The spatial arrangement of methyl groups significantly influences the reaction pathways available during decomposition. For D12MCH, the proximity of methyl groups facilitates specific ring-opening sequences that enhance high-temperature decomposition rates. Conversely, the separation between methyl groups in D13MCH creates more favorable energetics for low-temperature chain-branching pathways through hydroperoxide chemistry [1].

Speciation Data and Product Formation

Table 2: Key intermediate species concentrations in DMCH oxidation

Species Category	Specific Compounds	1,2-DMCH Oxidation	1,3-DMCH Oxidation	Formation Pathways
Olefins	C₂-C₄ alkenes	Higher yield at high T	Higher yield at low T	β-scission of alkoxy radicals
Oxygenates	Carbonyl compounds, cyclic ethers	Moderate	Prominent at low T	QOOH radical isomerization
Aromatics	Benzene, toluene	Higher peak concentrations	Lower peak concentrations	Ring enlargement; C₅ RSR chemistry
Radical Pool	ȮH, HO₂˙	Higher ȮH at high T	Enhanced ȮH at low T	H-abstraction/β-scission sequences

The molecular structure effects are particularly evident in aromatics formation, where the peak concentration of aromatics is generally higher in D12MCH oxidation than in D13MCH oxidation [1]. This result aligns with the understanding that aromatics are mainly formed by five-membered-ring chemistry involving C₅ resonantly stabilized radicals and six-membered-ring chemistry involving the traditional H-abstraction/β-scission sequence, which is determined by the fuel decomposition reactivity [1].

The ring-opening reactions of DMCH isomers have been extensively studied on iridium catalysts, revealing that the addition of potassium to Ir/SiO₂ catalysts tunes the selectivity toward cleavage of substituted C-C bonds, favoring the formation of unbranched products desirable in diesel fuel [63]. This catalytic ring opening proceeds through different mechanisms: the dicarbene pathway (favored on unpromoted Ir/SiO₂) leads to branched products via unsubstituted C-C bond cleavage, while the metallocyclobutane pathway (favored on K-promoted Ir/SiO₂) facilitates unbranched products through substituted C-C bond cleavage [63].

Kinetic Modeling Framework

Model Development and Validation

The construction of detailed kinetic models for D12MCH and D13MCH should begin with established foundational mechanisms, such as the n-heptane oxidation model covering detailed C₀-C₇ chemistry, and incorporate combustion mechanisms of MCH as a starting point [1]. Model development requires careful consideration of the unique reaction classes for cyclic hydrocarbons:

• Initial H-abstraction reactions: Site-specific rate constants for tertiary and secondary hydrogen atoms, influenced by substituent positions
• Radical isomerization pathways: Conformation-dependent intramolecular H-migration reactions
• Ring-opening sequences: Scission of cyclic structures to form acyclic radicals
• Low-temperature oxidation: Peroxy radical (QOOH) isomerization and decomposition
• Aromatic precursors formation: Cyclization pathways leading to benzene and alkylbenzenes

Model validation should be performed against experimental speciation data obtained from flow reactor studies under both lean and rich conditions at atmospheric pressure, covering a temperature range that captures both low-temperature and high-temperature oxidation regimes [1]. Critical validation targets include fuel consumption rates, intermediate species profiles (olefins, carbonyls, cyclic ethers), and aromatic species formation.

Conformational Analysis Considerations

The conformational landscapes of DMCH isomers significantly influence their oxidation kinetics. Computational investigations reveal complex inversion-topomerization processes for substituted cyclohexanes, with distinct energy barriers for chair-chair interconversions [64]. For cis- and trans-1,2-dimethylcyclohexanes, comprehensive potential energy surfaces map the transitions between conformational minima, which can impact the accessibility of specific reaction pathways [64].

These conformational features play a particularly important role in low-temperature oxidation chemistry, where molecular geometry affects hydrogen accessibility for 1,4 or 1,5 H-migration reactions, subsequently influencing chain branching probabilities that determine overall fuel reactivity [64]. Kinetic models should incorporate conformation-dependent reaction pathways for accurate prediction of low-temperature ignition behavior.

Experimental Protocols

Flow Reactor Oxidation Studies

Objective: Quantify species evolution and fuel consumption rates during DMCH oxidation under controlled temperature and equivalence ratio conditions.

Materials and Equipment:

• Laminar flow tubular reactor (1000 mm quartz tube, 6 mm inner diameter)
• Preheating and mixing system for vaporized fuel/O₂/N₂ mixtures
• Tubular furnace with 550 mm total length (350 mm heating region)
• K-type thermocouple for temperature profiling
• Online gas chromatography (GC) system with flame ionization detector
• Gas chromatography-mass spectrometry (GC-MS) for species identification
• DMCH isomers (≥99% purity), high-purity oxygen (≥99.995%), nitrogen (≥99.999%)

Procedure:

• Prepare fuel/O₂/N₂ mixtures at target equivalence ratios (typically ϕ = 0.25 for lean, ϕ = 1.5 for rich conditions)
• Vaporize the mixture at 473 K and introduce into the flow reactor
• Maintain system at atmospheric pressure with residence times of 1.5-2.0 seconds
• Heat reactor from 500 K to 1100 K with controlled temperature ramp
• Sample reaction products at discrete temperature intervals using heated sampling line
• Quantify species mole fractions using calibrated GC and GC-MS systems
• Repeat experiments for both D12MCH and D13MCH isomers under identical conditions

Data Analysis:

• Plot species mole fractions as functions of temperature
• Calculate fuel consumption rates and product formation selectivities
• Compare intermediate species profiles between isomers
• Identify temperature regimes of maximum reactivity for each isomer

Ignition Delay Time Measurements

Objective: Determine autoignition characteristics of DMCH isomers under engine-relevant conditions.

Materials and Equipment:

• Modified Cooperative Fuel Research (CFR) engine or rapid compression machine
• Pressure transducers for ignition detection
• High-speed data acquisition system
• Temperature-controlled fuel injection system
• Heated intake manifold for mixture preparation

Procedure:

• Prepare fuel/air mixtures at target equivalence ratios (ϕ = 0.5-1.5)
• Compress mixture to elevated temperatures (650-1100 K) and pressures (10-40 bar)
• Monitor pressure-time histories to detect ignition events
• Record ignition delay times as function of temperature, pressure, and equivalence ratio
• Compare reactivity trends between D12MCH, D13MCH, and reference fuels

Catalytic Ring-Opening Experiments

Objective: Evaluate selective ring-opening pathways of DMCH isomers on promoted catalysts.

Materials and Equipment:

• Ir/SiO₂ catalysts (1 wt% Ir) prepared by incipient wetness impregnation
• Potassium-promoted Ir/SiO₂ catalysts with varying K⁺ loadings (0-5.1 atoms nm⁻²)
• Fixed-bed flow reactor system with online product analysis
• H₂ chemisorption apparatus for metal dispersion measurements
• Temperature-programmed reduction (TPR) system

Procedure:

• Reduce catalysts in flowing H₂ at 673 K for 2 hours
• Introduce 1,3-DMCH vapor in H₂ carrier gas at appropriate weight hourly space velocity
• Vary reaction temperature between 473-573 K
• Analyze products using online GC
• Determine selectivity ratios for substituted vs. unsubstituted C-C bond cleavage
• Correlate catalytic performance with promoter loading and metal dispersion

Research Reagent Solutions

Table 3: Essential research reagents and materials for DMCH oxidation studies

Reagent/Material	Specifications	Application Purpose	Key Considerations
1,2-DMCH	≥99% purity, stereoisomer mixture	Primary reactant for oxidation kinetics	Store under inert atmosphere; check for peroxides
1,3-DMCH	≥99% purity, stereoisomer mixture	Comparative reactivity studies	Confirm isomer composition by GC-MS
Iridium Catalysts	1 wt% Ir/SiO₂, K-promoted variants	Catalytic ring-opening studies	Pre-reduce in H₂ at 673 K before use
High-Purity Gases	O₂ (≥99.995%), N₂ (≥99.999%), H₂ (≥99.999%)	Reactor diluent and oxidizer sources	Use appropriate purifiers for trace contamination removal
Calibration Standards	Authentic hydrocarbon/oxygenate standards	GC-FID and GC-MS quantification	Prepare fresh calibration curves for each experiment series
Potassium Promoter	K₂CO₃ (99.5% purity)	Catalyst modification for selectivity tuning	Control loading density (atoms nm⁻²) precisely

Visualization of Reactivity Pathways

DMCH Oxidation and Ring-Opening Pathways

Diagram 1: Reaction network for DMCH oxidation and catalytic ring-opening pathways. D12MCH and D13MCH follow distinct oxidation routes, with branching between low-temperature and high-temperature mechanisms. Catalytic ring-opening selectivity depends on catalyst formulation, with potassium promotion shifting selectivity toward substituted C-C bond cleavage.

Experimental Workflow for Kinetic Modeling

Diagram 2: Kinetic modeling workflow for DMCH oxidation chemistry. The process begins with experimental data collection, proceeds through model construction and validation, and employs iterative refinement to achieve predictive capability for fuel performance under diverse conditions.

The comparative analysis of 1,2-DMCH and 1,3-DMCH reactivity reveals significant structure-dependent oxidation characteristics that profoundly impact their combustion behavior and application in sustainable fuels. The higher high-temperature reactivity of D12MCH, coupled with its greater propensity for aromatic formation, positions it differently in combustion applications compared to D13MCH, which exhibits superior low-temperature reactivity. These fundamental insights enable more accurate surrogate fuel formulation and combustion system optimization.

The kinetic modeling frameworks and experimental protocols outlined in this application note provide researchers with comprehensive tools for investigating cycloalkane combustion chemistry. The integration of detailed chemical mechanisms, conformational analysis, and catalyst design principles facilitates a multidimensional understanding of fuel reactivity that spans molecular-level interactions to system-level performance. Future research directions should focus on extending these methodologies to more complex polysubstituted cycloalkanes, investigating synergistic effects in multicomponent fuel blends, and validating model predictions under practical combustion conditions.

Analyzing Isomeric Effects on Product Yields and Soot Propensity

Within the broader context of kinetic modeling of dimethylcyclohexane (DMCH) oxidation chemistry, understanding the inherent differences between isomers is crucial for predicting combustion behavior and emissions. This application note provides a detailed experimental and theoretical framework for analyzing how structural differences in 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH) impact product yields and soot propensity. The protocols outlined enable researchers to connect molecular structure to combustion performance through specialized reactor experiments, analytical techniques, and kinetic modeling approaches, providing essential data for surrogate fuel development and cleaner combustion strategies.

Comparative Oxidation Kinetics of DMCH Isomers

Experimental Reactivity Profiles

Flow reactor studies reveal distinct oxidation characteristics between DMCH isomers under systematically controlled conditions. Quantitative data extracted from laminar flow tubular reactor experiments demonstrate temperature-dependent reactivity differences critical for kinetic model validation.

Table 1: Comparative Reactivity and Product Formation in DMCH Isomer Oxidation

Parameter	1,2-DMCH (D12MCH)	1,3-DMCH (D13MCH)	Experimental Conditions
High-temperature reactivity	Higher	Lower	Atmospheric flow reactor, lean & rich conditions
Low-temperature reactivity	Lower	Higher	Atmospheric flow reactor, lean & rich conditions
Aromatic compounds formation	Higher peak concentrations	Lower peak concentrations	Temperature range: 500-1100 K
Primary decomposition pathways	H-abstraction/β-scission sequences	Complex low-temperature pathways	Equivalence ratios (φ): 0.25 and 1.5
Key differentiating factor	Bond dissociation energies & carbon flux	ȮH formation contributions	Analysis: ROP and sensitivity

Structural Influences on Reaction Pathways

The spatial arrangement of methyl groups fundamentally alters decomposition mechanisms. D12MCH exhibits superior high-temperature reactivity due to favorable bond dissociation enthalpies in its molecular configuration, while D13MCH demonstrates enhanced low-temperature oxidation through more efficient ȮH radical formation channels [1]. These distinctions manifest quantitatively in product spectra, with D12MCH generating substantially higher aromatic precursor concentrations through five-membered-ring chemistry involving C5 resonantly stabilized radicals and traditional H-abstraction/β-scission sequences [1].

Soot Propensity in Cyclic Hydrocarbons

Molecular Structure-Soot Relationship

Sooting tendencies demonstrate exceptional sensitivity to molecular architecture, particularly in cyclic compounds where subtle positional isomers produce dramatically different emissions.

Table 2: Sooting Tendencies of Cyclic Hydrocarbons

Compound	Sooting Tendency	Key Finding	Experimental Method
Cyclopentane	Stronger than cyclohexane	Prefers decomposition to odd-carbon radicals (cyclopentadienyl, allyl)	Counterflow diffusion flame
3-methyl-1-cyclohexene	Higher YSI (Yield Sooting Index)	Preferential dehydrogenation to cyclohexadienes and toluene	Flow reactor + DFT simulations
1-methyl-1-cyclohexene	Lower YSI	Dominant retro-Diels-Alder pathway causing ring opening	Flow reactor + DFT simulations
4-methyl-1-cyclohexene	Lower YSI	Dominant retro-Diels-Alder pathway causing ring opening	Flow reactor + DFT simulations

Methylcyclohexene isomers exemplify how minimal structural variations dramatically alter sooting propensity, with 3-methyl-1-cyclohexene exhibiting significantly higher Yield Sooting Index (YSI) than its positional isomers [65] [66]. This divergence stems from competing decomposition mechanisms: 1- and 4-methylcyclohexene preferentially undergo retro-Diels-Alder reactions leading to ring opening and molecular weight reduction, while 3-methyl-1-cyclohexene favors dehydrogenation pathways yielding cyclohexadienes and toluene—efficient aromatic precursors that enhance soot formation [66]. The relative stability of the first radical intermediate determines the branching ratio between these channels, underscoring how minimal structural features can dramatically alter carbon fate during combustion [66].

Experimental Assessment Methods

Sooting tendency evaluation employs multiple complementary methodologies, each offering unique insights. Counterflow diffusion flames (CDFs) configured as soot formation (SF) types isolate soot inception and growth processes by transporting particles away from oxidizing zones, providing fundamental data on nascent soot formation without oxidation interference [67]. This approach contrasts with coflow diffusion flames—used for Yield Sooting Index (YSI) determination—which represent soot formation/oxidation (SFO) environments where soot undergoes both formation and destruction processes [67]. Additional metrics include sooting limits (critical flame conditions where soot first appears), soot volume fraction measurements via laser-induced incandescence (LII), and temperature-based indices like Sooting Temperature Index (STI) [67].

Experimental Protocols

Flow Reactor Oxidation Studies

Objective: Quantify species concentrations and global reactivity parameters for DMCH isomer oxidation at varying temperatures and equivalence ratios.

Materials and Equipment:

• Laminar flow tubular reactor (quartz, 6 mm ID, 1000 mm length)
• Heated tubular furnace (550 mm total length, 350 mm heating region)
• Online gas chromatograph (GC) and GC-MS system
• K-type thermocouple for temperature profiling
• Precision syringe pump for liquid fuel delivery
• Mass flow controllers for gas streams (O₂, N₂, He)
• 1,2-dimethylcyclohexane and 1,3-dimethylcyclohexane standards (≥99% purity)

Procedure:

• System Preparation: Calibrate mass flow controllers and GC/MS system. Verify temperature profile along reactor axis using movable thermocouple.
• Fuel Vaporization: Deliver liquid DMCH isomers via syringe pump to vaporization chamber maintained at 473 K. Mix vaporized fuel with preheated oxygen and nitrogen diluent.
• Reaction Conditions: Establish lean (φ=0.25) and rich (φ=1.5) mixtures at atmospheric pressure. Total flow rate: 1.0 slpm, residence time: ~2 seconds.
• Temperature Profiling: Conduct experiments across temperature range 500-1100 K, focusing on low-temperature (500-800 K) and high-temperature (800-1100 K) regimes.
• Species Identification: Sample reactor effluent via heated transfer line. Quantify stable intermediates, oxygenates, and aromatic compounds using GC-FID/TCD and GC-MS.
• Data Collection: Record mole fractions of CO, CO₂, H₂, CH₄, C₂H₄, C₂H₂, benzene, toluene, and oxygenated species as function of temperature.
• Model Validation: Compare experimental data against detailed kinetic model predictions for fuel consumption rates and product distributions.

Sooting Tendency Assessment

Objective: Determine comparative sooting propensities of cyclic hydrocarbons using counterflow diffusion flames.

Materials and Equipment:

• Counterflow diffusion flame burner
• Liquid fuel vaporization system
• Mie scattering apparatus for soot detection
• Laser-induced incandescence (LII) system for soot volume fraction
• Nd:YAG laser (532 nm) for LII excitation
• ICCD camera for signal detection
• Temperature-controlled fuel reservoir

Procedure:

• Flame Configuration: Establish counterflow diffusion flames with fuel stream (vaporized hydrocarbon in nitrogen) opposing oxidizer stream (oxygen in nitrogen).
• Sooting Limit Determination: Gradually increase fuel concentration while maintaining constant strain rate. Identify critical fuel mole fraction at which soot first appears via Mie scattering.
• Soot Volume Fraction Measurement: At fixed conditions above sooting limit, measure two-dimensional soot volume fields using LII calibration procedure.
• Comparative Analysis: Determine relative sooting tendencies for compound series (C5-C8 n-alkanes, cycloalkanes, alkenes) under identical aerodynamic conditions.
• Kinetic Interpretation: Complement experimental data with numerical modeling of fuel pyrolysis pathways to identify key radical intermediates and aromatic precursors.

Kinetic Modeling Framework

Model Development Protocol

Objective: Construct detailed chemical kinetic models for DMCH isomers covering low-to-high-temperature oxidation chemistry.

Procedure:

• Base Mechanism Selection: Begin with validated n-heptane oxidation mechanism covering C0-C7 chemistry [1].
• Fuel-Specific Reactions: Incorporate DMCH isomer decomposition pathways:
  • H-atom abstraction sites (tertiary vs. secondary H)
  • Alkyl radical isomerization
  • Cycloalkane ring-opening β-scission reactions
  • Low-temperature chain-branching sequences
• Thermochemical Parameters: Calculate bond dissociation energies for each isomer using computational methods (e.g., CBS-QB3).
• Rate Parameter Assignment: Employ analogy rules from similar cycloalkanes (methylcyclohexane), with adjustments for substituent effects.
• Validation: Compare model predictions against experimental speciation data from flow reactor and ignition delay measurements.
• Analysis Tools: Implement Rate of Production (ROP) and sensitivity analysis to identify dominant reaction pathways.

Kinetic Model Workflow:

Pathway Analysis Methods

Rate of Production (ROP) Analysis:

• Calculate contribution of individual reactions to species formation/consumption
• Identify dominant fuel decomposition pathways for each isomer
• Quantify branching ratios at critical junctures (e.g., ring-opening vs. dehydrogenation)

Sensitivity Analysis:

• Determine elementary reactions with strongest influence on target outputs (fuel consumption, aromatic species formation)
• Identify key rate parameters requiring refinement
• Reveal mechanistic differences between isomers

Flux Analysis:

• Visualize carbon atom flow through reaction network
• Identify major channels to products (CO, CO₂, aromatics)
• Quantify differences in carbon allocation between isomers

The Scientist's Toolkit

Table 3: Essential Research Reagents and Equipment

Category	Specific Items	Function/Application
Reference Fuels	1,2-dimethylcyclohexane, 1,3-dimethylcyclohexane (≥99%)	Primary substrates for isomeric comparison studies
Oxidizers & Gases	Oxygen (UHP), Nitrogen (UHP), Helium (UHP)	Reactant and diluent gases for controlled oxidation environments
Analytical Standards	n-Alkanes (C1-C8), alkenes, cycloalkanes, aromatic compounds	GC/MS calibration for species quantification
Catalytic Materials	Platinum-based catalysts (e.g., SI-2)	Isomerization studies and catalyst performance evaluation
Computational Tools	RMG kinetic modeling software, DFT packages (Gaussian, ORCA)	Reaction mechanism generation, thermochemical calculation, transition state analysis
Oxidation Catalysts	Iron(PDP)-type complexes, metalloporphyrins	Selective C–H bond oxidation for mechanistic studies

Visualization of Structure-Reactivity Relationships

Molecular Structure to Combustion Outcomes:

This application note establishes comprehensive protocols for analyzing isomeric effects on product yields and soot propensity in dimethylcyclohexane systems. The integrated experimental and modeling approach enables researchers to connect molecular structure to combustion behavior through controlled oxidation studies, detailed speciation analysis, and kinetic modeling. The documented differences between 1,2- and 1,3-DMCH—particularly their contrasting temperature-dependent reactivity and aromatic yields—provide critical validation targets for predictive combustion models. These methodologies support the development of accurate surrogate fuel models and emission reduction strategies essential for advancing sustainable aviation fuels and cleaner combustion technologies.

Performance Comparison of Published DMCH Kinetic Mechanisms

Dimethylcyclohexane (DMCH) isomers are critical cyclic hydrocarbons found in conventional fossil fuels and are emerging as vital components in next-generation, lignin-derived sustainable aviation fuels (SAFs) [1]. The development of accurate chemical kinetic models for these isomers is essential for predicting combustion behavior, optimizing engine performance, and reducing soot and greenhouse gas emissions [1]. This Application Note provides a structured comparison of published DMCH kinetic mechanisms, detailing their experimental validation, performance characteristics, and implementation protocols to assist researchers in the selection and application of these models.

The simplest DMCH isomers, 1,2-dimethylcyclohexane (D12MCH) and 1,3-dimethylcyclohexane (D13MCH), exhibit distinct combustion properties due to differences in molecular structure and bond dissociation energies [1]. D13MCH demonstrates higher low-temperature reactivity, whereas D12MCH exhibits higher high-temperature reactivity and produces higher concentrations of aromatic compounds, which are precursors to soot formation [1]. These differences underscore the necessity for isomer-specific kinetic models.

Key experimental investigations have provided the data necessary for model development and validation:

• Eldeeb et al. (2016): Conducted high-temperature ignition delay and pyrolysis studies for D13MCH behind reflected shock waves (1049–1544 K, 3–12 atm) [16].
• Recent Flow Reactor Study (2025): Provided comprehensive oxidation data for both D12MCH and D13MCH in a laminar flow tubular reactor under lean and rich conditions at atmospheric pressure, measuring vital species concentrations using online GC and GC–MS techniques [1].

Comparative Analysis of Kinetic Mechanisms

The following table summarizes the key features and validation ranges of the primary DMCH kinetic mechanisms available in the literature.

Table 1: Published DMCH Kinetic Mechanisms and Their Validation

Mechanism / Study	DMCH Isomer	Validation Targets	Temperature Range	Pressure Range	Key Model Characteristics
Eldeeb et al. (2016) [16]	D13MCH	Ignition Delay Times (IDT), Fuel Concentration Histories	1049 – 1544 K	3.0 – 12 atm	High-temperature focused; reasonably predicts IDT and pyrolysis trends.
Recent Model (2025) [1]	D12MCH & D13MCH	Species Concentrations (Flow Reactor)	Low- to High-Temperature	Atmospheric	Comprehensive low- and high-temperature chemistry; explains isomer-specific reactivity and aromatics formation.

Table 2: Performance Characteristics of DMCH Kinetic Mechanisms

Mechanism / Study	Predicted Reactivity Trend	Strengths	Limitations / Uncertainties
Eldeeb et al. (2016) [16]	Longer IDT for D13MCH vs. ethylcyclohexane	Good performance at high temperatures and varied equivalence ratios.	Accuracy decreases at high pressure and low dilution; lacks low-temperature chemistry validation.
Recent Model (2025) [1]	D12MCH > D13MCH (High-T); D13MCH > D12MCH (Low-T)	Validated against extensive speciation data; identifies key fuel-specific pathways for major products and aromatics.	Primarily validated at atmospheric pressure; further validation at higher pressures is needed.

Detailed Experimental Protocols for Mechanism Validation

Ignition Delay Time Measurements behind Reflected Shock Waves

This protocol, used for high-temperature mechanism validation [16], measures the time interval between the arrival of the shock wave and the subsequent rapid pressure rise or light emission signifying ignition.

Key Apparatus and Procedures:

• Shock Tube: A high-pressure shock tube equipped with pressure transducers (e.g., Kistler 603B) and optical diagnostics.
• Mixture Preparation: DMCH vapor is manometrically mixed with oxidizer (e.g., O₂) and inert bath gas (e.g., Ar or N₂) in a heated vessel. Equivalence ratios (φ) typically range from 0.5 to 2.0.
• Experimental Procedure:
  • The driven section is evacuated and filled with the test mixture to a specified pressure.
  • The driver section is pressurized until the diaphragm ruptures, generating a incident shock wave.
  • The shock wave reflects from the endwall, creating a uniform region of high-temperature and high-pressure gas.
  • Ignition Delay Time Definition: The time interval between the pressure rise associated with the reflected shock and the maximum rate of pressure rise (or CH* chemiluminescence) during ignition [16].
• Data Recording: Record pressure histories and/or light emission signals using photomultiplier tubes or monochromators. Experiments are repeated across a temperature range (950–1500 K) and pressures of 5–20 bar.

Species Concentration Measurements in a Laminar Flow Reactor

This protocol provides speciation data for mechanism validation under both low- and high-temperature conditions [1].

Key Apparatus and Procedures:

• Flow Reactor: An atmospheric laminar flow reactor consisting of a quartz tube (e.g., 6 mm inner diameter, 1000 mm length) heated by a tubular furnace with a controlled temperature profile.
• Reactant Delivery System: A fuel vaporization system where liquid DMCH is fed via a syringe pump, vaporized, and mixed with pre-heated oxidizer (O₂) and diluent (N₂ or He). The mixture flows into the heated reactor.
• Online Sampling and Analysis:
  • Gas Chromatography (GC): Samples are extracted from the reactor outlet and analyzed via online GC for permanent gases and light hydrocarbons.
  • Gas Chromatography-Mass Spectrometry (GC-MS): Used for precise identification and quantification of heavier hydrocarbon species and oxygenated intermediates.
• Data Acquisition: Measure species mole fractions as a function of reactor temperature for different equivalence ratios (e.g., φ = 0.25 for lean, φ = 1.5 for rich) [1].

The Scientist's Toolkit: Key Research Reagents and Materials

Table 3: Essential Research Reagents and Materials for DMCH Combustion Studies

Item	Function / Application	Specifications / Notes
DMCH Isomers	Primary Reactant: High-purity chemical feedstock for pyrolysis and oxidation experiments.	Use >99% purity isomers (e.g., 1,2-DMCH, 1,3-DMCH). Store under inert atmosphere.
Oxidizers	Co-reactant: Provides oxygen for oxidation chemistry.	High-purity O₂. For simulated air, use O₂/N₂ or O₂/Ar mixtures at 3.76:1 ratio.
Diluent Gases	Bath Gas: Controls reactor density and acts as thermal buffer.	Chemically inert; high-purity Ar, N₂, or He. He offers high diffusivity.
Calibration Gases	Analytical Standard: Quantification of reactants, products, and intermediates.	Certified standard mixtures for CO, CO₂, O₂, H₂, and light hydrocarbons (C1-C6).
Shock Tube Diaphragms	Pressure Barrier: Contains driver section pressure until rupture initiates experiment.	Material (e.g., aluminum, steel) and thickness determine burst pressure.

Critical Reaction Pathways and Modeling Insights

Kinetic modeling analysis reveals distinct consumption pathways and reactivity trends for DMCH isomers. The following diagram illustrates key reaction channels controlling DMCH oxidation.

Modeling Insights from Pathway Analysis:

• Isomer-Specific Reactivity: The higher high-temperature reactivity of D12MCH is attributed to more favorable bond dissociation energies and β-scission pathways from its initial radicals. In contrast, D13MCH radicals facilitate more efficient O₂ addition at low temperatures, enhancing its low-temperature reactivity [1].
• Aromatics Formation: Aromatic compound yield is generally higher in D12MCH oxidation. This results from competing pathways involving five-membered-ring chemistry with C₅ resonantly stabilized radicals and traditional H-abstraction/β-scission sequences from the six-membered ring [1].
• Model Construction Strategy: Hierarchical model development begins with a core mechanism for light species (e.g., a validated n-heptane model). DMCH-specific reactions are added, focusing on H-abstraction reactions forming various DMCH radicals, followed by subsequent radical isomerization, decomposition, and oxidation channels [1] [68].

This analysis compares the current landscape of chemical kinetic models for dimethylcyclohexane isomers, highlighting the availability of detailed mechanisms for D12MCH and D13MCH validated across different temperature regimes and experimental targets. The choice of an appropriate mechanism depends critically on the specific application: high-temperature ignition (e.g., the Eldeeb et al. model for D13MCH) versus wide-range oxidation with detailed speciation (e.g., the recent 2025 model for both isomers). Future model development should focus on extending validation to higher pressures, broader temperature ranges, and further refinement of rate parameters for key aromatics-forming pathways to enhance predictive accuracy for soot emissions.

Conclusion

The kinetic modeling of dimethylcyclohexane oxidation represents a mature yet rapidly advancing field, crucial for the development of next-generation sustainable aviation fuels. This review has synthesized key findings, demonstrating that detailed mechanisms can accurately capture the complex oxidation behavior of DMCH isomers, including distinctive features like NTC chemistry. The comparative analysis reveals significant isomeric effects on reactivity and product distribution, underscoring the need for isomer-specific models. Future research directions should focus on refining low-temperature reaction pathways, expanding mechanisms to include tri-substituted cycloalkanes, and integrating kinetic models with computational fluid dynamics for real-world engine simulations. These advancements will ultimately enable the design of high-performance, low-emission bio-based fuels, directly impacting the decarbonization of the aviation and transportation sectors.

References

• 1. A comparative experimental and kinetic modeling study on ... [https://www.sciencedirect.com/science/article/abs/pii/S0016236125001413]
• 2. Temperature- and pressure-dependent branching ratios for 1,4 ... [https://ui.adsabs.harvard.edu/abs/2024Fuel..37832833T/abstract]
• 3. Cyclohexane, 1,1-dimethyl- - the NIST WebBook [https://webbook.nist.gov/cgi/cbook.cgi?ID=C590669&Mask=1]
• 4. Experimental and kinetic model studies of 2,3- ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218024004905]
• 5. Hydroxy lactones with the gem-dimethylcyclohexane system [https://arabjchem.org/hydroxy-lactones-with-the-gem-dimethylcyclohexane-system-synthesis-and-antimicrobial-activity/]
• 6. Understanding the impact of cycloalkane additives on ... [https://www.sciencedirect.com/science/article/abs/pii/S1540748925000173]
• 7. From food waste to sustainable aviation fuel: cobalt ... [https://www.nature.com/articles/s41467-025-64645-y]
• 8. Understanding the Compositional Effects of SAFs on ... [https://www.frontiersin.org/journals/energy-research/articles/10.3389/fenrg.2022.830236/full]
• 9. Cycloalkane-rich sustainable aviation fuel production via ... [https://pubs.rsc.org/en/content/articlelanding/2024/se/d4se01151a]
• 10. Advancing sustainable aviation fuel with high-energy ... [https://www.sciencedirect.com/science/article/pii/S2666386425002917]
• 11. and 1,3-dimethylcyclohexanes: Key cyclic components in ... [https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=202502229137600806]
• 12. 2.16: Conformations of Disubstituted Cyclohexanes [https://chem.libretexts.org/Courses/Brevard_College/CHE_201%3A_Organic_Chemistry_I/02%3A_Alkanes_and_Cycloalkanes/2.16%3A_Conformations_of_Disubstituted_Cyclohexanes]
• 13. 4.8 Conformations of Disubstituted Cyclohexanes [https://ncstate.pressbooks.pub/organicchem/chapter/conformations-of-disubstituted-cyclohexanes/]
• 14. Cyclohexane Chair Conformation Stability: Which One Is ... [https://www.masterorganicchemistry.com/2014/07/23/which-cyclohexane-chair-is-of-lower-energy/]
• 15. 6.10: Disubstituted Cyclohexanes [https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_Structure_and_Reactivity_in_Organic_Biological_and_Inorganic_Chemistry_(Schaller)/I%3A__Chemical_Structure_and_Properties/06%3A_Conformational_Analysis/6.10%3A_Disubstituted_Cyclohexanes]
• 16. Experimental and Chemical Kinetic Modeling Study of ... [https://figshare.com/articles/dataset/Experimental_and_Chemical_Kinetic_Modeling_Study_of_Dimethylcyclohexane_Oxidation_and_Pyrolysis/3824424]
• 17. LT-HyChem - A physics-based chemical kinetic modeling ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218024005613]
• 18. Insights into the high-temperature oxidation of ... [https://www.sciencedirect.com/science/article/abs/pii/S001623611832074X]
• 19. Role of decomposition products in the oxidation ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10192294/]
• 20. negative temperature coefficient (NTC) Explained - DXM [https://www.dxmht.com/article/negative-temperature-coefficient-ntc-thermistor-is-what.html]
• 21. Using rapid compression machines for chemical kinetics ... [https://www.sciencedirect.com/science/article/abs/pii/S0360128514000148]
• 22. An experimental and kinetic modeling investigation on low ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218022003807]
• 23. A Rapid Compression Machine for Chemical Kinetics Studies ... [https://combdiaglab.engr.uconn.edu/projects/chemical-kinetics-investigation-using-rapid-compression-machine/a-rapid-compression-machine-for-chemical-kinetics-studies-at-elevated-pressures-and-temperatures/]
• 24. Rapid Compression Machine RCM [https://www.hgd.rwth-aachen.de/cms/hgd/forschung/experimentelle-anlagen/~kfobp/rapid-compression-machine-rcm/?lidx=1]
• 25. Shock tube and kinetic modeling study on high- ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218024002645]
• 26. Flow Reactor Study of NH3/DEE Oxidation Chemistry - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC12400427/]
• 27. Selectivity in the Aliphatic C–H Bonds Oxidation ... [https://www.mdpi.com/2073-4344/13/1/121]
• 28. If C–H Bonds Could Talk – Selective C–H Bond Oxidation [https://pmc.ncbi.nlm.nih.gov/articles/PMC3980681/]
• 29. Efficient catalytic oxidation of alkanes by Lewis acid/[Os(VI) ... [https://pubmed.ncbi.nlm.nih.gov/18642814/]
• 30. An experimental and modeling study of the low [https://www.sciencedirect.com/science/article/abs/pii/S0010218013002034]
• 31. Cyclohexane, 1,2-dimethyl-, cis- - the NIST WebBook [https://webbook.nist.gov/cgi/cbook.cgi?ID=C2207014&Mask=1]
• 32. RMG - Reaction Mechanism Generator [https://rmg.mit.edu/]
• 33. Computer based generation of reaction mechanisms for ... [https://pubmed.ncbi.nlm.nih.gov/10890364/]
• 34. A comparative experimental and kinetic modeling study on ... [https://www.sciencedirect.com/science/article/pii/S0016236125001413]
• 35. Tools for kinetics & combustion [https://akrmys.com/tools4kin.html.en]
• 36. Resources [https://rmg.mit.edu/resources]
• 37. Oxidation chemistry of cyclic hydrocarbons in a motored ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218009002338]
• 38. Experimental and modeling study on effects of N2 and CO2 ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC4348458/]
• 39. from the Electronic Structure to Model Applications [https://pubmed.ncbi.nlm.nih.gov/38804972/]
• 40. Experimental and Chemical Kinetic Modeling Study of ... [https://acs.figshare.com/articles/dataset/Experimental_and_Chemical_Kinetic_Modeling_Study_of_Dimethylcyclohexane_Oxidation_and_Pyrolysis/3824424]
• 41. Sensitivity analysis of complex kinetic systems. Tools and ... [https://link.springer.com/article/10.1007/BF01166355]
• 42. Mathematical and sensitivity analysis for chemical species ... [https://www.sciencedirect.com/science/article/pii/S2405844024087784]
• 43. 3.2.3: Rate Determining Step [https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/03%3A_Rate_Laws/3.02%3A_Reaction_Mechanisms/3.2.03%3A_Rate_Determining_Step]
• 44. Rate-determining step [https://en.wikipedia.org/wiki/Rate-determining_step]
• 45. Reaction Profiles; Rate Limiting Steps (M13Q10) – CHEM ... [https://wisc.pb.unizin.org/chem104workingcopy/chapter/mechanisms-and-multistep-reactions-reaction-profiles-rate-limiting-steps-m13q10/]
• 46. Identification of Rate-limiting Reaction Steps - Protheragen [https://wavefunction.protheragen.ai/services/identification-of-rate-limiting-reaction-steps.html]
• 47. and pressure-dependent branching ratios for 1,4 ... [https://www.sciencedirect.com/science/article/pii/S0016236124019823]
• 48. Fuel decomposition and aromatic species formation in ... [https://www.sciencedirect.com/science/article/abs/pii/S0016236125019489]
• 49. A comprehensive combustion chemistry study of n- ... [https://www.sciencedirect.com/science/article/pii/S0010218021003199]
• 50. An experimental and kinetic modeling study on the high- ... [https://www.sciencedirect.com/science/article/abs/pii/S0010218023001530]
• 51. Kinetic modeling [https://bio-protocol.org/exchange/minidetail?id=8570401&type=30]
• 52. Effect of methyl side chain positions on dimethylhexane ... [https://www.sciencedirect.com/science/article/abs/pii/S1743967125002910]
• 53. Speciation studies of methyl butanoate ignition [https://www.sciencedirect.com/science/article/abs/pii/S0016236111000305]
• 54. Jet-stirred reactor temperature and species profiles [https://cantera.org/dev/examples/python/kinetics/jet_stirred_reactor.html]
• 55. Towards cleaner combustion engines through ... - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC3586671/]
• 56. Experimental study and modeling of shock tube ignition ... [https://www.sciencedirect.com/science/article/pii/S1540748908000230]
• 57. Shock Tube Study of Ignition Delay Times for Hydrogen– ... [https://www.mdpi.com/2571-6255/6/11/435]
• 58. Shock tube ignition delay times and modeling of jet fuel mixtures [https://hanson.stanford.edu/publications/shock-tube-ignition-delay-times-and-modeling-jet-fuel-mixtures]
• 59. Shock tube ignition measurements of 2,5 dimethylhexane [https://squ.elsevierpure.com/en/publications/shock-tube-ignition-measurements-of-25-dimethylhexane/]
• 60. Kinetic modeling of gasoline surrogate components and ... [https://www.sciencedirect.com/science/article/abs/pii/S1540748910000787]
• 61. An experimental and modeling study of oxidation of 1,2,4- ... [https://www.sciencedirect.com/science/article/abs/pii/S1540748918304474]
• 62. An experimental and modeling study on the low ... [https://www.sciencedirect.com/science/article/abs/pii/S0016236121002507]
• 63. Tuning the ring-opening reaction of 1,3- ... [https://www.sciencedirect.com/science/article/abs/pii/S1385894707005554]
• 64. Conformational inversion-topomerization processes of ... [https://www.sciencedirect.com/science/article/abs/pii/S0040402018314984]
• 65. Experimental and theoretical insight into the soot ... [https://ora.ox.ac.uk/objects/uuid:c299cd18-bd51-41f3-b628-ca363acb839b]
• 66. Experimental and theoretical insight into the soot ... [https://www.sciencedirect.com/science/article/abs/pii/S1540748918302785]
• 67. A comparative study of the sooting tendencies of various C5 ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC7557285/]
• 68. Developing chemical kinetic models for thermochemical ... [https://www.nature.com/articles/s41596-025-01195-z]