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Extracting meaningful standard enthalpies and entropies of activation for surface reactions from kinetic rates
While analyses based on the Arrhenius kinetic model have been successfully applied since its introduction, the Arrhenius model neglects to describe pre-exponential factor in a scientifically meaningful fashion. Since the 1930s, transition-state theory (TST), has met with success in interpreting the pre-exponential factor’s value, allowing a standard entropy of activation to be estimated. However, analyses based on TST’s assumptions have been applied inconsistently in the literature, particularly in corrosion science, leading to difficulty in comparison of standard entropy of activations from different studies. In this work, the foundational principles of TST and standard states are discussed and a standard method to apply TST in analyzing rates of surface reactions is recommended. When full details are not available, reacting species’ concentrations should be normalized to the concentration of active surface sites. For corrosion reactions, conversion relationships are given to convert from units of corrosion rate to surface reaction rate, consistent with TST. This method is dubbed a surface reactant equi-density approximation. Application of this standard to reported data results in adjustments of the standard entropy of activation between - 65 and +50 J/mol K and brings reported entropies into a narrower range of values.
Theoretical and kinetic modeling study of hydrazine oxidation
The present work constitutes the first theoretical and kinetic modeling study of hydrazine oxidation, which may be important for burnout in ammonia-fueled combustion. The kinetics of the oxidation of N 2 H 4 , N 2 H 3 and tHNNH by molecular oxygen were investigated via a quantum chemistry/canonical transition state theory approach. Geometries and anharmonic frequencies were obtained with density functional theory, and energies from coupled cluster calculations (CCSD(T)) extrapolated to the infinite basis set limit, with corrections for core-valence electron correlation, scalar relativistic effects, and higher level correlation up to lambda coupled cluster, CCSDT(Q) Λ . The key reactions occurred on the N 2 H 4 O 2 potential energy surface, where the results indicated a fast reaction of N 2 H 3 with HO 2 via singlet adducts to yield tHNNH + H 2 O 2 and HNN(H)O + H 2 O, while reaction on the triplet surface proceeds via a bound complex followed by a tight, submerged barrier to yield N 2 H 4 + O 2 . The results were incorporated in a detailed reaction mechanism, which was used to interpret the shock tube results from Michel and Wagner (1965) on the effect of O 2 on hydrazine conversion at 1100–1400 K. The kinetic model captured qualitatively the observed behavior, but underestimated the reaction rate under oxidizing conditions. The hydrazine pyrolysis chemistry dominated conversion at reducing conditions and/or high temperature. At oxidizing conditions and intermediate temperatures (≲ 1400 K), reactions of N 2 -amines with HO 2 and O 2 were important for the oxidation rate.
Lattice Boltzmann simulation of the dissolution of slag in alkaline solution using real-shape particles
Highlights: • A dissolution numerical model was proposed to capture the real dissolution kinetics of slag in alkaline solution. • The log forward dissolution rate of Si was described as a function of NBO/T and solution pH. • A threshold solid volume fraction of 0.688 was found for a voxel in 3D, 63.8% larger than that for a pixel in 2D. • The proposed dissolution numerical model provides a reliable alternative to study the dissolution kinetics of slag. A dissolution numerical model was proposed in this study to capture the real dissolution kinetics of slag in alkaline solution. It consists of three modules, i.e. (i) simulation of the initial particle parking structure of slag in alkaline solution using real-shape particles of slag, (ii) simulation of the chemical reactions between slag and solution based on the transition state theory, and (iii) simulation of the physical transport of aqueous ions using the lattice Boltzmann method. This dissolution numerical model was verified using experimental results, showing reasonable accuracy. After verification, the dissolution numerical model was implemented to study the influences of temperature and particle shape using a proper recipe of slag in alkaline solution. This recipe was designed to avoid solid phase precipitation or gel formation via thermodynamic analysis. The simulation results showed faster dissolution kinetics of slag when using higher temperatures and more irregular particle shapes.
GeoMicro3D: A novel numerical model for simulating the reaction process and microstructure formation of alkali-activated slag
Highlights: • The GeoMicro3D model was innovatively developed for simulating the reaction process and microstructure formation of AAS. • In GeoMicro3D, the dissolution of slag and reactions of aqueous ions are fundamentally described in the local lattice cell. • A novel approach is proposed to speed up the nucleation simulations. • GeoMicro3D was implemented and verified with the relevant experimental data and thermodynamic calculation results. For the first time, this study developed a novel model, named GeoMicro3D, to simulate the reaction process and microstructure formation of alkali-activated slag. The GeoMicro3D model consists of four modules that are designed to simulate, respectively: (i) the initial spatial distribution of real-shape slag particles in alkaline activator, (ii) the dissolution of slag and diffusion of ions via the transition state theory and lattice Boltzmann method, respectively, (iii) the spatial distribution of reaction products using a nucleation probability theory, and (iv) the chemical reactions with thermodynamic modelling. Afterwards the GeoMicro3D model was implemented and verified. The simulation results were discussed and compared with the relevant experimental data and thermodynamic calculation results using GEMS. A good agreement was found in the comparisons, showing the strong simulation capability of GeoMicro3D.
An experimental and kinetic modeling study of the pyrolysis of isoprene, a significant biogenic hydrocarbon in naturally occurring vegetation fires
Isoprene dominates the carbon flux emitted by vegetation and constitutes 40% of non-methane biogenic emissions worldwide. Despite pyrolysis experiments at temperatures above 1000 K showing a link between isoprene combustion and aromatic species formation, comprehensive mechanistic research on isoprene is scarce in the literature. Here, in this work, we carry out an experimental and theoretical study to build, for the first time, a chemical kinetic model describing isoprene pyrolysis. The formation of polycyclic aromatic hydrocarbon (PAH) precursor species, often observed in vegetation fire plumes, is partially explained by isoprene pyrolysis experiments and theoretical modeling. Molecular dynamics (MD) simulations unveil reaction pathways from allylic isoprenyl radicals to allene and cyclopentadiene (CPD) intermediates, two relevant species detected in the experiments. Rate constants for these identified pathways are calculated using variational transition state theory to update the kinetic model, which is validated against single-pulse shock tube (SPST), and jet-stirred reactor (JSR) experimental data in the temperature range of 850–1690 K. The kinetic model presents satisfactory agreement with the SPST experimental data, and a reaction pathway analysis shows that association of propargyl radicals results in benzene formation. The JSR pathway analysis also identifies the prominent reactions for CPD, benzene, styrene, and toluene formation. Our model does not reproduce the CPD experimental profiles, indicating that additional studies are necessary. Overall, our findings advance the understanding of isoprene pyrolysis and its related atmospheric pollutants in naturally occurring vegetation fires where smoldering and oxygen-deficient combustion processes are present.
Experimental and modeling study of the autoignition behavior of a saturated heterocycle: Pyrrolidine
Experiments are conducted in both rapid compression machine (RCM) and shock tube (ST) to better quantify autoignition behavior (e.g., ignition delay, heat release) and understand heteroatomic effects in heterocyclic compounds, which are important reference components for the combustion of biomass-derived liquid fuels. These tests focus on the nitrogen-containing, five-membered saturated ring, pyrrolidine, at diluted conditions covering pressures of 20 and 50 bar, temperatures of 720–1450 K and a range of stoichiometries (ϕ = 0.5–2). A chemical kinetic model is developed and coupled to an existing combustion kinetics framework describing key nitrogen containing intermediates (e.g. pyrrole, ammonia and NOx). H-abstraction reactions by OH, H, CH 3 and HO 2 , are determined using ab-initio transition state theory methods, while analogies to cyclopentane are adopted for many other reactions, such as ring-opening. Here, the autoignition measurements reveal the lack of negative temperature coefficient (NTC) behavior and low-temperature chemistry for pyrrolidine, as opposed to its saturated hydrocarbon analogue, cyclopentane. Interestingly, at the lowest temperatures (T < 750 K), the reactivity of cyclopentane is greater than pyrrolidine, while at higher temperatures, pyrrolidine becomes more reactive. Agreement between the experimental measurements and the model is good, and it is found that H-abstraction reactions by HO 2 and ensuing chemistry play key roles in controlling the reactivity of this cyclic amine. Most of the fluxes, i.e., >70 %, are predicted to move through 1- or 2-pyrroline (C 4 H 7 N) and then the cyclic C 4 H 6 N radical, at both lower and higher temperatures, to form either CH 2 CHCHCHNH via ring-opening or pyrrole via β-scission. It appears that the ring opens more easily at lower temperature whereas the C–H β-scission dominates at higher temperature and lower pressure, such that the reaction of the fuel radical intermediate carrying an unpaired electron on the nitrogen atom with HO 2 is the next most notable in promoting oxidation. When comparing pyrrolidine and cyclopentane, which exhibits distinct pathways in different temperature regimes, the pyrrolidine pathways and sensitivity analysis align more closely to the high temperature case of cyclopentane where the important role of HO 2 radicals is seen to provide chain branching through HO 2 reaction with the fuel, accompanied by H 2 O 2 formation and decomposition to OH. The formation of 5-membered diene rings and ring opening reactions are also found to be highly relevant. Of particular note, it is found that there is little influence of small molecule nitrogen-chemistry, e.g., NH 2 , HCN, NO/NO 2 on the reactivity of the pyrrolidine mixtures investigated here where no recirculated combustion gases are included.
Best of both worlds: Enforcing detailed balance in machine learning models of transition rates
The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and Kinetic Monte-Carlo (kMC) algorithms, where the state-to-state evolution of the system is represented in terms of a continuous-time Markov chain, are instead frequently relied upon to efficiently predict long-time evolution. The accuracy of kMC simulations however relies on the complete and accurate knowledge of reaction pathways and corresponding kinetics. This requirement becomes extremely stringent in complex systems such as concentrated alloys where the astronomical number of local atomic configurations makes the a priori tabulation of all possible transitions impractical. Machine learning models of transition kinetics have been used to mitigate this problem by enabling the efficient on-the-fly prediction of kinetic parameters. While conventional KMC methods based on transition state theory naturally yield reversible dynamics that exactly obey the detailed balance criterion, providing strong guarantees on the properties of the stationary distribution, many recently-proposed ML-based approaches to barrier predictions provide no such guarantees. In this study, we derive conditions under which physics-informed ML architectures exactly enforce the detailed balance condition by construction, even when relying on non-extensive descriptions of states in terms of local environments around mobile defects. In conclusion, using the diffusion of a vacancy in a concentrated alloy as an example, we show that such ML architectures also exhibit superior performance in terms of prediction accuracy, demonstrating that the imposition of physical constraints can facilitate the accurate learning of barriers at no increase in computational cost.
The kinetics of the reactions of ground-state NH with N 2 O and implications for ammonia combustion
Quantum chemistry and canonical transition state theory have been applied to derive rate constants k for reactions of 3 Σ − imidogen with nitrous oxide. 3 channels were quantified. The fastest leads to NNH+NO and may be summarized as k = 2.8 × 10 7 T 1.68 exp.(−23.1 kcal mol −1 /RT) cm 3 mole −1 s −1 . Two much slower pathways lead to N 2 + 3 HNO and spin-forbidden 1 HNO. Modeling of literature data, from an NH 3 /O 2 flame and jet-stirred reactor measurements on dilute NH 3 /N 2 O mixtures, with the new kinetic information suggests that these channels are too slow to consume N 2 O significantly, and confirms that a widely used proposed rate constant for NH+N 2 O overestimates the reactivity.
Thermodynamically consistent forward and reverse degrees of rate control in reversible reactions
The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per k B T decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the apparent initial states and the apparent transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step at equilibrium. Here, this apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, $\bar{σ}$ The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.
Experimental and modeling study of water time histories during H 2 S-N 2 O combustion in a shock tube
Here, with the interest in directly burning sour gas in gas turbines, and the fact that even small amounts of H 2 S or its combustion products can alter combustion characteristics, many research studies have been performed to better understand the combustion chemistry of H 2 S. In the present study, the water formation was followed by laser absorption with N 2 O as an oxidant, instead of O 2 . Nitrous Oxide being essentially consumed via N 2 O (+M) ⇌ N 2 + O (+M), the water formation via the H 2 S + O route can then be probed to further validate the models. Three H 2 S/N 2 O mixtures diluted in 98% Ar were studied to cover the following range of equivalence ratios: 0.5, 1.0, and 2.0, over a wide range of temperatures (1580–1940 K) around atmospheric pressure. A chemical kinetic model was then developed first by validating the base N 2 O kinetics mechanism, then by investigating the experimental results presented herein. The N 2 O kinetics mechanism was updated with recent work on the low- and high-pressure limits for N 2 O decomposition (N 2 O (+M) ⇌ N 2 + O (+M)) as well as a review of rate coefficients for N 2 O + H ⇌ N 2 + OH from the literature. Good agreement is shown for H 2 /N 2 O mixtures. Updates were then made to the H 2 S kinetics mechanism, specifically, an update from the literature on SO 2 + H (+M) ⇌ SO + OH (+M) and an adjustment to SO + SH ⇌ S 2 + OH. Additionally, reactions between SH and N 2 O were determined using W1BD data and transition state theory which required the addition of an NNS sub-mechanism. With these updates, the mechanism provides good agreement with the H 2 S/N 2 O experiments.
Pressure-dependent kinetics of cyclopentene consumption
Recent experiments have uncovered deficiencies in the ability of current kinetic models for cyclopentane combustion to predict species profiles as a function of O2 concentration. One likely source of these discrepancies flows from the limited availability of relevant kinetic data for key functionalized intermediates, requiring the use of distant analogies to estimate their rates. This work fills this gap for cyclopentene, the most prominent C5 intermediate in low-temperature cyclopentane combustion. Ab initio transition-state-theory based master equation methods are used to calculate pressure-dependent rate constants across four potential energy surfaces (C5H8 + OH, C5H8 + HO2, C5H7, and C5H7 + O2). Potential energy surfaces are characterized at the CCSD(T)-F12/cc-pVDZ-F12//revDSD-PBEP86-D3BJ/def2-TZVPP level of theory. Pressure-dependent rate constants and branching fractions are determined via 1D master equation calculations. The results are used to analyze the competition for radicals between cyclopentene and cyclopentane in the intermediate temperature region, and to identify the dominant pathways flowing from these initiation channels. On the OH initiation surface, we find good agreement with recently published experimental rate constants at high temperature, and we elucidate the complex temperature dependence below 800 K, where 𝜋𝜋 addition becomes prominent. On the HO2 initiation surface, we find an interesting alternative route to bicyclic ether formation via well-skipping over the HO2 adduct well. On the cyclopentenyl radical surface, the major product is cyclopentadiene plus H. On the cyclopentenyl + O2 surface, we find that resonance stabilization largely prevents the allylic radical from undergoing oxidation, whereas the alkylic radical has a somewhat elevated propensity for oxidation pathways relative to cyclopentyl.
The P( 4 S) + NH( 3 Σ – ) and N( 4 S) + PH( 3 Σ – )reactions as sources of interstellar phosphorus nitride
Phosphorus nitride (PN) is believed to be one of the major reservoirs of phosphorus in the interstellar medium (ISM). For this reason, understanding which reactions produce PN in space and predicting their rate coefficients is important for modelling the relative abundances of P-bearing species and clarifying the role of phosphorus in astrochemistry. Here, in this work, we explore the potential energy surfaces of the $\textrm{P}(^4\textrm{S}) + \textrm{NH}(^3\Sigma^-)$ and $\textrm{N}(^4\textrm{S}) + \textrm{PH}(^3\Sigma^-)$ reactions and the formation of $\textrm{H}(^2\textrm{S}) + \textrm{PN}(^1\Sigma^+)$ through high accuracy ab initio calculations and the variable reaction coordinate transition state theory (VRC-TST). We found that both reactions proceed without an activation barrier and with similar rate coefficients that can be described by a modified Arrhenius equation ( $k(T)=\alpha\!\left( T/300 \right)^{\beta} \exp\!{(\!-\!\gamma/T)})$ with $\alpha=0.93\times 10^{-10}\rm cm^3\,s^{-1}$ , $\beta=-0.18$ and $\gamma=0.24\, \rm K$ for the $\textrm{P} + \textrm{NH} \longrightarrow \textrm{H} + \textrm{PN}$ reaction and $\alpha=0.88\times 10^{-10}\rm cm^3\,s^{-1}$ , $\beta=-0.18$ and $\gamma=1.01\, \rm K$ for the $\textrm{N} + \textrm{PH} \longrightarrow \textrm{H} + \textrm{PN}$ one. Both reactions are expected to be relevant for modelling PN abundances even in the cold environments of the ISM. Given the abundance of hydrogen in space, we have also predicted rate coefficients for the destruction of PN via H + PN collisions.
Non-Boltzmann Effects in Chain Branching and Pathway Branching for Diethyl Ether Oxidation
Low-temperature (LT) engine applications have several potential benefits, including reduced emissions and increased efficiency. Attaining these benefits requires accurate kinetic modeling of LT chain branching, which depends heavily on ketohydroperoxide (KHP) decomposition. For diethyl ether (DEE), a promising biofuel, current estimates of the KHP decomposition rate constant are largely based on empirical fits to data. In this study, we investigate the most important KHP isomer in DEE LT oxidation by applying variable reaction coordinate transition state theory to the main pathway for KHP decomposition: OO bond fission to produce •OH and a keto-alkoxy radical, •OQ'O. We also use ab initio kinetics methods to investigate the decomposition of •OQ'O, where we find dominant branching to acetic acid, with the remaining flux going to CH 3 C(O)OCHO. Additionally, new time-resolved measurements of DEE and acetic acid concentrations during LT (450–600 K) DEE oxidation are obtained in a laser photolysis flow reactor coupled with multiplexed photoionization mass spectrometry. These new experimental data, along with jet-stirred reactor data in the literature, are compared with the predictions of a recent DEE mechanism (Tran et al. Proc. Comb. Inst. 2019, 37, 511-519) that was modified with the newly calculated ab initio rate constants for KHP and •OQ'O decomposition. The predictions of the modified mechanism are quite poor when compared to the experimental data; this is primarily due to the new KHP ⇌ •OQ'O + •OH rate constant, which is 1–2 orders of magnitude slower than empirical values employed in recent mechanisms. To reconcile the new KHP rate constant and the experimental data, we explore and quantify the possible role of non-Boltzmann (nB) reaction sequences. The nB reactions have a substantial effect on both the overall mechanism reactivity and the •OQ'O branching to acetic acid. We also provide guidance on the proper implementation of nB reactions in kinetic mechanisms.
Diffusion and Adsorption of 2-Methylpentane and 3-Methylpentane in MFI-Type Zeolite Crystals
Due to the intimate contact of guest molecules with the inner surface of microporous adsorbents, slight changes in the structure of the guest molecules may lead to remarkable changes in their microdynamics. As an impressive example, in this work, diffusion measurements via IR microimaging (IRM) show that the transport diffusivity of 2-methylpentane (2MP) exceeds the value attained for 3-methylpentane (3MP) by a factor of 2−4.5 in silicalite- 1, an MFI-type zeolite crystal and a technically relevant porous host system. This experimental finding is rationalized by comparison with the outcome of dynamically corrected transition state theory (dcTST) simulations.
Kinetics and Mechanism of the Singlet Oxygen Atom Reaction with Dimethyl Ether
Here, we combine in situ laser spectroscopy, quantum chemistry, and kinetic calculations to study the reaction of a singlet oxygen atom with dimethyl ether. Infrared laser absorption spectroscopy and Faraday rotation spectroscopy are used for the detection and quantification of the reaction products OH, H 2 O, HO 2 , and CH 2 O on submillisecond time scales. Fitting temporal profiles of products with simulations using an in-house reaction mechanism allows product branching to be quantified at 30, 60, and 150 Torr. The experimentally determined product branching agrees well with master equation calculations based on electronic structure data and transition state theory. The calculations demonstrate that the dimethyl peroxide (CH 3 OOCH 3 ) generated via O-insertion into the C–O bond undergoes subsequent dissociation to CH 3 O + CH 3 O through energetically favored reactions without an intrinsic barrier. This O-insertion mechanism can be important for understanding the fate of biofuels leaking into the atmosphere and for plasma-based biofuel processing technologies.
Simple Approximation for the Ideal Reference State of Gases Adsorbed on Solid-State Surfaces
Reference states are useful as models for facilitating calculations of equilibrium constants, and they may also serve as standard states that are convenient for organizing and tabulating thermodynamic data; however, standard state conventions and appropriate reference states for adsorbed species have received less attention than those for pure substances and solutes. Here, we compare seven choices of reference states for calculations of equilibrium constants and transition state theory rate constants for flat surfaces, in particular (1) an ideal 2D harmonic oscillator, (2) an ideal rigid-molecule harmonic oscillator, (3) an ideal 2D harmonic oscillator with separable surface modes, (4) a 2D ideal gas, (5) an ideal 2D hindered translator, (6) an ideal 2D hindered translator with lowest-order barriers, and (7) a simple ideal 2D hindered translator proposed in this work. The advantage of models 5–7 is that they can treat both mobile and localized adsorbates in a consistent way, whereas models 1–3 are only appropriate for localized adsorbates, and model 4 is only appropriate for a freely translating adsorbate. Furthermore, models 6 and 7 reduce the computational cost without the user having to calculate barrier heights for diffusion. An advantage of the simple ideal 2D hindered translator is that it has a physical high-temperature limit. We also propose a reference state for nonflat surfaces. Here, the user is encouraged to choose a reference state based on the appropriateness of the model and the practicality of the calculations.