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Wu Y, Hu Y, Li Z, Ma J. Molecular Dynamics Simulation of Thermal Nonequilibrium and Chemical Reaction Processes in Hydrogen Combustion. J Phys Chem A 2024; 128:2643-2655. [PMID: 38530707 DOI: 10.1021/acs.jpca.3c08131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/28/2024]
Abstract
Using reactive force field (ReaxFF) and molecular dynamics simulation, we investigate the combustion process of hydrogen-oxygen systems in initial thermal nonequilibrium states with different translational and rovibrational temperatures for oxygen. The system studied in this work contains 300 oxygen molecules and 700 hydrogen molecules with a density of 7 times the air density. For this system, the characteristic relaxation times of oxygen and hydrogen vibrational energies are 0.173 and 0.249 ns, respectively. 0.6% of hydrogen undergoes a chemical reaction with oxygen during the thermal nonequilibrium relaxation stage. For the distribution of translational energy and vibrational energy of oxygen in the thermal nonequilibrium state, the maximum mean error of the statistical distribution in the simulation and the Boltzmann distribution at temperature calculated from the average kinetic energy of molecules is about 2.25 × 10-5. At the same time, it was observed in the simulation that many-body interactions play a certain role in the combustion process. Furthermore, we compare the ignition time and temperature rise behavior of different combustion mechanisms and molecular dynamics simulations starting from the thermal equilibrium state. These results will provide meaningful references for the construction of thermal nonequilibrium combustion chemical reaction mechanisms.
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Affiliation(s)
- Yimiao Wu
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China
| | - Yongxin Hu
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China
| | - Zhiwei Li
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China
| | - Jianyi Ma
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China
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2
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Hanel R, Corominas-Murtra B. The Typical Set and Entropy in Stochastic Systems with Arbitrary Phase Space Growth. ENTROPY (BASEL, SWITZERLAND) 2023; 25:350. [PMID: 36832717 PMCID: PMC9954961 DOI: 10.3390/e25020350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Revised: 02/03/2023] [Accepted: 02/05/2023] [Indexed: 06/18/2023]
Abstract
The existence of the typical set is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given its central role underlying the emergence of stable, almost deterministic statistical patterns, a question arises whether typical sets exist in much more general scenarios. We demonstrate here that the typical set can be defined and characterized from general forms of entropy for a much wider class of stochastic processes than was previously thought. This includes processes showing arbitrary path dependence, long range correlations or dynamic sampling spaces, suggesting that typicality is a generic property of stochastic processes, regardless of their complexity. We argue that the potential emergence of robust properties in complex stochastic systems provided by the existence of typical sets has special relevance to biological systems.
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Affiliation(s)
- Rudolf Hanel
- Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria
- Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
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3
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Bone RA, Green JR. Optimizing dynamical functions for speed with stochastic paths. J Chem Phys 2022; 157:224101. [PMID: 36546817 DOI: 10.1063/5.0125479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Living systems are built from microscopic components that function dynamically; they generate work with molecular motors, assemble and disassemble structures such as microtubules, keep time with circadian clocks, and catalyze the replication of DNA. How do we implement these functions in synthetic nanostructured materials to execute them before the onset of dissipative losses? Answering this question requires a quantitative understanding of when we can improve performance and speed while minimizing the dissipative losses associated with operating in a fluctuating environment. Here, we show that there are four modalities for optimizing dynamical functions that can guide the design of nanoscale systems. We analyze Markov models that span the design space: a clock, ratchet, replicator, and self-assembling system. Using stochastic thermodynamics and an exact expression for path probabilities, we classify these models of dynamical functions based on the correlation of speed with dissipation and with the chosen performance metric. We also analyze random networks to identify the model features that affect their classification and the optimization of their functionality. Overall, our results show that the possible nonequilibrium paths can determine our ability to optimize the performance of dynamical functions, despite ever-present dissipation, when there is a need for speed.
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Affiliation(s)
- Rebecca A Bone
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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4
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Mondal S, Greenberg JS, Green JR. Dynamic scaling of stochastic thermodynamic observables for chemical reactions at and away from equilibrium. J Chem Phys 2022; 157:194105. [DOI: 10.1063/5.0106714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions.
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Affiliation(s)
- Shrabani Mondal
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Chemistry, Physical Chemistry Section, Jadavpur University, Kolkata 700032, India
| | - Jonah S. Greenberg
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
| | - Jason R. Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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5
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Bone RA, Sharpe DJ, Wales DJ, Green JR. Stochastic paths controlling speed and dissipation. Phys Rev E 2022; 106:054151. [PMID: 36559408 DOI: 10.1103/physreve.106.054151] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 10/28/2022] [Indexed: 11/24/2022]
Abstract
Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.
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Affiliation(s)
- Rebecca A Bone
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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Bertels LW, Newcomb LB, Alaghemandi M, Green JR, Head-Gordon M. Benchmarking the Performance of the ReaxFF Reactive Force Field on Hydrogen Combustion Systems. J Phys Chem A 2020; 124:5631-5645. [DOI: 10.1021/acs.jpca.0c02734] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Luke W. Bertels
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Lucas B. Newcomb
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
| | - Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
| | - Jason R. Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
- Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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7
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Nicholson SB, Bone RA, Green JR. Typical Stochastic Paths in the Transient Assembly of Fibrous Materials. J Phys Chem B 2019; 123:4792-4802. [PMID: 31063371 DOI: 10.1021/acs.jpcb.9b02811] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
When chemically fueled, molecular self-assembly can sustain dynamic aggregates of polymeric fibers-hydrogels-with tunable properties. If the fuel supply is finite, the hydrogel is transient, as competing reactions switch molecular subunits between active and inactive states, drive fiber growth and collapse, and dissipate energy. Because the process is away from equilibrium, the structure and mechanical properties can reflect the history of preparation. As a result, the formation of these active materials is not readily susceptible to a statistical treatment in which the configuration and properties of the molecular building blocks specify the resulting material structure. Here, we illustrate a stochastic-thermodynamic and information-theoretic framework for this purpose and apply it to these self-annihilating materials. Among the possible paths, the framework variationally identifies those that are typical-loosely, the minimum number with the majority of the probability. We derive these paths from computer simulations of experimentally-informed stochastic chemical kinetics and a physical kinetics model for the growth of an active hydrogel. The model reproduces features observed by confocal microscopy, including the fiber length, lifetime, and abundance as well as the observation of fast fiber growth and stochastic fiber collapse. The typical mesoscopic paths we extract are less than 0.23% of those possible, but they accurately reproduce material properties such as mean fiber length.
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Affiliation(s)
- Schuyler B Nicholson
- Department of Chemistry , University of Massachusetts Boston , Boston , Massachusetts 02125 , United States
| | - Rebecca A Bone
- Department of Chemistry , University of Massachusetts Boston , Boston , Massachusetts 02125 , United States
| | - Jason R Green
- Department of Chemistry , University of Massachusetts Boston , Boston , Massachusetts 02125 , United States.,Department of Physics , University of Massachusetts Boston , Boston , Massachusetts 02125 , United States.,Center for Quantum and Nonequilibrium Systems , University of Massachusetts Boston , Boston , Massachusetts 02125 , United States
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8
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Jizba P, Korbel J. Maximum Entropy Principle in Statistical Inference: Case for Non-Shannonian Entropies. PHYSICAL REVIEW LETTERS 2019; 122:120601. [PMID: 30978043 DOI: 10.1103/physrevlett.122.120601] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2018] [Revised: 01/12/2019] [Indexed: 06/09/2023]
Abstract
In this Letter, we show that the Shore-Johnson axioms for the maximum entropy principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof where a one-parameter class of admissible entropies is identified, we substantiate our point by analyzing the effect of weak correlations and by discussing two pertinent examples: two-qubit quantum system and transverse-momentum behavior of hadrons in high-energy proton-proton collisions.
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Affiliation(s)
- Petr Jizba
- FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague, Czech Republic
| | - Jan Korbel
- FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague, Czech Republic
- Section for Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria
- Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria
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9
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Nicholson SB, Greenberg JS, Green JR. Entrance and escape dynamics for the typical set. Phys Rev E 2018; 97:012146. [PMID: 29448403 DOI: 10.1103/physreve.97.012146] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2017] [Indexed: 11/07/2022]
Abstract
According to the asymptotic equipartition property, sufficiently long sequences of random variables converge to a set that is typical. While the size and probability of this set are central to information theory and statistical mechanics, they can often only be estimated accurately in the asymptotic limit due to the exponential growth in possible sequences. Here we derive a time-inhomogeneous dynamics that constructs the properties of the typical set for all finite length sequences of independent and identically distributed random variables. These dynamics link the finite properties of the typical set to asymptotic results and allow the typical set to be applied to small and transient systems. The main result is a geometric mapping-the triangle map-relating sequences of random variables of length n to those of length n+1. We show that the number of points in this map needed to quantify the properties of the typical set grows linearly with sequence length, despite the exponential growth in the number of typical sequences. We illustrate the framework for the Bernoulli process and the Schlögl model for autocatalytic chemical reactions and demonstrate both the convergence to asymptotic limits and the ability to reproduce exact calculations.
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Affiliation(s)
- Schuyler B Nicholson
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jonah S Greenberg
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Center for Quantum and Nonequilibrium Systems, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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10
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Nicholson SB, Alaghemandi M, Green JR. Effects of temperature and mass conservation on the typical chemical sequences of hydrogen oxidation. J Chem Phys 2018; 148:044102. [PMID: 29390841 DOI: 10.1063/1.5012760] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Macroscopic properties of reacting mixtures are necessary to design synthetic strategies, determine yield, and improve the energy and atom efficiency of many chemical processes. The set of time-ordered sequences of chemical species are one representation of the evolution from reactants to products. However, only a fraction of the possible sequences is typical, having the majority of the joint probability and characterizing the succession of chemical nonequilibrium states. Here, we extend a variational measure of typicality and apply it to atomistic simulations of a model for hydrogen oxidation over a range of temperatures. We demonstrate an information-theoretic methodology to identify typical sequences under the constraints of mass conservation. Including these constraints leads to an improved ability to learn the chemical sequence mechanism from experimentally accessible data. From these typical sequences, we show that two quantities defining the variational typical set of sequences-the joint entropy rate and the topological entropy rate-increase linearly with temperature. These results suggest that, away from explosion limits, data over a narrow range of thermodynamic parameters could be sufficient to extrapolate these typical features of combustion chemistry to other conditions.
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Affiliation(s)
- Schuyler B Nicholson
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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11
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Newcomb LB, Alaghemandi M, Green JR. Nonequilibrium phase coexistence and criticality near the second explosion limit of hydrogen combustion. J Chem Phys 2017; 147:034108. [PMID: 28734297 DOI: 10.1063/1.4994265] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While hydrogen is a promising source of clean energy, the safety and optimization of hydrogen technologies rely on controlling ignition through explosion limits: pressure-temperature boundaries separating explosive behavior from comparatively slow burning. Here, we show that the emergent nonequilibrium chemistry of combustible mixtures can exhibit the quantitative features of a phase transition. With stochastic simulations of the chemical kinetics for a model mechanism of hydrogen combustion, we show that the boundaries marking explosive domains of kinetic behavior are nonequilibrium critical points. Near the pressure of the second explosion limit, these critical points terminate the transient coexistence of dynamical phases-one that autoignites and another that progresses slowly. Below the critical point temperature, the chemistry of these phases is indistinguishable. In the large system limit, the pseudo-critical temperature converges to the temperature of the second explosion limit derived from mass-action kinetics.
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Affiliation(s)
- Lucas B Newcomb
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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12
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Alaghemandi M, Newcomb LB, Green JR. Ignition in an Atomistic Model of Hydrogen Oxidation. J Phys Chem A 2017; 121:1686-1692. [DOI: 10.1021/acs.jpca.7b00249] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mohammad Alaghemandi
- Department
of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
| | - Lucas B. Newcomb
- Department
of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
| | - Jason R. Green
- Department
of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
- Department
of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
- Center
for Quantum and Nonequilibrium Systems, University of Massachusetts Boston, Boston, Massachusetts 02125, United States
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13
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Monge-Palacios M, Rafatijo H. On the role of the termolecular reactions 2O 2 + H 2 → 2HO 2 and 2O 2 + H 2 → H + HO 2 + O 2 in formation of the first radicals in hydrogen combustion: ab initio predictions of energy barriers. Phys Chem Chem Phys 2017; 19:2175-2185. [PMID: 28045141 DOI: 10.1039/c6cp07029a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We have investigated the role of termolecular reactions in the early chemistry of hydrogen combustion. We performed molecular chemical dynamics simulations using ReaxFF in LAMMPS to identify potential initial reactions for a 1 : 4 mixture of H2 : O2 in the NVT ensemble at density 276.3 kg m-3 and ∼3000 K (∼4000 atm) and ∼4000 K (∼5000 atm), and then characterized the saddle points for those reactions using ab initio methods: CCSD(T) = FC/cc-pVTZ//MP2/6-31G, CCSD(T) = FULL/aug-cc-pVTZ//CCSD = FC/cc-pVTZ and CASSCF MP2/6-31G//MP2/6-31G. The main initial reaction is H2 + O2 → H + HO2, frequently occurring in the presence of a second O2 as a third body; that is, 2O2 + H2 → H + HO2 + O2. The second most frequent reaction is 2O2 + H2 → 2HO2. We found three saddle points on the triplet PES of these termolecular reactions: one for 2O2 + H2 → H + HO2 + O2 and two for 2O2 + H2 → 2HO2. In the latter case, one has a symmetric structure consistent with simultaneous formation of two HO2 and the other corresponds to a bimolecular reaction between O2 and H2 that is "interrupted" by a second O2 before going to completion. The classical barrier height of the symmetric saddle point for 2O2 + H2 → 2HO2 is 49.8 kcal mol-1. The barrier to H2 + O2 → H + HO2 is 58.9 kcal mol-1. The termolecular reaction will be competitive with H2 + O2 → H + HO2 only at sufficiently high pressures.
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Affiliation(s)
- M Monge-Palacios
- Department of Chemistry, University of Missouri-Columbia, Columbia, MO 65211-7600, USA.
| | - Homayoon Rafatijo
- Department of Chemistry, University of Missouri-Columbia, Columbia, MO 65211-7600, USA.
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