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A: Kinetics and Dynamics

Molecular Dynamics Study of Combustion Reactions in a Supercritical Environment. Part 3: Boxed MD Study of CH + HO -> CHO + OH Reaction Kinetics 3

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Sergey Valer'evich Panteleev, Artem E. Masunov, and Subith S Vasu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12233 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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The Journal of Physical Chemistry

Molecular Dynamics Study of Combustion Reactions in Supercritical Environment. Part 3: Boxed MD Study of CH3 + HO2 CH3O + OH Reaction Kinetics

Sergey V. Panteleev,1,2 Artëm E. Masunov,*1,3,4,5 Subith S. Vasu6 1

NanoScienece Technology Center, University of Central Florida, 12424 Research Parkway, Ste 400, Orlando, FL 32826, USA 2

N.I. Lobachevsky State University of Nizhny Novgorod, Gagarin Av. 23, Nizhny Novgorod 603950, Russia

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Department of Chemistry, and Department of Physics, University of Central Florida, 4111 Libra Dr., Orlando, FL 32816, USA 4

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South Ural State University, Lenin pr. 76, Chelyabinsk 454080, Russia

National Research Nuclear University MEPhI, Kashirskoye shosse 31, Moscow, 115409, Russia

Center for Advanced Turbomachinery and Energy Research (CATER), Mechanical and

Aerospace Engineering University of Central Florida, Orlando, Florida, 32816, USA *Corresponding Email: [email protected]

Abstract The kinetics of reaction CH3 + HO2 CH3O + OH in supercritical carbon dioxide media at pressures from 0.3 to 1000 atm in the temperature range (600-1600) K was studied using boxed molecular dynamics simulations at QM/MM theory level with periodical boundary conditions. The mechanism of this process includes two consecutive steps: formation and decomposition of CH3OOH intermediate. We calculated the activation free energies and rate constants of each step, then used Bodenstein’s quasistationary concentrations approximation to estimate the rate constants of the reaction. Based on the temperature dependence of the rate constants, parameters in the extended Arrhenius equation were determined. We found that reaction rate of each step, as well as overall reaction, increases with increasing CO2 pressure in the system. The most effective zone for the process is T = 1000-1200 K and the CO2 pressure is about 100 atm. 1

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1. INTRODUCTION Oxy-fuel combustion technology, where CO2 replaces nitrogen as diluent to control the flame temperature, holds a great promise of increased energy efficiency,1 reduced nitroxide pollution2-3 and an opportunity for carbon sequestration.4,5 In many studies the standard combustion mechanisms are presumed to be valid at CO2-reach conditions for data interpretation and modeling the flame composition,6,7 or turbine design.8 Although several kinetic models for the methane combustion mechanism were developed, none of them was designed for oxycombustion specifically.9,10 These mechanisms involve a large number of elementary reactions, and some of them may be altered by the presence of carbon dioxide in large concentrations and high pressures.11 Recently we extended our efforts toward development and validation of kinetic mechanisms specific for oxy-fuel combustion. With this purpose, we investigated potential surfaces of elementary combustion reactions in the presence of CO2 molecule and predicted catalytic effects of carbon dioxide on reaction rates.12,13,14,15 Shock tube experimental study of CO2 effects on ignition delay time were conducted.16-19 The high-pressure conditions in supercritical CO2 environment, however, present a great challenge for experimental measurements and cannot be simulated by quantum chemistry methods alone. For these reasons we employed classical Molecular Dynamics (MD) methods to model combustion reactions in supercritical conditions. In the first paper of this series20 we established that the H/C/O parameterization of ReaxFF force field (which is used by other groups to simulate oxy-fuel combustion21 and supercritical environment22) does not reproduce the pressure-density curves for

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neither H2O, nor CO2 fluids. Reparameterization is required, which distorts reactive potential surfaces considerably. Our second paper of this series23 was focused on reaction CO + OH CO2 + H. We employed QM/MM approach, where reactive system was treated by quantum chemistry, and CO2 fluid was described by transferable potentials for phase equilibria (TraPPE).43 TraPPE is molecular mechanics force field, designed to reproduce pressure-density curve very accurately. In order to simulate the infrequent event of reactive system crossing the activation barrier, we employed Boxed Molecular Dynamics (BXD). BXD is a particular implementation of the enhanced sampling techniques, where reactive system is confined to a narrow interval of the reaction coordinate, statistics is collected, and the free energy slope is obtained. When intervals cover the entire range of reaction coordinate, the free energy profile is obtained, and reaction constant can be calculated. Even though the sampling is enhanced, reliable statistics requires the trajectory with tens of millions of steps, which makes this method unfeasible at ab initio MD level. For more details on this approach the reader is referred to Computational Details section. Here we apply the same methodology to study another elementary reaction, important in combustions: 24-30 CH3 + HO2 CH3O + OH,

(R1)

The first detailed study of R1 reaction was performed by Colket.31 According to the obtained experimental data, the rate constant of the process R1 at T = 1030-1115 K and normal pressure in nitrogen was estimated as 2·1013 cc/mol·s. Such values are characteristic of very rapid transformations: most other similar processes have rate constants that are lower by several orders of magnitude.31-33 Colket concluded this reaction proceeds without a barrier and has zero energy

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of activation. His study also established that R1 proceeds through the formation of a stable intermediate - methylhydroperoxide: CH3 + HO2 CH3OOH,

(R2)

CH3OOH CH3O + OH,

(R3)

However, the product methoxy radical CH3O is unstable and nay lose hydrogen atom to form CH2O easily.32 The enthalpies of R2 and R3 processes according to Colket are -70 and 44 kcal/mol, respectively, which is very close to the recently predicted values of -66.9 and 43.4 kcal/mol.33 According to Lightfoot et al.,34 the decomposition of methylhydroperoxide at room temperature and below is very slow, and the rate of R3 becomes significant only above 600 K. They also reported that the temperature dependence of the reaction rate constants R3 in the temperature range from 600 to 719 K and atmospheric pressure is close to linear. The potential energy surfaces of the reaction CH3O + OH Products were predicted by Zhu et al.35 Various channels were reported, including (R1a) CH4 + 3O2, (R1b) CH4 + 1O2, (R1c) CH2O + H2O, (R1d) CH3O + OH. Thus, the process R1 should be considered as one of the possible reaction channels. The computational kinetics study of the reaction CH3O + OH Products revealed the independence of the total rate constant from pressure of up to 50 atm in the temperature range from 300 to 3000 K.35 The calculated rate constant was in a good agreement with the value obtained earlier by Colket.31 This may indicate that the process R1 is one of the fastest in the group of reaction channels R1a-d. The authors of this study also established that at T 100 atm. This behavior is typical for the direct process R2 and for the inverse R2r reaction, however, for R2 the pressure increase has a lesser effect on k than for R2r, while the temperature factor plays a decisive role here. In Fig. 2a, b, two regions can be clearly distinguished: 1 - in the pressure range from 0.3 to 100 atm (approximately), 2 - at P > 100 atm. For the first region almost linear and sharp increasing in k is observed with an increase in P, for the second, a sharp slowing of k growth with increasing P and an exit to the plateau.

3.2 Reactions R3 and R3r In Supplementary Materials in Tables S6 and S7 are free energies and rate constants respectively of conversion R3 calculated for the different temperatures and the number of CO2 molecules in system in accordance with the Eyring-Polany equation (2). In Tables S8 and S9, similar data are presented, but for the inverse process R3r. Tables 5 and 6 show the rate constants of reactions R3 and R3r, obtained as a result of numerical approximations k from Tables S7 and S9 on the range of interesting pressure values at different temperatures. Table 5. Rate constants k (s-1), predicted for R3 reaction. T, K Pressure of CO2, atm. 0.3 1 3 10 30 600 3.46·104 4.62·104 6.92·104 1.36·105 5.98·105 800 4.82·107 5.58·107 6.56·107 9.12·107 1.81·108 1000 4.48·109 4.92·109 5.55·109 6.88·109 9.14·109 1200 6.04·1010 6.38·1010 6.75·1010 7.36·1010 8.51·1010 1400 3.77·1011 3.89·1011 4.07·1011 4.35·1011 4.72·1011 1600 1.42·1012 1.46·1012 1.51·1012 1.58·1012 1.66·1012

Table 6. Rate constants k (cc/mol·s), predicted for R3r reaction.

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100 3.55·106 4.12·108 1.32·1010 9.96·1010 5.14·1011 1.78·1012

300 1.54·107 8.13·108 1.87·1010 1.19·1011 5.67·1011 1.89·1012

1000 5.77·107 1.74·109 2.58·1010 1.43·1011 6.18·1011 1.98·1012


T, K 600 800 1000 1200 1400 1600

0.3 1 3 5.01·103 3.84·103 2.96·103 6.29·107 3.92·107 2.38·107 1.26·1010 6.53·109 3.17·109 2.64·1011 1.39·1011 6.61·1010 8.98·1011 5.42·1011 3.42·1011 1.55·1012 1.39·1012 1.19·1012

Pressure of CO2, atm. 10 30 2.29·103 1.57·103 1.44·107 8.81·106 1.54·109 7.73·108 3.52·1010 1.75·1010 2.38·1011 1.64·1011 1.01·1012 8.76·1011

100 300 1000 1.18·103 8.42·102 6.24·102 5.74·106 3.51·106 2.32·106 4.59·108 2.95·108 1.88·108 9.62·109 5.94·109 4.07·109 1.13·1011 8.00·1010 5.83·1010 7.39·1011 6.09·1011 4.78·1011

These rate constants correspond to values of the free activation energy in the range from 9.0 to 23.5 kcal/mol and from 13.5 to 26.0 kcal/mol for direct and reverse reactions, respectively. The lg k dependences of the reactions R3 and R3r on the reciprocal temperature (1/T) are shown in Fig. 3. 2.E+12 3.E+10 2.E+10 3.E+08

P=0.3 atm P=1.0 atm

2.E+08

k, cc/mol·s

k, s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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P=3 atm P=10 atm P=30 atm P=100 atm

2.E+06

P=0.3 atm P=1.0 atm P=3 atm P=10 atm P=30 atm P=100 atm P=300 atm P=1000 atm

3.E+06

3.E+04

P=300 atm P=1000 atm

2.E+04 0.6

0.8

1

3.E+02 1.2

1.4

1.6

0.6

1000/T, K-1

0.8

1

1.2

1.4

1.6

1000/T, K-1

a b Fig. 3. Dependence of ln k on 1000/T: a - reaction R3, b - reaction R3r. Rate constants plot vs. in logarithmic scale.

The linearized dependence lg k – 1000/T indicates a close to Arrhenius character of the temperature dependence of rate constants R3 reaction in temperature range from 600 to 1600 K. For the inverse R3r process, one can see bend in the region of elevated temperatures: approximately at T > 1200 K. What is interesting, with increasing CO2 pressure, the bend degenerates and at P > 100 atm is not observed at all.

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Table 7 shows the numerical values of the parameters in extended Arrhenius equation (3) for the reaction R3, in Table 8 for the reaction R3r.

Table 7. Parameters of extended Arrhenius equation for the reaction R3 in temperature range (600-1600) K Parameters of Extended Arrhenius equation Pressure Plog, atm A, s-1 n Ea, cal/mol 15 0.3 (6.40±0.13)·10 -0.075±0.004 30360±190 14 1.0 (7.09±0.15)·10 0.185±0.006 29380±170 3.0 (1.37±0.13)·1014 0.394±0.009 28540±170 13 10 (9.63±0.12)·10 0.475±0.012 27920±180 30 (2.45±0.12)·1013 0.521±0.014 26630±160 13 100 (1.16±0.14)·10 0.863±0.017 24470±140 11 300 (3.33±0.09)·10 1.309±0.024 21880±140 1000 (8.20±0.13)·1012 0.914±0.021 21120±130 Table 8. Parameters of extended Arrhenius equation for the reaction R3r in temperature range (600-1600) K Pressure Plog, Parameters of Extended Arrhenius equation atm A, cc/mol·s n Ea, cal/mol 0.3 (2.50±0.03)·1023 -3.489±0.033 27460±120 1.0 (8.89±0.05)·1022 -3.354±0.030 27580±120 3.0 (5.31±0.07)·1021 -2.832±0.026 28510±140 20 10 (1.11±0.11)·10 -2.079±0.025 29950±120 19 30 (1.05±0.10)·10 -1.667±0.019 30740±160 100 (7.40±0.08)·1018 -1.495±0.016 31950±180 17 300 (2.82±0.02)·10 -0.947±0.012 32650±170 1000 (1.93±0.05)·1017 -0.862±0.014 33200±200

With increasing pressure in system, the reaction rate constant R3 increases, whereas for the reverse pressure it decreases, which is generally not typical for such reactions (Fig. 4).

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T=600 K

2.E+12

T=600 K

3.E+12

T=800 K

T=800 K

2.E+11

T=1000 K

T=1000 K

2.E+10

T=1200 K

2.E+09

T=1400 K T=1600 K

2.E+08 2.E+07 2.E+06

3.E+10

k, cc/mol∙s

k, s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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T=1200 K T=1400 K

3.E+08

T=1600 K

3.E+06 3.E+04

2.E+05 2.E+04

3.E+02

0

500 P, atm

1000

0

500

1000

P, atm

a b Fig. 4. Dependence of rate constants R3 (a) and R3r (b) on pressure in the system produced by CO2 molecules at different temperatures. The ordinate axis is logarithmic It is interesting to note that the reaction rate constant R3r, according to the data obtained decreases with increasing pressure, and especially sharply in the region of low pressures, slowly emerging on a shallow plateau at high pressures. It can be assumed that such atypical behavior is associated with the solvation of the active OH radical stabilized by the environment of CO2 molecules.

3.3 Reaction R1 The reaction rate constants R1 were calculated in accordance with the principle of quasistationary Bodenstein concentrations, assuming that the R3r process can be neglected. Thus, the whole process can be formally described by the following scheme:

The rate constant k1 in this case can be expressed in terms of the components k2, k3, k-2 (the derivation of this expression is given in Supplementary Materials):

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k1 =

k 2 k3 k − 2 + k3

(4)

The calculated values of k1 are given in Table. 9. Using the values of k2, k3, k-2, obtained at the previous stage (see Tables 1, 5, 6), k1 was calculated (Table 9).

Table 9. Rate constants k (cc/mol·s), predicted for R1 reaction. T, K Pressure of CO2, atm. 0.3 1 3 10 30 600 4.29·109 4.55·109 4.95·109 5.42·109 5.98·109 800 6.79·1010 6.77·1010 6.80·1010 7.32·1010 9.17·1010 1000 2.85·1011 2.92·1011 3.06·1011 3.35·1011 3.78·1011 1200 7.44·1011 7.91·1011 8.40·1011 8.90·1011 9.68·1011 1400 1.60·1012 1.68·1012 1.78·1012 1.89·1012 2.02·1012 1600 3.47·1012 3.63·1012 3.84·1012 4.00·1012 4.20·1012

100 6.64·109 1.15·1011 4.38·1011 1.06·1012 2.19·1012 4.49·1012

300 7.44·109 1.34·1011 5.04·1011 1.19·1012 2.40·1012 4.89·1012

1000 8.23·109 1.57·1011 5.76·1011 1.34·1012 2.62·1012 5.16·1012

The lg k dependences of the reactions R3 and R3r on the 1000/T are shown in Fig. 5a. The dependence of the rate constant of the gross reaction k1 on pressure is shown in Fig. 5b. T=600 K 3.E+12

T=800 K

3.E+12

T=1000 K T=1200 K

k, cc/mol∙s

3.E+11

k, cc/mol·s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P=0.3 atm P=1.0 atm P=3.0 atm P=10 atm P=30 atm P=100 atm P=300 atm

3.E+10

3.E+09

3.E+11

T=1400 K T=1600 K

3.E+10

3.E+09 0.6

0.8

1

1.2

1000/T,

K-1

1.4

1.6

0

a

17

500

P, atm

b


1000


Fig. 5. Reaction R1: a - dependence of ln k1 on 1000/T at different pressures of CO2, b dependence of k1 on CO2 pressure at different temperatures. Rate constants plot vs. in logarithmic scale.

One can see from Fig. 5 that temperature dependence of the rate constants has a character close to Arrhenius. In Table. 10 shows the parameters of extended Arrhenius equation for reaction R1 for each of the pressures.

Table 10. Parameters of extended Arrhenius equation for reaction R1 in temperature range (6001600) K Pressure Plog, Parameters of Extended Arrhenius equation atm A, cc/mol·s n Ea, cal/mol 15 0.3 (2.51±0.19)·10 0.004±0.002 15860±140 1.0 (6.04±0.23)·1016 -0.594±0.012 15020±140 3.0 (8.04±0.22)·1016 -0.705±0.017 14420±150 17 10 (1.13±0.19)·10 -0.784±0.017 14120±120 30 (1.62±0.24)·1017 -0.834±0.019 14040±120 17 100 (1.71±0.25)·10 -0.886±0.015 13590±120 300 (1.79±0.24)·1017 -0.944±0.018 13060±120 17 1000 (1.86±0.26)·10 -0.992±0.020 12620±110

With increasing CO2 pressure in system, the rate constant k1 of the gross process increases, and this effect increases with decreasing temperature. In high-pressure region (P ≥ 100 atm), k1 practically ceases to grow with increasing pressure, and the dependence k1(P) reaches a shallow plateau. Thus, 100 atm is the most optimal CO2 pressure in the reactor from the point of view of its influence on the rate of the developed process. The results of comparison of obtained values k1 with data of previous studies are given in Table 11.

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Table 11. Comparison of k1 values obtained in this study with previous studies Rate constant, cc/mol·s Pressure, atm. 1.0 3.0 100.0 13 a 12 c Experiment 3.5·10 6.0·10 8.9·1012 e 9.0·1012 f Prediction 1.68·1012 b 8.4·1011 d 1.1·1012 d 4.49·1012 g 35

a) N2 diluent, pressure up to 50 atm., temperature Ref. b) Temperature 1000 K 32 c) Ar diluent, pressure 3.5 atm, temperature range: 1054-1249 K, Ref. d) Temperature 1200 K 37 e) He diluent, pressure range: 1.0-1000 atm., temperature 1200 K, Ref. 37 f) He diluent, pressure range: 1.0-1000 atm., temperature 1200-1600 K, Ref. g) Temperature 1600 K

This comparison indicates lower values of k1 compared to previous studies. This is partly due to the nature of the collider (CO2), which is different from previous studies, in part because the present study is specifically focused on the problem of pressure effect on kinetics of the process, while all previous studies proposed a single Arrhenius equation operating over a wide range of pressures, the parameters of which were not put in dependence on P.

4. CONCLUSIONS We reported free energy profiles and rate constants predicted by the method of boxed molecular dynamics in hybrid quantum-classical theory level (QM/MM). Both forward steps R2 and R3, reverse processes R2r and R3r, as well as the total transformation of R1, were investigated under different temperatures and pressures. The results obtained make it possible to draw the following generalizations: 1. The temperature dependences of rate constants for the forward reaction R2, R3, reverse processes R2r and R3r, as well as the gross reaction k1, are close to Arrhenius. The

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calculated numerical parameters of extended Arrhenius equation are presented in Tables 3, 4, 7, 8, 10. 2. With increasing CO2 pressure in the system, rate constant for R1 reaction rises in the pressure range from 0.3 to 100 atm, and almost does not depend on pressure at higher values of P. 3. An analogous growth of the rate constants with increasing total pressure is observed for the elementary processes R2, R2r and R3. However, for the R3r process, there is an opposite trend: decrease in the rate constant with increasing P, also with access to the plateau in the region of high pressures. Presumably, this effect is due to solvation effects involving OH radicals. 4. Comparison of values of the rate constants with previous experimental data indicates the need to take into account the pressure in system when calculating the parameters of extended Arrhenius equation. The effect of CO2 on the growth of reaction rate constants R1-R3 allows us to assume that the buffer gases based on it are potentially effective colliders for combustion reaction.

Supporting Information. Calculated pressures, activation free energies, and rate constants for each number of CO2 molecules and temperature. Profiles of potential energies, and free energies of reactive systems vs. reaction coordinate. Derivation of Eq. 6. Samples of CHARMM input files.

Acknowledgements

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The authors are grateful to Dr. Glowacki for his assistance with AXD program module. This work was supported in part by the Department of Energy (grant number: DE-FE0025260). The authors also acknowledge the National Energy Research Scientific Computing Center (NERSC), and the University of Central Florida Advanced Research Computing Center (https://arcc.ist.ucf.edu)

for

providing

computational

resources

and

support.

A.E.M.

acknowledges support by the Act 211 Government of the Russian Federation (contract no. 02.A03.21.0011) and by the “improving of the competitiveness” program of the National Research Nuclear University MEPhI. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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