1. Hydrogen Oxidation by MD Simulations
ME346 TERM PROJECT
Hark Lee
Department of Mechanical Engineering
Stanford University

2. Hydrogen Oxidation

3. Introduction
This primary branching reaction involves two different atoms and four species.
Considering the typical thermodynamic approach and the scale (spatial, time) of the MD simulation, this is indeed a macroscopic phenomenon.
To investigate the potential of MD simulation as a link between macroscopic and microscopic regimes is my primary objective.

4. Reaction Chamber
The reaction chamber is initially divided to two different sub-chambers separating hydrogen atoms from oxygen molecules.
The number of particles are fixed.
( H atom : 400 / O2 molecule : 400 )
The reaction chamber is variable in its volume.
By changing the intermolecular spacing we can control the number density and pressure of gases in the system.
(Constant Temperature)
As reference condition, I set spacing to 80(angstrom), Pressure to 7bar and Temperature to 360K.
Initial spacing between particles : 80
Initial pressure of each species : 7 bar
Initial temperature of the system : 360K
Number of total atoms : 1200

5. Reaction Chamber
After a certain time of preliminary run, the imaginary plane between sub-chambers disappears, and gases start to mix.
If a hydrogen atom and an oxygen molecule collide with sufficient kinetic energy and geometric configuration they undergo chemical reaction.
By varying the pressure, we can observe the dependency of the reaction rate on the system pressure
Initial spacing between particles : 80
Initial pressure of each species : 7 bar
Initial temperature of the system : 378K
Number of total atoms : 1200

6. Four Main Concerns LJ Potential Boundary Condition Chemical Reaction
Unification of Representation Method for Position / Velocity / Acceleration Matrices and Equation of Motion for Atoms and Molecules
LJ Potential
Boundary Condition
Chemical Reaction

7. Matrices
All position, velocity and acceleration matrices are set to 800 by 3 matrices
1st and 2nd column usually indicates x-component and y component of center of mass. 3rd column is related to the angular property.
For Atoms, all 3rd column components set to zero since the rotational motion of an atom is almost negligible.
395
396
397
398
399
400
401
402
403
404
123.45
336.12
583.10
004.10
124.85
764.46
347.21
411.23
596.12
431.10
933.45
126.12
323.10
514.10
914.85
234.46
577.21
111.23
006.12
801.10
0.0000
1.2351
0.3155
2.1541
5.1231
Atom
Molecule
MR : Position Matrix

8. Describing Particle Positions
Since there are two different types of particles (atom / molecule) and four different species, establishing unified description of position / velocity / acceleration matrices is essential.
For example : Specifying molecule positions (OH, O2)

9. Particle Composition List
Need to specify species and composing atoms of a particle.
Forward composition list FPCL and reverse list RPCL are devised
Assigned species indices to all particles
( H : 1 / O : 2 / OH : 3 / O2 : 4)
1st and 2nd columns of MCL indicate the index numbers of composition atoms and third column contains species index
For an atom, second column set to zero
110
111
112
113
114
115
116
117
118
119 98
741
594
899 11
1032
302
912
692
511
126
900
913
512 1 3 2 4
FPCL : Composition List

10. LJ Potential Between Different Atoms
Since there are two different atoms present in this simulation, we need to consider total three interactions when calculating potentials
Those are H-H, O-O and O-H interactions and all of them have different equilibrium energy and equilibrium separation
Interaction
ε0(eV)
s0(A)
H-H
7.410e-4
2.810
O-H
1.983e-3
2.880
O-O
5.310e-3
2.950 o
M.P.Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford Science Publications, (1987,1989), p22

11. Specular Boundary Condition
If a particle hit the boundary wall of the main chamber or separating plane, it would be reflected like a ray of light reflected by a mirror.
Criteria
1. If a particle is outside of the main chamber
2. If the velocity is still outward
t=t1
t=t1+1

12. Typical LJ-potential Curve
Chemical Reaction - 1
Setting Adequate Criteria
Proximity Criterion
(Only when H and O2 are sufficiently close)
Kinetic Energy Criterion
(Only when the kinetic energy of reactants is greater than the O2 dissociation energy)
Energy Criterion
If two particles get close to each other, their kinetic energy is likely to be transformed into potential energy.
So setting up a proper criteria is not so simple.
My decision
Bond lengths = equilibrium lengths(s0)
Capture Radius = equilibrium lengths
Kinetic energy = net energy change
Typical LJ-potential Curve

13. Chemical Reaction - 2 Embed Two Criteria
First find any hydrogen atom inside the OH potential equilibrium length from the point of an O2 molecule (Proximity Criterion)
Calculate the relative velocity of H atom with respect to the COM of O2 molecule and project of the relative velocity on the line which connects H atom and O2 COM
Compute the kinetic energy with the projected velocity vector to figure out whether the H atom has enough kinetic energy to break O-O bond
If the kinetic energy is sufficient initiate the chemical reaction

14. Chemical Reaction - 3

15. Chemical Reaction - 4

16. Troubleshooting
Loaded Gun Effect

17. Computation Process Potential F to MA MR to R
Calculate Atomic Force from R(t) Using LJ-potential
F to MA
Convert Calculated Force F(t) to Acceleration Matrix MA(t)
Velocity Verlet
Calculate Velocity MV(t) and Position MR(t+1) Matrices
MR to R
Convert COM Positions MR(t+1) to Atom Positions R(t+1)
Chemical
Reaction
If there is a pair of particles meet reaction criteria, proceed chemical reaction
Specular B.C
Neighbor List
Check if all particles stay inside boundary
Check if reconstruction of Verlet list is required

18. Results – Temperature and Energy

19. Results – Reaction Rate

20. Physical Interpretation
Ideal Gas Law
P=nkBT where n=N/V
PV=Const. in this case (N,T=Const.)
Reactive Collision Rate [ per unit volume time]
ZAB=nA*nB*f(T)
V*ZAB=V*nA*nB*f(T)
=PH*PO2*V*g(T)
-> Proportional to Pressure!

21. Conclusions
MD simulation can be applied to a chemically reacting system.
To make this feasible, simplified models for the chemical reaction and kinetic behavior of particles are inevitable.
To account for the details of chemical reaction, more refined models and expensive hardware are needed.