Hydrogen Oxidation by MD Simulations ME346 TERM PROJECT 2005. 12. 15 Hark Lee Department of Mechanical Engineering Stanford University

Hydrogen Oxidation

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.

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

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

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

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

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)

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

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

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

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

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

Chemical Reaction - 3

Chemical Reaction - 4

Troubleshooting Loaded Gun Effect

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

Results – Temperature and Energy

Results – Reaction Rate

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!

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.