Molecular dynamics simulation of a system of Lennard-Jones particles
This program implements a molecular dynamics simulation of particles in two dimensions interacting
via the Lennard-Jones potential. The output includes the velocity distribution, mean pressure, temperature, and the heat capacity.
The algorithm for simulating the evolution of the particles is summarized by the following:
- Compute the forces on all the particles due to the other particles. By Newton's second law the acceleration
of each particle is given by the total force on the particle divided
by its mass, which we set to unity.
- Use a numerical algorithm to update the positions and velocities of
all the particles at a time t + Δt later. The program uses the Verlet algorithm.
- Accumulate data for various averages.
- The particles are initially placed on a square lattice. The velocities are initially distributed randomly and uniformly such that the mean kinetic energy yields the desired initial temperature and the center of mass momentum in each direction is zero. Run the simulation for a while and observe the velocity distribution. Does it appear to be a Gaussian? Estimate
the width of the distribution and record the average temperature. Repeat for several different densities and initial kinetic energies per particle. Plot the temperature versus the width of the
velocity distribution. You should obtain a linear dependence.
- Determine the ratio PA/NkT for several different densities starting with L = 24. What should this ratio be for an ideal gas? How does the ratio change as the density is increased? For N = 64 the linear dimension cannot be chosen to be much less than L = 8 with Δt = 0.01. Why?
- Use the default parameters and run the simulation until the system is more or less in equilibrium. Then change the quench rate (velocity rescaling) λ to 0.999. The effect of the quench rate is to multiply each velocity component by λ after each time step. What happens to the temperature of the system when λ ≠ 1? Is there evidence of a phase transition between
a gas and a liquid? If you increase the number of particles (and increase the linear dimension of the system) and choose different values of the quench rate, you will be able to see a configuration where
two phases coexist. Can you tell the difference between a liquid and a gas?
- Estimate the magnitude of the
temperature fluctuations. Are they approximately proportional to the heat capacity? The latter can be calculated approximately from the numerical derivative of the temperature versus energy curve.
Updated 19 July 2015.