How to perform random walk simulation of diffusion

Hi all, i am a begginer in simulation. can any one help me in understanding how to perform random walk simulation of diffusion.I need help to understand how simulation is done in the following paper 1.Self-assembly of ink molecules in dip-pen nanolithography: A diffusion model J.Jang et al.,J.Chem. Phys.115,2721(2001). Thankyou in advance Saravanan

1. Hi,

I have not had an opportunity to read the paper you cited, but I do have some experience with Kinetic Monte Carlo diffusion models. Many random walk simulations of diffusion occur on a lattice; if the diffusion medium is not crystalline, usually you can impose a simple cubic lattice on it. Pick a “walker” (a diffusing particle) at random and move it to a neighbor site; calculate the energy of the new configuration (usually the sum of all the pair interactions within a certain interaction range). If the new energy is lower, keep the new configuration. If the new energy is not lower, keep the new configuration with a Boltzmann probability, exp(-deltaE/2kT), where deltaE is the change in energy, k is Boltzmann’s constant, and T is the temperature. If you choose not to keep the new configuration, move the walker back to its original site and go on to another randomly chosen particle.

The implicit assumption in this method is that the time scale of a diffusive event is much shorter than the overall time scale on which the system approaches equilibrium. This allows you to assume that you are moving particles at a local equilibrium.

With all simulations like this, your confidence in the results increases as you do more simulations with identical initial conditions and calculate mean results.

A more difficult question involves how to include time in such a simulation. You need to know the energy barriers for each diffusive hop in order to calculate the hopping frequencies. This is a more complicated point, and this answer is already long enough. I hope this is enough to get you started.