# Approach to model solvent in a lattice: e.g. H2O in NaCl

If a lattice contains a solvent, lets say $\ce{NaCl}$ and water of crystallisation, what is the condition for a solvent molecule to change it's location?

From my current point of view I assume that such a water molecule is bound to a lattice ion by ion-dipole forces. It vibrates at that location until, randomly, the particle energy exceeds the binding energy. Then it goes to a new location, in the direction that minimizes Gibbs free energy.

How is the water molecule energy distributed? Currently I use Maxwell-Boltzmann distribution. However, Maxwell-Boltzmann is for non-interacting particles and therefore not quite a good fit for molecules that interact with a ion. Further, my chemistry book suggest that ion-dipole bonds have a binding energy of >$50~\mathrm{kJ~mol^{-1}}$, which will in my calculations rarely allow a jump at all.

I ask this question because I'm working on a particle-drying simulation. I intend to use a Random Walk simulation to obtain diffusion coefficients under special circumstances: e.g. if the lattice salvation behaviour is somehow weird. The model must not be physically correct in all details. Even bigger "model" error will most likely be small in the simulation results.

This is a bit outside my realm of expertise - you'd want to look at molecular dynamics (MD) simulations for more details. Let me take your question in a few parts.

1) A water molecule in a lattice is likely bound by electrostatic (and hydrogen-bond) interactions. So your general assumption is a good one.

2) MD simulations usually have a "thermostat" depending on the type of ensemble used. Your thermal energy will be distributed into different degrees of freedom, such as rotations, translations, and vibrations. So I'd work out the amount of translational free energy from statistical mechanics, and then use the electrostatic interactions to determine the path for jumps. (Your main question here seems like the activation barrier, since each lattice site should have the same energy, right?)

3) If the moves are rare, you might want to look into "rare event sampling" methods, which preserve the correct statistics, but allow you to more efficiently run your model.

Many of these techniques are already implemented in simulation codes. You might want to look at something like LAMMPS which can handle different levels of particles (e.g., atoms, molecules, crystal domains, etc.)

Hope that helps - I can only talk in broad generalities here.

• Thank you for your answer. I will consider LAMMPS as a next step when I made some experience with by own approach. – dani Sep 24 '14 at 14:45