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Päällikkö

Homework Helper

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## Main Question or Discussion Point

My question is not so much about the Lennard-Jones potential, although I mentioned it in the title, but of the "force field" thinking in general.

So a lot of people are (were) interested in the phase transition temperature of the Ising model. How realistic is the model in the sense that it assumes an interaction energy of J, which is independent of temperature, between neighboring sites? If instead of magnets, we think of solutions, the very same Ising model is called the regular solution model (in the Bragg-Williams mean field approximation). Now is it true that, say, water and oil mix the way described by the model (i.e. no explicit temperature dependence)?

These are of course simple toy models, but real scientists employ Lennard-Jones potentials in their molecular dynamics codes, but never seem to give too much thought, or at least discussion in the publications, to this matter. The van der Waals forces (which the attractive part of the Lennard-Jones potential represents) for neutral particles is due to London dispersion forces, which if I recall is supposed to vary as 1/T. This is to my knowledge never accounted for in actual molecular dynamics force fields. Why?

When can I be sure that the interaction energies between two (or more) particles do not explicitly depend on temperature? When does this approximation break down? Naturally, I'd also be quite interested in how other state variables, such as pressure, might affect the microscopic interactions, and when I can ignore their effects.

So a lot of people are (were) interested in the phase transition temperature of the Ising model. How realistic is the model in the sense that it assumes an interaction energy of J, which is independent of temperature, between neighboring sites? If instead of magnets, we think of solutions, the very same Ising model is called the regular solution model (in the Bragg-Williams mean field approximation). Now is it true that, say, water and oil mix the way described by the model (i.e. no explicit temperature dependence)?

These are of course simple toy models, but real scientists employ Lennard-Jones potentials in their molecular dynamics codes, but never seem to give too much thought, or at least discussion in the publications, to this matter. The van der Waals forces (which the attractive part of the Lennard-Jones potential represents) for neutral particles is due to London dispersion forces, which if I recall is supposed to vary as 1/T. This is to my knowledge never accounted for in actual molecular dynamics force fields. Why?

When can I be sure that the interaction energies between two (or more) particles do not explicitly depend on temperature? When does this approximation break down? Naturally, I'd also be quite interested in how other state variables, such as pressure, might affect the microscopic interactions, and when I can ignore their effects.