During our discussion this week I mentioned DLVO theory, named after the work of Derjaguin and Landau, Verwey and Overbeek. The theory, (well chemist call it a theory but physicists would probably call it a model) describes the potential of two colloidal particles in solution as a function of their separation distance. The total potential is expressed as the sum of the attractive and repulsive potentials, where the attractive term is solely due to van der Waals forces and the repulsive term due to the interaction of the particle's diffuse double layers.
The derivation of both the attractive and repulsive terms involve a number of approximations, without which the final result would be truly horrendous and unusable. However, in spite of the approximations, it works surprisingly well both as a qualitative guide and at making quantitative predictions. Due to it's successes it's very popular with colloidal chemists and nano-tech people; so popular in fact it even has it's own facebook page!
If you would like more information send me an email and I'll send you some lecture notes, the information I've found on the web is rather scattered and not very helpful.
These approximations of which you speak... do they go beyond the mean-field?
ReplyDeleteYeah, for example the solution to the Poisson-Boltzmann equation is found using the Debye-Huckel approximation and on the van der Waals side of things, the particles are assumed to be homogeneous in size and that the separation distance is much less than the particle radius.
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