Mean field theory of Potts model:

Relationship between order parameters and conformational energy

Abstract

One of the most fundamental questions in chemistry is how does structurally modifying a molecule with substituents affect thermodynamic properties of a condensed molecular system. Itoh et al. reported a reduced viscosity in a fluorinated derivative of the 1-butyl-3-methylimidazolium (bmim) salts. At first, we suspected that the reduced viscosity was caused by modification of the molecular motion induced by the fluorine atoms, because the rotational potential calculated for the fluorinated bmim cation was different from that for the bmim cation. Unfortunately, the difference of the rotational potential could not be ascribed to the reduced viscosity. This implies that the effect of the substituents on the thermodynamic properties should be studied with the same approach as many body problems. To answer the question, we defined the molecular conformations by Potts spin variables as a general coordinate. The mean field Hamiltonian was formulated as a quadratic form of the Potts spins and applied to 1-methyl-3-propylimidazolium chloride (pmimCl) derivatives. Now we report the temperature dependence of the order parameters and the relationship with the conformational energies in the pmimCl derivatives.