STATISTICAL-MECHANICS OF A MULTIPOLAR GAS - A LATTICE FIELD-THEORY APPROACH

A recently proposed lattice field theory approach to the statistical m echanics of a classical Coulomb gas (J. Chem. Phys. 1992, 97, 5653) is generalized to treat particles with arbitrary electric multipole mome nts. Explicit development of the mean-field approximation is given for the case of mobile dipoles and monopoles (ions) surrounding an arbitr ary collection of fixed charges embedded in macroions. In particular, a modified Poisson-Boltzmann (PB) equation is derived in which the mob ile dipoles provide an effective spatially dependent dielectric consta nt. This equation implies a self-consistent iteration procedure by whi ch the monopole and dipole densities are simultaneously determined in terms of single scalar (PB) field. Moreover, this equation can be deri ved from a minimum principle; an annealing strategy for computing the PB field is thereby suggested. In addition, explicit mean-field expres sions for thermodynamic free energies are obtained as simple functiona ls of the PB field. Connection to the well-known Langevin dipole model is made. A numerical application to a system consisting of two parall el plates is presented in order to illustrate the utility of the formu lation.