A variational field theory for solutions of charged, rigid particles

A general field theoretic formalism is developed for dealing with solutions of particles with rigid charge distributions. Combined with the mean-field approximation, the resulting theory extends the Poisson–Boltzmann equation to incorporate the presence of structured ions (e.g., uniformly charged rods or disks). When combined with a first-order variational approximation, the resulting theory, in the low density limit, is a generalization of the Debye–Hückel theory to extended charge distributions and reduces to the standard expressions when applied to point charges. A first-order variational theory is applied to solutions of uniformly charged disks and to solutions of uniformly charged disks with a neutralizing ring charge to examine the influence of electrostatic interactions on the isotropic-nematic transition.