Statistical mechanics of charged polymers in electrolyte solutions: a lattice field theory approach.

The lattice field theory approach to the statistical mechanics of a classical Coulomb gas [R.D. Coalson and A. Duncan, J. Chem. Phys. 97, 5653 (1992)] is generalized to include charged polymer chains. Saddle-point analysis is done on the functional integral representing the partition function of the full system. Mean-field level analysis requires extremization of a real-valued functional which possesses a single minimum, thus guaranteeing a unique solution. The full mean-field equations for such a coupled system are derived, as well as the leading (one-loop) fluctuation corrections. Two different numerical real-space lattice procedures are developed to implement the generalized theory; these are applied to the problem of a charged polymer confined to a spherical cavity in an electrolyte solution. The results provide insight into the physics of confined polyelectrolytes.