A new approach to polymer solution theory

Abstract

Shows that in the usual treatment of the O(n) symmetric Ginzburg-Landau-Wilson field theory Goldstone modes induce a negative susceptibility for n<1 as the co-existence curve is approached. This situation affects the whole of the semi-dilute regime of polymer solutions. To examine the role of Goldstone modes within this formalism, the authors consider the generalised Heisenberg model of H.E. Stanley (1969) with self-avoiding constraint on a d=2 square lattice in the limit n to 0. By taking highly anisotropic couplings, the authors take the continuum limit in one direction for the transfer matrix and obtain a quantum mechanical Hamiltonian on a d=1 lattice. This is used to obtain perturbation series in the coupling between lattice sites for the inverse correlation length and susceptibility. The authors obtain the equation of state to second order, and show the existence of spontaneous magnetisation even though it is absent in d=1. The susceptibility is well behaved and positive. The calculations can be readily extended to systems of higher dimensionality.