Self-consistent variational theory for globules

Max-Planck-Institute for Polymer Research - Ackermannweg 10, 55128 Mainz, Germany

Received: 17 March 2005
Accepted: 4 May 2005

Abstract

A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoinding chain, is restricted to a good-solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor-solvent regime where the balance between the two-body attractive and the three-body repulsive interactions leads to contraction of the chain to form a globule. By employing the Ginzburg criterion, we recover the correct scaling for the θ-temperature. The introduction of the three-body interaction term in the variational scheme recovers the correct scaling for the two important length scales in the globule —its overall size R, and the thermal blob size . Since these two length scales follow very different statistics —Gaussian on length scales , and space filling on length scale R— our approach extends the validity of the uniform expansion method to non-uniform contraction rendering it applicable to polymeric systems with attractive interactions. We present one such application by studying the Rayleigh instability of polyelectrolyte globules in poor solvents. At a critical fraction of charged monomers, f_c, along the chain backbone, we observe a clear indication of a first-order transition from a globular state at small f to a stretched state at large f; in the intermediate regime the bistable equilibrium between these two states shows the existence of a pearl-necklace structure.