Polymers below the theta point: Renormalization group considerations

Abstract

The average size of long chains below the theta point is discussed in terms of a continuum model in which the chain is viewed as a collapsed phase perturbed by repulsive pair interactions. The representation of the collapsed phase makes use of the path integral formulation of a colored noise process introduced in an earlier paper [J. Chem. Phys. 99, 9230 (1993)], while the pair interactions are approximated as delta function pseudopotentials of strength v0. By treating the excluded volume perturbatively, the model can be described (at first order in v0) by renormalization group (RG) methods using dimensional regularization, ε expansion and minimal subtraction of poles. The nature of the fixed points of the RG transformation suggests that the collapse transition may be first order.