Renormalized field theory of polymer solutions. I. Scaling laws

Abstract

The large scale spatial correlations in a dilute solution of long chain molecules are dominated by excluded volume effects. We extend the field‐theoretic methods of Des Cloizeaux and De Gennes to describe these correlations. We derive general scaling laws which the experimentally measured correlation functions must obey. The dependence on (scattering) wave number, concentration, and chain length is thereby reduced to a function of two variables. This function may moreover be calculated via well‐studied approximations, leaving only an excluded volume parameter and a microscopic length parameter. Using the scaling law, we derive several experimentally observed power laws for parameters such as the radius of gyration, including limiting behavior for small overlap (independent chains), large overlap, and large wave vector.