Formation of hydrodynamically coupled networks of chain polymer molecules in solution. Criteria for the transition from dilute to semidilute behaviour

Abstract

Two improved simple models are proposed for estimating c^*, the critical concentration for the transition between dilute and semidilute behaviour in polymer solutions. One model predicts the onset of long-range coupling between hydrodynamically interacting coils: c^* corresponds to the formation of infinitely large networks of successively overlapping randomly placed spherical molecules. An alternative model takes c^* as the maximum concentration for randomly assorted non-penetrating spherical molecules. The estimated critical concentrations are lower than those predicted by many former and rather arbitrary criteria, but agree well with the empirical observation that c^*≈ 1/[η].