Coil-to-Globule Transition in Polymeric Solvents

Abstract

We study the coil-to-globule (C–G) transition of a test polymer of chain length N1 in a polymeric solvent of chain length N using the self-consistent field theory. For short-chain solvents, the C–G transition point is given by (χN)_(tr)–1/2 ∼ (pN)^(3/4)N₁^(–1/2), consistent with an extended Lifshitz theory, where p = b²/v_m^(2/3) is the stiffness parameter. However, for long-chain solvents, the C–G transition becomes strongly first order, with the transition point given by (χN)_(tr)–1/2 ∼ pNN₁^(–2/3). A scaling analysis suggests that the transition point for any chain length combination is a universal function of the scaling variable x ≡ (pN)^(3/2)/N₁, which has the clear interpretation as the ratio between the pervaded volume of the solvent chain and the physical volume of the test chain and that a crossover between the two transition scenarios occurs at x ∼ 1. Furthermore, when properly nondimensionalized, the density profile in the globule state and the center density and the interfacial thickness of the globule at the transition also exhibit universal behavior. For both the short-chain and long-chain solvent cases, the C–G transition corresponds to the point when the interfacial thickness of the globule becomes comparable to the core size.