Two-Step Coil-to-Globule Transition in Mixed Mono-/Polymeric Solvents

We observe a two-step coil-to-globule (C–G) transition of a solute chain with length N1 in a mixed solvent with polymeric solvents of chain length N and monomeric solvent. The lower transition point, labeled as a superscript L and a subscript tr, is induced by the polymeric solvent with (χNxp)trL−1/2∼(Np)3/4xp1/2N1−1/2 and (χNxp)trL−1/2∼(Np)xp2/3N1−2/3 (xp is the volume fraction of the polymeric solvent in the mixed solvent and p is the stiffness parameter) for the short-chain and long-chain limit, respectively, while the higher one with a superscript H is intrigued by the monomeric solvent, with the transition point given by χtrH – 1/2 ∼ N1–1/2p3/4, independent of xp and chain length N. A theoretical analysis exhibits that the lower transition point at various combinations of solvent composition and chain length can be unified by the proposed variable x ≡ (pN)3/2xp/N1, where x can be treated as the ratio between the solvent pervaded volume and the swollen-solute volume. Interestingly, the density profile and center density at the transition show universal behavior when scaled with x too.