Polymer collapse in dilute solution: Equilibrium and dynamical aspects

Publisher Website
Google Scholar
Abstract
The pairwise, long‐range attractions experienced by a polymer chain in poor solvent, are resisted by the screened (two‐body) and by the three‐body interactions. While the former are due to the nonzero effective chain thickness and are especially important for relatively short chains, the latter arise from interdependence among the two‐body attractions, and prevail for very long chains. We adopt the Gaussian approximation for the interatomic long‐range distances with a lower cutoff for the chain contacts, and a Fourier description of the chain configurational modes. If the average chain diameter is small enough compared with Kuhn’s segment length, a polymer with a sufficiently large molecular mass undergoes a coil→globule first‐order transition upon cooling below the Θ temperature; otherwise, the transition is of the second order. For the case of atactic polystyrene, we predict a first‐order transition. Within the collapsed globule, polymer portions are essentially unperturbed if their root‐mean‐square length does not exceed the globule’s diameter, otherwise their end‐to‐end distance becomes independent of the contour length, thus leading to a complete randomness among the long‐range interatomic contacts; however, the end segments of the chain are predicted to get closer to each other than the average intersegment distance. The resulting picture indicates that the collective Fourier‐configuration modes undergo a much stronger shrinkage than the localized ones, upon collapse, which implies in turn that the relaxation times of the collective modes are drastically shortened in proportion with the average. These conclusions appear to be in essential agreement with the dynamical, light‐scattering results obtained by Nishio, Swislow, Sun, and Tanaka on very dilute cyclohexane solutions of high‐molecular weight polystyrene.