Statistics of Polymer Solutions from Scaling Concepts for Geometry and Relativistic Self-Diffusion in Liquids

Abstract

Basic results on conformational statistics of polymer solutions are derived from recent scaling concepts for geometry and a relativistic picture for Brownian self-diffusion in liquid media. Any chain conformation is interpreted as a geometrical state affected by its end-to-end dimension, which here denotes the mean deviation between geodesic paths diffusing in the relativistic liquid phase. Statistical polymer length distributions solve an ondulatory equation in non-Euclidean manifolds for coil extension and shape. When length scale is vanishing, the size scaling is found again in terms of parallelism angle rotations. The characteristic chain ratio identifies instead an average metric coefficient, originating topologically from rotational degrees of freedom internal to single molecules.

Keywords:

• Polymer Solutions
• Conformational Statistics
• Geometrical Scaling Laws