ON THE APPLICATION OF GEOMETRIC PROBABILITY-THEORY TO POLYMER NETWORKS AND SUSPENSIONS .2.

The theory of stochastic processes and integral geometry is applied to polymer networks and suspensions. Averaged monomer density is calculated for adsorbed and depleted layers of single-chain polymers modelled as brownian paths near plane and spherical surfaces, and exact solutions are given for an adsorbed layer with a force field. Asymptotic expressions are deduced for the available space fraction for a small solute in such layers. A measure of the typical asymmetry of a single-chain polymer modelled as a brownian path is obtained by calculating the averaged integral of the mean curvature, surface area and volume of its convex hull. The averaged integral of the mean curvature and surface area also give the first two terms of an asymptotic expression for the depletion near a smooth, slightly curved surface and an upper bound on the averaged capacitance. These qualities are also calculated for model polymer aggregates, brownian rings and brownian paths with drift. From the latter, we deduce averages of powers of the end-to-end distance of a brownian path weighted by the integral of the mean curvature and surface area of its convex hull. The depletion due to a lamina with a smooth, slightly curved boundary in a solution of single-chain polymers is calculated, and the result is interpreted in terms of averaged geometrical properties of brownian paths.