Unperturbed Dimension and Translational Friction Constant of Branched Polymers

A theory of the conformational properties of random-flight branched molecules is developed for estimating the branching effect on the translational friction constant Ξb as well as on the mean-square statistical radius 〈S2〉b½. Calculations are made for three types of branching—star, normal (or linear), and random types, and for two types of distribution of the branch units—uniform and random types. It is found that the contraction of molecular dimensions produced by branching occurs to the highest degree in the star types of branching and to the lowest degree in the normal type of branching, and that the heterogeneity in the distance between the nearest pair of branch units generally diminishes the degree of the molecular contraction. The applicability of the Flory-type equation, Ξb=η0Pb〈S2〉b½, to the branched molecules is discussed with the intention of searching the experimental method for determination of the number of branch units involved in the various types of branched molecules. Here η0 is the viscosity of solvent and Pb is the proportional factor corresponding to Flory's universal constant in the linear polymers.