Polydisperse polymers with random trifunctional branching. II. Weight‐averaging of chosen molecular size‐dependent functions and a restatement of the approximate distribution function

Abstract

AbstractThe product gzbZa is weight‐averaged over the distribution of molecular species in a polydisperse polymer possessing randomly distributed trifunctional branch points. This permits comparison between branched and nonbranched polydisperse polymers of certain physical properties that depend upon the relative degree of polymerization, z, and upon the ratio of branched to nonbranched molecule mean‐square radii, g = Rbr2/Rl2. Values of a, b, and γ (a branching index) are chosen for specific physical reasons and the computed ratios, \documentclass{article}\pagestyle{empty}\begin{document}$ (1 - \gamma )^a \int_0^\infty {g_z ^b z^a } W_z dz/\int_0^\infty {z^{a + 1} e^{ - z} dz} $\end{document} are tabulated. The distribution function for the polydisperse polymer possessing randomly distributed trifunctional branch points is restated in terms of a modified Bessel function of the first kind. This form is of use since properties of the Bessel function are known and the tabulated values of this function are generally available.