Light scattering power of randomly cut random coils with application to the determination of depolymerization rates

Abstract

The scattering of light by a dilute monodisperse population of random-coil molecules is approximately described by the well-known function P(θ)=(2/u2)(e−u+u−1), where u=R2gq2, Rg is the radius of gyration of the random coils, and q=(4πn/λ)sin(θ/2) is the magnitude of the scattering vector. We show that if the molecules in this population undergo random scission, then P(θ) is still given by the above formula where, however, u is now equal to R2goq2+r, where r is the average number of scissions per molecule in the originally monodisperse population and Rgo is the original radius of gyration. It is suggested that this could be useful for determining depolymerization rate constants, and for investigating whether various forms of scission are actually random. Results from initial experiments which apply the theory to the acid hydrolysis of hyaluronic acid are presented. The rate constants found are in reasonable agreement with values in the literature.