Method for Calculating Average Molecular Weights and Molecular Weight Distributions of Polymeric Materials from Sedimentation Equilibrium Experiments

Abstract

A method is proposed for the determination of average molecular weights and molecular weight distributions of polymeric materials from sedimentation equilibrium experiments in theta solvents. The data required are the refractive index gradients at the center of the ultracentrifuge cell as a function of a parameter λ = (1—v̄ρ0) (r22—r12)ω2/2RT; here v̄ is the partial specific volume of the polymer solute in the given solvent, ρ0 is the density of the solvent, ω is the rotor speed, r1 and r2 are the radial distances from the rotor axis to the meniscus and the bottom of the cell, respectively, T is the absolute temperature, and R is the gas constant. The most important feature of the proposed method is that it allows calculation of the number-average molecular weight. The desired distribution of molecular weights of a given sample can be obtained by solving an integral equation of the Fredholm type.