Relationship between chain length and the concentration dependence of polymer and oligomer self-diffusion in solution

A complex relationship between chain length and the concentration dependence of polymer self-diffusion, D-p(c)/D-p(0), is revealed from analysis of polystyrene (PS) and oligostyrene self-diffusion in solution. Pulsed-field-gradient NMR measurements of PS self-diffusion in styrene and toluene were compared with literature results for PS self-diffusion in benzene, tetrahydrafuran, toluene, and carbon tetrachloride. An empirical relationship was used to correlate D-p(c)/D-p(0) to the concentration dependence of solvent self-diffusion, D-s(c)/D-s(0): D-p(c)/D-p(0) = [D-s(c)/D-s(0)](beta) where beta quantifies the relationship between chain length and the concentration dependence of D-p. (This power law, with a chain-length-independent, may be justified from Vrentas-Duda free volume theory.) Accounting for differences in the free volume contribution of the solvent species, 0 values obtained in the five solvents can be normalized to a single solvent, styrene, revealing universality in the relationship between chain length and the concentration dependence of PS self-diffusion in solution. A strong dependence of beta on chain length was observed for oligomers, increasing from 1.0 for styrene (1-unit chain) to similar to2.3 for a 20-unit chain. For unentangled PS, is nearly chain-length-independent, ranging from 2.5 to 3.4 for chain lengths of similar to55 to similar to1000 units. For longer chains, there is a sharp rise in beta with increasing chain length, consistent with entanglement effects. The beta values for PS correspond with those from analysis of limited poly(methyl methacrylate) self-diffusion data, supporting the notion that polymers with similar glass transitions and critical chain lengths for entanglement should exhibit similar impact of chain length on the concentration dependence of D-p in solution.