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)]^β where β quantifies the relationship between chain length and the concentration dependence of D_p. (This power law, with a chain-length-independent β, may be justified from Vrentas-Duda free volume theory.) Accounting for differences in the free volume contribution of the solvent species, β 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 β on chain length was observed for oligomers, increasing from 1.0 for styrene (1-unit chain) to ∼2.3 for a 20-unit chain. For unentangled PS, β is nearly chain-length-independent, ranging from 2.5 to 3.4 for chain lengths of ∼55 to ∼1000 units. For longer chains, there is a sharp rise in β with increasing chain length, consistent with entanglement effects. The β 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.