Relationship between Chain Length and the Concentration Dependence of Polymer and Oligomer Self-Diffusion in Solution

Citations Over TimeTop 13% of 2002 papers

Abstract

A complex relationship between chain length and the concentration dependence of polymer self-diffusion, Dp(c)/Dp(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 Dp(c)/Dp(0) to the concentration dependence of solvent self-diffusion, Ds(c)/Ds(0): Dp(c)/Dp(0) = [Ds(c)/Ds(0)]β where β quantifies the relationship between chain length and the concentration dependence of Dp. (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 Dp in solution.

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