Microscopic Theory of the Effect of Caging and Physical Bonding on Segmental Relaxation in Associating Copolymer Liquids

We construct a microscopic statistical mechanical theory for how strong short-range attractions between sticky groups regularly copolymerized in a chain backbone perturb the segmental dynamics of unentangled polymer liquids. Based on the segmental packing fraction or temperature, bare strength and range of attractive interactions, and fraction of stickers as input, PRISM integral equation theory is used to compute the equilibrium interchain pair correlation functions of associating copolymer liquids. This information is employed to construct a dynamic theory for the emergence of persistent cages and physical bonds and the associated high-frequency glassy elastic shear modulus and real space transient localization lengths. Longer time relaxation dynamics for the activated nonsticker hopping (alpha process) time scale is formulated based on the dynamic free energy concept in the strong association (cross-linked network-like) regime where physical bonds are stable on the relevant time scale. Predictions for how physical bonds can strongly modify nonsticker relaxation are made as a function of system parameters. A nearly linear increase of the glass transition temperature and supraexponential growth of the alpha relaxation time with sticker fraction is predicted. Comparison with limited experiments suggests the theoretical predictions for association-induced slowing down of structural relaxation, weak changes of the high-frequency shear modulus, and elevation of the vitrification temperature are consistent with observations.