Mode-coupling theory of the dynamics of polymer liquids: Qualitative predictions for flexible chain and ring melts

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Abstract

The qualitative predictions of the mode-mode-coupling (MMC) theory developed in the preceding paper are determined for various transport properties and time correlation functions. The degree of polymerization N dependence of the self-diffusion constant D of long flexible chain and rigid rod melts are found to be in agreement with the reptation/tube model scaling predictions. Ideal ring polymer liquids also follow D ∝ N-2 law, but for collapsed non-Gaussian rings a stronger power law dependence is obtained. The viscoelastic properties of chain melts are derived from a linear generalized Langevin equation (GLE), which at long times consists of the usual Rouse terms plus a chain length and internal normal mode-dependent frictional contribution. The latter novel term gives rise to of order N slow internal modes, and hence a plateau modulus, and a shear viscosity and recoverable compliance which scale as N3 and N0;, respectively. All the predictions are derived from the MMC dynamic memory function by neglecting end effects, and without a priori invoking the existence of static entanglements, a confining tube, nor curvilinear diffusion. The molecular weight dependent renormalizations arise from time-dependent intermolecular force fluctuations on the radius of gyration and longer length scales. An alternative mathematical approximation for the viscosity memory function leads to an asymptotic scaling law of N3.5 for chain melts. This nonreptation prediction follows from the physical assumption that the fluctuating repulsive forces exerted by the surrounding matrix on the internal modes of a probe polymer can fully relax only after a time proportional to the probe translational diffusion time. The qualitative form of the mode-coupling GLE in the terminal relaxation regime can be approximately interpreted in terms of curvilinear reptation à la the Doi-Edwards formulation. However, this physical interpretation is not uniquely established, and the alternative possibility of isotropic, but highly cooperative, motion is not precluded. The viscoelastic properties of flexible ring melts are found to be qualitatively similar to their chain polymer counterparts. A general microscopic approach for including the effects of matrix polymer mobility is formulated in terms of the collective dynamic structure factor of the melt. The qualitative implications for self-diffusion and crossover phenomena are studied, and a self-consistent theory for the shear viscosity is derived.

Original languageEnglish (US)
Pages (from-to)5822-5839
Number of pages18
JournalThe Journal of Chemical Physics
Volume91
Issue number9
DOIs
StatePublished - Jan 1 1989
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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