Parallel Emergence of Rigidity and Collective Motion in a Family of Simulated Glass-Forming Polymer Fluids

Abstract

The emergence of the solid state in glass-forming materials upon cooling is accompanied by changes in both thermodynamic and viscoelastic properties and by a precipitous drop in fluidity. Here, we investigate changes in basic elastic properties upon cooling in a family of simulated polymer fluids, as characterized by a number of stiffness measures, such as the “glassy plateau shear modulus” G p, the “non-ergodicity parameter” f s, q *, the bulk modulus B, the Poisson ratio ν, and the “Debye–Waller parameter” ⟨ u 2 ⟩, where G p, f s, q *, and ⟨ u 2 ⟩ correspond to the shear stress relaxation function G ( t ), the self-intermediate scattering function F s ( q *, t ), and the mean square displacement on a ps timescale, respectively. The time dependence of G ( t ) at elevated temperatures ( T ) resembles the power-law decay predicted by the Rouse model, but stress relaxation transitions to a stretched exponential form in the low- T liquid regime dominated by glassy segmental dynamics. In this “glassy dynamics” regime, the relaxation times from G ( t ) and F s ( q *, t ) closely track each other for all polymer models investigated, thereby justifying the identification of the α-relaxation time τ α from F s ( q *, t ) with the structural relaxation time τ G from G ( t ). We show that τ α can be expressed quantitatively both in terms of measures of the material “stiffness”, G p, and ⟨ u 2 ⟩, and the extent L of cooperative particle exchange motion in the form of strings, establishing a direct relation between the growth of emergent elasticity and collective motion. Moreover, the macroscopic stiffness parameters, G p, B, and f s, q *, can all be expressed quantitatively in terms of the molecular scale stiffness parameter, k B T /⟨ u 2 ⟩, with k B being Boltzmann’s constant, and we discuss the thermodynamic scaling of these properties. We also find that G p is related to the cohesive energy density Π CED, pointing to the critical importance of attractive interactions in the elasticity and dynamics of glass-forming liquids. Finally, we discuss fluctuations in the local stiffness parameter as a quantitative measure of elastic heterogeneity and their significance for understanding both the linear and nonlinear elastic properties of glassy materials.

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