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 τα from F s(q*, t) with the structural relaxation time τ G from G(t). We show that τα 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 ΠCED, 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.

Influence of Chain Stiffness on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

“…This scaling relationship has been subsequently observed in a wide range of polymeric and metallic glass-forming materials, such as polycarbonate, nanocellulose networks, thin polymer films, and Cu 64 Zr 36 metallic glass formers. − Here, we explore this scaling relationship for cross-linked networks with varying chain stiffness. The shear modulus G exhibits a linear relationship with the local stiffness k B T /⟨ u 2 ⟩ (Figure a), as observed in the fully flexible cross-linked networks with a wide range of cross-link densities and cohesive energy parameters. , Recently, Xu et al also observed this linear relationship in the linear polymer melts with variable pressure, chain stiffness, and chain length, where the slope and intercept were material- and pressure-dependent. The simulations on the Zr–Cu metallic glass, thin polymer films, and double-stranded DNA melts with varying bending stiffness all indicated that the k B T /⟨ u 2 ⟩ could be taken as an “effective force constant” characterizing the “stiffness” of the bonds in a molecule.…”

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

“…As the mass percentage becomes higher by modifying m from 5% to 50%, the G values and yield stress of the cross-linked thermosets are considerably reduced. Figure c shows the relationship between G and T at different mass percentages m and cross-link densities c , where G in its glassy state decreases significantly as the T increases. , In addition, G increases significantly with increasing c , and decreasing m for cross-linked thermosets, where these two variables have a competing effect. The softening of cross-linked thermosets with the introduction of additives is reminiscent of the plasticization phenomenon .…”

“…Douglas and Xu also reported a similar scaling relationship in simulations of linear polymer melts, indicating that this expression has some degree of universality over different materials. Xu et al utilized an approximate linear relation between G p and k B T /⟨ u 2 ⟩ in the GF polymer fluids having variable pressure, chain rigidity, chain length, and temperature. In the thermosets with additives, nearly all the data fall at the same linear relationship.…”

Solid-that-Flows Picture of Glass-Forming Liquids

“…A consequence of the above physical picture is that single-particle motion is predicted to be spatially heterogeneous on short time scales, but homogeneous on time scales longer than τ α . ,− That structural relaxation and thereby τ α is controlled by the slow particles is an old idea, ,− which has recently been confirmed in experiments, as well as in equilibrium , and aging simulations.…”

“…In the solid-that-flows picture it is obvious to assume that the flow-event activation energy likewise is proportional to the elastic constants, here those that characterize fast deformations, i.e., the high-frequency plateau shear and bulk moduli. This idea defines the elastic models that exist in several versions, , and which have been linked to models based on the decrease of free volume or increase of collective motion upon cooling. , Note that in some models elasticity accounts for only part of the activation energy. − …”