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

XL Xu and JF Douglas and WS Xu, MACROMOLECULES, 56, 4929-4951 (2023).

DOI: 10.1021/acs.macromol.3c00184

The emergence of the solid state in glass-forming materialsuponcooling is accompanied by changes in both thermodynamic and viscoelasticproperties and by a precipitous drop in fluidity. Here, we investigatechanges in basic elastic properties upon cooling in a family of simulatedpolymer 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 & nu;, and the "Debye-Wallerparameter" & LeftAngleBracket;u (2)& RightAngleBracket;,where G (p), f (s,q*), and & LeftAngleBracket;u (2)& RightAngleBracket;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 elevatedtemperatures (T) resembles the power-law decay predictedby the Rouse model, but stress relaxation transitions to a stretchedexponential form in the low-T liquid regime dominatedby 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 & alpha;-relaxation time & tau;(& alpha;) from F (s)(q*, t) with the structural relaxation time & tau; (G) from G(t). We show that & tau;(& alpha;) can be expressedquantitatively both in terms of measures of the material "stiffness", G (p), and & LeftAngleBracket;u (2)& RightAngleBracket;, and the extent L of cooperative particleexchange motion in the form of strings, establishing a direct relationbetween 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 molecularscale stiffness parameter, k (B) T/& LeftAngleBracket;u (2)& RightAngleBracket;, with k (B) being Boltzmann's constant, and we discuss thethermodynamic scaling of these properties. We also find that G (p) is related to the cohesive energy density & pi;(CED), pointing to the critical importance of attractiveinteractions in the elasticity and dynamics of glass-forming liquids.Finally, we discuss fluctuations in the local stiffness parameteras a quantitative measure of elastic heterogeneity and their significancefor understanding both the linear and nonlinear elastic propertiesof glassy materials.

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