Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

Abstract

The study of glass formation is largely framed by semiempirical models that emphasize the importance of progressively growing cooperative motion accompanying the drop in fluid configurational entropy, emergent elasticity, or the vanishing of accessible free volume available for molecular motion in cooled liquids. We investigate the extent to which these descriptions are related through computations on a model coarse-grained polymer melt, with and without nanoparticle additives, and for supported polymer films with smooth or rough surfaces, allowing for substantial variation of the glass transition temperature and the fragility of glass formation. We find quantitative relations between emergent elasticity, the average local volume accessible for particle motion, and the growth of collective motion in cooled liquids. Surprisingly, we find that each of these models of glass formation can equally well describe the relaxation data for all of the systems that we simulate. In this way, we uncover some unity in our understanding of glass-forming materials from perspectives formerly considered as distinct.glass formation | elasticity | cooperativity | free volume | strings T here are numerous theoretical approaches aiming to describe the universal liquid dynamics approaching the glass transition. One class of theories emphasizes the importance of the congested nature of the local atomic environment in cooled liquids, focusing on the amount of "free volume" available to facilitate molecular rearrangement (1). This free-volume approach is also linked to the more modern jamming model of glass formation (2). Older treatments of glass formation based on this perspective can be traced back to Batchinski (3), Doolittle (4), and Hildebrand (5) for small liquids, and to Williams and coworkers (6) and Duda and Vrentas (7, 8) for polymer materials. There is also more recent work based on the free-volume perspective, for example, positron lifetime measurements (9) that probe the cavity structure of glass-forming (GF) liquids. DebyeWaller measurements (9, 10), based on neutron, X-ray, or other scattering measurements, emphasize another type of free volume that is associated with the volume explored by particles as they rattle about their mean positions in a condensed material. This type of free-volume modeling has also been refined to take into account the shape of these "rattle" volumes (11,12).Another family of glass-formation models emphasizes the emergent elasticity in glassy materials (13). These approaches build on the idea that the solid-like nature of glasses is one of their most conspicuous, and perhaps defining, properties. Dyre (13) and Nemilov (14) have argued that the activation energy for transport should grow in proportion to the shear modulus. The models of Hall and Wolynes (15) and Leporini and coworkers (10, 16) can also be included in this class if the Debye-Waller factor is taken as a measure of local material stiffness.Approaches emphasizing the underlying complex potential energy surface have also found consider...

A unifying framework to quantify the effects of substrate interactions, stiffness, and roughness on the dynamics of thin supported polymer films

“…The second approach is to identify the temperature below which particle caging first emerges; caging can be defined by the presence of a minimum in the logarithmic derivative of the mean square displacements ∂ ln⟨r 2 (t)⟩/∂ ln t. The temperature at which this minima first appears on cooling defines T A . 57,68 Both definitions yield consistent T A values.…”

Thermodynamic scaling of vibrational dynamics and relaxation

“…Insight into the correlation is offered by the remark that the height of the barrier to be surmounted for structure rearrangement increases with the curvature near the minimum of the potential well temporarily trapping the particles, as first noted by Tobolsky et al [47] via a simple viscoelastic model and put on a firmer ground by Hall and Wolynes who related the barrier height to 1/ u 2 [49]. The correlation was reported in polymeric systems [72][73][74], binary atomic mixtures [39,73,75,79], colloidal gels [76] and antiplasticized polymers [56,78] and compared with the experimental data concerning several glassformers in a wide range of fragility -the steepness m of the temperature-dependence of the logarithm of the structural relaxation time at GT defined by Angell [89] -(20 ≤ m ≤ 191), including polymers, van der Waals and hydrogen-bonded liquids, metallic glasses, molten salts and the strongest inorganic glassformers [72,75,77,80,81,87]. The correlation between structural relaxation and fast mobility is summarized by the universal master curve [72]:…”

“…Eq.3 has been tested on experimental data [72,75,77,80,81,87] as well as numerical models of polymers [38,39,[72][73][74]82], colloids [76] and atomic liquids [39,73,75]. Douglas and coworkers developed a localization model predicting the alternative master curve F F M ( u 2 ) ∝ u 2 −3/2 relating the structural relaxation time and the fast mobility [56,78,79]. Both the latter form and Eq.3 account for the convexity of the master curve, evidenced by the experiments and simulations, and improve the original linear relation proposed by Hall and Wolynes in their pioneering work [49].…”

Weak links between fast mobility and local structure in molecular and atomic liquids

“…Renewed interest about the fast mobility was raised by extensive molecular-dynamics (MD) simulations evidencing the universal correlation between the structural relaxation time τ α * Electronic address: dino.leporini@df.unipi.it and u 2 were reported in polymeric systems [29][30][31], binary atomic mixtures [30,32], colloidal gels [33] and antiplasticized polymers [13,35] and compared with the experimental data concerning several glassformers in a wide fragility range (20 ≤ m ≤ 191) [29,32,34,36,37]. One major finding was that statesof a given physical system, say X and Y, with equal fast mobility u 2 have equal relaxation times τ α too:…”