Pressure-Dependent Dynamics of Polymer Melts from Arrhenius to Non-Arrhenius: The Cooperative Free Volume Rate Equation Tested against Simulation Data

Abstract

We apply the cooperative free volume (CFV) model to analyze the segmental relaxation times, τ(T,V), of a model 20-mer polymer melt simulated via molecular dynamics over a broad pressure range. Thermodynamic characterization of the 20-mer allows determination of the constant contribution from the hard-core volume (V hc ), which then yields predictions for the free volume, V free = V − V hc . The CFV rate model is based on an activation free energy that increases with the number of cooperating segments, n*, wherein the system's free volume, V free , is what determines n*. The model predicts that on isotherms ln τ vs 1/V free is linear with T-dependent slopes. The 20-mer melt data follow this linear behavior at all temperatures. Assuming a fixed activation energy per cooperating segment leads to a very simple analytic form that describes all of the 20-mer melt's high T behavior, including the Arrhenius to non-Arrhenius transition regime. This form reflects the importance of a gas kinetic contribution as well as both energetic and entropic contributions to the activation energy. Optimization of only one material-dependent parameter leads to collapse of the data. The results of this paper reveal that a key source of non-Arrhenius behavior with decreasing T along isobars is the reduction in V free , which means that segmental rearrangement will require increased cooperativity and higher activation energy. This effect explains the volume contribution to dynamics.

Solution filtering affects the glassy dynamics of spincoated thin films of poly(4-chlorostyrene)

“…By measuring the amount of chains irreversibly adsorbed onto the supporting substrate, we verified that the bulk-like response of the films obtained via unfiltered solutions is associated with a specific volume corresponding to bulk like response. These findings are in line with the prediction of the cooperative free volume rate model by White and Lipson [31][32][33][34].…”

“…In our recent work [42], we have shown that confinement effects on the segmental mobility of P4ClS can be quantitatively predicted by the cooperative free volume (CFV) rate model [31][32][33]. This theoretical framework is based on a description of the segmental relaxation times under general pressure-dependent conditions, τ (T, V ).…”

Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

“…60,61 The most widely used definitions of free volume in the literature and the differences between different definitions have been recently reviewed by White and Lipson, 61 who have developed a 'cooperative free volume' model to explain the dynamics of GF liquids. [202][203][204][205] While the general concept of packing frustration is rather vague, the GET 19 allows us to quantify this property of fluids in terms of how molecular parameters, such as the relative rigidities of the polymer backbone and side chains, chain length, monomer structure, and cohesive interaction strength, influence macroscopic properties such as the thermal expansion coefficient and isothermal compressibility that are highly dependent on the efficiency of molecular packing and the complex intermolecular interactions of molecular fluids. Early studies with the GET 19 indicated that these molecular parameters can greatly influence motivating the theoretical study of S-S polymers in more detail.…”

Dynamics across a Free Surface Reflect Interplay between Density and Cooperative Length: Application to Polystyrene

“…The effect of interfaces on the structural dynamics of polymers and other glass-forming materials has been of strong interest in experiments, theories, and simulations. − Some approaches yield results that show how an interface changes properties as averaged over the whole sample, while other more detailed methods track position-dependent dynamics on the nanometer scale. In a recent work − with the cooperative free volume (CFV) rate model, − we used an overall density value averaged over both outer and inner layers to predict the segmental relaxation times (τ) of polymer films as a whole sample. In this paper, we use the CFV model, but our focus is not on the sample average; instead, we turn to more detailed predictions for τ as a function of position across the interface and focus on changes in the segmental relaxation dynamics to depths of about 5 nm.…”