Abstract
Although many theories have been proposed to describe the nature of glass formation, its microscopic picture is still missing. Here, by a combination of neutron scattering and molecular dynamics simulation, we present the temperature-dependent atomic structure variation of polystyrene at the glass formation, free volume and cooperative rearrangement. When it is close to glass formation, the polymer is confined in tubes, whose diameter is the main chain–main chain distance, in a “static cage” from its neighbors. This definition can not only account for the kinetic pathway dependence of Williams-Landel-Ferry (WLF) free volume, but also be testified in a set of six polymers. However, the free volume which allows a monomer to move cannot be found in any frame of its real-space image. Monomers, thus, have to move cooperatively to be out of the cage. During glass formation, dynamic heterogeneity develops, and string-like cooperative rearrangement region (CRR) grows over a long range of time and length scales. All of these CRRs tend to walk through loose “static cages”. Our observation unifies the concepts of free volume and cooperative rearrangement. The former is a statistical average leading to a polydisperse “static cage” formation; while a loose “static cage” provides the way that CRRs move.
Highlights
Vogel first proposed the concept of free volume in 1921 [1]
The only experimental observation which may be related to the molecular packing density and possibly the “free volume” has been the small change in the scattering function, S(q), at the scattering vector (q) in the range of the monomer dimension [8]; while in the simulation, some groups have tried to use thermodynamic approaches to calculate the free volume [9,10,11,12] As a result, the William-Landau-Ferry (WLF) theory is often believed to be phenomenological [13,14]
Neutron total scattering profiles of six samples (PS-d8, PS-d5, PS-h8, 50 mol% PSd8/50 mol% PS-h8, 50 mol% PS-d8/50 mol% PS-d5 and 50 mol% PS-d5/50 mol% PS-h8) as shown in Figure 1b and Figure S1 were compared with the Fourier Transforms of molecular dynamics simulations
Summary
Vogel first proposed the concept of free volume in 1921 [1]. In theory, it looks easy to understand, i.e., a polymer can move only when it has the space to do so. The only experimental observation which may be related to the molecular packing density and possibly the “free volume” has been the small change in the scattering function, S(q), at the scattering vector (q) in the range of the monomer dimension [8]; while in the simulation, some groups have tried to use thermodynamic approaches to calculate the free volume [9,10,11,12] As a result, the William-Landau-Ferry (WLF) theory is often believed to be phenomenological [13,14] In contrast to this free volume approach, Adam and Gibbs proposed that the polymer could still move if they performed this in a cooperative way at a low temperature [15].
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