Abstract
The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from an analysis of the α-process in ordinary relaxation experiments is addressed. The mechanism whereby a CRR changes its configuration is viewed as consisting of two distinct steps: a reduced number of monomers reaches initially an activated state, allowing for some local rearrangement; then, the subsequent regression of the energy fluctuation may take place through the configurational degrees of freedom, thus allowing for further rearrangements on larger length scales. The latter are indeed those to which the well-known Donth's scheme refers. Local readjustments are described in the framework of a canonical formalism on a stationary ensemble of small-scale regions, distributed over all possible energy thresholds for rearrangement. Large-scale configurational changes, instead, are described as spontaneous processes. Two main regimes are envisaged, depending on whether the role played by the configurational degrees of freedom in the regression of the energy fluctuation is significant or not. It is argued that the latter case is related to the occurrence of an Arrhenian dependence of the central relaxation rate. Consistency with Donth's scheme is demonstrated, and data from the literature confirm the agreement of the two methods of analysis when configurational degrees of freedom are relevant for the fluctuation regression. Poly(n-butyl methacrylate) is chosen in order to show how CRR size and temperature fluctuations at rearrangement can be estimated from stress relaxation experiments carried out by means of an atomic force microscopy setup. Cases in which the configurational pathway for regression is significantly hindered are considered. Relaxation in poly(dimethyl siloxane) confined in nanopores is taken as an example to suggest how a more complete view of the effects of configurational constraints would be possible if direct measurements of temperature fluctuations were combined with the proposed analysis.
Highlights
Segmental relaxation in polymers, when approaching the glass transition, is characterized by cooperativity
The existence of an associated length scale of dynamical correlations is inherently addressed by this picture and was put forward already by Adam and Gibbs (AG) in a seminal paper several decades ago, through the introduction of the concept of a cooperatively rearranging region (CRR) [1]
The scope of this paper is to provide a semiphenomenological model through which CRR sizes can be estimated by a method that differs from that of Donth
Summary
When approaching the glass transition, is characterized by cooperativity. This is a condition whereby a monomer moves provided the surrounding ones happen to move concurrently. The problem of estimating its limiting value was considered by Donth in a number of papers (see, e.g., [2]), and it was treated extensively in his book [3]. The relevance of this kind of motion, known as the α-process, has to do with an understanding of the glass transition
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