A method for estimating the cooperativity length in polymers

Abstract

The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from the analysis of the $α$-process in ordinary relaxation experiments is addressed. The system is treated with the canonical formalism as an ensemble of CRRs, which are described by a stationary distribution relative to the rearrangement energy threshold. The process 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 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. Two main regimes are envisaged, depending on wether 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 time. Data of the literature are rediscussed within this new framework.