The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from an analysis of the αprocess 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 wellknown Donth's scheme refers. Local readjustments are described in the framework of a canonical formalism on a stationary ensemble of smallscale regions, distributed over all possible energy thresholds for rearrangement. Largescale 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(nbutyl 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.
Method for estimating the cooperativity length in polymers / Pieruccini, Marco; Alessandrini, Andrea.  In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS.  ISSN 15393755.  STAMPA.  91:5(2015), pp. 111. [10.1103/PhysRevE.91.052603]
Method for estimating the cooperativity length in polymers
ALESSANDRINI, Andrea
2015
Abstract
The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from an analysis of the αprocess 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 wellknown Donth's scheme refers. Local readjustments are described in the framework of a canonical formalism on a stationary ensemble of smallscale regions, distributed over all possible energy thresholds for rearrangement. Largescale 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(nbutyl 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.File  Dimensione  Formato  

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