AN APPROACH TO FLUCTUATION AND ELASTICITY IN POLYMER NETWORKS

The fluctuation of strands and junctions in fully crosslinked polymer networks under deformation is investigated along with the deformation free energy and elasticity. Nonergodic, disordered system as it is, st atistical properties of a polymer networks need to be described on the basis of average over the partial configuration space accessible to t he chains. In this work, we reconsider the ensemble average for the bu lk and single-chain properties and devise a response theory to relate the fluctuations of the single strand with an external deformation. In the light of this formulation, we assess the ''cooperative network'' theory of Ronca and Allegra (RA), which represents a statistical mecha nical theory with no adjustable parameters yielding good agreements wi th experiments. Their formulation of the fluctuation under strains is rather ad hoc, since it is adjusted to meet the empirically expected b ehaviors in the affine and phantom network limits. We find their free energy can be put into a form much more significant and suggestive, wh ich combines with our approach to yield an alternative theory. An appr oximation within our approach yields better agreements with the experi ments on elasticity