Polydisperse polymer networks : elasticity, orientational properties, and small angle neutron scattering

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Abstract
The properties of polymer networks may be expected to depend upon the distribution, f(S), of chain lengths between crosslinks. We develop a formalism for treating phantom networks which allows the explicit inclusion of an arbitrary f(S) distribution. In bimodal networks we investigate chain orientation in the strained network by calculating and for the long and the short chains separately. The responses of the two species differ markedly from each other, although it is found that the overall network birefringence is dependent only on the mean chain length. Similarly, although the typical degree of extension of the chains upon straining the network differs widely between the species, the network modulus is formally independent of f( S). We investigate scattering from a long labelled chain crosslinked in a network at many randomly-positioned points, and explicitly account for the Poisson distribution of lengths between crosslinks. The scattering function is calculated exactly if the simplification of affine deformation of the junction points is made, and if the junctions are allowed to fluctuate freely, then an approximate solution is possible. The former model (Polydisperse Junction Affine model) agrees much better with the experimental data than the existing theories, both as regards the shape of the Kratky plot and the iso-intensity contours. There remain, however, features of the data which cannot be reproduced by any of the models considered. It is shown by the calculation of limit curves that these differences can only be accounted for by a treatment which goes beyond the idea of phantom chains