Non-affine deformation and spatial fluctuations of the modulus observed in heterogeneous networks and nanocomposites

Abstract

The anisotropic small-angle neutron scattering from two different materials is considered. One is a polymer network permeated by free, uncross-linked, deuteriated chains. These free chains behave as mobile species. The other is made up of two networks, one being deuteriated, grown interwoven with each other. They are made of two different polymers which are immiscible, one being in a soft, rubbery state, the other in a hard, glassy state.

The scattering of the two systems displays an unusual dependence upon the direction with respect to the stretching axis. The scattered intensity recorded along any direction which corresponds to an increase in the dimensions increases strongly with the elongation ratio. The isointensity patterns, so-called butterflies, have the shape of 8s, oriented along the stretching axis.

We propose a general explanation: in both cases this increase is due to the separation between some hard, weakly deformed regions inside a softer matrix.

This implies, for the network permeated by free chains, that a scattering contrast is created between hard and soft regions: the free chains migrate into the soft regions. The increase of the correlation length, ξ, along any extended direction of the sample (such as the one parallel to the stretching) reveals an intermediate regime at lower and lower values of the scattering vector, q. In this q range, the intensity, I(q), is superimposed on a limit curve, characteristic of each sample. The perpendicular scattering is essentially unaffected. Different continuous-medium elasticity theories have tried to explain such an anisotropy of the spatial fluctuations of concentration. Rather accurate measurements allow us to detect disagreements between these theories and experiment. In our opinion, this confirms our more direct picture: the progressive unscreening of the structure of the spatial distribution of the modulus.