Scattering from deformed swollen gels with heterogeneities

When elastic materials are anisotropically deformed, heterogeneities in stiffness generally produce long-range density variations. The effect is particularly enhanced in swollen gels. We calculate the structure factor from such frozen density deviations under general alline deformations. It is maximized in the most stretched direction, whereas that from the thermal fluctuations is minimized in the same direction. As a result, under uniaxial extension, a crossover occurs from normal to abnormal butterfly scattering patterns with increase of the strength of inhomogeneity or the swelling ratio in accord with recent scattering experiments. Furthermore, scattering patterns under shear deformation closely resemble those from phase-separating semidilute polymer solutions under shear flow.