Scattering from network polydispersity in polymer gels

Abstract

Swollen networks possess permanent elastic constraints that induce static variations 〈\ensuremath{\delta}${\mathit{\ensuremath{\varphi}}}^{2}$${\mathrm{〉}}_{\mathit{s}}$ at a microscopic scale in the polymer volume fraction \ensuremath{\varphi}. It is shown that the concentration polydispersity 〈\ensuremath{\delta}${\mathit{\ensuremath{\varphi}}}^{2}$${\mathrm{〉}}_{\mathit{s}}$/${\mathit{\ensuremath{\varphi}}}^{2}$ is related to the macroscopic osmotic and elastic properties of the gel. An expression is derived for the dependence of 〈\ensuremath{\delta}${\mathit{\ensuremath{\varphi}}}^{2}$${\mathrm{〉}}_{\mathit{s}}$/${\mathit{\ensuremath{\varphi}}}^{2}$ on swelling. Good agreement is found with previously reported small-angle neutron scattering measurements in randomly cross-linked polyvinyl acetate and end-linked polydimethyl siloxane networks swollen in toluene.