Nuclerar magnetic relaxation and nonaffine deformation in cross-linked elastomers

A pulsed NMR-experiment was carried out and the dependence of the second moment $M_2$ of the residual dipole-dipole interaction on the stretch ratio $\lambda$ of cross-linked elastomer was established. The theoretical dependencies $M_2(\lambda)$ calculated on the basis of traditional approaches saying that function of interval distribution between chemical cross-links is Gaussian and the deformation is affine, do not agree with the experimental data. The account of the nonaffine deformation of the sample which is a consequence of the distribution of density of chemical cross-links, and replacement of distribution of the Gaussian chains by the Langevin ones allowed to achieve full coincidence of the theoretical and experimental dependences of the second moment on the stretch ratio.