STATISTICAL-MECHANICS OF COAL TREATED AS A DENSELY CROSS-LINKED NETWORK

An analysis of the statistical mechanics of a densely cross-linked sys tem is presented. It is argued that for such systems fluctuations of t he cross-link points will be severely inhibited and the assumption of affine deformation should be reasonable. It is first demonstrated that the usual result obtained by classical theories can be obtained by an alternative method without assuming Gaussian statistics or the Langev in approximation for the partition function, For values of N, the numb er of ''statistical segments'' (freely hinged and rotating) between cr oss-link points, less than or equal to 2, the Gaussian results cannot apply. For small deformations of networks with N greater than or equal to 3, the Gaussian approximation is shown to be valid. This latter re sult will be employed in studies of the deformation of swollen coal ge ls in future work.