A Note on “Modified Chain Displacement Function of Gaussian Networks” by A. H. Crossland

Crossland claims that the development of the conventional Gaussian theory of rubber elasticity does not take into account the requirement that the polymer chain end-to-end vector must be equal in direction to the network junction-to-junction vector. Reintroducing the directional probability, he develops a novel Gaussian strain-energy function. H correct, Crossland's work is a significant contribution, resulting in notable improvements in important models in rubber elasticity and polymer rheology. Unfortunately, there is an error in Crossland's analysis. Correction of the error reduces Crossland's results to those of the conventional Gaussian theory and shows that the conventional theory does correctly account for the directional probability. The “improved” strain-energy function, therefore, has no theoretical basis and, at best, must be considered purely empirical.