next up previous
Next: Appendix: Taylor Expanding Up: Rubber Elasticity with Finite Previous: Network Average


We have presented a perturbation method of deriving the end-to-end distribution function of a freely jointed chain, the . By performing a network average, we derive a fully tensorial expression for the rubber elasticity of a crosslinked network with finite extensibility. The elastic free energy is then obtained as an explicit function of tex2html_wrap_inline855 and tex2html_wrap_inline857 , the two invariants of the deformation tensor. The main conclusion of the paper is that the finite extensibility of polymer chains can give rise to the negative tex2html_wrap_inline697 , observed experimentally. The expansions in small deformation tensor tex2html_wrap_inline839 and the inverse strand length 1/N are performed. The deviation from the usual Gaussian behaviour is obtained. Work in progress aims to generalize the method presented here to nematic networks.

Acknowledgements: I would like to thank Dr. M. Warner and Dr. E. M. Terentjev for introducing me to the problem and their helpful suggestions, Prof. M. E. Cates, Dr. R. C. Ball for stimulating discussions. I thank the referees for critical but useful remarks. I am also grateful to Trinity College, Cambridge for a Research Studentship.

Yong Mao
Wed Apr 30 14:46:27 BST 1997