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
and 
, 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 
, observed experimentally.
The expansions in small deformation tensor 
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.