On the Unperturbed State of a Polymer Chain

The mean square end-to-end distances < R 2 >∝ N 2ν and the end-to-end vector distribution functions P ( R ) of a polymer chain at \(\)-point and in the polymer melt are considered in the framework of the self-consistent approximation developed by Edwards. The following conclusions are drawn. i) At \(\)-point 2ν=1, but P ( R ) is not gaussian in three dimensional space. ii) In the melt 2ν=1 and P ( R ) is very close to gaussian in three dimensional space. iii) The mechanisms making 2ν unity in the two cases above are different and hence < R 2 > are generally different in these two cases. iv) The parameter z of the two-parameter theory is not a good parameter for analyzing the data near \(\)-point.