On the Unperturbed State of a Polymer Chain

The mean square end-to-end distances ⟨R²⟩∝N^2ν and the end-to-end vector distribution functions P(R) of a polymer chain at Θ-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 Θ-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 ⟨R²⟩ 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 Θ-point.