Cross-over in polymer solutions

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Abstract
Using a small-angle neutron scattering experiment, we measured the pair correlation function P(r) in polymer solutions in the interval 3 RG ≥ r ≥ l, where RG is the radius of gyration and I the step length. At the theta temperature, this function is known to follow the characteristic Debye law P(r) ∼ r-1. In good solvents (high temperature limit) and in the limit of zero polymer concentration this function is uniformly proportional to r-4/3, as predicted by S. F. Edwards. We observe however, that at higher concentrations or intermediate temperatures, P(r) exhibits both characteristic behaviours, depending on the range of r. The cross-over distances r* which separate the patterns are found to depend upon concentration and temperature. The scaling of r* is related to the scaling of the screening length ξ and the radius R G in the temperature-concentration diagram