Variation of the screening length with temperature

The study of the dependence of the screening length on temperature is also very significant. We know that in the semi-dilute regime, the screening length e is proportional to the Kuhnian overlap length. By definition 

Let us now examine the experimental results. Cotton et al.21 measured the screening length associated with polystyrene (Mw = 1.4 x 106) solutions in deuterated cyclohexane, at fixed concentration p, for different temperatures. The result is seen in Table 15.14. We verify that decreases as temperature increases. 

Moreover, using the values of this table, we are going to verify that, in good solvent and in the overlap regime, the screening length obeys eqn (15.4.40). We shall observe that below a certain temperature this law ceases to be valid, as predicted from theory. 

For this, let us relate the screening length to the two-body interaction b. By definition, we have, 

We have already verified that, in good solvent, interaction b varies linearly with l/T, for T close to TF [see (15.3.5]. Therefore, for a good solvent and 

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