Form function of an isolated chain semi-phenomenological approaches, thermic sequences

3 Form function of an isolated chain semi-phenomenological approaches, thermic sequences  

An approximate expression of h(x) for a chain with a critical exponent v can be obtained in a very simple way as was done by Peterlin (1955)31, and also Ptitsyn (1957)32 and Benoit (1957).33 The basic assumptions are that 

Unfortunately, the result (13.1.167) is not as good as could be expected, for reasons already explained in connection with the calculation of the radius of gyration (Chapter 4, Section 2.1.2). In fact, eqns (13.1.164) and (13.1.165) represent reality only very crudely (see Section 1.5.6 and Chapter 10, Section 7.2). Actually, the equality (13.1.166) can be tested by comparison with exact results. 

the value of h, which can be deduced from it, is given by (13.1.167) and 

Moreover, starting from (13.1.167) and expanding in powers of x, we find 

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