Expanded chains pair distribution function

Combining all the information collected so far, for the single chain pair distribution function in a semidilute solution we can predict an overall shape as indicated in Fig. 3.8. For the presentation we choose a plot of 4nr g r) versus r. The curve is a composite of different functions in four ranges, with cross-overs at the persistence length Ips, the thermic correlation length and the screening length Up to r we find the properties of the expanded chain, which... 

It is possible to deduce from the scaling law Eq. (2.83) the fractal dimension of expanded chains, as well as characteristic properties of the pair distribution function and the structure function. The fractal dimension d follows from the same argument as applied above for the ideal chains, by estimating the average number of monomers included in a sphere of radius r which is now given by... 

More detailed considerations show that, as in the case of the ideal chains, the pair distribution function of expanded chains may also be presented in a reduced form... 

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