Chain size and the molecular expansion factor

Consider a linear polymer made up of monomer segments of length a. A freely jointed chain of n segments would have an average square of the end-to-end distance, given by (Flory, 1953)  

However, this describes a completely random orientation problem where each segment may double back on adjacent segments and may approach 

The quantity r is considered to be related to the unperturbed or unswollen chain length of the polymer. Note that the actual mean square end-to-end 

In practice, the experimentally determined mean square of the end-to-end distance of the polymer will not be the same as the unperturbed value. The size of the polymer chain in solution will depend on the solvent. In a good 

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