Theorem of Corresponding States for r-mers

The reduced equation of state (16.5.6) leads us to consider more dosely the possibility of an extension of the theorem of corresponding states to polymers (Prigogine, Beixemans and Colin-naar [1957]). This extension which we shall introduce in tins paragraph opens the way to a treatment of polymer solutions by an appropriate modification of the average potential method (cf. Ch. IX-XII). 

First we note that for purely dimensional reasons we may write for the lattice energy 

We then obtain the configurational partition function in the form (cf. 16.3.19) 

This formula already expresses a theorem of corresponding states in terms of , r. r, c and z. This theorem is however less general than the theorem of corresponding states for monomers, for it is bound to the existence of a quasi-lattice and thus can oiily be applied to condensed states. Furthermore the number of parameters which appear in (16.7.4) is too large to make this expression really useful at present. 

To reduce the number of parafiieters we shall therefore make one farther assumption the cell partition function per point centre depends only on v 

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