Representation of the partition functions and symmetry factors

A set of molecules belonging to m types can be defined by giving for every sd sd = 1,. . . , m), the number of molecules of type sd belonging to the set. This is what we have done until now and consequently we represented the partition function of such a set by using the symbol Qa( V Nt,. . . , Nm) where V is the volume of space occupied by the molecules. 

It is also possible to define a set of N molecules in a different way, by listing the molecules contained in , and this other representation is more adapted to the study of sets of homogeneous polymers. 

In fact, a homogeneous polymer can be characterized by its number N of monomers (or links) polymers having different numbers of monomers belong to different species, and therefore it is possible to identify sd with N(N - Nn). Thus can be defined by the set (N1,. . . , NH) of the numbers of monomers contained in the chains constituting obviously, the corresponding Nn are thus given by 

In the same spirit, we can represent the partition function associated with a set S of N polymers by the symbol ZG (V Nit. .., Nn). Everywhere in the following pages of this book ZG (V Nt,.. ., NH) are always calculated as if the polymers were distinguishable (actually they may or may not be so), and as if they had a distinguishable origin (dissymmetrical polymers). 

Actually, the synthetic polymers which are used in experiments are generally dissymmetrical, but in both cases, the properties of solutions of long polymers are the same. On the other hand, the theoretical implications of the presence or the absence of a symmetry are trivial. 

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