The Combinatorial Factor for Mixtures of chain molecules

Consider a group of r sites congruent with an r-mer. Such a group may be occupied in many distinguishable ways among which two are outstandingly ample  

Let us call and the probability of these events and define the ratio of P, to P  

We shall now relate a to the thermod3mamic properties of the system. The lattice partition fimction (3.2.5) of the system of Na monomers and Nb r-mers is here (equating the energy of the contacts to zero) 

The lattice partition function reduces to the combinatorial factor g. Let us now calculate the corresponding grand partition function. According to (2.3.4) it is obtained by summation over all values of Na and Nb of the partition function, each term of the sum being multiplied by the factor exp Naiha + Nb/ b) which represents the statistical weight of the configuration Na, Nb) for given value of / a, /ab, T and T. To take account of the incompressibility of the lattice we introduce moreover the function such that 

In the present case the lattice grand partition function is therefore 

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THE COMBINATORIAL FACTOR FOR MIXTURES OF CHAIN MOLECULES 73 sites is given by the product of the two preceding independent events... 

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