Explicit Expression for the Excess Volume

We have given a general expression for the excess volume F in (17.4.5). This expression can be expanded in f at sufiSciently low temperatures. Keeping terms of first or second order only, we have 

Owing to the complexity of this expression we shall discuss it graphically. We take = 1 and ra - 00. It is then convenient to 

In each case, 6 is taken equal to 0. The reference component A is argon near its boiling point (cf. Table 9.5 1) (Xa =. STn 0.5) 

Let us consider mixtures of monomers and imagine that we increase the chain-length f of the second molecular species. We may thus e q ect a kind of periodic behaviour for the excess volume with ininiina when the length of the second species is approximately an integral multiple of that of the first one. This should provide quite a direct test for the quasicrystalline structure of liquid mixtures. At present, however, no appropriate experimental data seem to he available. 

We now turn to the comparison of the theory with the eiqpecun tal data. In this section we shall discuss the occurence of inversions of the sign of some excess functions with composition. In the two next sections we shall consider the case of monomer-dimer mixtures and monomer-high pol3uner mixtures. 

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