Critical region correlation functions, direct

So, c(q = 0) is a finite quantity even when the isothermal compressibility %T tends to diverge in the critical region of any fluid. As will be seen, the former quantity is useful, because of being accessible from direct experiment [12] thanks to recent SANS measurements (see Section V). At variance from g(r), the direct correlation function c(r) in not zero inside the core region (r < a) and its knowledge is crucial in this range of distances, since it is directly related to y T so that... 

The correlation length E, along the imaginary time direction is the other quantity we can use to determine the critical region. The correlation length is defined as the asymptotic behavior of the correlation function... 

Thus, Ornslein-Zcrnike s equation 84 introduces the direct correlation function C(r) which is short-range in the critical region. On the other hand, the form of C(q) given by other relationships of statistical physics, or by a simpler approximation, enables one to obtain the functional dependence of the pair correlation function h r). 

To describe the liquid behaviour in the critical region, the pair correlation function h r) and the direct correlation function C(r) are introduced. 

The generalized Krichevskii parameter or its equivalent, the direct correlation function integral, Cu, is well behaved in the critical region, as shown in Figure 2.18, and on this is based Equation (2.85) (O Connell et al., 1996), which was used to fit the standard partial molar volume of nonelectrolytes all over the density range. 

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