Because the compressibility of pure water has a singularity at the critical point. Equation (2.11) predicts that the standard partial molar volume should diverge in the critical point. The sign of the critical divergence, determined by the spatial integral of the direct correlation function, C 2, depends on the nature of the solute-solvent interaction. [Pg.157]

If the finite size of the system is ignored (after all, A is probably 10 or greater), the compressibility is essentially infinite at the critical point, and then so are the fluctuations. In reality, however, the compressibility diverges more sharply than classical theory allows (the exponent y is significantly greater dian 1), and thus so do the fluctuations. [Pg.647]

Fluctuations of Pi,(r) can be caused by density or concentration fluctuations. Real density fluctuations in simple (one-component) fluids occur near the critical point, where the isothermal compressibility of the liquid diverges. In multicomponent fluids, the concentration fluctuations can be observed when (at least one of) the components want to demix. Naturally, in more complex samples, like colloids in some solvents, fluctuations are present because, on the atomic length scale point of view, there are several (at least two) different phases present. SANS (and also, its X-ray counterpart SAXS) can be applied with success in these latter instances. [Pg.1540]

The remaining bulk thermodynamic exponent a determines the rate of divergence of the constant-volume heat capacity Cv at the liquid-vapour critical point of a one-component fluid [or that of the constant-pressure heat capacity Cp, or of the literal mechanical (rather than osmotic) compressibility k, or of the coefficient of thermal expansion, of a liquid mixture near its consolute point]. At fixed p = p , the heat capacity Cv as a function of temperature has the shape shown schematically in Fig. 9.3(a) with [Pg.262]

Contrary to the tail of the correlation function, which is directly connected with the strong divergence of the compressibility, the tirst peak of the correlation function, as pointed out by Stell and H0ye [11), bears a subtle relation to the internal energy. The latter property behaves smoothly at the critical point, but its first temperature derivative, the heat capacity Cv, has a weak divergence. [Pg.12]

The second, or indirect, mechanism by which a solute may alter the density of a compressible fluid is dependent upon the correlation length of the fluid (equation 4), which diverges with the compressibility kt as the critical point is approached. Recall that a correlation of length implies that if there is a fluctuation in the local density of the fluid at some position x, e.g., Sp x) = p(x) - p > 0, where p is the bulk density, then the density fluctuation at any other [Pg.2831]

Figure 1 also shows a P p isotherm for the liquid phase of WAG silica. Notably, this isotherm also exhibits an inflection, indicating the presence of a compressibility maximum in the liquid state [19]. In simulations of supercooled liquid water, the same thermodynamic feature occms, and as T decreases, the compressibility maximum in simulated water grows into a divergence at a critical point [20]. Below the temperatme of this critical point, two thermodynamically distinct liquid phases of simulated water occur, each with a distinct density, reflecting the occurrence of a first order LLPT. [Pg.376]

See also in sourсe #XX -- [ Pg.384 ]

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