Isomorphic Critical Behaviour of Mixtures

In the simplest case the vapour-liquid critical points of the two components may be connected by a continuous locus of vapour-liquid critical points of mixtures at various concentrations with or without additional liquid-liquid immiscibility. In other cases the locus of vapour-liquid critical points is interrupted and starting from one of the components may wonder off to higher temperatures or may crossover to an upper or a lower consolute point. The principle of isomorphic critical behaviour asserts that the thermodynamic behaviour associated with the critical behaviour in mixtures can still be described by the scaling-law expression of eq 10.1 in terms of two independent scaling fields, hi and hj, and a dependent scaling field hi. The different types of critical phenomena observed experimentally are caused by different relationship of these scaling fields with the actual physical fields.  

In binary mixtures, we need to consider four physical fields, namely, the (dimensionless) temperature t=T Tc, pressure P=PlpcRTc, chemical potential of the solvent pi =pilRTc, chemical potential of the solute p.2 = P2IRT, or chemical-potential difference fj.2i = P2-Pu and the deviation variables A7 =7 -l, AP = P-P, Api = pi-fiic, and Ap2 = Pi-pic, or A/I21 = A21-A21C Complete scaling asserts that the scaling fields depend on all four field variables. In linear approximation one obtains instead of eq 10.35  

It should be pointed out that all system-dependent parameters, namely the coefficients bi, and c, in the expressions for the scaling fields and the critical parameters Tc, Pc, Hic, and now depend parametrically on the actual position on the critical locus that may be specified by any of the four critical parameters. The two theoretical scaling fields 4 and f 2 continue to be defined as (joi = (dhsldhi)/, and (p2 = (dh3ldh2 - Since 

It has been shown that the principle of isomorphic critical behaviour accounts not only for the thermodynamic behaviour of mixtures near vapour-liquid critical points and near critical liquid-liquid mixing critical points, but also near special critical points, like azeotropic critical points, critical points where the critical temperature exhibits a maximum or a minimum as a function of temperature, re-entrant critical points and critical double points, depending on the values of the coefficients a,-, bi, and c,- in the expressions for the scaling fields. In this chapter we restrict ourselves to some more common cases of critical phase behaviour in mixtures. 

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