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2 Thermodynamics of Critical Phenomena

In this Chapter the theoretical background of the thermodynamics of critical phenomena in binary and ternary liquid systems, phase transitions as well as the static and dynamic scaling hypotheses are presented. Furthermore, critical exponents and their important role for the description of second order phase transitions are shown. Moreover, typical binary and ternary phase diagrams are presented.

2.1 Phase transitions

Figure 2.1: Discontinuous and continuous shape of the entropy of phase transitions: discont. ∆S ̸= 0 ⇔∆Q = T0∆S; cont. S is a continuous function of T ⇒∆Q = 0

The first attempt to classify phase transitions was done by Ehrenfest (1933). The Ehrenfest classifica- tion scheme was based on grouping of phase transi- tions into their degree of non-analyticity. Phase tran- sitions were labeled by the lowest derivative of the Gibbs free energy G(T, p) that is discontinuous at the phase transition. Taking a closer look at the increas- ing degree of derivation, the differences between the phases on consideration get smaller. In fact, it is nec- essary to raise the question about the sense of differing between phases in this way. It is more practicable to consider derivatives of lower degree only. This leads to the description of so-called first-order phase tran- sitions or discontinuous phase transitions. Charac- teristic of first-order phase transitions is the disconti- nuity of the first derivation of the Gibbs free energy G(T, p). Within the scope of critical phenomena in liquids, another kind of phase transitions plays an im- portant role, the so-called second-order phase transi- tions or the continuous phase transitions (see Fig.(2.1)). In this case, the first derivative of Gibbs free energy is continuous and especially in liquid systems the conception of latent heat does no longer exist. Another characteristic parameter of continuous phase

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