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2 Thermodynamics of Critical Phenomena

2.3.4 Renormalization of critical exponents

Taking a closer look at literature of last decades which deals with the theoretical and experimental investigations of critical behavior in three-component fluids it turns out that the binary fluids conception has to be adjusted to apply to ternary fluids. Adjustment can be made by renormalization of critical exponents. Bak and Goldburg 1969 [37], [38], have performed light scattering measurements. They found larger critical exponents for the osmotic susceptibility in the critical ternary system bromobenzene-ethanol-water. Based on these results Fisher proposed a renormalization of critical exponents from calculations of the free electron Ising model [9], [10]. His idea was to keep the formalism developed for binary fluids and to consider the third component as an ”impurity” of the system. The free energy of a binary liquid system is given by F = F0(T,h), where h is the field that corresponds with the other thermodynamic parameters. In the case of ternary fluids the free energy is determined by F(T,h,h3), where h3 is the field which is coupled to the ”impurity” with concentration x3. A more detailed description can be found in the papers by M¨uller [40], [41].

2.3.5 Critical opalescence and equal volume criterions

Critical opalescence is a phenomenon in liquids close to their critical point. A normally transparent liquid appears milky due to density fluctuations at all possible wavelengths. In 1908 Smoluchowski [42] was the first one who connected density fluctuations with the opalescence. In 1910 Einstein [43] showed the relationship between critical opalescence and Rayleigh scattering. Since then, critical opalescence is one of the most important indications for the existence of a critical point. However, another substantial criterion for the existence of a critical point is the so-called equal volume criterion. Only when the volumes of considered components are equal when approaching the consolute point, that point can be assumed to be a critical point. According to both criterions it is possible to determine the critical point visually.

2.4 Phase diagrams

The correct knowledge of the phase diagrams of the critical systems under consideration is essential for measurements at and close to the critical point.

2.4.1 Phase diagrams for binary liquids at constant pressure

It is common practice to present the coexistence curve of a binary mixture in a T-x- diagram as is shown in Fig.(2.3), where T denotes the temperature and x denotes the mole fraction of one constituent. Fig.(2.3) demonstrates the common types of phase diagrams.

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