Stability and Critical Phenomena in Binary Solutions

In region BL of Fig. 13.2 the system is a supersaturated vapor and may begin to condense if nucleation can occur. This is a metastable state. Similarly, in region AJ we have a superheated liquid that will vaporize if there is nucleation of the vapor phase. The stable, metastable and unstable regions are indicated in Fig. 13.2. Finally, at the critical point C, both the first and second derivatives of p with respect to Vequal zero. Here the stability is determined by the higher-order derivatives. For stable mechanical equilibrium at the critical point, we have 

In solutions, depending on the temperature, the various components can segregate into separate phases. For simplicity, we shall only consider binary mixtures. The phenomenon is similar to the critical phenomenon in a liquid-vapor transition in that across one range of temperature the system is in one homogeneous phase (solution) but across an another range of temperature the system becomes unstable and the two components separate into two phases. The critical temperature that separates these two ranges depends on the composition of the mixture. This can happen in three ways, as illustrated by the following examples. 

At atmospheric pressure the liquids n-hexane and nitrobenzene are miscible in all proportions when the temperature is above 19 °C. Below 19 °C the mixture separates into two distinct phases, one rich in nitrobenzene and the other in n- 

Let us now look at the phase separation in binary mixtures from the viewpoint of stability. The separation of phases occurs when the system becomes unstable with respect to diffusion of the two components, i.e. if the separation of the two components produces an increase in entropy then the fluctuations in the mole number due to diffusion in a given volume grow, resulting in the separation of the two components. As we have seen in section 12.4, the condition for stability against diffusion of the components is 

At a fixed T, for binary mixtures, this can be written in the explicit form 

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