Diffusion in the Region of a Critical Point

Consider diffusion in a binary liquid mixture exhibiting an upper critical solution temperature (UCST) or lower critical solution temperature (LCST) (see Fig. 3.1). Let us take a mixture at the critical composition x at point A just above the UCST. Any concentration fluctuation at A will tend to be smeared out due to the effects of diffusion in this homogeneous mixture. On the other hand, any fluctuation of a system at point B, infinitesimally below the UCST, will lead to separation in two phases. Similarly, the mixture at point D, just below the LCST is stable whereas the mixture at point C, just above the LCST is unstable and will separate into two phases. 

For thermodynamically stable binary systems the second derivative of the Gibbs free energy with respect to the mole fraction x is positive 

It follows that the Fick diffusion coefficient must tend towards zero as the spinodal curve is approached. This has been experimentally confirmed for a few systems, the data of Haase and Siry (1968) for the systems water-triethylamine and n-hexane-nitrobenzene are shown in Figs. 3.2 and 3.3 (see, also, Claesson and Sundeldf, 1957 Myerson and Senol, 1984). Vitagliano et al. (1980) and Clark and Rowley (1986) determined spinodal compositions by extrapolating diffusivity data to zero. 

For thermodynamic stability in a multicomponent system the matrix [G] must be positive definite. Thus 

For a ternary system the requirement D = 0 at the critical point implies that 

---