Phase equilibria and the Landau—Ginzburg functional

• Published in: Fluid phase equilibria Vol. 45; no. 2; pp. 229 - 250
• Main Authors: Nauman, E.B., Balsara, Nitash P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.1989; Elsevier Science
• Subjects: Chemistry; Exact sciences and technology; General and physical chemistry; Phase equilibria; Theoretical study; Chemical potential; Thermodynamic properties; Phase equilibrium; Binary system; Free energy
• ISSN: 0378-3812; 1879-0224
• DOI: 10.1016/0378-3812(89)80260-2

New, more restrictive conditions are derived for the minimization of free energy in binary liquid systems. These conditions are an extension of chemical potential theory as developed by Gibbs to systems involving gradient energy. The new conditions eliminate nonphysical and pseudoequilibrium solutions found in previous treatments. They also give the surprising result that the bifurcation from single-phase to two-phase behavior occurs at a finite value of the gradient energy parameter. There is a minimum possible size below which a system cannot separate into two phases. This minimum size is a function of average composition. It ranges from infinity at the binodal composition to an absolute minimum at some point within the spinodal. Within the spinodal region, the minimum size of a two-phase system approaches the minimum size for growth as predicted by Cahn's linearized theory of spinodal decomposition. The non-linear Cahn—Hilliard diffusion equation requires a subtle modification to be consistent with the present theory. However, this modification does not affect the linearized theory or the long-time predictions of the full equation.