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We set up the problem of finding the transition state for phase nucleation inmulti-component fluid mixtures, within the Landau-Ginzburg density functional.We establish an expression for the coordinate-dependent local pressure thatapplies to mixtures, arbitrary geometries, and certain non-equilibriumconfigurations. The expression allows one to explicitly evaluate the pressurein spherical geometry, \`a la van der Waals. Pascal's law is recovered withinthe Landau-Ginzburg density functional theory, formally analogously to howconservation of energy is recovered in the Lagrangian formulation of mechanics.We establish proper boundary conditions for certain singular functional formsof the bulk free energy density that allow one to obtain droplet solutions withthick walls in essentially closed form. The hydrodynamic modes responsible formixing near the interface are explicitly identified in the treatment; thecomposition at the interface is found to depend only weakly on the dropletsize. Next we develop a Landau-Ginzburg treatment of the effects of amphiphileson the surface tension; the amphiphilic action is seen as a violation ofPascal's law. We explicitly obtain the binding potential for the detergent atthe interface and the dependence of the down-renormalization of the surfacetension on the activity of the detergent. Finally, we argue that therenormalization of the activation barrier for escape from long-lived structuresin glassy liquids can be viewed as an action of uniformly seeded, randomlyoriented amphiphilic molecules on the interface separating two dissimilaraperiodic structures. This renormalization is also considered as a "wetting" ofthe interface. The resulting conclusions are consistent with the random firstorder transition (RFOT) theory.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Pressure in the Landau-Ginzburg Functional: Pascal's Law, Nucleation in  Fluid Mixtures, a Meanfield Theory of Amphiphilic Action, and Interface  Wetting in Glassy Liquids