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

TL;DR

This paper develops a comprehensive Landau-Ginzburg framework for analyzing pressure, nucleation, amphiphilic effects, and wetting phenomena in complex fluid mixtures and glassy liquids, linking classical laws with modern theories.

Contribution

It introduces a generalized pressure expression within Landau-Ginzburg theory, incorporates amphiphilic effects on surface tension, and connects interface wetting to glassy dynamics, advancing understanding of phase transitions.

Findings

Derived a coordinate-dependent local pressure expression for mixtures.

Revealed how amphiphiles violate Pascal's law and affect surface tension.

Linked interface wetting phenomena to glassy liquid dynamics and RFOT theory.

Abstract

We set up the problem of finding the transition state for phase nucleation in multi-component fluid mixtures, within the Landau-Ginzburg density functional. We establish an expression for the coordinate-dependent local pressure that applies to mixtures, arbitrary geometries, and certain non-equilibrium configurations. The expression allows one to explicitly evaluate the pressure in spherical geometry, \`a la van der Waals. Pascal's law is recovered within the Landau-Ginzburg density functional theory, formally analogously to how conservation of energy is recovered in the Lagrangian formulation of mechanics. We establish proper boundary conditions for certain singular functional forms of the bulk free energy density that allow one to obtain droplet solutions with thick walls in essentially closed form. The hydrodynamic modes responsible for mixing near the interface are explicitly identified in the treatment; the composition at the interface is found to depend only weakly on the droplet size. Next we develop a Landau-Ginzburg treatment of the effects of amphiphiles on the surface tension; the amphiphilic action is seen as a violation of Pascal's law. We explicitly obtain the binding potential for the detergent at the interface and the dependence of the down-renormalization of the surface tension on the activity of the detergent. Finally, we argue that the renormalization of the activation barrier for escape from long-lived structures in glassy liquids can be viewed as an action of uniformly seeded, randomly oriented amphiphilic molecules on the interface separating two dissimilar aperiodic structures. This renormalization is also considered as a "wetting" of the interface. The resulting conclusions are consistent with the random first order transition (RFOT) theory.