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Landau-Safran theory of network fluids at structured surfaces

A broad class of associating fluids (microemulsions, patchy colloids, dipolar fluids) shares striking properties (e.g. re-entrant phase diagrams, ultra-low surface tensions, low liquid densities, etc.). These can be traced to the self-assembly into chains of the basic constituents (monomers) of the fluid.

Although a full description of these systems is difficult, a simple Landau-like theory captures the essential features and explains the universal behavior of these different materials. The Landau-Safran free-energy is written as an expansion of a scalar order parameter but the chaining and branching contribute non-analytic terms to the free-energy, with powers 1/2 (accounting for the free-energy cost of the chain ends) and 3/2 (accounting for the free-energy cost of chain branching) of the order parameter, which in the low density limit dominate the free energy. The thermodynamic analysis of the Landau-Safran free-energy describes the re-entrant phase diagram and the low density liquid.

We investigated the interfacial properties and found that the ultra-low surface tension of the liquid-vapor interface is also described. A standard analysis of interfacial phenomena also reveals peculiar features of the wetting behaviour. Due to the re-entrant phase diagram and the low density of the liquid phase at low temperatures, the liquid wets any surface at low temperatures. At higher temperatures, as the critical temperature is approached, the surface is also always wet but it may be wet by the vapor phase (dry) depending on the properties of the surface. The adsorption vs temperature reveals two wetting transitions (one as the temperature increases, and the other as the temperature decreases) which collide when the density at the surface increases.

In this project we aim to study the Landau-Safran theory for wetting at structured surfaces. The re-entrance is bound to lead to novel effects for wetting and filling of capillaries, capped capillaries, wedges, sinusoidal gratings, etc.

References

• Reentrant wetting of network fluids, N. R. Bernardino and M. M. Telo da Gama, Physical Review Letters 109, 116103 (2012)