C. Rascón

Geometry-dominated fluid adsorption on sculpted solid substrates

The shape and chemical composition of solid surfaces can be controlled at a mesoscopic scale. Exposing such structured substrates to a gas that is close to coexistence with its liquid phase can produce quite distinct adsorption characteristics compared to those of planar systems, which may be important for technologies such as super-repellent surfaces or micro-fluidics. Recent studies have concentrated on the adsorption of liquids on rough and heterogeneous substrates, and the characterization of nanoscopic liquid films. But the fundamental effect of geometry on the adsorption of a fluid from the gas phase has hardly been addressed. Here we present a simple theoretical model which shows that varying the shape of the substrate can exert a profound influence on the adsorption isotherms of liquids. The model smoothly connects wetting and capillary condensation through a number of examples of fluid interfacial phenomena, and opens the possibility of tailoring the adsorption properties of solid substrates by sculpting their surface shape.

Critical effects at 3D wedge wetting

We show that continuous filling transitions are possible in 3D wedge geometries made from substrates exhibiting first-order wetting transitions, and develop a fluctuation theory yielding a complete classification of the critical behavior. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also on an exact transfer-matrix analysis of a novel effective Hamiltonian that we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness xi( perpendicular) approximately (T(F)-T)(-1/4) on approaching the filling temperature T(F), valid for all possible types of intermolecular forces.

Universality for 2D Wedge Wetting

We study 2D wedge wetting using a continuum interfacial Hamiltonian model which is solved by transfer-matrix methods. For arbitrary binding potentials, we are able to exactly calculate the wedge free-energy and interface height distribution function and, thus, can completely classify all types of critical behaviour. We show that critical filling is characterized by strongly universal fluctuation dominated critical exponents, whilst complete filling is determined by the geometry rather than fluctuation effects. Related phenomena for interface depinning from defect lines in the bulk are also considered.

Wedge filling, cone filling and the strong-fluctuation regime

Interfacial fluctuation effects occurring at wedge- and cone-filling transitions are investigated and shown to exhibit very different characteristics. For both geometries we argue that the conditions for observing critical (continuous) filling are much less restrictive than for critical wetting, which is known to require the fine tuning of the Hamaker constants. Wedge filling is critical if the wetting binding potential does not exhibit a local maximum, whilst conic filling is critical if the line tension is negative. This latter scenario is particularly encouraging for future experimental studies. Using mean-field and effective Hamiltonian approaches, which allow for breather-mode fluctuations which translate the interface up and down the sides of the confining geometry, we are able to completely classify the possible critical behaviours (for purely thermal disorder). For the three-dimensional wedge, the interfacial fluctuations are very strong and characterized by a universal roughness critical exponent ν⊥W = 1/4 independent of the range of the forces. For the physical dimensions d = 2 and d = 3, we show that the effect of the cone geometry on the fluctuations at critical filling is to mimic the analogous interfacial behaviour occurring at critical wetting in the strong-fluctuation regime. In particular, for d = 3 and for quite arbitrary choices of the intermolecular potential, the filling height and roughness show the same critical properties as those predicted for three-dimensional critical wetting with short-ranged forces in the large-wetting-parameter (ω>2) regime.

Phase diagrams of systems of particles interacting via repulsive potentials

We use a recently developed density-functional perturbation theory, which has been applied successfully to predict phase diagrams of systems of attractive particles, to describe the phase diagram of particles interacting via repulsive potentials. We consider potentials composed of a hard-sphere core plus a repulsive term. Specifically, we have investigated square shoulder and repulsive Yukawa terms. We show that, when the range of the interaction is very short, the shoulder potential leads to solid–solid coexistence involving two face-centered cubic structures, in analogy to an attractive square-well potential. Comparison with simulation results shows that the theory is quantitatively correct. If the range of the potentials is sufficiently long, we also find that a body-centered cubic structure can be stabilized. By considering the phase behavior at zero temperature, we argue that several triple points, involving coexistence of fluid and/or solid phases, may occur. A repulsive Yukawa term also shows a reg...

Theoretical approach to the correlations of a classical crystal

We present the first theoretical approach to the angular-average of the two-body correlation function

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

\tilde g(r)

Covariance for cone and wedge complete filling.

for simple solids. It is based on three sum rules for

Perturbation Theory for Classical Solids.

\tilde g(r)

Wetting at nonplanar substrates: Unbending and unbinding

: the compressibility and virial equations and the normalization. We apply the theory to determine this correlation function for the case of the FCC solid phase of hard spheres. The agreement with simulation data is excellent over all the density range. The application to other simple systems is discussed. The approach opens a new route to perturbation theories for simple solids.