Phase transitions of fluids in heterogeneous pores

We study phase behaviour of a model fluid confined between two unlike parallel walls in the presence of long range (dispersion) forces. Predictions obtained from macroscopic (geometric) and mesoscopic arguments are compared with numerical solutions of a non-local density functional theory. Two capillary models are considered. For a capillary comprising of two (differently) adsorbing walls we show that simple geometric arguments lead to the generalized Kelvin equation locating capillary condensation very accurately, provided both walls are only partially wet. If at least one of the walls is in complete wetting regime, the Kelvin equation should be modified by capturing the effect of thick wetting films by including Derjaguin's correction. Within the second model, we consider a capillary formed of two competing walls, so that one tends to be wet and the other dry. In this case, an interface localized-delocalized transition occurs at bulk two-phase coexistence and a temperature $T^*(L)$ depending on the pore width $L$. A mean-field analysis shows that for walls exhibiting first-order wetting transition at a temperature $T_{w}$, $T_{s}>T^*(L)>T_{w}$, where the spinodal temperature $T_{s}$ can be associated with the prewetting critical point, which also determines a critical pore width below which the interface localized-delocalized transition does not occur. If the walls exhibit critical wetting, the transition is shifted below $T_{w}$ and for a model with the binding potential $W(\ell)=A(T)\ell^{-2}+B(T)\ell^{-3}+\cdots$, where $\ell$ is the location of the liquid-gas interface, the transition can be characterized by a dimensionless parameter $\kappa=B/(AL)$, so that the fluid configuration with delocalized interface is stable in the interval between $\kappa=-2/3$ and $\kappa\approx-0.23$.Comment: 18 pages, 12 figure

Bridging transitions for spheres and cylinders

We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius $R$ separated by a distance $H$ that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density functional theory and finite-size scaling theory we study the location and order of the bridging transition and also the stability of the liquid bridges which determines spinodal lines. The location of the bridging transitions is similar for cylinders and spheres, so that for example, at bulk coexistence the distance $H_b$ at which a transition between bridged and unbridged configurations occurs, is proportional to the colloid radius $R$. However all other aspects, and, in particular, the stability of liquid bridges, are very different in the two systems. Thus, for cylinders the bridging transition is typically strongly first-order, while for spheres it may be first-order, critical or rounded as determined by a critical radius $R_c$. The influence of thick wetting films and fluctuation effects beyond mean-field are also discussed in depth

Filling transitions in acute and open wedges

We present numerical studies of first-order and continuous filling transitions, in wedges of arbitrary opening angle $\psi$, using a microscopic fundamental measure density functional model with short-ranged fluid-fluid forces and long-ranged wall-fluid forces. In this system the wetting transition characteristic of the planar wall-fluid interface is always first-order regardless of the strength of the wall-fluid potential $\varepsilon_w$. In the wedge geometry however the order of the filling transition depends not only on $\varepsilon_w$ but also the opening angle $\psi$. In particular we show that even if the wetting transition is strongly first-order the filling transition is continuous for sufficient acute wedges. We show further that the change in the order of the transition occurs via a tricritical point as opposed to a critical-end point. These results extend previous effective Hamiltonian predictions which were limited only to shallow wedges

Crossover scaling of apparent first-order wetting in two dimensional systems with short-ranged forces

Recent analyses of wetting in the semi-infinite two dimensional Ising model, extended to include both a surface coupling enhancement and a surface field, have shown that the wetting transition may be effectively first-order and that surprisingly the surface susceptibility develops a divergence described by an anomalous exponent with value $\gamma_{11}^{\rm eff}=\frac{3}{2}$. We reproduce these results using an interfacial Hamiltonian model making connection with previous studies of two dimensional wetting and show that they follow from the simple crossover scaling of the singular contribution to the surface free-energy which describes the change from apparent first-order to continuous (critical) wetting due to interfacial tunnelling. The crossover scaling functions are calculated explicitly within both the strong-fluctuation and intermediate-fluctuation regimes and determine uniquely and more generally the value of $\gamma_{11}^{\rm eff}$ which is non-universal for the latter regime. The location and the rounding of a line of pseudo pre-wetting transitions occurring above the wetting temperature and off bulk coexistence, together with the crossover scaling of the parallel correlation length, is also discussed in detail

The Influence of Intermolecular Forces at Critical Point Wedge Filling

We use microscopic density functional theory to study filling transitions in systems with long-ranged wall-fluid and short-ranged fluid-fluid forces occurring in a right-angle wedge. By changing the strength of the wall-fluid interaction we can induce both wetting and filling transitions over a wide range of temperatures and study the order of these transitions. At low temperatures we find that both wetting and filling transitions are first-order in keeping with predictions of simple local effective Hamiltonian models. However close to the bulk critical point the filling transition is observed to be continuous even though the wetting transition remains first-order and the wetting binding potential still exhibits a small activation barrier. The critical singularities for adsorption for the continuous filling transitions depend on whether retarded or non-retarded wall-fluid forces are present and are in excellent agreement with predictions of effective Hamiltonian theory even though the change in the order of the transition was not anticipated