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In this work, the morphology of nematic capillary nanobridges in slit pores separated by a vertical distance $D$ will be characterised by Monte Carlo simulations for oblate molecules nematogen modelled by the Gay-Berne potential. Previous studies on droplets show that the molecules are arranged homeotropically at the nematic-vapour interface and form spherical droplets with an annular disclination located in their equatorial plane. In the presence of pores with attractive substrates that favour homeotropic anchoring, the formation of nanobridges characterised by anchoring angles that decrease with increasing particle-substrate interaction intensity is observed. When the orientational field in the nanobridge is analysed, the formation of an annular disclination of topological charge $+1/2$ located in the plane perpendicular to the $z$-axis that passes through the centre of mass of the nanobridge is observed for small $D$. However, when considering higher values of $D$, a change to a biaxial orientational profile within the nanobridge is observed, where now the annular disclination is arranged in a plane perpendicular to one direction of the $xy$ plane. These results are indicative of the existence of an orientational phase transition for an intermediate $D$ value between a uniaxial and a biaxial orientational configuration in the capillary nanobridge., Comment: 20 pages, 8 figures. This article has been accepted for publication in Liquid Crystals, published by Taylor & Francis

In this Letter we present evidences of the occurrence of a tricritical filling transition for an Ising model in a linear wedge. We perform Monte Carlo simulations in a double wedge where antisymmetric fields act at the top and bottom wedges, decorated with specific field acting only along the wegde axes. A finite-size scaling analysis of these simulations shows a novel critical phenomenon, which is distinct from the critical filling. We adapt to tricritical filling the phenomenological theory which successfully was applied to the finite-size analysis of the critical filling in this geometry, observing good agreement between the simulations and the theoretical predictions for tricritical filling., Comment: 5 pages, 3 figures

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favours homeotropic anchoring, as a function of the wavenumber of the surface structure $q$, the tilt angle $\alpha$ and the surface anchoring strength $w$. In addition to the previously reported non-analytic contribution proportional to $q\ln q$, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to $q$ for a given substrate roughness, in agreement with Berreman's predictions. We characterise this term, finding that it has two contributions: the deviations of the nematic director field with respect to the corresponding to the isolated disclination lines, and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit $wL>1$, when strong anchoring conditions are effectively achieved., Comment: 13 pages, 9 figures; revised version submitted to Phys. Rev. E

Close to sinusoidal substrates, simple fluids may undergo a filling transition, in which the fluid passes from a dry to a filled state, where the interface remains unbent but bound to the substrate. Increasing the surface field, the interface unbinds and a wetting transition occurs. We show that this double-transition sequence may be strongly modified in the case of ordered fluids, such as nematic liquid crystals. Depending on the preferred orientation of the nematic molecules at the structured substrate and at the isotropic-nematic interface, the filling transition may not exist, and the fluid passes directly from a dry to a complete-wet state, with the interface far from the substrate. More interestingly, in other situations, the complete wetting transition may be prevented, and the fluid passes from a dry to a filled state, and remains in this configuration, with the interface always attached to the substrate, even for very large surface fields. Both transitions are only observed for a same substrate in a narrow range of amplitudes.

In our first paper, we showed how a non-local effective Hamiltionian for short-ranged wetting may be derived from an underlying Landau-Ginzburg-Wilson model. Here, we combine the Green's function method with standard perturbation theory to determine the general diagrammatic form of the binding potential functional beyond the double-parabola approximation for the Landau-Ginzburg-Wilson bulk potential. The main influence of cubic and quartic interactions is simply to alter the coefficients of the double parabola-like zig-zag diagrams and also to introduce curvature and tube-interaction corrections (also represented diagrammatically), which are of minor importance. Non-locality generates effective long-ranged many-body interfacial interactions due to the reflection of tube-like fluctuations from the wall. Alternative wall boundary conditions (with a surface field and enhancement) and the diagrammatic description of tricritical wetting are also discussed., Comment: (14 pages, 2 figures) Submitted J. Phys. Condens. Matter

We study filling phenomena in 3D wedge geometries paying particular attention to the role played by a line tension associated with the wedge bottom. Our study is based on transfer matrix analysis of an effective one dimensional model of 3D filling which accounts for the breather-mode excitations of the interfacial height. The transition may be first-order or continuous (critical) depending on the strength of the line tension associated with the wedge bottom. Exact results are reported for the interfacial properties near filling with both short-ranged (contact) forces and also van der Waals interactions. For sufficiently short-ranged forces we show the lines of critical and first-order filling meet at a tricritical point. This contrasts with the case of dispersion forces for which the lines meet at a critical end-point. Our transfer matrix analysis is compared with generalized random-walk arguments based on a necklace model and is shown to be a thermodynamically consistent description of fluctuation effects at filling. Connections with the predictions of conformal invariance for droplet shapes in wedges is also made., Comment: Revised version with two added figures, accepted for publication in New Journal of Physics

We show that the 3D wedge filling transition in the presence of short-ranged interactions can be first-order or second order depending on the strength of the line tension associated with to the wedge bottom. This fact implies the existence of a tricritical point characterized by a short-distance expansion which differs from the usual continuous filling transition. Our analysis is based on an effective one-dimensional model for the 3D wedge filling which arises from the identification of the breather modes as the only relevant interfacial fluctuations. From such analysis we find a correspondence between continuous 3D filling at bulk coexistence and 2D wetting transitions with random-bond disorder., Comment: 7 pages, 3 figures, 6th Liquid Matter Conference Proceedings (to be published in J. Phys.: Condens. Matter)

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively., Comment: 7 pages, 3 figures, accepted for publication in Europhysics Letters

The liquid-gas transition of an electroneutral mixture of oppositely charged colloids, studied by Monte Carlo simulations, is found in the low temperature -- low density region. The critical temperature shows a non-monotonous behavior as a function of the interaction range, $\kappa^{-1}$, with a maximum at $\kappa \sigma \approx 10$, implying an island of coexistence in the $\kappa$-$\rho$ plane. The system is arranged in such a way that each particle is surrounded by shells of particles with alternating charge. In contrast with the electrolyte primitive model, both neutral and charged clusters are obtained in the vapor phase, Comment: 6 pages

We have employed the Density Functional Theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyse the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropic-like to nematic-like states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interface-like states which allow to continuously transform the nematic-like phase to the isotropic-like phase without undergoing a phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematic-like state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematic-like state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematic-like states., Comment: 31 pages, 10 figures, submitted to J. Chem. Phys

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential \emph{functional} depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition., Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Lett

We investigate interfacial structural and fluctuation effects occurring at continuous filling transitions in 3D wedge geometries. We show that fluctuation-induced wedge covariance relations that have been reported recently for 2D filling and wetting have mean-field or classical analogues that apply to higher-dimensional systems. Classical wedge covariance emerges from analysis of filling in shallow wedges based on a simple interfacial Hamiltonian model and is supported by detailed numerical investigations of filling within a more microscopic Landau-like density functional theory. For sufficiently short-ranged forces mean-field predictions for the filling critical exponents and covariance are destroyed by pseudo-one-dimensional interfacial fluctuations. In this filling fluctuation regime we argue that the critical exponents describing the divergence of lengthscales are related to values of the interfacial wandering exponent $\zeta(d)$ defined for planar interfaces in (bulk) two-dimensional ($d=2$) and three-dimensional ($d=3$) systems, recovering the known results for pure (thermal disorder) systems and predicting universal critical exponents for the case of random-bond disorder. Finally we revisit the transfer matrix theory of three-dimensional filling based on an effective interfacial Hamiltonian model and discuss the interplay between breather, tilt and torsional interfacial fluctuations., Comment: 30 pages, 9 figures, submitted to J. Phys.: Condens. Matter

Interfacial structure and correlation functions near a two-dimensional (2D) wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant., Comment: 14 two-column pages, 3 figures, submitted to Physical Review E

Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group (RG) and mean field analysis (MF) shows this covariance is obeyed in 2D, 3D and for long and short ranged forces. This connection should be experimentally accesible and provides a means of checking theoretical predictions for critical wetting., Comment: 4 pages, 1 figure, submitted to Physical Review Letters

We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere the physical mechanism involved in the appearance of these phase diagrams, leading to an enhanced tendency to phase separate below the lower critical solution point. Three different cases are considered: a planar solid surface in contact with a bulk fluid, while the other two represent two models of porous systems, namely a slit and an array on infinitely long parallel cylinders. We confirm that surface transitions, as well as capillary transitions for a large area/volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed., Comment: 12 two-column pages, 12 figures, accepted for publication in Physical Review E; corrected version

We present a systematic study of the effect of the ion pairing on the gas-liquid phase transition of hard-core 1:1 electrolyte models. We study a class of dipolar dimer models that depend on a parameter R_c, the maximum separation between the ions that compose the dimer. This parameter can vary from sigma_{+/-} that corresponds to the tightly tethered dipolar dimer model, to R_c --> infinity, that corresponds to the Stillinger-Lovett description of the free ion system. The coexistence curve and critical point parameters are obtained as a function of R_c by grand canonical Monte Carlo techniques. Our results show that this dependence is smooth but non-monotonic and converges asymptotically towards the free ion case for relatively small values of R_c. This fact allows us to describe the gas-liquid transition in the free ion model as a transition between two dimerized fluid phases. The role of the unpaired ions can be considered as a perturbation of this picture., Comment: 16 pages, 13 figures, submitted to Physical Review E

The effect of confinement on the orientational structure of a nematic liquid crystal model has been investigated by using a version of density-functional theory (DFT). We have focused on the case of a nematic confined by opposing flat surfaces, in slab geometry (slit pore), which favor planar molecular alignment (parallel to the surface) and homeotropic alignment (perpendicular to the surface), respectively. The spatial dependence of the tilt angle of the director with respect to the surface normal has been studied, as well as the tensorial order parameter describing the molecular order around the director. For a pore of given width, we find that, for weak surface fields, the alignment of the nematic director is perpendicular to the surface in a region next to the surface favoring homeotropic alignment, and parallel along the rest of the pore, with a interface separating these regions (S phase). For strong surface fields, the director is distorted uniformly, the tilt angle exhibiting a linear dependence with the distance normal to the surface (L phase). Our calculations reveal the existence of a first-order transition between the two director configurations, which is driven by changes in the surface field strength, and also by changes in the pore width. In the latter case the transition occurs, for a given surface field, between the S phase for narrow pores and the L phase for wider pores. A link between the L-S transition and the anchoring transition observed for the semi-infinite case is proposed. We also provide calculations with a phenomenological approach that yields the same main result that DFT in the scale length where this is valid., Comment: submitted to PRE

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma_{-}/\sigma_{+}=1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma_{+-}=(sigma_{+} + sigma_{-})/2 relevant for the low densities in question, both Tc* (=kB Tc sigma_{+-}/q^2 and rhoc* (= rhoc sigma _{+-}^{3}) decrease rapidly (from ~ 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with Tc* lower by ~ 0-11% and rhoc* greater by 37-12%)., Comment: 4 pages, 5 figures