Micelle Formation in Aqueous Solutions of Room Temperature Ionic Liquids: A Molecular Dynamics Study.

1-Alkyl-3-methylimidazolium cations in the presence of water are used as a test system to study by molecular dynamics the formation of micelles in aqueous mixtures of highly anisotropic room temperature ionic liquids (IL). Structural properties, i.e., radial distribution functions (RDF) and transport parameters, such as diffusion coefficients and conductivities, are computed as a function of the IL/water mole fraction. The concentration plots reveal a sharp change of the slope of both the cation self-diffusion coefficient and the first peak of the head-head RDF at approximately the same value of the concentration. This transition, considered as a measure of a critical micellar concentration, appears only for the most anisotropic systems, composed of longer alkyl chains. The formation of the micelles is confirmed from the analysis of the tail-tail and cation-water RDFs. As a general result, we found that the larger the anisotropy of the ionic liquid the lower the critical concentration and the larger the proportion of monomers forming part of the micelles. The molecular dynamics predictions are in line with the experimental evidence reported for these systems.

Flue gas adsorption by single-wall carbon nanotubes: A Monte Carlo study.

Adsorption of flue gases by single-wall carbon nanotubes (SWCNT) has been studied by means of Monte Carlo simulations. The flue gas is modeled as a ternary mixture of N2, CO2, and O2, emulating realistic compositions of the emissions from power plants. The adsorbed flue gas is in equilibrium with a bulk gas characterized by temperature T, pressure p, and mixture composition. We have considered different SWCNTs with different chiralities and diameters in a range between 7 and 20 Å. Our results show that the CO2 adsorption properties depend mainly on the bulk flue gas thermodynamic conditions and the SWCNT diameter. Narrow SWCNTs with diameter around 7 Å show high CO2 adsorption capacity and selectivity, but they decrease abruptly as the SWCNT diameter is increased. For wide SWCNT, CO2 adsorption capacity and selectivity, much smaller in value than for the narrow case, decrease mildly with the SWCNT diameter. In the intermediate range of SWCNT diameters, the CO2 adsorption properties may show a peculiar behavior, which depend strongly on the bulk flue gas conditions. Thus, for high bulk CO2 concentrations and low temperatures, the CO2 adsorption capacity remains high in a wide range of SWCNT diameters, although the corresponding selectivity is moderate. We correlate these findings with the microscopic structure of the adsorbed gas inside the SWCNTs.

Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate.

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 favors homeotropic anchoring as a function of the wave number of the surface structure q, the tilt angle α, and the surface anchoring strength w. In addition to the previously reported nonanalytic 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 characterize this term, finding that it has two contributions: the deviations of the nematic director field with respect to a reference field 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.

Nematic wetting and filling of crenellated surfaces.

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau-de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.

Computer simulations of nematic drops: coupling between drop shape and nematic order.

We perform Monte Carlo computer simulations of nematic drops in equilibrium with their vapor using a Gay-Berne interaction between the rod-like molecules. To generate the drops, we initially perform NPT simulations close to the nematic-vapor coexistence region, allow the system to equilibrate and subsequently induce a sudden volume expansion, followed with NVT simulations. The resultant drops coexist with their vapor and are generally not spherical but elongated, have the rod-like particles tangentially aligned at the surface and an overall nematic orientation along the main axis of the drop. We find that the drop eccentricity increases with increasing molecular elongation, κ. For small κ the nematic texture in the drop is bipolar with two surface defects, or boojums, maximizing their distance along this same axis. For sufficiently high κ, the shape of the drop becomes singular in the vicinity of the defects, and there is a crossover to an almost homogeneous texture; this reflects a transition from a spheroidal to a spindle-like drop.

The order of filling transitions in acute wedges.

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.

Filling and wetting transitions of nematic liquid crystals on sinusoidal substrates.

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 observed only for a same substrate in a narrow range of amplitudes.

Derivation of a non-local interfacial model for 3D wetting in an external field.

We extend recent studies of 3D short-ranged wetting transitions by deriving an interfacial Hamiltonian in the presence of an arbitrary external field. The binding potential functional, describing the interaction of the interface and the substrate, can still be written in a diagrammatic form, but now includes new classes of diagrams due to the coupling to the external potential, which are determined exactly. Applications to systems with long-ranged (algebraically decaying) and short-ranged (exponentially decaying) external potentials are considered at length. We show how the familiar 'sharp-kink' approximation to the binding potential emerges, and determine the corrections to this arising from interactions between bulk-like fluctuations and the external field. A connection is made with earlier local effective interfacial Hamiltonian approaches. It is shown that, for the case of an exponentially decaying potential, non-local effects have a particularly strong influence on the approach to the critical regime at second-order wetting transitions, even when they appear to be sub-dominant. This is confirmed by Monte Carlo simulation studies of a discretized version of a non-local interfacial model.

3D short-range wetting and nonlocality.

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.

Wetting transition of a nematic liquid crystal on a periodic wedge-structured substrate.

It is known that the wetting behaviour of a fluid is deeply altered by the presence of rough or structured substrates. We first review some simple considerations about isotropic fluids and rough substrates, and then we generalize Wenzel's law, which assigns an effective contact angle to a droplet on a rough substrate, when the wetting layer has an ordered phase, like a nematic. We estimate the conditions for which the wetting behavior of an ordered fluid can be qualitatively different from that usually found in a simple fluid. To support our general considerations, we use the Landau-de Gennes mean field approach to investigate theoretically and numerically the wetting transition of a nematic phase on a periodic triangular structured substrate.

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: II. General diagrammatic structure.

In our first paper, we showed how a non-local effective Hamiltonian 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 zigzag 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.

Freezing of hard spheres confined in narrow cylindrical pores.

Monte Carlo simulations for the equation of state and phase behavior of hard spheres confined inside very narrow hard tubes are presented. For pores whose radii are greater than 1.1 hard sphere diameters, a sudden change in the density and the microscopic structure of the fluid is neatly observed, indicating the onset of freezing. In the high-density structure the particles rearrange in such a way that groups of three particles fit in sections across the pore.

Liquid-gas separation in colloidal electrolytes.

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 nonmonotonous behavior as a function of the interaction range, kappa(-1), with a maximum at kappasigma approximately 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.

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

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Green's function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the small-gradient limit.

Density functional theory study of the nematic-isotropic transition in an hybrid cell.

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 analyze 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 isotropiclike to nematiclike 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 interfacelike states which allow us to continuously transform the nematiclike phase to the isotropiclike phase without undergoing a sharp phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematiclike 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 nematiclike state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematiclike states.

Nonlocality and short-range wetting phenomena.

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike 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 nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study.

Interfacial structure and correlation functions near a two-dimensional 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.

Surface and capillary transitions in an associating binary mixture model.

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 that displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere with 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 surface area to volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.

Fluid adsorption near an apex: covariance between complete and critical wetting.

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, and mean-field analysis show that this covariance is obeyed in 2D and 3D and for long- and short-ranged forces. This connection should be experimentally accessible and provides a means of checking theoretical predictions for critical wetting.

Dipolar origin of the gas-liquid coexistence of the hard-core 1:1 electrolyte model.

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 nonmonotonic 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.