Fluid-wall Potential Research Articles

Extension of the effective solid-fluid Steele potential for Mie force fields

Molecular simulation of fluid systems in the presence of surfaces require computationally expensive calculations due to the large number of solid–fluid pair interactions involved. Representing the explicit solid as a continuous wall with an effective potential can significantly reduce the computational time and allows exploring larger temporal and spatial scales. The well-known (10-4-3) Steele potential is one such analytic expression that faithfully represents the effective solid–fluid interactions for homonuclear crystalline solids with hexagonal lattice symmetry. However, this and most of the effective potentials found in the literature have been developed for fluids and solids interacting exclusively through Lennard-Jones potentials. In this work, we extend the Steele model to obtain the effective wall–fluid potentials for Mie force fields. We perform molecular dynamics simulations of coarse-grained fluids modelled via the SAFT force field approach in the presence of explicit and implicit surfaces to compare structural and dynamic properties in both representations. Also, we study the adsorption of ethane into slit-like pores with explicit and implicit surfaces via grand canonical Monte Carlo simulations. We explore the validity and the improvement in the simulation performance as well as the limitations of the proposed expression.

Adsorption behaviors of supercritical Lennard-Jones fluid in slit-like pores

Understanding the adsorption behaviors of supercritical fluid in confined space is pivotal for coupling the supercritical technology and the membrane separation technology. Based on grand canonical Monte Carlo simulations, the adsorption behaviors of a Lennard-Jones (LJ) fluid in slit-like pores at reduced temperatures over the critical temperature, Tc* = 1.312, are investigated; and impacts of the wall-fluid interactions, the pore width, and the temperature are taken into account. It is found that even if under supercritical conditions, the LJ fluid can undergo a “vapor-liquid phase transition” in confined space, i.e., the adsorption density undergoes a sudden increase with the bulk density. A greater wall-fluid attractive potential, a smaller pore width, and a lower temperature will bring about a stronger confinement effect. Besides, the adsorption pressure reaches a local minimum when the bulk density equals to a certain value, independent of the wall-fluid potential or pore width. The insights in this work have both practical and theoretical significances.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory.

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν∥, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring.

In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.

Investigation of some well known bulk fluid regularities for Lennard–Jones confined fluid in nanoslit pore

The modified fundamental measure theory has been employed to investigate some well known regularities of bulk fluid for the Lennard–Jones fluid confined in nanoslit pore. The regularities investigated include common compression point, common bulk modulus point, Tait–Murnaghan equation, and the linear regularity between pressure and temperature for each isochore. All these regularities have been investigated for two different components of pressure for confined fluid. Our results show that the common compression and common bulk modulus point remain valid for fluids confined in nanoslit pores of different sizes and with different wall–fluid potentials. The density of the common compression and common bulk modulus point are different from corresponding ones for the bulk fluid. Our observations also show that the Tait–Murnaghan equation and pressure–temperature linear regularity also hold for confined fluid. The sign of the intercept of pressure–temperature regularity is determined by the difference between attraction and repulsion terms in the compressibility factor.

Prediction of n-Alkane Adsorption on Activated Carbon Using the SAFT–FMT–DFT Approach

The SAFT–FMT–DFT approach to adsorption equilibrium combines elements of the statistical associating fluid theory (SAFT), fundamental measure theory (FMT), and classical density functional theory (DFT) to create a framework to model fluids described as chain molecules in the presence of external fields. In this paper, the SAFT–FMT–DFT approach is used to calculate single pore isotherms to develop a pore size distribution for BPL activated carbon, described by the 10–4–3 fluid-wall potential, based on nitrogen adsorption at 77 K. The nitrogen pore isotherms show a progression of monolayer transitions, pore filling, and pore condensation. The pore size distribution is used to predict excess adsorption isotherms for methane, ethane, n-butane, n-pentane, and n-hexane adsorbed on the carbon at 298.15 and 348.15 K. Parameters for interaction of the molecules with the solid are obtained using experimental data for adsorption of each alkane on the planar wall of a nonporous graphitized carbon. The predicted excess n-alkane isotherms agree well with experimental isotherms.

Density functional study of complete, first-order and critical wedge filling transitions

We present numerical studies of complete, first-order and critical wedge filling transitions, at a right angle corner, using a microscopic fundamental measure density functional theory. We consider systems with short-ranged, cut-off Lennard-Jones, fluid–fluid forces and two types of wall–fluid potential: a purely repulsive hard wall and also a long-ranged potential with three different strengths. For each of these systems we first determine the wetting properties occurring at a planar wall, including any wetting transition and the dependence of the contact angle on temperature. The hard wall corner is completely filled by vapour on approaching bulk coexistence and the numerical results for the growth of the meniscus thickness are in excellent agreement with effective Hamiltonian predictions for the critical exponents and amplitudes, at leading and next-to-leading order. In the presence of the attractive wall–fluid interaction, the corresponding planar wall–fluid interface exhibits a first-order wetting transition for each of the interaction strengths considered. In the right angle wedge geometry the two strongest interactions produce first-order filling transitions while for the weakest interaction strength, for which wetting and filling occur closest to the bulk critical point, the filling transition is second-order. For this continuous transition the critical exponent describing the divergence of the meniscus thickness is found to be in good agreement with effective Hamiltonian predictions.

Two interacting particles in a spherical pore

In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrate and between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle density distribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhard interaction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle. We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding a spherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hard wall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-null zero order term in the Tolman length.

Simulation study of the disjoining pressure profile through a three-phase contact line

Computer simulations are performed to measure the disjoining pressure profile Pi(y) across the three-phase contact line formed by a liquid-vapor interface intersecting a planar substrate wall lying in the xy plane. The method makes use of an exact expression for the disjoining pressure in terms of the density profile and the wall-fluid interaction. Pi(y) is reported for three distinct values of the wall-fluid attractive potential, representing differing levels of partial wetting by macroscopic adsorbed drops. Mechanical force-balance normal to the substrate is confirmed by direct evaluation of the required analog to Young's equation. For the model system under study, the disjoining pressure profiles are well-fitted by inverted Gaussians. The fitted results are used with an extension (to large values of Young's contact angle theta) of the interface Hamiltonian theory of Indekeu, thereby enabling us to report the line tension tau(theta).

Impact of surface charges on the solvation forces in confined colloidal solutions

Combining computer simulations and experiments we address the impact of charged surfaces on the solvation forces of a confined, charged colloidal suspension (slit-pore geometry). Investigations based on the colloidal-probe atomic-force-microscope technique indicate that an increase in surface charges markedly enhances the oscillations of the force in terms of their amplitude. To understand this effect on a theoretical level we perform grand-canonical Monte-Carlo simulations (GCMC) of a coarse-grained model system. It turns out that various established approaches of the interaction between a charged colloid and a charged wall, such as linearized Poisson-Boltzmann (PB) theory involving the bulk screening length, do not reproduce the experimental observations. We thus introduce a modified PB potential with a space-dependent screening parameter. The latter takes into account, in an approximate way, the fact that the charged walls release additional (wall) counterions which accumulate in a thin layer at the surface(s). The resulting, still purely repulsive fluid-wall potential displays a nonmonotonic behavior as function of the surface potential with respect to the strength and range of repulsion. GCMC simulations based on this potential reproduce the experimentally observed charge-induced enhancement in the force oscillations. We also show, both by experiment and by simulations, that the asymptotic wave- and decay length of the oscillating force do not change with the wall charge, in agreement with predictions from density functional theory.

A stepwise approximation for modeling of the wall–fluid potential of a mesoscopic pore

A common computational method for the characterization of porous materials is to calculate the adsorption isotherm of fluids in the materials from the preassumed wall–fluid potential. If the wall–fluid potential is unknown, the common computational method becomes invalid. In a realistic experiment, however, it is common to know the experimental adsorption isotherm of nitrogen and not to know the wall–fluid potential. Here we propose a stepwise approximation for modeling wall–fluid potential under conditions where only the adsorption isotherm of nitrogen is measured experimentally. Based on the modeled wall–fluid potential, we can characterize the porous materials and predict the adsorption of other adsorbates on the materials. It is expected that the approach would provide a powerful means for the characterization of novel materials under conditions where only the experimental adsorption isotherm is available.

Square-well fluids in confined space with discretely attractive wall-fluid potentials: Critical point shift

In this work the effects of the wall-fluid interaction on the critical point shift are studied by using a discrete and attractive wall-fluid interaction and density functional theory. In contrast to the previous assumption, it is found that the dependence of critical temperature shift on the wall-fluid interaction does not simply show a monotonic manner, but increases with the strength of the interaction for weak surfaces, then decreases for strong surfaces. The similar trend holds for the systems with different fluid-fluid interactions and different confined spaces. Unlike the capillary critical temperature, the critical density of square-well fluids in a confined space increases monotonically as the wall-fluid interaction becomes more attractive.

Mesoscopic modeling of a two-phase flow in the presence of boundaries: The contact angle

We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone [J. Fluid. Mech. 489, 55 (2003)] and J. Philip [Z. Angew. Math. Phys. 23, 960 (1972)] for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen [Phys. Rev. E 49, 2941 (1994)] and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

Behavior of a wetting phase near a solid boundary: vapor near a weakly attractive surface

Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed.

Statistical mechanics of fluids adsorbed in planar wedges: finite contact angle.

I consider the statistical mechanics of inhomogeneous fluids applied to fluids adsorbed in planar wedges. Exact results are described that belong to an infinite subset of models defined as the intersection of any two identical semi-infinite planar wall-fluid potentials. This geometry is interesting as a generic example of adsorption onto structured interfaces and of interfacial phase transitions controlled by the substrate geometry. Previously described virial theorems are extended to the case of a general wall-fluid model. This enables the consideration of wedge filling when Young's contact angle far from the wedge apex is finite. The virial theorems generate two important relations: the wedge sum rules. The first sum rule links the interfacial free energy far from the wedge apex to the structure induced at the apex. The second sum rule links the free energy of the apex region to the structure induced by the apex. When Young's contact angle at the wedge walls is finite these relations further yield an exact result for the macroscopic contact angle in terms of the nanoscopic structure at the three-phase contact line (the intersection of the liquid-vapor surface with a wedge wall): the contact angle sum rule. These exact results are of direct relevance to computer simulation studies of adsorbed films. In addition, they take on special significance in the vicinity of continuous interfacial phase transitions: an approach to complete filling and the filling transition at bulk liquid-vapor coexistence.

Lennard-Jones fluids confined in nanoscopic slits: evidence for reentrant filling transitions.

By using grand canonical and canonical ensemble Monte Carlo simulations, the structure and phase behavior of a Lennard-Jones (LJ) fluid confined between the parallel (100) planes of a face-centered cubic crystal are studied. Slit pores with a width which allows three adsorbate layers to form are used. It is shown that the filled pore consists of three commensurate layers over a wide range of the surface potential strength, while the pore-filling mechanism and the topology of the phase diagram change when the strength of this fluid-wall potential is varied. Condensation may occur in one step or via two layering-like transitions. The structure of monolayer films depends on the strength and corrugation of the surface potential, and the condensation of the middle layer may induce a reentrant first-order transition.

Solvation force for long-ranged wall--fluid potentials.

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long-ranged wall-fluid potentials decaying as -Az(-p),z--> infinity, for various values of p. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field h=0 by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force f(solv) for the Ising film is repulsive and decays for large wall separations L in the same fashion as the boundary field f(solv) approximately L(-p), whereas for temperatures larger than the bulk critical temperature f(solv) is attractive and the asymptotic decay is f(solv) approximately L(-(p+1)). For the LJ fluid system f(solv) is always repulsive away from the critical region and decays for large L with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behavior of the solvation force.

The structure of fluids confined in crystalline slitlike nanoscopic pores: bilayers.

Grand canonical and canonical ensemble Monte Carlo simulation methods are used to study the structure and phase behavior of Lennard-Jones fluids confined between the parallel (100) planes of the face centered cubic crystal. Ultra thin slit pores of the width allowing for the formation of only two adsorbate layers are considered. It is demonstrated that the structure of adsorbed phases is very sensitive to the wall-wall separation and to the strength of the fluid-wall potential. It is also shown that the structure of low temperature (solid) phases strongly depends on the fluid density. In particular, when the surface field is sufficiently strong, then the high density phases may exhibit a domain wall structure, quite the same as found in monolayer films adsorbed at a single substrate wall. On the other hand, the weakening of the surface potential leads to the regime in which only the hexagonally ordered bilayer structure is stable. The phase diagrams for a series of systems are estimated. It is shown that, depending on the pore width and the temperature, the condensation leads to the formation of the commensurate or incommensurate phases. The incommensurate phases may have the domain-wall or the hexagonal structure depending on the pore width and the strength of the fluid-wall potential.

Wetting in thebinary Gaussian core model

Using a simple mean-field density functional approach weinvestigate the adsorption of a binary fluid mixture ofrepulsive Gaussian core particles at a repulsive planar wall.For certain choices of wall-fluid potential we find afirst-order wetting transition, and the accompanying pre-wettingline, whereby the fluid phase rich in the larger speciescompletely wets the interface between the wall and the fluidphase rich in the smaller species. We show that in the completewetting regime the film thickness diverges as l~-l0ln (x-xcoex), where (x-xcoex) is the deviation inconcentration x of the smaller species from the bulk binodal,for all the (short-ranged) wall potentials that we have consideredbut the amplitude l0 depends on the precise details of thesepotentials.

Capillary Condensation in Pores with Energetically Heterogeneous Walls: Density Functional versus Monte Carlo Calculations

We investigate adsorption of a Lennard–Jones fluid in slit-like pores with energetically heterogeneous walls by using Grand Canonical Monte Carlo simulations and a density functional approach. The model of a fluid-wall potential is qualitatively similar to that invoked by Röcken et al. (J. Chem. Phys.108, 8089, (1999); i.e., it consists of a homogeneous part that varies in the direction perpendicular to the wall and a periodic part, varying also in one direction parallel to the wall, but in contrast to the above mentioned work, both parts of the fluid-wall potential are modeled by Lennard–Jones (9, 3) type functions. The structure of the adsorbed film is characterized by local densities. We evaluate the phase diagrams for several systems characterized by different corrugation of the adsorbing potential and discuss the discrepancies between theoretical predictions and computer simulations.