On the solvation force of water-like fluid models with square-well attraction and site–site association in slit-like pores: density functional approach

The solvation force of the water-like fluid models with square-well attraction and site–site chemical association confined to slit-like pores has been explored. Theoretical procedure is based on the application of the density functional approach with mean-field approximation for the attractive interparticle interactions. The chemical association effects are treated by using the first-order thermodynamic perturbation theory of Wertheim. Trends of behaviour of the solvation force are put in correspondence with the distribution of molecules in the pores and with the average density of the adsorbate. Moreover, the distribution of non-bonded species on pore width is described. The influence of the width of the square-well and of the gas–solid attraction is discussed. A comparison of theoretical predictions with computer simulations results for water models in slit-like pores is performed.     

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.     

A simulation study of the effects of adsorbent energy on the diffusion of molecules in slit pores: 1 commensurate slit widths

Equilibrium molecular dynamics simulation has been used to study the self-diffusion coefficients (from correlation of the molecular velocity) and the collective, or centre of mass diffusion coefficients (from correlation of the streaming velocity) of a Lennard-Jones fluid in model slit pores. The slit widths were chosen to be integer multiples of the Lennard-Jones adsorbate diameter, and therefore are close to being commensurate with layered adsorbate structures. Slits of reduced width H* = 3 and 5 were examined at a reduced temperature of T* = 1.0. The adsorbate densities ranged from 0.3 to 0.9 in reduced units. The adsorbent adsorbate interaction was modelled as a simple potential with inverse 4th power attraction plus hard wall repulsion, and systems with reduced parameter u₀* ranging from ?5 to +5 were studied. Molecule-wall scattering was represented by a diffuse reflection algorithm. The density distributions show strong layering in the attractive system, but this is absent in the most repulsive slits, except at very high densities. Self-diffusion is only weakly dependent on u₀* and slit width at high densities, but a strong dependence on u₀* appears at low densities. The collective diffusion coefficient is less easy to calculate with high accuracy; nevertheless, it is clear that there is a strong dependence of this property on u₀* Trajectory plots show zones in which the particles are more or less strongly localized, but undergo irregular oscillatory motion corresponding to regions of high density in the single-particle distributions.     

受限于对称性破缺狭缝间氢键流体的相平衡研究

利用密度泛函理论并结合改进的基本度量理论研究了受限于对称性破缺狭缝间氢键流体的相平衡. 首先根据氢键流体的吸附-脱附等温线及相应巨势获得不同条件下氢键流体的相图. 进一步讨论了氢键作用、狭缝间距、狭缝与流体分子间相互作用及对称性破缺程度等因素对氢键流体相平衡的影响. 结果表明, 由于狭缝与流体分子及流体分子间的相互作用存在竞争, 使得受限于对称性破缺条件下的氢键流体呈现更为复杂的相态特征.     

Absence of simulation evidence for critical depletion in slit pores

Recent Monte Carlo simulation studies of a Lennard-Jones fluid confined to a mesoscopic slit pore have reported evidence of "critical depletion" in the pore local number density near the liquid-vapor critical point. In this Brief Report we demonstrate that the observed depletion effect is in fact a simulation artifact arising from small systematic errors associated with the use of long range corrections for the potential truncation. Owing to the large near-critical compressibility, these errors lead to significant changes in the pore local number density. We suggest ways of avoiding similar problems in future studies of confined fluids.     

Thermal diffusion in micropores by molecular dynamics computer simulations

This work focuses on the identification of the main microscopic processes that influence thermal diffusion (the Soret effect) in a fluid mixture confined in an uncorrugated slit pore. To achieve this purpose, a boundary driven nonequilibrium molecular dynamics scheme is applied on binary mixtures of super-critical Lennard–Jones (LJ) spheres representing methane and n-decane. Following previous work, we perform a systematic study of the influence of the parameters used to describe a model slit pore on an effective thermal diffusion factor. Among these parameters are: The nature of the reflection of the diffusing particles on the walls (specular or diffusive), the pore width with respect to the particle size and the fluid-wall potential strength. Simulations were run both on equimolar and non-equimolar mixtures. The results indicate that thermal diffusion is effectively lowered only for strong fluid–wall interactions. It is shown that the general trends, which are different under sub- and super-critical conditions, can be explained by a careful analysis of the relative sorption energies of the two compounds.     

The effects of interaction range,porosity and molecular association on the phase equilibrium of a fluid confined in a disordered porous media

Grand-canonical transition-matrix Monte Carlo (GC-TMMC) is employed to analyse the effects of range of interaction, packing fraction and molecular association on phase coexistence properties of square-well (SW) based fluids in disordered pores. The nature of the phase equilibria were studied inside a repulsive disordered porous media with packing fractions, η _m = 0.05 and 0.10. Three values of the SW attractive well range parameter were studied: λ = 1.5, 1.75, and 2.0. Coexistence number probability distribution reflects the signature of the disordered structure of the porous matrix. Yet, no multiple fluid–fluid transition was observed. The effect of strength of molecular association on coexistence densities, density profile, saturation pressure, and monomer fraction for the SW based dimerizing fluids inside a repulsive disordered media is reported. Association is found to increase as the packing fraction of the matrix increase. Critical properties of these confined fluids are calculated via a rectilinear diameter approach. Fractional shift in the critical temperature linearly decreases with the increase in the attractive well width for non-associating fluids. The rate of decrease in the critical temperature shift increases with the increase in packing fraction. Associating sites are found to suppress the shift in the critical temperature.     

Equilibrium partitioning of a simple fluid in a matrix-filled cylindrical pores with adsorbing walls: A grand canonical Monte Carlo study

We have studied a model of a hard sphere fluid adsorbed in a cylindrical pore filled with quenched disordered matrix of hard sphere particles using Grand canonical Monte Carlo simulations. The interactions between matrix species and pore walls are assumed of a hard sphere type. However, the pore walls exert a short-range attraction upon adsorbed fluid particles. We discuss the adsorption isotherms and the density profiles of fluid particles in pores with different microporosity for several values of the pore radius. We have observed that like in homogeneous microporous media the adsorption increases with increasing porosity. However, trends of behavior of the isotherms also reflect layering of adsorbed fluid. The data obtained in this study may serve as a benchmark for the development of the theory of confined quenched-annealed systems and for computer simulation investigation of models permitting phase transitions in pores. This project has been supported in parts by DGAPA of the UNAM under research grant IN111597, by the National Council for Science and Technology (CONACyT), grant No. 25301-E.     

Freezing and melting of binary mixtures confined in a nanopore

This paper reports on a Grand Canonical Monte Carlo study of the freezing and melting of Lennard–Jones Ar/Kr mixtures confined in a slit pore composed of two strongly attractive structureless walls. For all molar compositions and temperatures, the pore, which has a width of 1.44?nm, accommodates two contact layers and one inner layer. Different wall/fluid interactions are considered, corresponding to pore walls that have a larger affinity for either Ar or Kr. The solid/liquid phase diagram of the confined mixture is determined and results compared with data for the bulk mixture. The structure of the confined mixture is studied using 2D order parameters and both positional g(r) and bond orientational G₆(r) pair correlation functions. It is found that in the confined solid phase, both the contact and inner layers have a hexagonal crystal structure. It is shown that the freezing temperature of the Ar/Kr confined mixture is higher than the bulk freezing point for all molar compositions. Also, it is found that the freezing temperature becomes larger as the ratio α of the wall/fluid to the fluid/fluid interactions increases, in agreement with previous simulation studies on pure substances confined in nanopores. In the case of pore walls having a stronger affinity for Kr atoms (ε _Ar/W<ε _Kr/W), it is observed that both the contact and inner layers of the confined mixture undergo, at the same temperature, a transition from the liquid phase to the crystal phase. The freezing of Ar/Kr mixtures confined between the walls having a stronger affinity for Ar (ε _Ar/W?>?ε _Kr/W) is more complex: for Kr molar concentration lower than 0.35, we observe the presence of an intermediate state between all layers being 2D hexagonal crystals and all the layers being liquid. This intermediate state consists of a crystalline contact layer and a liquid-like inner layer. It is also shown that the qualitative variations of the increase of freezing temperature with the molar composition depend on the affinity of the pore wall for the different components. These results confirm that, in addition to the parameter α the ratio of the wall/fluid interactions for the two species, η=?_Ar/W/?_Kr/W, is a key variable in determining the freezing and melting behaviour of the confined mixture.     

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

Based on the free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard-Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for the design and characterization of novel materials.     

Further observations on the polarized absorption spectrum of benzene crystals at 2000 Å

The structure of a hard sphere fluid confined by model slit and cylindrical pores is investigated. Results from grand canonical Monte Carlo (GCMC) simulations and from the hypernetted chain/mean spherical approximation (HNC/MSA) equation are reported. GCMC results are compared with those from the HNC/MSA equation, and agreement is good. The effect of confinement on liquids at the same chemical potentials is that the absorption of the hard sphere fluid into the pores decreases with increasing confinement, i.e., when going from planar to cylindrical geometry or by narrowing the pores. The adsorption on the pore walls has, in general, the opposite behaviour. For high bulk concentrations and certain values of cylindrical pore diameter the concentration profile is higher at the centre of the pore than next to the pore wall. A very strong, but continuous, transition occurs in the concentration profile, as a function of the cylinder's diameter. These results could be of some interest in catalysis studies.     

The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

Structure of liquid-vapor interface of square well fluid confined in a cylindrical pore

By means of the canonical Monte Carlo simulations, the vapor-liquid (VL) equilibrium and structure of square well (SW) fluids confined in a single cylindrical pore with repulsive surface, have been studied. Coexistence curves of the confined VL interface are determined for a wide range of temperatures and pore diameters. It is demonstrated that the confinement not only reduces the VL coexistence region but also induces strong inhomogeneities of the VL interface: coexistence liquid densities are different at the pore center and at the wall surface. It may be considered as a preliminary step for an isolated droplet formation inside the pore, as well as a tentative reason of the two VL phase transitions of simple fluids adsorbed into disordered porous media.     

Investigation of vapour--liquid nucleation properties for spherical and chain-like fluids by density functional theory

The excess Helmholtz free energy functional for nonpolar chain-like molecules is formulated in terms of a weighted density approximation （WDA） for short-range interactions and a Weaks Chandler Andersen （WCA） approximation and a Barker Henderson （BH） theory for long-range attraction. Within the framework of density functional theory （DFT）, vapour liquid interracial properties including density profile and surface tension, and vapour-liquid nucleation properties including density profile, work of formation and number of particles are investigated for spherical and chain- like molecules. The obtained vapour liquid surface tension and the number of particles in critical nucleus for Lennard- Jones （L J） fluids are consistent with the simulation results. The influences of supersaturation, temperature and chain length on vapour liquid nucleation properties are discussed.[第一段]     

D2/H2 quantum sieving in microporous carbons: a theoretical study on the effects of pore size and pressure

The adsorption of hydrogen and deuterium in slit-shaped carbon pores is studied by grand canonical Monte Carlo simulations. All interactions are assumed to be of Lennard–Jones type, while the Feynman–Hibbs expression is used to account for quantum effects. The interaction energy of both isotopes inside the slit pore space is discussed thoroughly. Furthermore, pure component adsorption isotherms of both isotopes were simulated at 77?K for pressures up to 20?bar in slit pores having widths of up to 2.0?nm. According to our simulations, in equilibrium, slit pores reveal slight deuterium selectivity over hydrogen, and this quantum-based selectivity depends both on pressure and pore size.     

Diffusion within a near-critical nanopore fluid

Results are presented for grand canonical Monte Carlo (GCMC) and both equilibrium and non-equilibrium molecular dynamics simulations (EMD and NEMD) conducted over a range of densities and temperatures that span the two-phase coexistence and supercritical regions for a pure fluid adsorbed within a model crystalline nanopore. The GCMC simulations provided the low temperature coexistence points for the open pore fluid and were used to locate the capillary critical temperature for the system. The equilibrium configurational states obtained from these simulations were then used as input data for the EMD simulations in which the self-diffusion coefficients were computed using the Einstein equation. NEMD colour diffusion simulations were also conducted to validate the use of a system averaged Einstein analysis for this inhomogeneous fluid. In all cases excellent agreement was observed between the equilibrium (linear response theory) predictions for the diffusivities and non-equilibrium colour diffusivities. The simulation results are also compared with a recently published quasi-hydrodynamic theory of Pozhar and Gubbins (Pozhar, L. A., and Gubbins, K. E., 1993, J. Chem. Phys., 99, 8970; 1997, Phys. Rev. E, 56, 5367.). The model fluid and the nature of the fluid wall interactions employed conform to the decomposition of the particle–particle interaction potential explicitly used by Pozhar and Gubbins. The local self-diffusivity was calculated from the local fluid–fluid and fluid wall hard core collision frequencies. While this theory provides reasonable results at moderate pore fluid densities, poor agreement is observed in the low density limit.     

Adsorption isotherm of a Lennard-Jones nitrogen in a carbon slitlike pore

A density functional perturbation approximation based both on second-order perturbation theory and on the pore average density has been proposed to study the adsorption hysteresis of nitrogen in a carbon slit pore. The main advantage of the present approximation is that it is computationally much simpler than the original density functional approximation based on the second-order perturbation theory of liquids, and can be applied to several model fluids confined in a strong external field in order to study their structural and thermodynamic properties. The calculated adsorption hysteresis for the confined Lennard-Jones nitrogen is in very good agreement with computer simulation, even if its accuracy slightly deteriorates for the desorption branch. The calculated equilibrium particle density distributions also compare well with computer simulations, and are better than those of a density functional theory based on the so-called mean-field approximation.     

Evaluation of bridge function for hard sphere fluid confined in a narrow slit-pore via TMMC Mayer-sampling

The bridge function required to yield a singlet integral equation (IE) up to the second order in density expansion for the hard sphere fluid confined in a slit-pore is evaluated. The slit-fluid bridge function can be divided into wall-particle bridge diagrams with h _b-bond, which were evaluated by recently proposed Transition Matrix Monte Carlo (TMMC) Mayer-sampling method. The bulk-fluid total correlation function h _b(r) used in cluster integrals is determined by solution of the bulk-fluid Ornstein–Zernike (OZ) equation with a hypernetted chain closure (HNC). The calculation is performed for the reduced density of bulk fluid in equilibrium with the fluid in slit-pores from 0.3 to 0.7 with narrow slit width of 3.0σ and 4.0σ. The quantity of the slit-fluid bridge function is assessed by comparison of the density profile obtained from the singlet IE theory and the grand canonical Monte Carlo (GCMC) simulation. Good agreement between the proposed approach and the GCMC data is observed. The reduced normal pressure is also calculated, and agrees well with the simulation data at low to medium densities but becomes a little larger at high density. It is expected that the result can be improved by adding higher order bridge coefficients. The direct evaluation of the slit-fluid bridge function seems to be practical since a great improvement of the quality of the singlet IE theory has been achieved for predicting the structural and thermodynamic properties of fluids confined in narrow slit pores.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Wall mediated transport in confined spaces: exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.