The structure of fluids confined in crystalline slitlike nanoscopic pores

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. Thin slit pores with a width allowing for the formation of only up to five atomic layers are considered. The phase diagrams of the systems characterized by different pore width as well as by different strength of the fluid-pore walls potential are determined. It is shown that an enormously large number of different phase diagram topologies can occur, depending on the parameters of the problem (pore width, strength of the fluid-pore walls potential, etc).     

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.     

Phase behavior of ionic fluids in slitlike pores: a density functional approach for the restricted primitive model

We present a density functional theory of nonuniform ionic fluids. This theory is based on the application of the electrostatic contribution to the free energy functional arising from mean spherical approximation for a bulk restricted primitive model and from the energy route bulk equation of state. In order to employ this functional we define a reference fluid and additional averaged densities, according to the approach introduced by Gillespie, Nonner and Eisenberg [J. Phys.: Condens. Matter 14, 12129 (2002)]. In the case of bulk systems the proposed theory reduces to the mean spherical approximation equation of state, arising from the energy route and thus it predicts the first-order phase transition. We use this theory to investigate the effects of confinement on the liquid-vapor equilibria. Two cases are considered, namely an electrolyte confined to the pore with uncharged walls and with charged walls. The dependence of the capillary evaporation diagrams on the pore width and on the electrostatic potential is determined.     

Phase behavior of the restricted primitive model of ionic fluids with association in slitlike pores. Density-functional approach

We present results of investigations of condensation of restricted primitive model of electrolyte solutions with association between oppositely charged ions confined to slitlike pores. The associative interaction leads to the formation of ionic pairs. It is accounted for by incorporating the first-order thermodynamic perturbation theory into the free energy functional. In order to elucidate the role of association, the phase diagrams are compared with those obtained by us recently [O. Pizio et al., J. Chem. Phys. 121, 11957 (2004)] for the restricted primitive model. The inclusion of the association into the theory leads to lowering the critical temperature for the fluid confined to pores with uncharged and with charged walls. We have observed that the average fraction of bonded ions is high along the coexistence envelope.     

Density functional description of adsorption in slitlike pores modified with chain molecules: a simple model for pillaredlike materials

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in slitlike pores modified by chain molecules. Specifically, the chains are bonded by their ends to the opposite pore walls, so they can form pillaredlike structure. Two models are studied. In the first model, the nonterminating segments of chains can change their configuration inside the pore upon adsorption of spherical species. In the second model, the chains configuration remains fixed, so that the system is similar to a nonuniform quenched-annealed mixture. We study capillary condensation of fluid species inside such modified pores and compare the results obtained for two models.     

Adsorption of fluids in slitlike pores containing a small amount of mobile ions

We apply density functional theory to investigate changes in the phase behavior of a fluid caused by the presence of mobile ions inside the pore. The approach has been based on the fundamental measure density functional theory and on the theory of nonuniform electrolytes developed recently by O. Pizio, A. Patrykiejew, S. Soko?owski [J. Chem. Phys. 121 (2005) 11,957]. We have evaluated capillary condensation phase diagrams for pores of different widths and for different concentrations of confined ions. The calculations have demonstrated that the presence of ions leads to lowering the critical temperature and to an increase of the value of the chemical potential at the capillary condensation point.     

A computational study of the chromatographic separation of racemic mixtures

Summary A model is devised using molecular mechanics to simulate chromatographic separations of enantiomers. Theoretical results derived from this model are compared with experimental findings obtained using supercritical fluid chromatography. The model is then developed to incorporate the effects of binding the stationary phase to a matrix. Computed results show that addition of the matrix into the model has significant effects on the ability of the stationary phase to separate racemic mixtures.     

A computational study of the chromatographic separation of racemic mixtures

Summary A model is devised using molecular mechanics to simulate chromatographic separations of enantiomers. Theoretical results derived from this model are compared with experimental findings obtained using supercritical fluid chromatography. The model is then developed to incorporate the effects of binding the stationary phase to a matrix. Computed results show that addition of the matrix into the model has significant effects on the ability of the stationary phase to separate racemic mixtures.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Permethylated cyclodextrins in the GC separation of racemic mixtures of volatiles: Part 1

The chromatographic separation of racemic mixtures of volatile compounds by 2,3,6-trimethyl-α-, β- and γ-cyclodextrins is discussed. Columns were prepared by mixing the derivatized cyclodextrin with OV-1701 or hydroxy-terminated OV-1701 (OV-1701-OH) following Schurig's method [1]. About 130 racemates with widely differing structures were used to test the performances of 2,3,6-permethylated-α, β- and, γ-cyclodextrins mixed with the polysiloxane polymers in different ratios. The influence of the different types of cyclodextrin on racemate separation is shown, and some phenomena which might be helpful in the elucidation of the chromatographic behavior involved are also described. The influence both of the percentage of cyclodextrin in the polysiloxane, and of the operating conditions (carrier gas, flow rate, and temperature) in the separation of flavor and fragrance racemates is also evaluated.     

Cyclodextrin derivatives in the GC separation of racemic mixtures of volatile compounds: Part IV

This paper reports the chromatographic performance of columns coated with 2,3,6-trimethyl-α-, β-, and γ-cyclodextrins (2,3,6-TriMe-α,- β-, and γ-CD) and their derivatives 2,6-dimethyl-3-trifluoroacetyl-α-, β-, and γ-cyclodextrins (2,6-DiMe-3-TFA-α-, β-, and γ-CD), all six diluted in polysiloxane, for the separation of the enantiomers of volatile compounds. The influence of column length and film thickness on separation is reported. Phenomena related to reproducibility and consistency, over a period of time, of columns prepared with these CD derivatives are also discussed, and a possible solution to some drawbacks reported here is proposed.     

A particle-hole model for light scattering by simple fluids

The intensity, I, of depolarized light scattered by simple fluids is calculated by modeling the fluid as a dilute gas of dielectric spheres at low density and as a dilute gas of spherical holes in a dielectric continuum at high density. It is shown that a pair of spheres has more inherent scattering power than a pair of holes. Thus, at liquid density, I is smaller than would be predicted by using gas-phase scattering theory plus liquid-state statistics, as has generally been done in the past; the implications of our result for existing theories are discussed.     

Phase behavior of binary symmetric mixtures in pillared slit-like pores: a density functional approach

Density functional approach is applied to study the phase behavior of symmetric binary Lennard-Jones(12,6) mixtures in pillared slit-like pores. Our focus is in the evaluation of the first-order phase transitions in adsorbed phases and lines delimiting mixed and demixed adsorbed phases. The scenario of phase changes is sensitive to the pore width, to the energy of fluid-solid interaction, the amount, and the length of the pillars. Quantitative trends and qualitative changes of the phase diagrams topology are examined depending on the values of these parameters. The presence of pillars provides additional excluded volume effects, besides the confinement due to the pore walls. The effects of attraction between fluid species and pillars counteract this additional confinement. We have observed that both the increasing surface pillar density and the augmenting strength of fluid-solid interactions can qualitatively change the phase diagrams topology for the model with sufficiently strong trends for demixing. If the length of pillars is sufficiently large comparing to the pore width at low temperatures, we observe additional phase transitions of the first and second order due to the symmetry breaking of the distribution of chain segments and fluid species with respect to the slit-like pore center. Re-entrant symmetry changes and additional critical points then are observed.     

Velocity cross correlations in binary mixtures of simple fluids

The velocity cross correlation integrals $$D_{{\text{ab}}}^{\text{J}} = (N/3)\mathop \smallint \limits_{\text{o}}^\infty< {\text{v}}_{{\text{1a}}} ({\text{t}}) \cdot {\text{v}}_{{\text{2b}}} (0) > {\text{dt,}} {\text{a}} {\text{ = }} {\text{1,2;}} {\text{b}} {\text{ = }} {\text{1,2}}$$ can be estimated from the intradiffusion coefficients D ₁ ^° and D ₂ ^° at each mole fraction x₁ of component 1 on the basis of the exact relations among the Onsager phenomenological coefficients together with an assumed equation relating the joint diffusion coefficients D _ab ^J . The results from several such equations are compared with experimental data and with similar results derived by Hertz in a different way to represent the behavior of f _ab ≡D _ab ^J x _b in ideal reference systems. In some cases the agreement with experimental data for relatively ideal systems is even better than given by Hertz's results. For greater accuracy in predicting the D _ab ^J from D _a ^dg data one would need a prediction of the limiting value of D _aa ^J at x_a=0 for a=1,2. Presently known theory does not give a basis for estimating this limit reliably.     

The transport of adsorbate mixtures in porous materials: Basic equations for pores with simple geometry

The basic equations governing the transport of single and binary adsorbate mixtures through single pores are considered. An irreversible thermodynamic formulation is adopted and both viscous and diffusive terms are incorporated following the earlier work of Mason and co-workers. The links between phenomenological coefficients and molecular properties are demonstrated. For single components, the gas phase and high density limits are considered. By using simple hydrodynamic models it is shown that the phenomenological coefficients in the mixture equations can all be expressed as functions of the coefficients for the individual components in the same pore, and the properties of the component adsorption isotherms. Whilst it is appreciated that the hydrodynamic approach will be of limited value in very small pores, it is argued that useful insights can be gained into the feasibility of membrane separation processes from this method. The general equations can be used in future development of network models for porous materials.     

Simplified crossover droplet model for adsorption of pure fluids in slit pores

We present a generalized crossover (GC) model for the excess adsorption of pure fluids at a flat solid-liquid interface, which reproduces scaling behavior of the excess adsorption in the critical region and is reduced to the classical, van der Waals-type analytical model far away from the bulk critical point. In developing this model, we used the density-functional theory (DFT) approach for the order parameter profile calculations with a generalized corresponding states model for the local free-energy density. The GC DFT model well represents the available experimental adsorption data for Kr/graphite, C2H4/graphite, C3H8/graphite, CO2/silica, and SF6/graphite systems in the entire density range 0 < rho < or = 3rhoc and temperatures up to 1.7Tc. In the critical region 0.5 rhoc < r < or = 1.5rhoc and T < or = 1.15Tc, the GC DFT model is consistent with the predictions of the asymptotic renormalization-group crossover model for the critical adsorption in a semi-infinite system developed earlier. For the excess adsorption on the critical isochore, both theories predict a scaling-law behavior Gamma proportional tau(-nu+beta), but fail to reproduce a "critical depletion" of the excess adsorption along the critical isochore of the SF6/graphite system near Tc. We show that an anomalous decrease of adsorption observed in this system at tau = T/Tc - 1 < 10(-2) can be explained by finite-size effect and develop a simplified crossover droplet (SCD) model for the excess adsorption in a slit pore. With the effective size of the pore of L = 50 nm, the SCD model reproduces all available experimental data for SF6/graphite, including the critical isochore data where tau-->0, within experimental accuracy. At L > xib (where xib is a bulk correlation length) the SCD model is transformed into the GC DFT model for semi-infinite systems. Application of the SCD model to the excess adsorption of carbon dioxide on the silica gel is also discussed.     

Approximation of contacts for calculating the velocity of the thermal motion of rodlike molecules in narrow slitlike pores

Expressions for calculating the thermal velocities of the motion of rodlike molecules in slitlike pores were obtained within the framework of a lattice gas model valid over a wide range of fluid densities (from rarefied gases to liquids) and temperatures, including the critical region. The translational and rotational motion of molecules was described using the transition-state theory for nonideal reaction systems, which takes into account the effect of the neighboring molecules on the activation barrier height. The local distributions of the components of the mixture under equilibrium conditions were calculated by describing lateral interactions in the approximation of isolated contacts. The equations of the model reflect the fact that the distributions of the components in the direction perpendicular to the pore walls (due to the effect of adsorption forces) and along the pore axis (if capillary condensation occurs) exhibit a strong anisotropy.     

Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures

A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.     

A trans-tetrahydrobenzoxanthene receptor for the resolution of racemic mixtures of sulfonylamino acids

An enantioselective cleft-type receptor for sulfonylamino acids has been prepared and its use for the resolution of the amino acid racemic mixture is shown.     

Concentration fluctuations in binary mixtures of model polar fluids

We present calculations of the mean square concentration fluctuations, S_α(0), for binary mixtures of model polar fluids. The assumed pair interactions are taken to be of the forms of a hard core plus either dipole-dipole, quadrupole-quadrupole or dipole- quadrupole terms. The calculations are carried out within a mean field approximation. We have considered in some detail the interplay between size differences and the difference in the strength and range of the potentials in deciding how S_α(0) deviates from the ideal behaviour.