Fluids adsorbed

M. Schoen, D. J. Diestler. Analytical treatment of a simple fluid adsorbed in a slit-pore. J Chem Phys 709 5596-5605, 1998. 

R. Evans. Fluids adsorbed in narrow pores phase equilibria and structure. J Phys Condens Matter 2 8989-9007, 1990. 

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

To solve the replica OZ equations, they must be completed by closure relations. Several closures have been tested against computer simulations for various models of fluids adsorbed in disordered porous media. In particular, common Percus-Yevick (PY) and hypernetted chain approximations have been applied [20]. Eq. (21) for the matrix correlations can be solved using any approximation. However, it has been shown by Given and Stell [17-19] that the PY closure for the fluid-fluid correlations simplifies the ROZ equation, the blocking effects of the matrix structure are neglected in this... 

The equlibrium between the bulk fluid and fluid adsorbed in disordered porous media must be discussed at fixed chemical potential. Evaluation of the chemical potential for adsorbed fluid is a key issue for the adsorption isotherms, in studying the phase diagram of adsorbed fluid, and for performing comparisons of the structure of a fluid in media of different microporosity. At present, one of the popular tools to obtain the chemical potentials is an approach proposed by Ford and Glandt [23]. From the detailed analysis of the cluster expansions, these authors have concluded that the derivative of the excess chemical potential with respect to the fluid density equals the connected part of the fluid-fluid direct correlation function (dcf). Then, it follows that the chemical potential of a fluid adsorbed in a disordered matrix, p ), is... 

We would like to discuss consistently the results obtained in the theory and simulations for a hard sphere fluid adsorbed in a matrix of chains with four, eight, and sixteen monomer beads (m = M = 4 8 16). 

To the best of our knowledge, there was only one attempt to consider inhomogeneous fluids adsorbed in disordered porous media [31] before our recent studies [32,33]. Inhomogeneous rephca Ornstein-Zernike equations, complemented by either the Born-Green-Yvon (BGY) or the Lovett-Mou-Buff-Wertheim (LMBW) equation for density profiles, have been proposed to study adsorption of a fluid near a plane boundary of a disordered matrix, which has been assumed uniform in a half-space [31]. However, the theory has not been complemented by any numerical solution. Our main goal is to consider a simple model for adsorption of a simple fluid in confined porous media and to solve it. In this section we follow our previously reported work [32,33]. 

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

Abstract We formulate the balance principles for an immiscible mixture of continua with micro structure in the broadest sense for include, e.g., phenomena of diffusion, adsorption and chemical reactions. After we consider the flow of a fluid/adsorbate mixture through big pores of an elastic solid skeleton and propose suitable constitutive equations to study the coupling of adsorption and diffusion under isothermal conditions. 

Figure 6, Profiles of the density as a fimction of z, the distance from the center of a parallel-walled slh. The vertical lines show the planes of solid that make up the pore. The density is shown for a conqjletely wet (part a) and a con letely dry (part b) surface. Both the fluid adsorbate and the solid adsorbent are made up of Lennard-Jones atoms with well-depth ratios % /% = 0.85 (part a) and 0.30 (part b). The simulations were performed under conditions such that each system was at bulk liquid-vapor coexistence for 0.7. From Ref [31], J. Stat. Phys.

The Gibbs-ensemble procedure lias also been employed to estimate adsorptionisothemis for simple systems. The approach is illustrated- by calculations for a straight cylindrical pore where both fluid/fluid and fluid/adsorbent molecular interactions can be represented by tlie Lemiard-Jones potential-energy function [Eq. (16.1)]. Simulation calculations have also been made for isothemis of methane and ethane adsorbed on a model carbonaceous slit pore. Isosteric heats of adsorption liave also been calculated. ... 

While studying adsorption in mesopores using the molecular continuum model we have found [4,6,7] that there exist two critical diameters based on thermodynamic analysis of the adsorption, and two more when the mechanical stabihty of the meniscus is considered. These criticalities refer to the critical pore diameter below which there either exists a different mechanism of adsorption, or the adsorption is reversible. Here we provide a brief outline of these criticalities. The chemical potential of the fluid adsorbed in a cyfindrical pore of radius R can be expressed as [6,7] (r,R) = /jj (r,R) + (f>(R-r,R) = constant(/ ). After considering... 

Consider now real materials with model micropores, that is to say with regular dimensions and whose pore walls consist of well-defined crystalline adsorption sites (including possible cationic sites). Such solids can be found within the realm of zeolites and associated materials such as the aluminophosphates. One can imagine the probability that a fluid adsorbed within such micropores may be influenced by the well-defined porosity and thus become itself "ordered. Such phenomena have already been highlighted with the aid of powerful but heavy techniques such as neutron diffraction and quasi-elastic incoherent neutron diffusion. The structural characterisation of several of the following systems was carried out with the aid of such techniques in collaboration with the mixed CNRS-CEA Leon Brillouin Laboratory at Saclay (France). 

One of the main purposes of developing structural models of porous solids is to predict the effects of confinement on the properties of adsorbed phases, e.g., adsorption isotherms, heats of adsorption, diffusion, phase transitions, and chemical reaction mechanisms. Once a structural model for a particular porous solid has been chosen or developed (see Section 5.3), it is necessary to assume an interaction potential between the solid (adsorbent) and the confined fluid (adsorbate), as well as a fluid-fluid potential, and to decide on a theory or simulation method to calculate the property of interest [58]. A great many such studies have been reported in the literature, particularly for simple pore geometry models, and we do not attempt to review them here. Instead we present a few examples of such stuches, with emphasis on those involving more realistic pore models. 

Other theoretical work on this problem is that of Henderson [42], who considered the properties of a fluid adsorbed in a parallel-walled pore with grooved walls Bryk et al. [43] simulated a gas adsorbed on a number of rough surfaces created by placing a disordered quenched layer of hard spheres on a substrate interacting with the adsorbed atoms via a LJ 9-3 potential. Simulations showed that the system exhibits wetting, prewetting, and partial wetting for... 

TABLE 10.10c Exponent of Jth Independent Fluid, Adsorbed, and Surfactant-Associated Species [BB(I,J) Array] ... 

From now on wc focus on situations where the fluid adsorbed by a disordered matrix is both homogeneous and isotropic after averaging over different mar trix configurations. In such a situation, the fluid s singlet density is just a constant that is,... 

Figure 7,4 Top Replica HNC predictions for the stability limits of the homogeneous isotropic phase of Stockmayer fluids adsorbed to disordered DHS matrices of density p,n = 0.1. Curves are labeled according to the reduced matrix dipole moment fJ m/ sTocr (the pure HS matrix corresponds to = 0). Bottom Dielectric constant of a dense adsorbed fluid as a function of the matrix dipole moment T = 0.5, f) = 0.7, Pm = 0.1). The inset shows the integrated blocking part of the dipole dipole correlation function.

Herring, A.R. and Henderson, J.R. (2007) Hard-sphere fluid adsorbed in an annular wedge The depletion force of hard-body colloidal physics. Phys. Rev. E, 75,011402. 

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