Computer simulations adsorbed fluids

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. 

Sec. 4 is concerned with the development of the theory of inhomogeneous partly quenched systems. The theory involves the inhomogeneous, or second-order, replica OZ equations and the Born-Green-Yvon equation for the density profile of adsorbed fluid in disordered media. Some computer simulation results are also given. 

Our final focus in this review is on charged quenched-annealed fluid systems. Very recently Bratko, Chakraborty and Chandler have addressed this problem [34-36]. A set of grand canonical computer simulation results for infinitely diluted electrolyte adsorbed in an electroneutral matrix of ions has been presented and an attempt to describe them at the level of... 

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... 

We also have studied fluid distribution in the pore H = 6 (Fig. 12(b)) at Ppq = 4.8147 and at two values of Pp, namely at 3.1136 (p cr = 0.4) and at 7.0026 (pqOq = 0.7 Fig. 12(b)). In this pore, we observe layering of the adsorbed fluid at high values of the chemical potential Pp. The maxima of the density profile pi(z) occur at distances that correspond to the diameter of fluid particles. With an increase of the fluid chemical potential, pore filhng takes place primarily at pore walls, but second-order maxima on the density profile pi (z) are also observed. The theory reproduces the computer simulation results quite well. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

Computer simulations of nanoscopic confined fluids have revealed many details of the dynamics under confinement. The nature of the confined fluids - especially in the immediate vicinity of attractive surface - has been shown to be strongly altered by the confining surfaces, and this is manifested by a behavior dramatically different from the bulk fluids in the local relaxation [38a], the mobility [38c] and rheological properties [39] of molecules near adsorbing surfaces. For monomeric systems many computer simulation studies [40] provide a clear enough picture for the dynamics of confined films of small spherical molecules. On the other hand, for confined oligomers and polymers less has been done, especially towards the understanding of the dynamics of nanoscopic films [41]. 

In recent years, the behavior of fluid molecules in small pores has been well studied by computer simulation [136,137]. Computer simulation can provide us with valuable information about the microscopic behavior of adsorbate molecules confined in small pores in terms of intermolecular and surface forces, thus enabling us to understand the fundamental behaviors of adsorbates in the potential field of the model pores. The current trend in the literature suggests that for physical adsorption in activated carbon, the adsorbate-adsorbate interaction and adsorbate-pore interaction are well represented by the LJ potential theory while the model micropore is a slit-shaped channel of infinite extent. This forms the basis for the appliction of the statistical method in adsorption processes. 

In the case of the adsorbate being a simple gas (rare gases, methane, etc.), the adsorbate-adsorbate interaction may be modeled with a L-J potential, so that fx is the excess chemical potential for the 2D L-J system with respect to an ideal gas. For an ideal gas, = 0 (there is no excess) and then the classical Henry equation, Eq. (1), is recovered. Reliable values of /x for 2D L-J fluids have been obtained from perturbation theories [19], integral theories [210], computer simulations [225], and equations of state [212,214,226]. Details of these approaches and comparison of results will be made in Sections IVB and IVC. 

This section is devoted to studying the 2D Lennard-Jones model in order to serve as the basis in applying Steele s theory. In Section IVA the main studies about that model are summarized and commented on. In Section IVB, the most useful expressions for the equation of state of the model are given. In Section IVC we present results about the application of these equations, which are compared with other theoretical approaches to studying adsorption of 2D Lennard-Jones fluids onto perfectly flat surfaces. In Section FVD, the comparison with experimental results is made, including results for the adsorption isotherms, the spreading pressure, and the isosteric heat. Finally, in Section IVE we indicate briefly some details about the use of computer simulations to model the properties both of an isolated 2D Lennard-Jones system and of adsorbate-adsorbent systems. 

A eomparison between theoretical and experimental values for the critical properties was first made by Tsien and Valleau [283]. Following Tsien and Valleau, the experimental data of Thorny and Duval [37] reduced with the effeetive L-J parameters given by Wolfe and Sams [36] give reduced critical temperatures of 0.65, 0.61, and 0.60 for argon, krypton and xenon, respectively (see Tables 1, 8, and 11). The variation means, of course, that the L-J fluids can not model exactly the behavior of all the rare gases. Moreover, there is a major disagreement with respect to the theoretical or computer simulation values for 2D L-J fluids. Nevertheless, we note that if the most recent experimental values of the critical temperature are taken (except, obviously, for Kr), the reduced values come close to 0.5 for certain values of the L-J parameters, even in the case of adsorbed neon. 

In the preceding subsections we have considered computer simulations as a useful tool for relating the microscopic and the macroscopic behaviors of the substances involved, to test theoretical hypotheses, or as an aid in interpreting experimental results. They thus serve as a bridge between theory and experiment. In this subsection, more details will be given about computer simulations of 2D L-J fluids as models of adsorbed fluids and computer simulations which include a model for the adsorbent solid. These details will not include the techniques used or programming languages, which are available in other books [14,22]. 

---