Thermodynamic integration . solid-fluid

Adsorption is a surface phenomenon. When a multi-component fluid mixture is contacted with a solid adsorbent, certain components of the mixture (adsorbates) are preferentially concentrated (selectively adsorbed) near the solid surface creating an adsorbed phase. This is because of the differences in the fluid-solid molecular forces of attraction between the components of the mixture. The difference in the compositions of the adsorbed and the bulk fluid phases forms the basis of separation by adsorption. It is a thermodynamically spontaneous process, which is exothermic in nature. The reverse process by which the adsorbed molecules are removed from the solid surface to the bulk fluid phase is called desorption. Energy must be supplied to carry out the endothermic desorption process. Both adsorption and desorption form two vital and integral steps of a practical adsorptive separation process where the adsorbent is repeatedly used. This concept of regenerative use of the adsorbent is key to the commercial and economic viability of this technology. 

From a theoretical perspective, thermodynamics is then the central theory on which such a discussion must build. Below we use a formulation of thermodynamics usually applied to solid-like systems, because confined fluids have a lot in common with bulk solids in that they are highly inho-mogenc ous and anisotropic. However, unlike a solid, a confined fluid lacks any long-range spatial order. As we demonstrate in Chapter 1, symmetry considerations play an integral part of the current formulation of equilibrium thermodynamics with which the nonexpert in the field will not necessarily be accustomed. 

In the present chapter we have reviewed a numerically efficient and accurate equation of library state for high pressure fluids and solids. Thermodynamic cycle theories allow us to apply this model profitably to the reactions of energetic materials. The equation of state is based on HMSA integral equation theory, with a correction based on extensive Monte Carlo simulations. We have also shown that our equation of state can be used to accurately model the properties of molecular fluids and detonation products. The accuracy of the equation of state of polar fluids is significantly enhanced by using a multi-species or cluster representation of the fluid. 

Over the p t several years we and our collaborators have pursued a continuous space liquid state approach to developing a computationally convenient microscopic theory of the equilibrium properties of polymeric systems. Integral equations method [5-7], now widely employed to understand structure, thermodynamics and phase transitions in atomic, colloidal, and small molecule fluids, have been generalized to treat macromolecular materials. The purpose of this paper is to provide the first comprehensive review of this work referred to collectively as Polymer Reference Interaction Site Model (PRISM) theory. A few new results on polymer alloys are also presented. Besides providing a unified description of the equilibrium properties of the polymer liquid phase, the integral equation approach can be combined with density functional and/or other methods to treat a variety of inhomogeneous fluid and solid problems. 

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