Structured fluids mechanical properties theories

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

The availability of a satisfactory theory for simple fluids properties means that these last can successfully be predicted and described at the microscopic statistical mechanics level. This means, once the interparticle law force for a certain fluid has been fixed, one in principle should be able to determine, by means of exact equations relating the interaction potential to some structural functions and thermodynamical quantities, the properties the system will exhibit. However, in practice, a certain number of approximations need to be... 

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. 

In this section, we review some of the important formal results in the statistical mechanics of interaction site fluids. These results provide the basis for many of the approximate theories that will be described in Section III, and the calculation of correlation functions to describe the microscopic structure of fluids. We begin with a short review of the theory of the pair correlation function based upon cluster expansions. Although this material is featured in a number of other review articles, we have chosen to include a short account here so that the present article can be reasonably self-contained. Cluster expansion techniques have played an important part in the development of theories of interaction site fluids, and in order to fully grasp the significance of these developments, it is necessary to make contact with the results derived earlier for simple fluids. We will first describe the general cluster expansion theory for fluids, which is directly applicable to rigid nonspherical molecules by a simple addition of orientational coordinates. Next we will focus on the site-site correlation functions and describe the interaction site cluster expansion. After this, we review the calculation of thermodynamic properties from the correlation functions, and then we consider the calculation of the dielectric constant and the Kirkwood orientational correlation parameters. 

The object of any statistical mechanical theory of polymer systems is ultimately to relate the measurable physical properties of the system to the properties of the constituent monomers and their mutual interactions. It is imperative that the initial statistical mechanical theories of these physical properties of polymer systems not depend on the exact details of a particular polymer. Instead, these theories should reflect those generic properties of polymer systems that are a result of the chainlike structures of polymer molecules. Once the properties of simple, yet general, models of polymers are well understood, it is natural to focus attention upon the particular aspects of a polymer of interest. The initial use of simple models of polymers is not solely dictated by an attempt to obtain those general features of polymer systems. The mathematical simplicity of the model is required so that we avoid the use of uncontrollable mathematical approximations which necessarily arise with the use of more complicated models. When the model is sufficiently simple, yet physically nontrivial, we are able to test different approximation schemes to find those that are useful. Presumably these methods of approximation would also be useful for more complicated models. This emphasis upon mathematical simplicity has its analog in the theory of fluids. First hard-core interactions can be used to test the physical principles associated with various methods of approximation. Once physically sound approximation schemes have been obtained with this model, they may be applied with more realistic potentials, e.g., the Lennard-Jones potential, which require subsequent numerical approximations. Thus we wish to separate approximations of a physical origin from those of purely a numerical nature. This separation... 

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