Force-free hard sphere model

Air at room temperature and pressure consists of 99.9% void and 0.1% molecules of nitrogen and oxygen. In such a dilute gas, each individual molecule is free to travel at great speed without interference, except during brief moments when it undertakes a collision with another molecule or with the container walls. The intermolecular attractive and repulsive forces are assumed in the hard sphere model to be zero when two molecules are not in contact, but they rise to infinite repulsion upon contact. This model is applicable when the gas density is low, encountered at low pressure and high temperature. This model predicts that, even at very low temperature and high pressure, the ideal gas does not condense into a liquid and eventually a solid. 

In recent years, a number of investigators have studied the phase equilibria of simple fluids in pores by the application of density functional theory. Semina] studies were carried out by Evans and his co-workers (1985,1986). Their approach was considered to be the simplest realistic model for an inhomogeneous three-dimensional fluid . The starting point was a model intrinsic Helmholtz free energy functional F(p), with a mean-field approximation for the attractive forces and hard-sphere repulsion. As explained in Section 7.6, the equilibrium density profile of the fluid in a pore was obtained by minimizing the grand potential functional. 

Recent experimental studies (1-3), on systems of sterically stabilized colloidal particles that are dispersed in polymer solutions, have highlighted the role played by the free polymer molecules. These experiments are particularly relevant because the systems chosen are model dispersions in which the particles can be well approximated as monodisperse hard spheres. This simplifies the interpretation of the data and leads to a better understanding of the intcrparticle forces. DeHek and Vrij (1, 2) have added polystyrene molecules to sterically stabilized silica particles dispersed in cyclohexane and observed the separation of the mixtures into two phases—a silica-rich phase and a polystyrene-rich phase—when the concentration of the free polymer exceeds a certain limiting value. These experimental results indicate that the limiting polymer concentration decreases with increasing molecular weight of... 

The possibility of occurrence of instability of colloidal dispersions in the presence of free polymer was first predicted by Asakura and Oosawa (5), who have shown that the exclusion of the free polymer molecules from the interparticle space generates an attractive force between particles, DeHek and Vrij (1) have developed a model in which the particles and the polymer molecules are treated as hard spheres and rederived in a simple and illuminating way the interaction potential proposed by Asakura and Oosawa. Using this potential, they calculated the second virial coefficient for the particles as a function of the free polymer concentration and have shown that... 

While proper treatment of intermolecular interactions is very important, it should be remembered that entropy has a crucial role in the structure of condensed phases. Hydropho-bicity, e.g., is an entropy-driven effect and is intrinsically many-body in nature. One of the simplest solvation models envisages the solute as filling a cavity in a hard-sphere (i.e., billiard-bair like, without any attractive intermolecular interactions) fluid. Entropy-driven packing of the solvent around the solute results in a liquid structure and it is often helpful to represent this structure in terms of a potential of mean force, a fictitious intermolecular interaction constructed to mimic, in a hypothetical entropy-free world, the actual liquid structure. 

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