Scaled particle theory applications

Reiss H 1977 Scaled particle theory of hard sphere fluids Statistical Mechanics and Statistical Methods in Theory and Application ed U Landman (New York Plenum) pp 99-140... 

In this article, we have surveyed typical properties of isotropic and liquid crystal solutions of liquid-crystalline stiff-chain polymers. It had already been shown that dilute solution properties of these polymers can be successfully described by the wormlike chain (or wormlike cylinder) model. We have here concerned ourselves with the properties of their concentrated solutions, with the main interest in the applicability of two molecular theories to them. They are the scaled particle theory for static properties and the fuzzy cylinder model theory for dynamical properties, both formulated on the wormlike cylinder model. In most cases, the calculated results were shown to describe representative experimental data successfully in terms of the parameters equal or close to those derived from dilute solution data. 

The PDT that is a central feature of this book dates from this period (Widom, 1963 Jackson and Klein, 1964), as does the related but separately developed scaled-particle theory (Reiss et al, 1959). Both the PDT and scaled-particle approaches have been somewhat bypassed as features of molecular theory, in contrast to their evident utility in simulation and engineering applications. Scaled-particle theories have been helpful in the development of sophisticated solution models (Ashbaugh and Pratt, 2004). Yet the scaled-particle results have been almost orthogonal to pedagogical presentations of the theory of liquids. This may be due to the specialization of the presentations of scaled-particle theory (Barrat and Hansen, 2003). 

A hybrid approach of the extended scaled particle theory (SPT) and the Poisson-Boltzmann (PB) equation for the solvation free energy of non-polar and polar solutes has been proposed by us. This new method is applied for the hydration free energy of the protein, avian pancreatic polypeptide (36 residues). The contributions form the cavity formation and the attractive interaction between the solute and the solvent to the solvation free energy compensate each other. The electrostatic conffibution is much larger than other terms in this hyelration free energy, because hydrophilic residues are ionized in water. This work is the first step toward further applications of our new method to free energy difference calculation appeared in the stability analysis of protein. 

We have presented the first application of the newly developed method for calculating the solvation free energy to protein, which is based on the extended scaled particle theory and the Poisson-Boltzmann equation. Although the results are still preliminary, it demonstrates a possibility of obtaining the quantity theoretically, which is difficult even for the modem... 

Jackson, R. M. Sternberg, M. J. E. (1994). Application of scaled particle theory to model the hydrophobic effect implications for molecular association and protein stability. Prot. Eng. 7, 371-383. 

Wilhelm and Battino have extended their measurements of binary gas diffusion coefficients using the Stefan technique to mixtures of SF with four aliphatic hydrocarbons. Jaster and Kosky have completed a series of measurements of the solubility of SF, in four commercially-available fluorocarbon mixtures and Pierotti has published a recent review on the application of scaled-particle theory to the estimation of gas solubilities. 

The usual explanation given for the high surface tension of water is that at the surface a water molecule cannot form four tetrahedraUy directed hydrogen bonds with other water molecules but only three, hence water tends to minimize the surface area in order to minimize the energetic expense of the loss of hydrogen bonds. Therefore, a value of 5 of Eq. (4.7) of the order of two molecular diameters, 0.5 nm, should have been expected. Anyway, only very tiny droplets would have a surface tension smaller than that of bulk water with a flat surface. However, with regard to the application of the scaled particle theory, Eqs. (4.3) to (4.6), the question of the finite curvature of the cavity remains. 

Relation (4.4.40) suggests a novel application of the scaled particle theory to the problem of H0O interactions. In spite of some serious reservations that one may have regarding the application of the scaled particle theory to fluids such as water, the results computed by the SPT show the same trends as those for H(pO interactions. [A more detailed examination of the application of the scaled particle theory for this problem was... 

Relation (8.83) permits a novel application of the scaled particle theory to the problem of Table 8.8 gives some computed values of for water and various nonaqueous solvents. [See Ben-Naim (1971a).] It is quite clear that the values of zlyUns largest in water, which, by virtue of (8.83), means that in water, the HI is the strongest. In spite of some serious reservations that one may have regarding the application of the scaled particle theory to fluids such as water (see Section 7.3), the results of Table 8.8 show the same trend we witnessed in Section 8.6. [Recently, a more detailed examination of the application of the scaled particle theory for this problem has been reported by Wilhelm and Battino (1972). We have discussed here only spherical solutes, for which one needs a spherical cavity. An extension of the scaled particle theory to particles of arbitrary shape has been reported by Gibbons (1969).]... 

The diameters of solvents play a role in theoretical considerations, such as the application of the scaled particle theory. For gaseous solvent molecules, the collision diameter, o, is related to the Lennard-Jones pair potential energy,... 

There is naturally a wealth of publications on aspects of solvation and a comprehensive review would need a whole book. Hence, it is not practical to wade through all the developments in solvent effect theory, especially as other articles in this encyclopedia also deal with some aspects of solvation (see Related Articles at the end of this article). Instead, the focus will be on the methods used for the evaluation of the thermodynamics of cavity formation (TCF), which is a large part of solvation thermodynamics, and in particular on the application of the most successful statistical mechanical theory for this purpose, namely, the scaled particle theory (SPT) for hard sphere fluids (see Scaled Particle Theory). This article gives a brief introduction to the thermodynamic aspects of the solvation process, defines energy terms associated with solvation steps and presents a short review of statistical mechanical and empirical... 

In many cases, the solvent systems determined by analytical TLC are directly applicable to PLC with similar results. A proper mobile phase selected for PLC should have a resolution more than 1.5 in the analytical scale. According to theory, PLC resolution, however, decreases with increasing particle size. Improved separa-... 

Remaining above all a physicist, Ya.B. always departs from a concrete physical problem. But in those cases where the results have a general mathematical character, they are also applicable to physical situations which go far beyond the boundaries of the original problem. Thus, for example, Ya.B. s analysis (1970) [34 ] of particle cluster formation in a dust medium in his theory of the formation of the large-scale structure of the Universe simultaneously describes the appearance of optical caustics, as was shown, in particular, in his article with A. V. Mamaev and S. F. Shandarin [63]. 

Studies on the application of the theory of statistical moments in the description of grinding in ball mills have been carried out in the Department of Process Equipment, Lodz Technical University [1-3]. The research was carried out in a laboratory scale for selected mineral materials. Results obtained confirmed applicability of the theory of statistical moments in the description of particle size distribution during grinding. 

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