Particle theory

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... 

Gibbons R M 1969 Scaled particle theory for particles of arbitrary shape Mol. Phys. 17 81... 

Reiss H and Hammerich ADS 1986 Hard spheres scaled particle theory and exact relations on the existence and structure of the fluid/solid phase transition J. Phys. Chem. 90 6252... 

Stillinger F 1973 Structure in aqueous solutions from the standpoint of scaled particle theory J. Solution Chem. 2 141 Widom B 1967 Intermolecular forces and the nature of the liquid state Sc/e/ ce 375 157 Longuet-Higgins H C and Widom B 1964 A rigid sphere model for the melting of argon Mol. Phys. 8 549... 

The diversity of approaches based on HF (section B3.2.3.4) is small at present compared to the diversity found for DFT. For solids, HF appears to yield results inferior to DFT due to the neglect of electron correlation, but being a genuine many-particle theory it offers the possibility for consistent corrections, in contrast to DFT. Finally, the QMC teclmiqiies (section B3.2.3.41 hold promise for genuine many-particle calculations, yet they are still far from able to offer the same quantities for the same range of materials and geometries as the theories mentioned before. With this wide range of methods now introduced, we will look at their application to chemisorption on solid surfaces. 

Alternative integral equations for the cavity functions of hard spheres can be derived [61,62] using geometrical and physical arguments. Theories and results for hard sphere systems based on geometric approaches include the scaled particle theory [63,64], and related theories [65,66], and approaches based on zero-separation theorems [67,68]. These geometric theories have been reviewed by Stell [69]. 

Nussbaum, J. (1998). History and philosophy of science and the preparation for constructivist teaching The case of particle theory. In J. J. Mintzes, J. H. Wandersee, J. D. Novak (Eds.), Teaching. science for understanding—A human constructivist view (Ch. 2). London Academic... 

The wave theory for light provides a satisfactory explanation for these observations. It was, indeed, this very experiment conducted by T. Young (1802) that, in the nineteenth century, led to the replacement of Newton s particle theory of light by a wave theory. 

To exploit the concept of PMF to represent solvent in free energy calculations, practical approximations must be constructed. A common approach is to treat the two components Z H/"P(X) and Z lYelec(X) separately. Approximations for the nonpolar term are usually derived from geometric considerations, as in scaled particle theory, for example [62], The electrostatic contribution is usually derived from continuum electrostatics. We consider these two contributions in turn. 

Stillinger, F., Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory, J. Sol. Chem. 1973, 2, 141-158... 

Pierotti, R.A., A scaled particle theory of aqueous and nonaqueous solutions, Chem. Rev. 1976, 76, 717-726... 

The reason why classical mechanics is inadequate at the sub-atomic level is because it ignores quantum effects. Not only matter, but also radiation is discontinuous at the sub-microscopic level. Matter occurs as separate atoms and radiation as small packets, quanta or photons. At this level the two descriptions become identical - matter behaves like radiation and radiation behaves like matter. This is appropriate since matter and energy are interconvertible according to the relativistic relationship, E = me2. Wave and particle theories must therefore merge at the quantum level. 

Awkward questions about the electromagnetic and gravitational fields of infinitely many particles in the vacuum remain unanswered. Also, the Dirac theory, amended by the hole proposition is certainly not a one-particle theory, and hence not a relativistic generalization of Schrodinger s equation. 

Some workers have attempted to treat particular effects more rigorously, e g., by scaled-particle theory [142] or by extending [95, 103] Linder s theory [143] of dispersion interactions to the case of an SCRF treatment of solute-solvent interactions. We will not review these approaches here. 

Finally we address the issue of contributions. In our view it is unbalanced to concentrate on a converged treatment of electrostatics but to ignore other effects. As discussed in section 2.2, first-solvation-shell effects may be included in continuum models in terms of surface tensions. An alternative way to try to include some of them is by scaled particle theory and/or by some ab initio theory... 

Some qualities of light are best explained if we describe it as consisting of moving particles, often called photons or quanta (called the particle theory of light). Other qualities are best explained if... 

They cannot be directly measured because of the chemical reactions of the dissolved molecular components, but must be calculated theoretically or estimated by correlation. Electrostatic theory does not predict negative coefficients, which are characteristic of ammonia with some salts. To us, it appears that scaled particle theory(22) is probably the best method of calculation, but the required parameters (polarizability and ion size) are not available for the salts of interest. 

Masterton, W.L. Lee, T.P. "Salting Coefficients from Scaled Particle Theory," J. Phys. Chem., 1970, 74, 1776-80. 

Prediction of salting out effect based on scaled particle theory... 

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