Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Jan 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phdt........80k&link_type=abstract
Thesis (PH.D.)--STATE UNIVERSITY OF NEW YORK AT STONY BROOK, 1990.Source: Dissertation Abstracts International, Volume: 52-03,
Physics
Condensed Matter
Statistical Mechanics
1
Scientific paper
Theories of Statistical Mechanics are applied to the distinct topics of Percolation in a Simple Model Fluid (Chapter I), Thermodynamics for a Hard-Sphere Polydisperse System (Chapter II), Light Scattering of a Hard-Sphere Polydisperse System (Chapter III), Effective Conductivity of a Polydisperse Two-Phase System of Fully Penetrable Spheres (Chapter IV), and Diffusion in a Square-Well Lorentz Gas (Chapter V). Chapter I: Analytical results are derived for percolation in a one-component simple model fluid system of particles with hard cores and Yukawa attractive tails. For the percolation part, the Ornstein-Zernike-like connectedness equation is analytically solved in the Mean Spherical Approximation with hard core and Yukawa tail closures. Methods are developed for placing percolation and thermodynamic phase transitions on the same conceptual footing. Chapter II: The radial distribution function for a hard-sphere polydisperse system is determined through first order in density. The virial equation of state is derived through third order in density. Chapter III: An exact analytic expression is derived for the intensity of light scattering of a polydisperse system of hard-spheres through third order in density. An approximate expression which can be used to add attractive tails to the polydisperse hard cores is derived. Our results are expected to have utility for solutions up to five percent by weight. Chapter IV: A homogeneous and isotropic two-phase system of fully penetrable polydisperse spheres dispersed in a continuous matrix is considered. The two-point matrix function is analytically determined. Beran and Brown bounds for the effective thermal conductivity are obtained for different degrees of polydispersity. An excellent approximation is derived for a microstructural parameter appearing in these bounds. Polydispersity is found to have only a slight effect on the bounds. Chapter V: Computation of the collision cross-sections of a square-well dilute gas mixture is reduced to the evaluation of one-dimensional integrals. Our results are used to evaluate the exact diffusion coefficient of a Lorentz gas, which is then compared with its first and second Chapman-Enskog approximations, and with its second Kihara approximation, D_2^{K }. The D_2K is of high accuracy over the whole range of parameters studied.
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