Cell model of a fluid with hard-core repulsive long-range attractive potential

"A model of a one-dimensional fluid is investigated in which the praticles [sic] are embedded in a cellular space grid and interact with a modified Lennart-Jones potential. It is shown that with an appropriate change in the potential function the model is also suitable for a two- or three-dimensional fluid with more restricted interactions. The man-fermion-like nature of the system resulting from the hard-rod repulsive part of the modified Lennard-Jones potential makes possible an isomorphism between occupation numbers (number operators) and spin states (spin operators) of an Ising ferromagnet, permitting a convenient mathematical formulation of the problem in terms of the Ising model formalism. While the spinor-algebraic method of Onsager and Kaufman is seen not to lead to a solution of this problem, a method is found for linearizing the partition function which results in a useful series solution. The validity of the solution is first proved by applying it to a one-dimensional model with nearest-neighbor interactions for which the exact partition function is known in closed form. The series solution is shown to offer a convenient and unified method for obtaining, algebraically, correct low-temperature expansions of the partition function for two- and three-dimensional fluids with nearest-neighbor interactions and similar potentials incorporating only a limited number of bonds. Application of the solution to several infinite systems produced consistent and realistic results in various limits and leas to a correct picture of a phase transition under certain conditions without recourse to the Maxwell construction. A numerical evaluation and analysis of the series solution, by means of high-speed computer, for small one-, two-, and three-dimensional systems shows realistic thermodynamic behavior and confirms other estimates of the critical temperature of the three-dimensional system"--Abstract, pages ii-iii.

Name thesis:degree_name

Ph. D. in Physics

Grantor

University of Missouri at Rolla

Year dc:date.available

2016

Author dc:creator

• Tross, Ralph G.

• Physics

Repository record dc:identifier

https://scholarsmine.mst.edu/doctoral_dissertations/2065

OAI identifier oai:identifier

oai:scholarsmine.mst.edu:doctoral_dissertations-3067