In this dissertation I present three projects united by the idea of using statistical mechanics to study systems in which the main component is an ensemble of particles. Each project studies a distribution of particles either in an interacting ensemble by itself or in a host medium. I analyze connections between the internal properties of individual particles and the resulting macroscopic properties of the material with many particles.
The first project is research on thermal conductivity in suspensions of nanoparticles in base fluids. We develop a model for heat conduction through a fluid containing nanoparticles and agglomerates of various geometries. The calculations show that elongated and dendritic structures are more efficient in enhancing the thermal conductivity than compact spherical structures of the same volume fraction. Results prove that the geometry, agglomeration state, and surface resistance of nanoparticles are the main variables controlling thermal conductivity enhancement in nanofluids.
In the second project, the system of interest is a liquid crystal with a suspension of ferroelectric particles. Experiments on these suspensions have reported enhancement of the isotropic-nematic transition temperature, and enhanced sensitivity to applied electric fields. We present two theories to explain these enhancements: first a Landau-like theory, which provides a simple approach to the statistical mechanics of the suspension, and then a Maier-Saupe-type model, which gives more detailed predictions. These predictions apply even when electrostatic interactions are partially screened by moderate concentrations of ions, and are in good agreement with experiments.
In the third project we examine the jamming transition in a two-dimensional granular polymer system. The jamming density decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with recent experiments. The jamming density can be further reduced in mixtures of granular chains and granular rings, also as observed in experiment. We show that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for polydisperse two-dimensional disk systems. This result indicates that there is more than one type of jamming transition.