Statistical Mechanics
Required reading for MATE 509 (Statistical Mechanics of Simple Materials)
(2nd edition, Hardcover, available from Materials Department secretary)
On small length scales, matter is particulate. Mass is distributed in discrete atoms, and these individual particles move. On large length scales, matter is smooth, continuous, and motion is collective. Such are the natural consequences of the existence of atoms and molecules. As Thomas Hobbes observed, “whereas sense and memory are but knowledge of fact, … science is the knowledge of consequences.” Statistical Mechanics is the science of the consequences of the atomic theory of matter. Topics covered include heat capacity, equation of state, gas adsorption on surfaces, blackbody radiation, superfluidity, superconductivity, the formation of black holes, electrical conductivity, the Curie temperature, and Monte Carlo simulation. In addition to Statistical Mechanics, the tools used in the explanation of these “consequences” include thermodynamics, quantum mechanics, free electron theory, renormalization group theory, and mean field theory.
Polymers
Required reading for MATE 351 (Introduction to Polymeric Materials)
(2nd edition, Hardcover, available from Materials Department secretary)
Polymeric and macromolecular materials are essential for modern life – indeed, essential for all life because the building blocks of both plants and animals are macromolecules. The challenge of polymer science is to explain the properties of macromolecular materials - whether polyethylene or protein - in terms of structures and organization at the molecular level. The richness of detail at this level makes it a daunting task to describe the molecular to macroscopic link in a unified manner. David Hume expressed this scientific goal succinctly as “tho’ the effects be many, the principles, from which they arise, are commonly but few and simple.” The principles of polymer science, although not as few or as simple as one would like, are based on a particulate view of matter. The mathematics used to express these principles is, by necessity, largely statistical in nature because the properties of many individual molecules must be averaged over in order to describe their collective behavior. Topics covered include synthetic polymers, proteins, rubber elasticity, soap films, free radical synthesis, condensation synthesis, random walks, gelation, viscosity, diffusion and the glass transition. Tools used in the explanation of these topics include statistics, probability, scaling theory, thermodynamics, chemical kinetics, statistical mechanics and differential/integral equations.
Thermodynamics
Required reading for MATE 350 (Materials Thermodynamics) and CHEME349 (Chemical Engineering Thermodynamics)
(2nd edition, Hardcover, available from Materials Department secretary)
Thermodynamics strives to explain both the relationship between heat and work as well as the nature of heat. It achieves these goals by expressing in the language of partial differential equations two experimental results that are, to quote Descartes, “clearly and obviously conceived.” First, temperature can be increased by either heat or work, and, second, heat flows from high to low temperature. Consistency between the two experiments cannot be maintained solely through conservation laws, and the non-conservative aspect of “heat” addresses many of the central concepts in modern science such as equilibrium, stability, and the arrow of time.
This text builds an understanding of the equations governing heat and work through a careful treatment of the basic definition of terms and through the mathematical encoding of the experimental results. Although the primary applications addressed are associated with phase stability, the broader goal is to enable the student to understand the thermodynamic perspectives essential to the chemical, physical and biological sciences.