Book contents
- Frontmatter
- Contents
- Nomenclature
- Preface
- 1 Introduction
- 2 Foundations
- 3 The Ideal Gas
- 4 Excess Function Models
- 5 Equation of State Models
- Appendix 1 Fundamental Constants and Atomic Units
- Appendix 2 Stirling's Formula
- Appendix 3 Relative Probability of a Microstate
- Appendix 4 Spherical Harmonics, Rotation Matrices, and Clebsch–Gordan Coefficients
- Appendix 5 Higher-Order Perturbation Terms for the Intermolecular Potential Energy of Simple Molecules
- Appendix 6 Rules for Integration
- Appendix 7 Internal Rotation Contributions
- Appendix 8 Quasichemical Approximation for the Degeneracy in a Lattice
- Appendix 9 Off-Lattice Formulation of the Quasichemical Approximation
- Appendix 10 Combinatorial Contribution to the Excess Entropy in a Lattice
- Appendix 11 Integration Variables for Three-Body Interactions
- Appendix 12 Multipole Perturbation Terms for the High-Temperature Expansion
- Index
2 - Foundations
Published online by Cambridge University Press: 11 March 2010
- Frontmatter
- Contents
- Nomenclature
- Preface
- 1 Introduction
- 2 Foundations
- 3 The Ideal Gas
- 4 Excess Function Models
- 5 Equation of State Models
- Appendix 1 Fundamental Constants and Atomic Units
- Appendix 2 Stirling's Formula
- Appendix 3 Relative Probability of a Microstate
- Appendix 4 Spherical Harmonics, Rotation Matrices, and Clebsch–Gordan Coefficients
- Appendix 5 Higher-Order Perturbation Terms for the Intermolecular Potential Energy of Simple Molecules
- Appendix 6 Rules for Integration
- Appendix 7 Internal Rotation Contributions
- Appendix 8 Quasichemical Approximation for the Degeneracy in a Lattice
- Appendix 9 Off-Lattice Formulation of the Quasichemical Approximation
- Appendix 10 Combinatorial Contribution to the Excess Entropy in a Lattice
- Appendix 11 Integration Variables for Three-Body Interactions
- Appendix 12 Multipole Perturbation Terms for the High-Temperature Expansion
- Index
Summary
The book deals with the prediction of the macroscopic behavior of fluids from the properties of their molecular constituents. The basis of such prediction is the availability of molecular models. Designing molecular models for fluids has an interdisciplinary background of foundations. Their thorough understanding is the basis for developing new models and appreciating the promise as well as the limitations of those that are established.
Molecular models are formulated in terms of the energy of a system of three-dimensional flexible bodies, i.e., the molecules. This molecular energy depends on the geometrical structures of the molecules and the force field they are moving in. The relation between the geometrical structure of a body and its energy is defined in mechanical terms. The force field results from the electrical properties of the molecules. On this level the models are thus based on classical mechanics and electrostatics. Classical theory, although most powerful even on the molecular scale, is, however, incomplete in the sense that it does not provide information on the geometry of the molecules or on their charge distributions as the origin of the electrical force field. This gap is closed by quantum mechanics, which also gives important corrections to the classical results in order to make them ultimately applicable to molecules. The link between the molecular energy of a system and its macroscopic thermodynamic functions is provided by statistical mechanics and by computer simulation. By using this link the molecular model leads to numerical data for the thermodynamic functions, from which the macroscopic behavior of a fluid can be calculated by the laws of classical thermodynamics.
- Type
- Chapter
- Information
- Molecular Models for Fluids , pp. 20 - 146Publisher: Cambridge University PressPrint publication year: 2007