Overview

ABOUT THE COURSE: With the current emphasis on nano- and biotechnologies, descriptions at the molecular level can be used to create effective predictions in chemical engineering and physical chemistry. Classical thermodynamics can be used to relate heat and work and to describe various processes, including phase behaviour, chemical reaction equilibria, and flows on changes of state, but it hardly acknowledges the existence of molecules. This information can also be obtained by statistical thermodynamics, which begins with a description of individual molecules. A molecular-level description and statistical thermodynamics helps us to gain useful insights. In this course, only equilibrium properties, not dynamic or kinetic properties such as the kinetic theory of gases or liquids, are examined; thus, the term statistical thermodynamics is used rather than the more comprehensive statistical mechanics.INTENDED AUDIENCE: Postgraduates from Chemical Engineering, Mechanical Engineering, Physics and ChemistryPREREQUISITES: Thermodynamics at Undergraduate Level INDUSTRY SUPPORT: This shall be useful for those industrial personnel who are using computer simulation techniques for analyzing the trajectories of the compounds. This is true for Pharmaceutical and Biotech companies as they frequently use these techniques where the basics lie in the statistical thermodynamic concepts.

Syllabus

Week 1 : Introduction to Statistical Thermodynamics
Lecture 1 - Probabilistic Description, Macroscopic States and Microscopic States
Lecture 2 - Quantum Mechanical Description of Microstates

Week 2 : Canonical Partition Function
Lecture 3 - Properties of the Canonical Partition Function
Lecture 4 - Canonical Partition Function and Thermodynamic Properties
Lecture 5 - Independent Energy Modes and Collection of Noninteracting Identical Atoms

Week 3 : Monoatomic and Polyatomic Gases
Lecture 6 - Canonical Partition Function and Thermodynamic Properties of the Ideal Monatomic Gas
Lecture 7 - Ideal Diatomic Gas and Thermodynamic Properties of the Ideal Diatomic Gas
Lecture 8 - Partition Function for an Ideal Polyatomic Gas and its Thermodynamic Properties

Week 4 : Chemical Reactions
Lecture 9 - Nonreacting Ideal Gas Mixture
Lecture 10 - Partition Function of a Reacting Ideal Chemical Mixture and Chemical Equilibrium Constant
Lecture 11 - Partition Function of a Reacting Ideal Chemical Mixture and Chemical Equilibrium Constant

Week 5 : Other Partition Functions
Lecture 12 - Microcanonical Ensemble for a Pure Fluid and Grand Canonical Ensemble
Lecture 13 - Isobaric-Isothermal Ensemble and Restricted Grand or Semi-Grand Canonical Ensemble 1

Week 6 : Intermolecular Potentials and Virial Coefficients
Lecture 14 - Virial Equation of State for Polyatomic Molecules
Lecture 15 - Second Virial Coef?cient in a Mixture
Lecture 16 - Interaction Potentials for Multi-atom, Nonspherical Molecules, Proteins and Colloids

Week 7 : Monoatomic Crystals
Lecture 17 - Einstein and Debye Model
Lecture 18 - Heat Capacity Models for a Crystal with Sublimation Pressure and Enthalpy

Week 8 : Lattice Models For Fluids
Lecture 19 - Equations of State from Lattice Theory
Lecture 20 - Activity Coef?cient Models for Similar-Size Molecules
Lecture 21 -Flory-Huggins for Polymer Systems and Ising Model

Week 9 : Interacting Molecular in Dense Fluids
Lecture 22 - Reduced Spatial Probability Density Functions and Pair Correlation Functions
Lecture 23 - Radial Distribution Function in Liquids
Lecture 24 - Radial Distribution Function based on Integral Equations

Week 10 : Computer Simulation Methods
Lecture 25 - Monte Carlo Simulation
Lecture 26 - Molecular Dynamics Simulation

Week 11 : Perturbation Theories
Lecture 27 - Perturbation Theory for Square Well Potential
Lecture 28 - First and Second Order Barker-Henderson Perturbation Theory

Week 12 : Dilute Electrolyte Solutions
Lecture 29 - Solutions Containing Ions and Electrons
Lecture 30 - Debye-H¨uckel Theory and Mean Ionic Activity Coef?cient