10592 - Physical Chemistry of Materials

Learning outcomes

The course aims to provide basic knowledge of statistical thermodynamics, introducing concepts of probability distribution, partition function, and major thermodynamic functions up to the definition of chemical potential. The student understands the physicochemical foundations characterizing cooperative (and non-cooperative) processes in the condensed state.

Course contents

The concepts of stochastic and Bayesian probabilities. Examples and applications. Link to multiplicity.

Further examples and applications of conditional probability. Multiplicity, distinguishability and indistinguishability, examples and applications. Introduction to probability distributions. The case of two events.

Binomial and multinomial probability distributions, applications and examples of chemical interest, mean value and variance, their meaning in physical chemistry.

First and second moments for some observables and probability densities. The case of the expectation value of cos(theta) and cos^2(theta). Use of moments for the energy equipartition principle. The Stirling approximation.

Random walk, from the discrete to the continuous model, generation of the Gaussian. Lagrange multipliers, introduction and simple applications. Boltzmann equation, application to ideal gases: equation of state, equilibrium pressure between different containers.

The Boltzmann distribution with entropy maximization, its modification in the presence of physical constraints, examples and applications.

Free energy and its meaning, Boltzmann distribution from free energy, partition functions, their applications, internal energy and entropy in terms of partition functions. Practical examples of partition functions, mean values and thermodynamic functions.

Brief introduction to units of measurement. Use of units of measurement, examples and applications. Calculation of the translational partition function, practical examples. Rotational partition function, vibrational partition function, applications and examples. The chemical potential from partition functions. Chemical equilibrium. Use for activated complex theory.

Probability in practice with a hands on practice.

Coulomb's law: units of measurement, additivity, superposition, charge distribution, electric field, electric potential. Laplace equation. Multi-pole expansion. Symmetry effects, dependence on the origin. Quantum formulation, perturbation theory. Intermolecular forces.

Introduction to the disordered lattice model. Vapor pressure, cavitation energy, surface tension, interfacial tension. Entropy, energy, free energy and chemical potential of a two-component system according to the disordered lattice model, Bragg-Williams model or mean field. Entropy, internal energy, free energy, chemical potential for ternary systems; meaning of standard potential and activity coefficient with the disordered lattice model.

Binodal curve and its analytical expression. Introduction to equilibrium models in statistical thermodynamics; isosbestic point; cooperative and non-cooperative transitions. Introduction to the Langmuir model with the disordered lattice. Multiple binding by means of binding polynomials; comparison of stoichiometric model and multisite model from titration data, Scatchard plot, Hill plot; micelle formation. Multilayer formation and BET model.

Readings/Bibliography

K.A. Dill, S. Bromberg, Molecular driving forces, Garland Science

Teaching methods

Blackboard teaching

Assessment methods

Written test with 4 numerical problems and 2 open questions on the theory presented during the lectures

Teaching tools

Overhead projector together with the openboard software if the blackboard is inadequate

Office hours

See the website of Francesco Zerbetto