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

A brief introduction to units of measurement. Use of units of measurement, examples, and applications.

The need for an exponential probability distribution starting from the principles of classical thermodynamics.

The concept of stochastic and Bayesian probability. Examples and applications. Connection 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, variance, and moments, and their meaning in physical chemistry. Calculating the first and second moments for some observables and probability densities. The case of the expectation value of cos(theta) and cos^2(theta). Using moments for the principle of equipartition of energy.

The Stirling approximation. Random walk, from discrete to continuous models, Gaussian generation. 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.

Calculation of the translational partition function, practical examples. Rotational partition function, vibrational partition function, applications and examples. Chemical potential from partition functions.

Chemical equilibrium. Use in activated complex theory. 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, and 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 noncooperative transitions. Introduction to the Langmuir model with the disordered lattice. Multiple binding using bond polynomials; comparison of the stoichiometric model and the multisite model from titration data; Scatchard plot, Hill plot; micelle formation. Multilayer formation and the BET model.

Readings/Bibliography

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

H.J. Kreuzer, I. Tamblyn, Thermodynamics, World Scientific

Lecture notes

Teaching methods

Blackboard teaching

Assessment methods

Written test with 4 numerical problems and 2 open questions on the theory presented during the lectures. The test may be split into 2 parts (if agreed with the students). In this case each test will consist of 3 numerical problems plus a theoretical question. Maximum mark 33/30 (cum laude if mark >31/30). If the exam is taken in multiple parts, usually 2, the final grade will be the average of the grades of the individual parts weighted by the number of credits associated with each part.

The use of AI tools during the exam is prohibited in any form, including chatbots, text generators, content synthesizers, and tools integrated into devices. Any use of AI is considered a violation of the principles of honesty and fairness set forth in the University Policy and may result in the exam being cancelled by the instructor, who remains responsible for ensuring the exam's validity.

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

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

Office hours

See the website of Francesco Zerbetto