91909 - Properties and Processes in the Condensed Phase

Learning outcomes

At the end of the course the student has acquired knowledge necessary to bridge molecular, surface and solid state properties and to investigate also dynamical aspects of matter.

Course contents

Part 1 (F. Zerbetto): The concept of probability: stochastic and Bayesian probabilities. Examples and applications. Link with the concept of multiplicity.
Further examples and applications of conditioned probability. Introduction to probability distributions: binomial and multinomial distributions, applications and examples of chemical interest, mean value and variance, their meaning in chemistry and physics.
Calculation of the first and second moment for some observables. The case of the expectation value of cos(theta) and cos ^ 2 (theta). Equipartition of energy. The Stirling's approximation.
Random walk: the discrete model generates a Gaussian function. Lagrange multipliers, introduction and simple applications.
Boltzmann equation, application to ideal gases: equation of state, pressure balance between different containers.
The Boltzmann distribution with maximization of entropy, its modification in the presence of physical constraints, examples and applications.
Free energy and its meaning, Boltzmann distribution of the 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 the unit'of measurement.
Use of units of measurement in simple examples and for simple applications. Calculation of the translational partition function, practical examples.
Partition functions of rotational and vibrational degrees of freedom, applications and examples. The chemical potential from partition functions. The theory of the activated complex.
Introduction to the model of the disordered lattice. Vapor pressure, cavitation energy, surface tension, interfacial tension.
Entropy, energy, free energy and chemical potential of a two-component system with the model of the disordered lattice, the Bragg-Williams or mean field model.
Entropy, internal energy, free energy, chemical potential for ternary systems; standard potential and significance of activity with the model of the disordered lattice, the binodal curve and its analytical expression. The spinodal curve, its expression and simple applications; critical point as the third derivative of the free energy.
Introduction to the physical chemistry of polymers. Entropy and internal energy according to Flory-Huggins, comparison with the case of non-polymeric solutions.
Flory-Huggins: free energy, chemical potential, miscibility of polymers, the partition coefficient, dependence on the length of the chain.
Flory-Huggins parameter at the critical point, <r> <r^2>, Kuhn's model, random walk and probability of cyclization.
Polymer radius; elasticity in one dimension; elasticity of many chains for generic deformations. Entropy, internal energy and free energy as a function of the density of the polymer: theta conditions, "poor" and "good" solvents.

Readings/Bibliography

K.A. Dill, S. Bromberg, Molecular Driving Forces, Garland Science

Lectures notes

Teaching methods

This course is formed by frontal lectures accompanied by problems solution aimed at applying the notions acquired to the study of chemical properties and inter-molecular interactions.

Assessment methods

In the semester and up to the beginning of the following one, the exam is split into two parts, each containing an open question and 3 numerical problems, similar to those discussed in the lectures. The time allocated for each test is 2 hours. The maximum mark is 33/30. The average mark of the two test must be at least 18/30. From the beginning of the subsequent semester, a single written test on the entire program.

The final mark of the course PROPERTIES AND PROCESSES IN THE CONDENSED PHASE” is calculated as the average mark of two modules: Module 1, Prof. Zerbetto, and Module 2, Prof. Paolucci.

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

Teaching is mainly carried out at the blackboard or by hand writing on a computer screen, depending on the facilities provided at the lecture theater.

Office hours

See the website of Francesco Zerbetto