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 probability conditioning. Introduction to probability distributions.
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 equilibrium models in statistical thermodynamics; isosbestic point; cooperative and non-cooperative transitions. Model for non-cooperative equilibrium, totally cooperative cases, and first neighbors or Zimm-Bragg cooperation model. Cooperative model with degeneration. Nucleation and crystallization. Ising model. Introduction to the Langmuir model with the disordered lattice model. Michaelis-Menten and its significance in materials science. Active transport and passive transport by means of a carrier through an interface. Sabatier's principle. Binding polynomials. Multiple binding by means of the binding polynomials, Scatchard plot, Hill plot; micelles.
Formation of multilayer and the BET model. Pauling's cooperativity model. Binding with relaxation; model of multiple binding with excluded volume.
Introduction to the physical chemistry of polymers. Entropy and internal energy according to Flory-Huggins, comparison with the case of non-polymeric solutions.
Introduction to Dissipative Particle Dynamics, comparison with the model of disordered lattice, computer simulations and practical examples.
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.

Part 3 (E. Bakalis): The condensed phase laboratory aims to introduce students to deal with complex systems. Matlab software is used and consequently an introduction is made to concepts such as variables, vectors, matrices, built-in functions for data analysis and visualization of data (2D, 3D plots and multiplots). Treating of complex systems; Handling probablity distributions with Matlab, creating histograms from data sets and fitting for the optimal probability distribution. Statistical analysis of data sets (moments), logical statements and creation of data sets. Moving out of equilibrium; Random walk models and Langevin equation.

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, two written tests with a number of questions and problems. The time allocated for each test is 2 hours. From the beginning of the subsequent semester, a single written test of two hours followed by a viva.

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

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

See the website of Evangelos Bakalis