Università Roma Tre

1 - Review of Thermodynamics and Statistical Mechanics.
Extensive and intensive thermodynamic functions. Conditions of equilibrium.
Legendre transforms and thermodynamic potentials. Phase stability conditions.
Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.
Characterization of the liquid state of matter. Characterization of soft materials.
Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.
Radial distribution function and relationship with thermodynamics.
The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.
Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.
Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.
Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.


4 - Dynamics of liquids and soft matter
Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.
Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.
Diffusion coefficient. Speed ​​correlation function. Hydrodynamics and collective modes. Scattering Brillouin.
Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.