Università Roma Tre

1- Thermodynamics and Statistical Mechanics.

Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.

2- Atomic interactions and short range order.

Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.

3- Computer simulation of fluid systems.

Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.

4- Liquid dynamics.

Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.

5- Metastable states, supercooled liquids and glass transtion.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.

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.
Supplementary notes.