Università Roma Tre

1 - Thermodynamics and Statistical Mechanics.


Extensive and intensive thermodynamic functions. Balance conditions. Legendre transforms and thermodynamic potentials. Phase stability conditions. Phase transitions and their classification. Van der Waals equation. Introduction to the theory of statistical ensembles. Fluctuations.


2 - Forces between atoms and short-range order in liquids.


Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in the canon and in the grand canon. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid with diffusion techniques. Hierarchical equation for distribution functions. Medium strength potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closing reports. Hyper-crosslinked chains (HNC) approximation. Percus-Yevick (PY) approximation. PY solution for hard ball liquid. Equation of state for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular liquids.


3 - Numerical simulation of fluid systems


Stochastic and deterministic simulation methods. Molecular dynamics method. Verlet algorithms. Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method. Monte Carlo simulation in different ensembles.


4 - Dynamics of liquids


Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Correlation functions of Van Hove. Principle of the detailed budget. Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of the particles. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective ways. Scattering Brillouin.


5 - Metastable states, undercooled liquids and glass transition.


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. Notes on the dynamic aspects and Mode Coupling theory. Configurational entropy and Kauzmann 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.