Physics of Liquid Matter

Ch.1- General introduction to the liquid state of matter

Description of the phenomenology of liquids. Defininition of conditions for the classical limit. Introduction of different classes of liquids: simple, metallic, molecular etc. Defininition of complex fluids. Statistical mechanics methods as necessary tools for liquids state studies.

Ch.2- Thermodynamics and statistical mechanics of fluid states.

Defininition of equilibrium and stability conditions. Phase transitions and their classification. Van der Waals equation and its critical behaviour. Concepts of Statistical Mechanics to be used in study the fluid states. Relation between fluctuations and thermodynamics in the fluid phases.

Ch.3- Structure of liquids.

Effective potentials for classical liquid systems. Distribution functions in the canonical ensemble and in the grand canonical ensemble. Relation between the radial distribution function and the thermodynamics. The X-ray and neutron diffraction in the elastic limit to measure the static structure factor and the radial distribution function. The static structure factor close to the gas-liquid critical point. Structure of multicomponent liquids. Molecular liquids and some examples of structure of complex liquids (colloids, proteins...).

Ch.4 - Microscopic models for the study of liquids.

How to calculate from the microscopic model the structure of a liquid with analytical approaches. Classical density functional theory. The Ornstein-Zernike equation and the closure relations. Different approximations to calculate the radial distribution functions. Some examples: fluid interfaces, colloidal suspensions.

Ch.5- Methods of computer simulation: molecular dynamics and Monte Carlo.

Connection between molecular dynamics and statistical mechanics. Algorithms for time evolution. Equilibration procedures. Long range corrections. Ewald method. MD in different ensembles. MD for molecular and complex liquids.

Monte Carlo integration and importance sampling. Markov processes. Ergodicity and detailed balance. Metropolis method. Monte Carlo sampling in different ensembles.

Ch.6 - Free energy and phase diagrams calculations by Computer simulation.

Description of the difficulties in computing the free energy in computer simulations. Different types of umbrella sampling methods. Finite size effects and finite size scaling methods. Simulation of critical phenomena.

Ch.7 - Time dependent correlation functions and response functions.

Definitions of the correlation functions. Linear response theory. Properties of the response functions. Fluctuation-dissipation theorem.

Ch.8 - Neutron and light scattering for liquid matter.

Neutron scattering and Light scattering in liquids.

Van Hove functions. Intermediate scattering functions. Dynamic structure factors. Relation with the response functions.

Ch.9 - Dynamics of liquids.

Brownian motion. Langevin equation.

Mean square displacement and diffusion. Hydrodynamic limit. Equations in the hydrodynamic limit. Viscoelastic regime. Langevin equation with memory effects. Memory functions.

Ch.10 - Supercooled liquids. Glass transition and Mode Coupling Theory.

Phenomenology of the glassy states. Thermodynamics of metastable states. Glass transition. Angell plot. The Adam-Gibbs theory. Dynamics of metastable states. The Mode Coupling Theory of the glass transition.

Ch.11 - Static and dynamical properties of water and aqueous solutions.

Water molecules and hydrogen bond. The phase diagram of water. Supercritical water. Supercooled water and its anomalous behavior. Glassy phases. Liquid-liquid transition hypothesis and its consequences. Confined water. W