Simple liquids. Pair correlation functions. Density expansion of g(r) and two- and three-body interaction potential. Theories of the liquid state. Static and dynamic structure factor, their measurements. Complex liquids. Thermodynamical equilibrium and out of equilibrium conditions. Phase transitions and glass transition. Molecular correlation functions. Langevin equation, memory function, and mode-coupling theory. Dynamics of aggregate and supercooled liquids. Non-linear optical spectroscopy.
J. P. Hansen, I. R. McDonald, “Theory of Simple Liquids”, (Academic Press, London, 1986)
Gray C. G., Gubbins K. E., “Theory of Molecular Fluids”, (Clarendon, Oxford, 1984).
U. Balucani and M. Zoppi “Dynamics of the Liquid State”
(Clarendon Press, Oxford, 1994).
B.J.Berne and R. Pecora "Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics" (Dover Publications, Inc. Mineola, New York, 2000).
R.Torre "Time-resolved spectroscopy in complex liquids" (Springer, New York, 2008).
Learning Objectives
Knowledge of the basic structural and dynamical properties of simple and complex liquids. Dynamical processes and regimes in liquids. Collective and self dynamics of disordered systems and their experimental determination by various spectroscopic techniques: neutron and x-rays scattering; non-linear optical spectroscopy..
Prerequisites
Advised: Mathematical Methods
Teaching Methods
Traditional lectures (6 CFU, about 55 hours) with some calculations carried out at the blackboard. Parallel use of transparencies for the description of experimental data and techniques, and for the outline of the fundamental formulas presented during the lecture.
Further information
Weekly availability for students: Guarini: Tuesday 11.00-13.00 at the Physics and Astronomy Department, room 229
Torre: Tuesday 11.00-13.00 at LENS, room 62
Type of Assessment
Oral exam with a possible short presentation (optional) on one of the subjects of the part regarding simple liquids.
Course program
Static structure of simple liquids. Classical statistical mechanics and ensemble averages: useful results to remember. n-particle configurational probability density. n-particle microscopic density. Pair distribution function g(r) as density-density autocorrelation function. Physical meaning and properties of g(r), and its relation with the many-body interaction potential. Pair theory of liquids and relation between g(r) and the thermodynamical properties of the liquid. The short and long-range interaction potential and phenomenological models for the two- and three-body interactions.
Density expansion of g(r). Introduction to the cluster expansion. Low-density limit of g(r) and relation with the pair potential. Theories for the liquid state. Pair correlation functions: total and direct correlation. Ornstein-Zernike equation. Percus-Yevick, Hypernetted Chain, Modified Hypernetted Chain approximations. The static structure factor, its relation with g(r), physical meaning and properties. Introduction to neutron and X-rays scattering. Recent structural studies in simple liquids by neutron and X-rays diffraction.
Generalization to the dynamical case: space-time correlation functions. Space and time dependent density-density autocorrelation function. Intermediate scattering function and dynamic structure factor. Collective and single-particle dynamics. Dynamical regimes. The self dynamic structure factor in the kinetic and diffusive regimes
The dynamic structure factor from hydrodynamic theory. Viscoelastic model and brief introduction to the memory function formalism. Extraction of collective modes dispersion curves in simple liquids and relaxation times of the memory function from inelastic neutron or X-rays scattering data.
Complex Liquids
Introduction: Types and general characteristics, thermodynamic aspects (equilibrium and off equilibrium), Phases and mesophase (liquid crystals and plastic).
Phase transitions phenomenology: basic theories (free energies, Ehrenfest classification, Theory of Landau-Ginburg). Metastable, supercooled and glass phases, Thermodynamics and stability ST diagram and relaxation phenomena, metastable liquids in nature and technology.
Physical and experimental observables for light scattering: average and coarse-graining (macro, meso and micro), the correlation functions in phase or Fourier space. Microscopic function of the dielectric constant and its correlations, power spectrum and dynamic structure factors.
Introduction to the dynamics of liquids: Fluctuations and equilibrium thermodynamics. hydrodynamic equations
Linear Spectroscopy: Scattering of light in frequency space, measured spectra and liquid dynamics, Diffusion phenomena and propagation modes.
Non-linear Spectroscopy: Non-linear polarization and susceptibility, Four-wave mixing techniques, Experimental observables, Response functions and liquid dynamics.
Time resolved experimental techniques: optical Kerr effect and Transient Grating.