The course will introduce the main characteristics of "soft condensed matter": mixtures of liquids, liquid crystals, polymers, gels, colloids and glasses. The presence of meso-phases and out-of- equilibrium phases is explained by simple models based on thermodynamics and statistical mechanics. We use the physic models to explain the peculiar mechanical, optical and electrical properties of these materials. Some phenomena will be illustrated through simple practical demonstrations.
R.A.L. Jones, Soft Condensed Matter, Oxford University Press 2002.
Learning Objectives
Knowledge of the fundamental structural and dynamical properties of complex fluids and soft matter. Understanding of fundamental theoretical models for the interpretation of static and dynamic phenomena in condensed matter.
Prerequisites
Basic knowledge of thermodynamics and statistical mechanics
Teaching Methods
Lectures (6 credits, about 48 hours) with calculations done on the board and parallel use of slides for data and experimental techniques visualization. Realization of simple demonstration experiments.
Further information
Office hours for students:
Guarini:Tuesday 11.00-13.00 presso il Dipartimento di Fisica e Astronomia, studio 229
Torre: Tuesday 11.00-13.00 at LENS, studio 62
Oral exam with eventual presentation of a brief report (optional) on one of the topics covered.
Course program
Introduction to soft matter physics: phenomenology and complexity of these materials. Systems in thermodynamic equilibrium: Phase diagrams and equations of state. Out-of- equilibrium systems: metastable and amorphous phases .
Intermolecular potentials: potential definition. Attractive and repulsive bonds.
Theories of the liquid state: Density of configurational probability and microscopic density. Density autocorrelation function. Physical meaning and bond with the interaction potentials. Pair theory of liquids and thermodynamic properties. Mechanical Properties: stress tensor, strain tensor and strain rate. Constitutive equation. Solids, Newtonian and non -Newtonian liquids. Viscoelastic materials and simple theoretical models.
Optical properties: scattering processes with sample application in the classroom. Definition of the scattering tensor. Inelastic light scattering. Techniques for detection of the scattered radiation. Molecular theory of scattering phenomena.
Phase transitions: state functions , free energies and their derivatives. Ehrenfest classification. Critical phenomena and critical exponents. Order-disorder phase transition and order parameters. Introduction to Landau theory.
Liquid-liquid mixtures: critical opalescence. Statistical theory of phase separation. Introduction to the concepts of stability and metastability.
Liquid Crystals: Nature of liquid crystalline phases. Nematic - isotropic transition: orientational order parameter. Optical properties of a nematic phase and experimental observation of birefringence: calculation of the transmitted intensity with crossed polarizers.
DeGennes-Landau theory for the isotropic-nematic transition.
Elastic properties: Frank energy . Electrical properties: interaction energy between the electric field and the liquid crystal. Competition between elastic properties and electrical properties, Frederiks transition and its technologic relevance (Liquid Crystal Display).
Polymers: physical-chemical characteristics, structure, polymerization processes and examples. Free-Chain model. Random walk models for the polymer chains, Gaussian coil. Calculation of the configurational entropy and free energy; Kratky - Porod model and radius of gyration. Scattering of light by a Gaussian polymer chain.
Gel phases: physical and chemical gels. Elastic properties: polymers and rubbers; phenomena of entropic elasticity; gel transition models and percolative theories.
Colloids: definition and types; Single particle and Stokes' law; stochastic interactions and Brownian motion; diffusive motion and Einstein's law ; Inter-particle forces; Phases and stability.
Glasses: types of glasses, metastable liquids and out-of-equilibrium systems, experimental evidence of transition, Kauzman paradox. Entropic and dynamic theories of the glass transition.
Introduction to dynamic phenomena: Langevin equation, diffusion theories, fluctuation - dissipation theorem, outline of memory functions.
Outline of experimental studies :
Introduction to X-ray and neutron scattering in simple liquids structural studies using neutron diffraction and X-ray. Time-space autocorrelation function of the density, intermediate scattering function and the dynamic structure factor.
Introduction to non-linear optical spectroscopy, non-linear polarization and susceptibility; four-wave mixing techniques, experimental observables, response function and dynamics. Time-resolved experimental techniques: Optical Kerr effect and Transient Grating . Visit to the laboratories.