10. M2 Soft Matter

Soft Matter: liquid crystals, polymers, foams & emulsions

Lecturer

C Oguey     ( oguey @ u-cergy.fr )     CM 15h, TD 15h

The field of complex liquids is rapidly expanding. Ranging from liquid crystals, soft solids to organic tissues, the subject covers a large variety of phases and structures with countless applications in cosmetics, food, synthetic materials, live matter, etc. We will examine the morphology and physical properties of these phases. Soft matter provides many opportunities to study, on concrete cases, some theories with broader scope.

Outline: chapters chosen in the list

1. Morphology
   1. Diffraction and scattering by liquid crystals
   2. Density, correlation functions
   3. Symmetries and order parameters
   4. Thermotropic liquid crystals: isotropic, nematic, cholesteric, smectic A and C, hexatic, discotic
2. Variational mean field theory
   1. Landau - deGennes theory of the isotropic nematic transition
   2. An inequality fo the partition function
   3. Optimisation Euler-Lagrange functional equations
   4. Application to the isotropic - nematic transition
3. Lyotropic systems
   1. Symmetries and phase diagram of amphiphilic solutions
   2. Micellar, lamellar, cubic mesophases, sponge phases, emulsions
   3. Diluted solutions, critical micellar concentration, distribution of aggregates
   4. Concentrated solutions, surfactant parameter and morphology of mesophases
4. Interfaces, films and membranes
   1. Geometry and energetics of surfaces: area, curvatures, surface tension
   2. Free energy of interfaces and films
   3. Profile of an interface by the Ginzburg-Landau approach
   4. Structures of quasi-equilibrium: constant mean curvature
   5. Fluctuations in the harmonic approximation
   6. Non linear effects: faceting, roughening
5. Heterogeneous systems, physics of foams
   1. Structure of foams in 2 and 3 dimensions, Laplace and Plateau laws
   2. Diffusion, Oswald ripening, scaling laws
   3. Topology and statistics of cellular assemblies: Euler-Poincaré, Aboav, Lewis
   4. Drainage
6. Polymers
   1. Free random walks
   2. Flory theory of interacting polymers
   3. Theta point and folding transition in dissolved polymers
7. Elastic properties and defects
   1. Fields, tensors, elastic free energy
   2. The case of nematics
   3. The case of smectics
   4. Topological theory of defects: vortex
   5. Disclinations, dislocations in smectics

References

1. P.M. Chaikin & T.C. Lubensky, Principles of condensed matter physics, Cambridge U.P. 1995.
2. P.G. de Gennes et J. Prost, The physics of liquid crystals, Oxford, Clarendon Press 1993
3. S.A. Safran, Statistical thermodynamics of surfaces, interfaces, and membranes Addison-Wesley 1994
4. P. Oswald et P. Pieranski, Les cristaux liquides : Concepts et propriétés physiques illustrés par des expériences, Tomes 1 et 2, Gordon and Breach 2000
5. M. Kléman et O.D. Lavrentovich, Soft matter physics : an introduction, Springer 2003
6. M. Laguës et A. Lesne, Invariances d’échelle : des changements d’états à la turbulence, Belin 2003

Problems & grading

C. Oguey, Sept. 2020