Polymer Physics

Polymer physics, of which this course is an introduction, is concerned with the physical properties of covalent assemblies in chains, from a few tens to a few millions of elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in solid, liquid, solution, colloidal or confined to an interface.

Their very particular physical properties have led to the development of specific theoretical tools and to the appearance of this new branch of physics with numerous applications.

- Compute a fractal dimension.

- Master Flory's theory for the conformation of an isolated chain.

- Know how to predict the conformation of a chain in solution for given physicochemical conditions.

- Be able to determine the size of relevant blobs for stressed chains and deduce the corresponding free energy and average conformation of these chains.

- Identify and master the concepts of static and dynamic correlation lengths of polymers in solution.

- Construct a phase diagram of a polymer mixture or solution.

- Know how to characterize the rheological properties (viscosity and elastic modulus) of polymeric liquids and gels.

- Numerically model (Python, C or C++) all the configurations of an ideal or self-evident chain.

Basic knowledge of surface physics, interfaces and colloids, and statistical equilibrium physics.

Mastery of programming in Python or C,C++ language

Continuous control

The first chapter deals with the conformations of an isolated, ideal and then real chain. In particular, the fundamental notion of entropic elasticity is studied in detail. The Flory theory of the conformation of a real chain is presented. The study of the conformations of an isolated chain under stress allows to illustrate the important notion of blob and scaling law. The role of the solvent quality on the conformation of an isolated chain is detailed.

The second chapter deals with the structure and conformation of a chain assembly in semi-diluted solution or in melt, as well as at the interfaces (adsorption, grafting or depletion).

The third chapter is devoted to the thermodynamics of polymer mixtures treated by the Flory-Huggins lattice theory and to the construction of the phase diagram of a binary polymer/solvent or polymer/polymer mixture.

The fourth chapter deals with polymeric networks (gels, rubbers) and in particular develops the affine model which allows to predict the elastic modulus of a polymeric gel.

The fifth chapter unfolds the essential aspects of understanding the dynamics of polymers, in solution or in melt: (Rouse dynamics, Zimm dynamics, respiration modes of a semi-enmeshed solution, reptation theory, for entangled chains).

Two sessions of numerical simulation will aim to build, using a programming language (Python, C, C++), the set of configurations of an ideal or self-evident chain.