Polymer Physics

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

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

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

- Calculate a fractal dimension.

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

- Predict the conformation of a chain in solution for given physico-chemical conditions.

- Be able to determine the size of the 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.

- Characterize the rheological properties (viscosity and elastic modulus) of polymeric liquids and gels.

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

Basic knowledge of the physics of surfaces, interfaces and colloids, and of equilibrium statistical physics.

Programming skills in Python or C,C++.

Full continuous assessment

In particular, the fundamental notion of entropy elasticity is studied in detail. Flory's theory of the conformation of a real chain is presented. The study of the conformations of an isolated chain under stress illustrates the important notions of blob and scaling law. The role of 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-dilute solution or melt, as well as at interfaces (adsorption, grafting or depletion).

The third chapter is devoted to the thermodynamics of polymer mixtures using 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 for predicting the elastic modulus of a polymeric gel.

The fifth chapter covers the essential aspects of understanding polymer dynamics, both in solution and in the melt: (Rouse dynamics, Zimm dynamics, respiration modes of a non-entangled semi-diluted solution, reptation theory for entangled chains).

The aim of two numerical simulation practical sessions is to use a programming language (Python, C, C++) to build a set of configurations for an ideal or self-evitating chain.