Polymer Physics

Polymer physics, to which this course provides an introduction, focuses on the physical properties of covalent chain assemblies, ranging from a few dozen to several million elementary molecules: polymers or macromolecules.

These synthetic or natural molecules can be observed in the solid state, liquid state, in solution, in a colloidal state, 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 a single chain.

- Be able to predict the conformation of a chain in solution for given physicochemical conditions.

- Be able to determine the size of relevant blobs for constrained 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.

- Digitally model (Python, C, or C++) all configurations of an ideal or self-avoiding chain.

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

Proficiency in Python or C, C++ programming languages

Continuous assessment

The first chapter deals with the conformations of an isolated chain, first ideal and then real. In particular, the fundamental concept of entropic 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 concepts of blobs and scaling laws. The role of solvent quality on the conformation of an isolated chain is detailed.

The second chapter deals with the structure and conformation of an assembly of chains in semi-diluted or molten solutions, as well as at interfaces (adsorption, grafting, or depletion).

The third chapter is devoted to the thermodynamics of polymer blends as treated by the Flory-Huggins network theory and to the construction of the phase diagram of a binary polymer/solvent or polymer/polymer blend.

The fourth chapter deals with polymer networks (gels, rubbers) and, in particular, develops the affine model that can be used to predict the elastic modulus of a polymer gel.

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

Two practical sessions on digital simulation will aim to build, using a programming language (Python, C, C++), all the configurations of an ideal or self-avoiding chain.