Polymer Physics

Polymer physics—to which this course serves as an introduction—focuses on the physical properties of covalently bonded chain-like assemblies ranging from a few dozen to a few 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 highly distinctive 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.

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

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

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

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

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

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

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

Proficiency in programming in Python or C, C++

Comprehensive Continuous Monitoring

The first chapter deals with the conformations of an isolated chain—first an ideal one, then a real one. 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 the blob and the scaling law. The role of solvent quality on the conformation of an isolated chain is detailed.

The second chapter discusses the structure and conformation of a chain assembly in semi-dilute solutions or melts, as well as at interfaces (adsorption, grafting, or depletion).

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

Chapter 4 deals with polymeric networks (gels, rubbers) and, in particular, discusses the affine model, which can be used to predict the elastic modulus of a polymeric gel.

Chapter 5 covers the essential aspects of understanding polymer dynamics, whether in solution or in the melt: (Rouse dynamics, Zimm dynamics, breathing modes of a non-entangled semidilute solution, and the theory of reptation for entangled chains).

Two computer simulation lab sessions will focus on using a programming language (Python, C, C++) to build all possible configurations of an ideal or self-avoiding chain.