Polymer Physics

Polymers are chain molecules made of a large number of covalently bonded elementary units, called monomers. The physics of polymers is a fairly young field that can roughly be divided into two pioneering time periods: From 1930 to 1960, fundamental concepts were developed about the conformation of a polymer, its dynamics, and the elasticity of rubbers. The main principles of modern polymer physics were then introduced in the subsequent 20 years (1960-1980), inspired in large part by the simultaneous development of the theory of critical phenomena and phase transitions. This course intends to give an introduction to the fascinating field of polymer physics, with a focus on the equilibrium statistical properties and equilibrium dynamics of polymers.

Classical statistical physics usually starts by positing a Hamiltonian. In the introductory chapter (Chapter 1), we will posit a Hamiltonian for a polymer before summarizing the main hypotheses for the following discussion. Chapters 2 & 3 deal with dilute solutions of polymers, where the polymer chains are isolated. The chapters introduce the main concepts for such single chains: the “ideal polymer” (persistence length, Gaussian chain model, structure factor of an ideal chain) and the “real polymer” (effect of solvent quality, Edwards Hamiltonian, Flory theory of chain size, relationship between polymers and critical phenomena). In chapter 4, the crossover from dilute solutions to polymer melts (i.e. polymer liquids without solvent) is discussed (semidilute solutions and scaling theory, Flory’s ideality hypothesis for polymer melts, temperature-concentration phase diagram, cursory introduction to polymer solids). The equilibrium properties, developed in chapters 2 to 4, form the basis for the discussion of the next two chapters. Chapter 5 introduces leading models for polymer dynamics (Rouse, Zimm, reptation models), which underlie our current molecular understanding of the practically important viscoelasticity of polymers (definition of stress and strain, stress-strain relation and viscoelasticity, Boltzmann’s superposition principle, shear relaxation modulus). We will see that the dynamics of long-chain polymer melts can be interpreted as if there existed long-lived physical crosslinks, due to topological interactions, between the polymers. The final chapter 6 then turns to the case where permanent crosslinks are introduced by purpose, e.g. chemical reactions (vulcanization), leading to a rubber. We study thermodynamic and viscoelastic properties of this specific polymer solid.

Bibliography

M. Rubinstein, R. H. Colby, Polymer Physics (Oxford University Press, Oxford, 2003)
M. Doi, S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986)
G. Strobl, The Physics of Polymers (Springer, Berlin-Heidelberg-New York, 2007)
Yn-Hwang Lin, Polymer Viscoelasticity (World Scientific, Singapore, 2011)