Statics and Dynamics of Dilute Polymer Solutions

Abstract

Polymers show universal behaviour at long length and time scales. In this chapter, the statics and dynamics of dilute polymer solutions are presented in terms of theoretical models that form the basis of polymer physics. The size of an ideal polymer is calculated from the freely jointed chain model, the freely rotating chain model and the Gaussian equivalent chain model. The Edwards Hamiltonian for a continuous ideal chain is obtained as a continuum limit of the Gaussian equivalent chain. The size of a real chain in good and poor solvents is estimated from the free energy that includes entropic and enthalpic contributions. The temperature dependence of chain size is discussed using the concept of thermal blobs. The force–extension relations for ideal and real polymers are illustrated using tension blobs. A brief introduction to stiff chains is presented in terms of the worm-like chain model. Starting from the Langevin equation for a Brownian particle, the salient features of the Rouse and Zimm models are presented. The behaviour of polymers under extensional, rotational, simple shear and linear-mixed flows is discussed using the finitely extensible Rouse chain.