Equilibrium and Dynamics of Dilute Polymer Solutions

Polymers show universal behavior at long length and time scales. In this chapter, the equilibrium and dynamics of dilute polymer solutions is 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 from a continuous limit of the Gaussian equivalent chains. 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 the tension blobs. A brief introduction to stiff chains is presented in terms of the wormlike chain model. Starting from the Langevin equation for a Brownian particle, the salient features of the Rouse and Zimm models are presented. The behavior of polymers under extensional, rotational, simple shear and linear-mixed flows is discussed using the finitely extensible Rouse chain.