Polymer Dynamics

Abstract Chapter 9 focuses on molecular models of polymer dynamics in solutions, melts and networks. The discussion begins with an overview of Brownian motion and a derivation of the Stokes–Einstein relationship between the self-diffusion coefficient and the friction coefficient in a dilute solution of particles. The result is obtained in the framework of Langevin dynamics. This approach is extended to relaxation dynamics of polymer chain by reformulating the Rouse and Zimm models in terms of the real-space mode representation instead or the usual Fourier mode analysis. The dynamics of semidilute polymer solutions is described in the framework of a scaling approach by taking into account the screening of the hydrodynamic interactions on length scales of the solution correlation length. The final sections of the chapter deal with chain entanglements in melts and solutions. It introduces an entanglement criterium by expressing the entanglement degree of polymerization in terms of the chain’s packing parameter. The concept of entanglements is extended to polymer solutions by representing polymers as chains of correlation blobs. The chapter ends with a brief overview of the reptation motion of stars and comb-like polymers in a melt.