Dynamics of semidilute solutions of polymers and associating polymers

A theory of dynamics and transport of polymers and polymer clusters in semidilute solutions is presented based on the coupling theory of the author generalized to include scaling concepts. In this theory the concentration fluctuation correlation function, phi(t) = <delta c(q)(t)delta c(-q)(t)>/<\delta c(q)/(2)> where delta c(q)(t) is the concentration fluctuation of wave-vector q, is a stretched exponential function of time, exp-(t/tau(q,c))(1-n(c)). The coupling parameter n(c) increases with c and the relaxation time tau(q,c) has the q(-2/(1-n(c))) dependence on q. These basic predictions are supported by several experimental investigations using dynamic light scattering of different systems including solutions of associating polymers, hydroxypropylcellulose/water solutions, and solutions of polymer cluster. Some of these experimental data will be revisited to bring out the detailed correspondence between theoretical predictions and experimental facts. The theory is further developed here and used to interpret the measured tracer diffusion coefficient (D) by Lodge and coworkers of linear and star-branched polystyrenes with molecular weights (M) in semidilute solutions of poly(vinyl methyl ether)/o-fluorotoluene for different matrix molecular weights (P) and concentrations (c). The theory is capable of explaining the M dependence of D at fixed P and c; the stretched exponential c dependence of D at constant M and P; and also the P dependence of D at constant c and M.