Intrinsic viscosities for linear and ring polymers using renormalisation group techniques

Intrinsic viscosity and dielectric relaxation of ring polymers in dilute solutions

The absence of chain ends makes ring polymers distinctly different from their linear analogues. The intrinsic viscosity, complex viscosity and the dielectric relaxation of ring polymers are investigated within the tenets of the optimized Rouse-Zimm theory. The distance dependent excluded volume interactions (EVIs) are obtained from Flory's mean field theory. The hydrodynamic interactions (HIs) between the pairs of monomers are estimated using the preaveraged Oseen tensor. The intrinsic viscosity of linear and ring polymers both with and without EVI are compared as a function of ring size. A monotonically increasing trend of the intrinsic viscosity is observed in both cases. The intrinsic viscosity of both linear and ring polymers both with and without EVI show a very good agreement with the experimental results of polystyrene over a wide range of molecular weights in both good and theta solvents, respectively. The fractal dimensions of the ring polymers with EVI lie between that of a random walk and a self-avoiding walk model of linear polymers in three dimensions. The ring size increases with EVI and the effect of EVI is stronger on larger rings than that on smaller rings. The dielectric relaxation follow a connectivity independent universal scaling behavior at low and high frequency regions. The imaginary part of the complex dielectric susceptibility displays a local maxima in the intermediate frequency region, which reveals a structure dependent behavior of the rings. The theoretically calculated dielectric loss of ring polymers with HI matches well with those obtained from experiments.

Dynamic renormalization in the framework of nonequilibrium thermodynamics

We show how the dynamic renormalization of nonequilibrium systems can be carried out within the general framework of nonequilibrium thermodynamics. Whereas the renormalization of Hamiltonians is well known from equilibrium thermodynamics, the renormalization of dissipative brackets, or friction matrices, is the main new feature for nonequilibrium systems. Renormalization is a reduction rather than a coarse-graining technique; that is, no new dissipative processes arise in the dynamic renormalization procedure. The general ideas are illustrated for dilute polymer solutions where, in renormalizing bead-spring chain models, dissipative hydrodynamic interactions between different smaller beads contribute to the friction coefficient of a single larger bead.