Rheology of Ring Copolymers in Dilute Solutions

We investigate the rheology of ring copolymers theoretically within the framework of the optimized Rouse-Zimm theory in dilute solutions. The ring copolymer is composed of two type of monomers (A and B) of different sizes (A < B), which is represented by unequal-sized beads connected via harmonic springs with different spring constants. The hydrodynamic interactions (HI) between the monomers is modeled using the preaveraged HI tensor. These interactions accelerate the collective relaxation modes and impede the local relaxation modes. In the presence of HI, the storage modulus shows a quasi-plateau regime, demonstrating a viscoelastic solid-like response of the polymer, while the loss modulus exhibits a bimodal pattern due to the difference in the mobilities of the monomers. The inverse of the crossover frequency represents the overall characteristic relaxation time, which is higher for the ring copolymers than for the Rouse rings, suggesting a slower relaxation of the ring copolymers due to the presence of relatively large sized monomers. The quasi-plateau in the storage modulus and the bimodality in the loss modulus are enhanced with an increase in the size and number fraction of B-type monomers. An increase in the size of the B-type monomers increases both storage and loss moduli, resulting in an overall decrease in the dynamics of the ring copolymers.