Viscoelastic Relaxation of Rouse Chains undergoing Head-to-Head Association and Dissociation: Motional Coupling through Chemical Equilibrium

For nonentangled Rouse chains undergoing head-to-head association and dissociation reaction, the viscoelastic relaxation functions g1(t) and g2(t) were formulated for a case that a given dissociated unimer chain rapidly reassociates with its original partner unimer. The relaxation of the unimer and dimer was essentially determined by ratios ra and rd of the Rouse relaxation time (in the absence of reaction) to the association and dissociation times. For small ra and rd, the reaction was slow so that the unimer and dimer relaxed through respective pure Rouse modes, as naturally expected. However, for most cases in wide ranges of ra and rd, the dimer relaxation was accelerated with increasing rd (>1), and g2 of the dimer was indistinguishable from the pure Rouse relaxation function of the unimer, g1,Rouse. For those cases, g1 of the unimer also coincided with g1,Rouse. These results demonstrate that the motional coupling between the unimer and dimer, occurring through the association/dissociation reaction, strongly affects the relaxation. The Rouse modes of the unimer and dimer were found to split in two series due to this coupling, and new relaxation modes due to the coupling emerged as well. Those new modes largely contribute to g1 and g2 for the cases of ra, rd > 1, thereby compensating the difference between the split modes (involved in gj) and the pure Rouse modes (in g1,Rouse) to provide the unimer and dimer with the superficial coincidence between their gj and g1,Rouse. In addition, in limited cases of moderately small rd, the relaxation of odd modes of the dimer was accelerated by the dissociation but remained still slower than the relaxation of g1,Rouse. For this case, the unimer relaxation was slower than its pure Rouse relaxation (namely, the unimer relaxation was retarded by the reaction), because of the coupling with the dimer odd modes. This result confirmed the significant effect of motional coupling on the relaxation of the unimer and dimer.