Minimal model of relaxation in an associating fluid: Viscoelastic and dielectric relaxations in equilibrium polymer solutions

Abstract

Cluster formation and disintegration greatly complicate the description of relaxation processes in complex fluids. We systematically contrast the viscoelastic and dielectric properties for models of equilibrium polymers whose thermodynamic properties have previously been established. In particular, the monomer-mediated model allows chain growth to proceed only by monomer addition, while the scission-recombination model enables all particles to associate democratically, so that chain scission and fusion occur at the interior segments as well as at chain ends. The minimal models neglect hydrodynamic and entanglement interactions and are designed to explore systematically the competition between chemical reaction and internal chain relaxation and how this coupling modifies the dynamics from that of a polydisperse solution of Rouse chains with fixed lengths (i.e., "frozen" chains). As expected, the stress relaxation is nearly single exponential when the assembly-disassembly reaction is fast on the time scale of structural chain rearrangements, while multiexponential or nearly stretched exponential relaxation is obtained when this reaction rate is slow compared to the broad relaxation spectrum of almost unperturbed, nearly "dead" chains of intrinsically polydisperse equilibrium polymer solutions. More generally, a complicated intermediate behavior emerges from the interplay between the chemical kinetic events and internal chain motions.