Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

Viscoelastic soft colloidal particles have been widely explored in mechanical, chemical, pharmaceutical and other engineering applications due to their unique combination of viscosity and elasticity. The characteristic viscoelastic relaxation time shows an Arrhenius-type (or super-Arrhenius due to temperature-dependent transition attempts) thermally-activated behavior, but a holistic explanation from the relevant transition-state theory remains elusive. In this paper, the viscoelastic relaxation times of Lennard-Jones soft colloidal particle systems, including a single particle type system and a binary particle mixture based on the Kob-Andersen model, are determined using molecular dynamics (MD) simulations as the benchmark. First, the particle systems show a non-Maxwellian behavior after comparing the MD-predicted viscoelastic relaxation time and dynamic moduli (storage and loss modulus) to the classic Maxwell viscoelastic model and the recent particle local connectivity theory. Surprisingly, neither the Maxwell relaxation time tau(Maxwell) (obtained from the static shear viscosity eta and the high-frequency shear modulus G(infinity)) nor the particle local connectivity lifetime tau(LC) can capture the super-Arrhenius temperature-dependent behavior in the MD-predicted relaxation time tau(MD). Then, the particle dissociation and association transition kinetics, fractal dimensions of the particle systems, and neighbor particle structure (obtained from the radial distribution functions) are shown to collectively determine the viscoelastic relaxation time. These factors are embedded into a new multi-dimensional transition kinetics model to directly estimate the viscoelastic relaxation time tau(Model), which is found to agree with the MD-predicted tau(MD) remarkably well. This work highlights the microscopic origin of viscoelastic relaxation dynamics of soft colloidal particles, and theoretically connects rheological dynamics and transition kinetics in soft matters.