Simulating Nanoparticle and Polymer Dynamics in Solution

The dynamics of nanoparticles in complex fluids are of great interest for applications in drug delivery, oil recovery, and materials processing. Particle mobility is well described by the generalized Stokes-Einstein (GSE) relation when the nanoparticles are much larger than the polymers. Violations of GSE predictions are observed, however, when the size of nanoparticles is comparable to or smaller than length scales in polymer solutions. We investigate the microscopic origin of this anomalous behaviour using multi-particle collision dynamics (MPCD), an advanced algorithm for rigorously modelling solvent-mediated hydrodynamic interactions in coarse-grained, mesoscale simulations. We apply MPCD to study transport in nanoparticle-polymer systems and the effects of many-body hydrodynamic interactions on this behaviour. We demonstrate that the translational center-of-mass motions of both nanoparticles and polymers are sub-diffusive on short times before transitioning into a diffusive regime on longer time scales. In solutions of flexible, linear polymer chains, the long-time diffusivities of nanoparticles collapse according to scaling predictions, in accord with recent experiments. The sub-diffusive behavior predicted by MPCD simulations, by contrast, agrees with experiments, but significantly deviates from theoretical predictions. We show that this disagreement is due to a hitherto unreported transport mechanism characterized by the tight coupling of the translational motions of the nanoparticle and polymer centers-of-masses, which is not accounted for in current theories. We explore the consequences of this new coupling mechanism and perform extensive MPCD studies to investigate how it is influenced by hydrodynamic interactions and polymer concentration, stiffness, and morphology.