Friction on small objects and the breakdown of hydrodynamics in solution: Rotation of anthracene in poly(isobutylene) from the small-molecule to polymer limits

The friction on a nanometer-sized object, as measured by the molecular rotation time of dissolved anthracene, is compared to the macroscopic viscosity in poly(isobutylene) (PIB) over a molecular-weight range extending from the small-molecule limit (isooctane, M = 114 g/mol) to the entangled polymer (M = 85 000 g/mol). Calibration studies in small-molecule solvents show that anthracene rotation is a near ideal example of Stokes-Einstein-Debye (SED) behavior with slip boundary conditions. The average rotation time follows SED behavior based on the macroscopic viscosity eta(infinity) for PIBs up to a moderate length (M = 615 g/mol, eta(infinity) 2000 cP). Beyond this length, the rotational friction shows a sharp transition to a weak dependence on the polymer length. The transition length is not associated with any standard length scale of the static polymer structure. In particular, SED behavior continues well beyond the point where the solvent length or volume exceeds the solute's dimensions. An additional transition from exponential to nonexponential rotational relaxation occurs at a shorter polymer length. The breakdown of simple hydrodynamics and the SED model is attributed to exceeding a dynamical length scale associated with torsional flexibility and not to exceeding a simple ratio of solvent-to-solute size.