Size-Dependent Diffusion in the n -Alkanes

The translational diffusion constants, D, of trans -stilbene, 1,4-dipheny-1,3-butadiene, 1,6-dipheny-1,3,5-hexatriene, 1,1,4,4,-tetraphenyl-1,3-butadiene, tetraphenylethylene, 9,10-diphenylanthracene, p -terphenyl, bibenzyl, 1,1‘-binaphthyl, [2.2]paracyclophane, triptycene, and dodecahydrotriphenylene have been determined in the n -alkanes using capillary flow techniques. The solutes showed deviations from the Stokes−Einstein (SE) relation ( D = k B T /(6πη r )); the values of the hydrodynamic radius, r, decrease as the viscosity, η, increases. The data can be fitted to D / T = A SE /η p with p < 1 ( p = 1 for the SE relation). The values of p increase as the solute size increases; they range from p = 0.712 for p -terphenyl to p = 0.942 for 1,1,4,4,-tetraphenyl-1,3-butadiene. The deviations from SE behavior are discussed in terms of the ratio V s / V p, where V s and V p are the van der Waals volumes of a solvent and diffusing probe, respectively. The diffusion constants also are discussed in terms of the Wilke−Chang equation. The values of D -1 for several of the solutes are compared with their rotational correlation times, τ θ, in the n -alkanes. The values of τ θ, which showed deviations from the Stokes−Einstein−Debye expression (τ θ = 4π r 3 η/(3 k B T )), have the same general dependence on viscosity as D -1 .