Diffusion of Buckminsterfullerene in n-Alkanes

Explicit expression for the Stokes-Einstein relation for pure Lennard-Jones liquids

An explicit expression of the Stokes-Einstein (SE) relation in molecular scale has been determined for pure Lennard-Jones (LJ) liquids on the saturated vapor line using a molecular dynamics calculation with the Green-Kubo formula, as Dη(sv)=kTξ(-1)(N/V)(1/3), where D is the self-diffusion coefficient, η(sv) the shear viscosity, k the Boltzmann constant, T the temperature, ξ the constant, and N the particle number included in the system volume V. To this end, the dependence of D and η(sv) on packing fraction, η, and T has been determined so as to complete their scaling equations. The equations for D and η(sv) in these states are m(-1/2)(N/V)(-1/3)(1-η)(4)ε(-1/2)T and m(1/2)(N/V)(2/3)(1-η)(-4)ε(1/2)T(0), respectively, where m and ε are the atomic mass and characteristic parameter of energy used in the LJ potentials, respectively. The equations can well describe the behaviors of D and η(sv) for both the LJ and the real rare-gas liquids. The obtained SE relation justifies the theoretical equation proposed by Eyring and Ree, although the value of ξ is slightly different from that given by them. The difference of the obtained expression from the original SE relation, Dη(sv)=(kT/2π)σ(-1), where σ means the particle size, is the presence of the η(1/3) term, since (N/V)(1/3)=(6/π)(1/3)σ(-1)η(1/3). Since the original SE relation is based on the fluid mechanics for continuum media, allowing the presence of voids in liquids is the origin of the η(1/3) term. Therefore, also from this viewpoint, the present expression is more justifiable in molecular scale than the original SE relation. As a result, the η(1/3) term cancels out the σ dependence from the original SE relation. The present result clearly shows that it is not necessary to attribute the deviation from the original SE relation to any temperature dependence of particle size or to introduce the fractional SE relation for pure LJ liquids. It turned out that the η dependence of both D and η(sv) is similar to that in the corresponding equations by the Enskog theory for hard sphere (HS) fluids, although the T dependence is very different, which means that the difference in the behaviors of D and η(sv) between the LJ and HS fluids are traceable simply to their temperature dependence. Although the SE relation for the HS fluids also follows Dη(sv)=kTξ(-1((N/V)(1/3), the value of ξ is significantly different from that for the LJ liquids.

Diffusion of squalene in n-alkanes and squalane

Squalene, an intermediate in the biosynthesis of cholesterol, has a 24-carbon backbone with six methyl groups and six isolated double bonds. Capillary flow techniques have been used to determine its translational diffusion constant, D, at room temperature in squalane, n-C16, and three n-C8-squalane mixtures. The D values have a weaker dependence on viscosity, η, than predicted by the Stokes-Einstein relation, D = kBT/(6πηr). A fit to the modified relation, D/T = ASE/η(p), gives p = 0.820 ± 0.028; p = 1 for the Stokes-Einstein limit. The translational motion of squalene appears to be much like that of n-alkane solutes with comparable chain lengths; their D values show similar deviations from the Stokes-Einstein model. The n-alkane with the same carbon chain length as squalene, n-C24, has a near-equal p value of 0.844 ± 0.018 in n-alkane solvents. The values of the hydrodynamic radius, r, for n-C24, squalene, and other n-alkane solutes decrease as the viscosity increases and have a common dependence on the van der Waals volumes of the solute and solvent. The possibility of studying squalene in lipid droplets and membranes is discussed.

Bimolecular encounters and re-encounters (cage effect) of a spin-labeled analogue of cholestane in a series of n-alkanes: effect of anisotropic exchange integral

Electron paramagnetic resonance (EPR) spectra of the nitroxide spin probe 3β-doxyl-5α-cholestane (CSL) are studied as functions of the molar concentration, c, and the temperature, T, in a series of n-alkanes. The results are compared with a similar study of a much smaller spin probe, perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (pDT). The Heisenberg spin exchange (HSE) rate constants, K(ex), of CSL are similar in hexane, octane, and decane and are about one-half of those for pDT in the same solvents. They are also about one-half of the Stokes-Einstein-Perrin prediction. This reduction in HSE efficiency is attributed to an effective steric factor, f(eff), which was evaluated by comparing the results with the Stokes-Einstein-Perrin prediction or with pDT, and it is equal to 0.49 ± 0.03, independent of temperature. The unpaired spin density in CSL is localized near one end of the long molecule, so the exchange integral, J, leading to HSE, is expected to be large in some collisions and small in others; thus, J is modeled by an ideal distribution of values of J = J(0) with probability f and J = 0 with probability (1 - f). Because of rotational and translation diffusion during contact and between re-encounters of the probe, the effective steric factor is predicted to be f(eff) = f(1/2). Estimating the fraction of the surface of CSL with rich spin density yields a theoretical estimate of f(eff) = 0.59 ± 0.08, in satisfactory agreement with experiment. HSE is well described by simple hydrodynamic theory, with only a small dependence on solvent-probe relative sizes at the same value of T/η, where η is the viscosity of the solvent. This result is probably due to a fortuitous interplay between long- and short-range effects that describe diffusion processes over relatively large distances. In contrast, dipole-dipole interactions (DD) as measured by the line broadening, B(dip), and the mean time between re-encounters within the cage, τ(RE), vary significantly with the solvent-probe size ratio at the same value of T/η. For these phenomena, dominated by short-range diffusion, the reciprocal fractional free volume V(0)/V(f) provides a better description of the diffusion. Thus, B(dip) and τ(RE) form common curves when plotted vs V(0)/V(f). As a result, the fractional broadening by DD occurs at an order of magnitude higher values of T/η for CSL compared with pDT.

Diffusion Coefficients of C60 and C60- in Benzonitrile and Dichloromethane Solutions Containing Tetrabutylammonium Perchlorate, Measured by Potential-step Chronoamperometry

The diffusion coefficients of C(60) in dichloromethane and benzonitrile solutions containing 0.1 M tetrabutylammonium perchlorate were determined by single potential-step chronoamperometry at small disk electrodes. The diffusion coefficients of C(60) were obtained by curve fitting of the chronoamperograms to a theoretical equation by Shoup and Szabo. The values were (1.4 +/- 0.3) x 10(-9) and (4.1 +/- 0.3) x 10(-10) m(2) s(-1), respectively (the errors are 95% confidence limits). The diffusion coefficients of C(60)(-) in these solutions were measured by double potential-step chronoamperometry. The ratios of the diffusion coefficients of C(60) to those of C(60)(-) were obtained from theoretical curves of the ratios of the current at the second potential step to the current at the first one. The values of the ratios were 1.2 +/- 0.2 and 1.0 +/- 0.3, respectively.