Bruce A. Kowert

Size-dependent diffusion in cycloalkanes

The translational diffusion constants, D, of biphenyl, trans-stilbene, 1,4-diphenyl-1,3-butadiene, 1,1,4,4-tetraphenyl-1,3-butadiene, 1,6-diphenyl-1,3,5-hexatriene, tetraphenylethylene, 9,10-diphenylanthracene, bibenzyl, triptycene, perylene and 2,3-benzanthracene (tetracene) have been measured in combinations of the cycloalkanes cyclohexane, methylcyclohexane, n-butylcyclohexane, cis-decalin and trans-decalin using capillary flow techniques. Tetracene and chrycene have been studied in a series of n-alkanes. Deviations from the Stokes–Einstein (SE) relation (D = k B T/6πηr) were found. For a given solute, the hydrodynamic radius r decreases as both the viscosity η and the solvent/solute size ratio increase; the data were fitted to D/T = A/η  p with p<1 (p = 1 for the SE relation). The p values in the cycloalkanes increase as the solute size increases, are compared to the values in the n-alkanes and are discussed in terms of the properties of the two types of solvent. The experimental D values also are compared to the predictions of the Wilke–Chang equation and a free volume model which includes both the masses and sizes of the solution components.

Diffusion of Organic Solutes in Squalane

The translational diffusion constants, D, of 26 hydrocarbons have been determined in squalane (2,6,10,15,19,23-hexamethyltetracosane) at room temperature using capillary flow techniques. These new data and previously published room-temperature D values for the same solutes in some (or all) of the n-alkanes n-C(6)-n-C(16) constitute a study of solute diffusion in media spanning a 100-fold change in viscosity; at 23 °C, η = 0.31 cP for n-C(6), 3.2 cP for n-C(16), and 30 cP for squalane. The D values in the n-alkanes and squalane show deviations from the Stokes-Einstein relation, D = k(B)T/(6πηr); the values of r, a solutes hydrodynamic radius, decrease as the viscosity increases. The deviations increase as the solute size decreases and are analyzed by fitting the diffusion constants to the modified Stokes-Einstein equation, D/T = A(SE)/η(p). Fits involving the n-alkane-only and combined n-alkane-squalane D values give comparable results with values of p < 1 that increase as the solute size increases; p = 1 for the Stokes-Einstein limit. The deviations from Stokes-Einstein behavior also are discussed in terms of the relative sizes of the solutes, the n-alkanes, and squalane.

Diffusion of dioxygen in 1-alkenes and biphenyl in perfluoro-n-alkanes

Abstract The translational diffusion constant, D , has been measured for O 2 in the even 1-alkenes 1-C 6 H 12 to 1-C 16 H 32 and biphenyl in n -C 6 F 14 and n -C 9 F 20 . Deviations from the Stokes–Einstein relation were found; the use of D / T = A / η p gave p =0.560±0.017 for O 2 in the 1-alkenes, the same (within experimental error) as found previously for O 2 in the n -alkanes. The charge transfer (CT) transition used to detect O 2 in the 1-alkenes is at 220 nm. The D values for biphenyl in the perfluoro- n -alkanes (PFAs) are consistent with those in the n -alkanes, where p =0.718±0.004. These results suggest that O 2 has similar solute–solvent interactions in both the 1-alkenes and n -alkanes as does biphenyl in the n -alkanes and PFAs.

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.

Self-exchange reaction of [Ni(mnt)2](1-,2-) in nonaqueous solutions.

The rate constant, k, for the homogeneous electron transfer (self-exchange) reaction between the diamagnetic bis(maleonitriledithiolato)nickel dianion, [Ni(mnt) 2] (2-), and the paramagnetic monoanion, [Ni(mnt) 2] (1-), has been determined in acetone and nitromethane (CH 3NO 2) using (13)C NMR line widths at 22 degrees C (mnt = 1,2-S 2C 2(CN) 2). The values of k (2.91 x 10 (6) M (-1) s (-1) in acetone, 5.78 x 10 (6) M (-1) s (-1) in CH 3NO 2) are faster than those for the electron transfer reactions of other Ni(III,II) couples; the structures of [Ni(mnt) 2] (1-) and [Ni(mnt) 2] (2-) allow for a favorable overlap that lowers the free energy of activation. The values of k are consistent with the predictions of Marcus theory. In addition to k, the spin-lattice relaxation time, T 1e, of [Ni(mnt) 2] (1-) is obtained from the NMR line width analysis; the values are consistent with those predicted by spin relaxation theory.

TRANSLATIONAL DIFFUSION OF TRANSITION METAL COMPLEXES

Abstract Capillary flow techniques have been used to measure D T , the translational diffusion constant at temperature T , for three transition metal complexes in several low-viscosity liquids. The translational radius, r t , for each of the complexes was obtained from D T using the Stokes–Einstein relation. The common value of r t of Ni(mnt) 2 − in n -butyl alcohol, acetonitrile (ACN), acetone, and ethyl alcohol (EtOH) indicates that the apparently different rotational radii (from ESR) in a series of polar solvents are due to solute–solvent interactions and not to solvation or ion pairing. Another complex, Ni(mnt) 2 2− , was also studied in ACN; our values of D T for Ni(mnt) 2 2− and Ni(mnt) 2 − in ACN are in agreement with electrochemical values. The reproducibility of our techniques was checked by using three different capillaries to make four separate determinations of D T for Ni(mnt) 2 − in EtOH; the values are in good agreement. Values of D T were measured for Mn(Cat–N–SQ) 2 , MnR 2 , in tetrahydrofuran, 2-methyltetrahydrofuran, diethyl ether, and acetone. This complex is of interest because of its screw-propeller geometry. The values of r t in our solvents are in agreement with each other and are consistent with ESR studies of the reorientational motion of MnR 2 .

Investigation of the reorientational dynamics of the bis (maleonitriledithiolato) nickel anion radical using electron spin resonance lineshapes

Abstract Electron spin resonance spectra of the bis(maleonitriledithiolato) nickel anion radical, Ni(mnt)2−, have been calculated and compared with the experimental results of Huang and Kivelson in n-butyl alcohol. The calculated spectra show that the well-defined principal line found experimentally (for all motional rates) is produced when the reorientational motion of Ni (mnt)2− is described by axially symmetric Brownian rotational diffusion. The long in-plane axis is the symmetry axis of the rotational diffusion tensor; the rotational diffusion constant for the reorientation about the symmetry axis is approximately three times larger than the rotational diffusion constant for the reorientation about the two axes perpendicular to the symmetry axis. This motional model also produces calculated widths of the principal line which are in agreement with the experimental widths when the reorientational modulation of the anisotropic Zeeman interaction makes the dominant contribution to the widths. There is a lack of agreement between the experimental and calculated widths in the fast motional region near the minimum experimental width. The lack of agreement is discussed in terms of the spin rotation and nonsecular Zeeman contributions as well as the temperature dependence of the g factors of Ni(mnt)2−. ESR spectra and principal linewidths calculated using computer programs with and without the nonsecular Zeeman (electron spin flip) terms have been compared for motional rates in the fast and intermediate motional regions.

d‐electron count, ion‐pairing and diagonal twist angles in metallo‐bis(dithiolene) complexes

Electronic structure calculations for late transition metals coordinated by two dithiolene ligands are found to be consistent with existing structures and also predict the geometries of Ni(I) species for which no solid state structures have been reported. Of particular interest are the compounds [M(mnt)2]n− (M = Ni, Pd, and Pt with n = 1, 2, 3; M = Cu with n = 2). Calculations have been performed with and without ion‐paring with M(diglyme)+ (M = Li, Na, K) and R4N+ (R = Me, Bu). The diagonal twist angle between two NiS2 planes is found to depend on (i) the metals d‐electron count, spanning from 0° (planar d7 and d8), to 42° (d9), to 90° (pseudo‐tetrahedral d10), and (ii) the identity of the ion‐paired cations. Calculated ion‐pairing energies are functions of the cation size and charge‐density, being larger for alkali‐metal coordinated diglyme and smaller for tetra‐alkyl ammonium cations.

Molecular motion of the bis(maleonitriledithiolato)nickel trianion in solution.

Electron spin resonance (ESR) has been used to study the reorientational motion of the bis(maleonitriledithiolato)nickel trianion, [Ni(mnt)(2)](3-), in diethylene glycol dimethyl ether (diglyme). [Ni(mnt)(2)](3-) has one unpaired electron and was prepared by reducing the dianion, [Ni(mnt)(2)](2-), with potassium metal. The trianion and dianion are members of the redox series [Ni(mnt)(2)](n-) with n = 0, 1, 2, and 3. The monoanion, [Ni(mnt)(2)](-), also has S = 1/2 and its rotational diffusion in diglyme was the subject of previous ESR studies. This made possible the comparison of the reorientational data for two different oxidation states of the same planar complex in the same solvent. Differences were found; isotropic rotational diffusion produced agreement between the trianions experimental and calculated spectra, whereas the monoanions simulations required axially symmetric reorientation with diffusion about the long in-plane axis three times faster than that about the two perpendicular axes. At a given temperature, the monoanions reorientation rates about the long in-plane axis and two perpendicular axes were faster than the trianions isotropic rate by factors of ∼27 and ∼9, respectively. These differences suggest that [Ni(mnt)(2)](-) and [Ni(mnt)(2)](3-) have different shapes and sizes in solution; the monoanion is approximately a prolate ellipsoid, whereas the trianion is larger and more spherical. [Ni(mnt)(2)](3-) appears to be ion-paired, whereas in accord with results from other techniques, [Ni(mnt)(2)](-) is not.

The use of electron spin resonance linewidths to obtain anisotropic g factors

Electron spin resonance linewidths have been used to obtain a considerable body of information concerning the reorientational motion of radicals with electron spin S = f; the investigations have been carried out in a wide variety of solvents (1, 2). The linewidths are also potential sources of structural data; linewidth analyses have been used to determine the sign or relative sign of the isotropic hyperfine splitting constants, ai, for magnetic nuclei in a number of different radicals (3). Another possibility is the use of ESR linewidths to estimate the three principal g factors (gX, g,,, gz) that characterize the Zeeman interaction between the electron spin and the bulk magnetic field (3). A generalization of the method that has previously been used to calculate the g factors (4, 5) from linewidth parameters is the purpose of this Note. We will consider a radical with S = f and hyperline splittings from two nuclei (i and j) with unequal isotropic hyperhne splitting constants (]ai] # ]Uj], i.e., no degenerate transitions). In the fast-motion (Redfield) limit, the ESR linewidths for this type of radical are given by (6, 7)