Diffusion of aromatic compounds in nonaqueous solvents: A study of solute, solvent, and temperature dependences

Do Electrostatics Control the Diffusive Dynamics of Solitary Water? NMR and MD Studies of Water Translation and Rotation in Dipolar and Ionic Solvents

NMR-based measurements of the diffusion coefficients and rotation times of solitary water and benzene at 300 K are reported in a diverse collection of 13 conventional organic solvents and 10 imidazolium ionic liquids. Proton chemical shifts of water are found to be correlated to water OH-stretching frequencies, confirming the importance of electrostatic interactions in these shifts. However, the influence of magnetic interactions in aromatic solvents renders chemical shifts a less reliable indicator of electrostatics. Diffusion coefficients (DB) and rotational correlation times (τB) of benzene in the solvents examined are accurately described as functions of viscosity (η) by DB ∝ η-0.81 and τB ∝ η0.64. Literature values of DB and τB in alkane and normal alcohols, which were not included among the solvents studied here, are systematically faster than predicted by these correlations, indicating that factors beyond solvent viscosity play a role in determining the friction on benzene. In contrast to benzene, water diffusion and rotation are poorly described in terms of viscosity alone, even in the dipolar and ionic solvents measured here. The present data and the substantial literature data already available on dilute water diffusion show a systematic dependence of DW on solvent polarity among isoviscous solvents. The aspect of solvent polarity most relevant to water dynamics is the ability of a solvent to accept hydrogen bonds from water, as conveniently quantified by the frequency of water's OH stretching band, ΔνOH. The friction on translation, ζtr = kBT/DW, and rotation, ζrot = kBTτW, are both well correlated by functions of the form ζ(η, ΔνOH) = a1ηa2 exp (a3ΔνOH), where the ai are adjustable parameters. Molecular dynamics simulations reveal a strong coupling between electrostatic and nonelectrostatic water-solvent interactions, which makes it impossible to dissect the friction on water into additive dielectric and hydrodynamic components. Simulations also provide a tentative explanation for the unusual form of the correlating function ζ(η, ΔνOH), at least in the case of ζrot.

Diffusion of Squalene in Nonaqueous Solvents

Capillary flow techniques have been used to determine the translational diffusion constant, D, of squalene in seven alkanes and five cyclohexanes. The alkanes are n-hexane, n-octane, n-decane, n-dodecane, n-tetradecane, 2,2,4,4,6,8,8-heptamethylnonane (isocetane), and 2,6,10,14-tetramethylpentadecane (pristane). The cyclohexanes are cyclohexane, n-butylcyclohexane, n-hexylcyclohexane, n-octylcyclohexane, and n-dodecylcyclohexane. When combined with published data in CD₂Cl₂, ethyl acetate, n-hexadecane, squalane, n-octane-squalane mixtures, and supercritical CO₂, the 35 diffusion constants and viscosities, η, vary by factors of ∼230 and ∼500, respectively. A fit to the modified Stokes-Einstein equation (MSE, D/T = A _SE/η ^p ) gives an average absolute percentage difference (AAPD) of 7.72% between the experimental and calculated D values where p and A _SE are constants, T is the absolute temperature, and the AAPD is the average value of (10²) (|D _calcd - D _exptl|/D _exptl). Two other MSE fits using subsets of the 35 diffusion constants may be useful for (a) estimating the viscosity of the hydrophobic core of lipid droplets, where squalene is a naturally occurring component, and (b) providing estimates of the D values needed to design extraction processes by which squalene is obtained from plant oils. The Wilke-Chang equation also was considered and found to give larger AAPDs than the corresponding MSE fits.

Double liquid-core cylindrical lens utilized to measure liquid diffusion coefficient

We design and fabricate an aplanatic double liquid-core cylindrical lens (DLCL), which is used to measure the binary liquid diffusion coefficient (D). The front lens of the DLCL is used as both a diffusion cell and a key imaging element; the refractive index (RI) of liquid filled in its core can be measured in the way of spatial resolution. The rear lens of the DLCL is used as an aplanatic component, and either the RI position of spherical aberration (SA) or the SA in a range of RI caused by the front lens can be regulated by selecting the liquid, of which RI is pre-prepared and filled in the rear liquid core. Equipped with the aplanatic DLCL, two methods have been applied to measure the D value of 0.33mol/L KCL aqueous solution at temperature 298.15K. The first method derives D value precisely from the drift rate of diffusion image and the measured D is 1.8508 × 10^-5 cm²/s. Meanwhile, the second method obtains the D value rapidly by analyzing an instantaneous diffusion image and the measured D is 1.8619 × 10^-5 cm²/s. The measured values are in good agreement with the literature value, demonstrating that the designed DLCL works well in measuring liquid diffusion coefficients.

Asymmetric liquid-core cylindrical lens used to measure liquid diffusion coefficient

We design and fabricate an asymmetric liquid-core cylindrical lens (ALCL), which is used to measure the binary liquid diffusion coefficient (D). Acting as both diffusion cell and key imaging element, ALCL is of the function to measure the refractive index (RI) of liquid filled in its core in the way of spatial resolution. Comparing the ALCL with a symmetric liquid-core cylindrical lens (SLCL), the spherical aberration is reduced from about 300 μm (SLCL) to less than 5 μm (ALCL) when the RI of filled liquid is near 1.333, while the measurement accuracy of the RI of the ALCL is superior to 0.0002, which is much better than that of the SLCL. Equipped with the ALCL, the D value of triethylene glycol diffusing in water is measured at 25°C. The result is D=0.7515×10⁻⁵ cm²/s, a value very close to the literature value. The rational design of ALCL gives the optical method for measuring the D value good measurement precision and direct observation of the diffusive process as well as a simple experimental instrument.

New method to measure liquid diffusivity by analyzing an instantaneous diffusion image

A novel optical method was applied to measure the binary liquid diffusion coefficient (D) quickly. Equipped with an asymmetric liquid-core cylindrical lens (ALCL), the spatially resolving ability of the ALCL in measuring refractive index of liquid was utilized to obtain the gradient distribution of the liquid concentration along diffusive direction. Based on Fick's second law, the D value was then calculated by analyzing diffusion images. It was worth mentioning that only one instantaneous diffusive image was required to measure D value by the method, reducing the measurement time greatly from several hours in traditional methods to a few seconds. The diffusion coefficients of ethylene glycol diffusing in pure water, at temperatures from 288.15 to 308.15 K, were measured by analyzing instantaneous diffusion images, the results were consistent well with the values measured by using holographic interferometry and Taylor dispersion methods. The method is characterized by faster measurement, direct observation of diffusive process, and easy operation, which provides a new method in measuring diffusion coefficient of liquids rapidly.

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.