Transient cavity dynamics and divergence from the Stokes–Einstein equation in organic aerosol

The diffusion of small molecules through viscous matrices formed by large organic molecules is important across a range of domains, including pharmaceutical science, materials chemistry, and atmospheric science, impacting on, for example, the formation of amorphous and crystalline phases. Here we report significant breakdowns in the Stokes–Einstein (SE) equation from measurements of the diffusion of water (spanning 5 decades) and viscosity (spanning 12 decades) in saccharide aerosol droplets. Molecular dynamics simulations show water diffusion is not continuous, but proceeds by discrete hops between transient cavities that arise and dissipate as a result of dynamical fluctuations within the saccharide lattice. The ratio of transient cavity volume to solvent volume increases with size of molecules making up the lattice, increasing divergence from SE predictions. This improved mechanistic understanding of diffusion in viscous matrices explains, for example, why organic compounds equilibrate according to SE predictions and water equilibrates more rapidly in aerosols.

The failure of the Stokes–Einstein relation is assessed in aerosol measurements and molecular dynamics simulations.     

Transport properties in two pyrrolidinium-based protic ionic liquids as determined by conductivity,viscosity and NMR self-diffusion measurements

Conductivity and viscosity measurements of pyrrolidinium hydrogen sulfate, [Pyrr][HSO₄], and pyrrolidinium trifluoroacetate [Pyrr][CF₃COO] were performed at various temperatures over a wide temperature range (i.e., from T = 273 K to 353 K). The results were utilized in the Stokes–Einstein equation to investigate the proton conductivity in both PILs. The self-diffusion coefficients (D) of the cation and anion species in both studied PILs were independently determined in the same temperature range by observing ¹H and ¹⁹F nuclei with the pulsed-field gradient spin-echo NMR technique. With regard to the mechanism of self-diffusion, based on the values of the coefficients, a relatively large difference was observed between the two ionic liquids (ILs). Independently of the temperature, the D values indicated that the diffusion of both ions was similar, signifying that they were tightly bound together as ion pairs. Nevertheless, mobile protons attached to nitrogen atoms exhibited D values five times higher than those of the pyrrolidinium cation or hydrogenosulfate anion in [Pyrr][HSO₄], and twofold those in the case of [Pyrr][CF₃CO₂]. In order to comment d.c. conductivities results, the self-diffusion coefficients determined by PGSE NMR were converted into charge diffusivity D by means of the Nernst–Einstein equation. In a similar way, a viscosity-related diffusivity D was calculated with the aid of the Stokes–Einstein equation. The temperature-independent cation transference number and the effective hydrodynamic radius were also deduced from these equations. Such parameters play an important role in charge and mass transports in ILs. Moreover, proton conduction follows a combination of Grotthuss- and vehicle-type mechanisms, which confirms that Brønsted acid–base ionic liquid systems are good candidates as proton conductors in fuel cells or supercapacitor electrolyte devices operating under anhydrous conditions at elevated temperatures.     

Voltammetric Analysis of Iodide and Diffusion Coefficients Between 25 and 85°C

The oxidation wave of iodide in 0.075 mol-L^–1 H₂SO₄ was analyzed at 25, 40, 55, 70, and 85°C. The reversibility of the I₂/I^– system was checked using logarithmic transforms, half-wave potentials, and by studying I ^–1 = f(^–1/2). The limiting currents obtained enabled us to determine the diffusion coefficient of I^– using Newman's equation. These experimental results were compared with Nernst's limiting values. The Stokes–Einstein equation is not verified. Hydration numbers for I^– at different temperatures were established. An empirical equation is proposed to predict the evolution of diffusion coefficients in a sulfuric acid medium with temperature.     

Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH₂)₃CH₃, –(CH₂)₇CH₃, and –(CH₂)₁₁CH₃ nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.     

Diffusion coefficients of ions through ion excange membrane in Donnan dialysis using ions of different valence

Donnan dialysis with an ion exchange membrane was investigated for ions of different valence. The effective diffusion coefficients (D_e) of various kinds of ions in the membrane were obtained by fitting of the equation derived from the Nernst–Planck equation to three or more sets of experimental data for Donnan dialysis. It became apparent that the value of D_e/D_s of monovalent ions (e.g., K⁺ or Na⁺ ions) at z_A=1 and z_B=2 (feed ions are monovalent ones and driving ions are bivalent ones) remained constant at ca. 1/210 and that of bivalent ions (e.g., Ca²⁺, Cu²⁺, or Mg²⁺ ions) remained constant at ca. 1/526 where D_s denotes the diffusion coefficient of ions at infinite dilution in water calculated from the Nernst–Einstein equation, and z_A and z_B represent the valences of the feed and driving ions, respectively. D_e/D_s of monovalent ions (e.g., H⁺, K⁺, or Na⁺ ions) at z_A=2 and z_B=1 (feed ions are bivalent ones and driving ions are monovalent ones) was constant at ca. 1/23.3 and that of bivalent ions remained constant at ca. 1/58.4. It was proved that D_e/D using D_e at z_A=1 and z_B=2 was constant at 1/3.0 and that at z_A=2 and z_B=1 remained constant at 3.0 where D represents the diffusion coefficient of ions in the membrane at z_A=z_B (the valences of both feed and driving ions are equal). Therefore, it was found that a large flux of ions could be obtained using the monovalent driving ions in Donnan dialysis. On the other hand, the small flux can be obtained using bi- or higher-valent driving ions.     

Particle size measurement of lipoprotein fractions using diffusion-ordered NMR spectroscopy

The sizes of certain types of lipoprotein particles have been associated with an increased risk of cardiovascular disease. However, there is currently no gold standard technique for the determination of this parameter. Here, we propose an analytical procedure to measure lipoprotein particles sizes using diffusion-ordered nuclear magnetic resonance spectroscopy (DOSY). The method was tested on six lipoprotein fractions, VLDL, IDL, LDL₁, LDL₂, HDL₂, and HDL₃, which were obtained by sequential ultracentrifugation from four patients. We performed a pulsed-field gradient experiment on each fraction to obtain a mean diffusion coefficient, and then determined the apparent hydrodynamic radius using the Stokes–Einstein equation. To validate the hydrodynamic radii obtained, the particle size distribution of these lipoprotein fractions was also measured using transmission electron microscopy (TEM). The standard errors of duplicate measurements of diffusion coefficient ranged from 0.5% to 1.3%, confirming the repeatability of the technique. The coefficient of determination between the hydrodynamic radii and the TEM-derived mean particle size was r ² = 0.96, and the agreement between the two techniques was 85%. Thus, DOSY experiments have proved to be accurate and reliable for estimating lipoprotein particle sizes.     

Molecular dynamics simulation study of friction and diffusion of a tracer in a Lennard–Jones solvent

The friction and diffusion coefficients of a tracer in a Lennard–Jones (LJ) solvent are evaluated by equilibrium molecular dynamics simulations in a microcanonical ensemble. The solvent molecules interact through a repulsive LJ force each other and the tracer of diameter σ₂ interacts with the solvent molecules through the same repulsive LJ force with a different LJ parameter σ. Positive deviation of the diffusion coefficient D of the tracer from a Stokes–Einstein behavior is observed and the plot of 1/D versus σ₂ shows a linear behavior. It is also observed that the friction coefficient ζ of the tracer varies linearly with σ₂ in accord with the prediction of the Stokes formula but shows a smaller slope than the Stokes prediction. When the values of ratios of sizes between the tracer and solvent molecules are higher than 5 approximately, the behavior of the friction and diffusion coefficients is well described by the Einstein relation D = k _B T/ζ, from which the tracer is considered as a Brownian particle.     

Diffusion Coefficients of Imidazolium Based Ionic Liquids in Aqueous Solutions

Diffusion coefficients of the ionic liquids [C₂MIM][EtSO₄], [C₄MIM][OcSO₄], [C₂MIM][NTf₂] and [C₄MIM][NTf₂] in water at high dilution have been measured using the Taylor dispersion technique. Data on the diffusion coefficients have been obtained for each solute at six temperatures between 288 and 313 K. The data have been fitted by the Arrhenius equation and activation energies of diffusion have been determined. Effective radii of the ionic liquid molecules have also been obtained using the Stokes–Einstein relationship.     

Synthesis and Characterization of Polyoxometalate–Polyamino Dendritic Hybrid Compounds

Organic–inorganic hybrid compounds were prepared by the reaction of a tin chloride-substituted polyoxometalate, [PSn(Cl)W₁₁O₃₉]⁴⁻ with tris(2-aminoethyl)amine, and poly(propylene)imine (DAB-Am) tetraamine and octaamine dendrimers. Translational diffusion coefficients of the hybrid compounds were measured in DMSO-d ₆ by the stimulated echo diffusion (STE) NMR technique. Molecular radii were derived from the diffusion coefficients by the Stokes–Einstein equation and appeared to be incorrect because of fast exchange on the NMR time scale of the counter cation in the solution, which led to an averaging of the NMR signal and high diffusion coefficients. An effective hydrodynamic diameter of the [PSn(Cl)W₁₁O₃₉]⁴⁻–polypropylenimine octaamine hybrid adduct was measured in a light scattering experiment.     

Diffusion with molecular association in chloroform + triethylamine and chloroform + dioxane mixtures

The Taylor dispersion method is used to measure the binary mutual diffusion coefficients of chloroform + triethylamine and chloroform +1,4-dioxane at 25°C. The components of these mixtures associate, forming chloroform-triethylamine and chloroform-dioxane, (chloroform)₂-dioxane molecular complexes. A modified Hartley-Crank equation is developed to express the binary diffusion coefficient as a weighted average of the diffusion coefficients of the free molecules and the molecular complexes. Counterintuitively, the contribution made by each molecular complex to the overall diffusion coefficient vanishes when the concentration of the complex reaches its maximum value. The measured and fitted diffusion coefficients agree within 3% or better over the complete composition range.     

Molecular Dynamics Simulation of Diffusion of Vitamin C in Water Solution

Under different temperatures and concentrations, the diffusion of Vitamin C (VC) in water solution was examined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein equation. The influences of temperature, concentration, and simulation time on the diffusion coefficient were discussed. The results showed that at higher temperature and lower concentration the normal diffusions appear relatively late, but the linear range of mean square displacement curves continues longer than that at lower temperature and higher concentration. At the same temperature, the normal diffusion time increases and the diffusion coefficient decreases as the simulation concentration increases. These simulation results are in good agreement with experiments. Analyses of the pair correlation functions of the simulation systems showed that hydrogen bonds are mainly formed between the hydrogen atoms of VC molecules and oxygen atoms of H₂O molecules, rather than between the O atoms of VC molecules and H atoms of H₂O molecules. The diffusion coefficient is higher as the interaction between water molecules and VC molecules is stronger when VC concentration is lower. The water in the model systems affects the diffusion of VC molecules by the short‐range repulsion of O(H₂O)‐O(H₂O) pairs and the non‐bond interaction of H(H₂O)‐H(H₂O) pairs. The short‐range repulsion of O(H₂O)‐O(H₂O) pairs is greater when VC concentration is higher, the diffusion of VC is weaker. The greater the non‐bond interaction of H(H₂O)‐H(H₂O) pairs is, the higher the VC diffusion is. It is expected that this study can provide a theoretical direction for the experiments on the mass transfer of VC in water solution.     

Pore structure of gel chitosan membranes. II. Modelling of the pore size distribution from solute diffusion measurements. Gaussian distribution—Mathematical limitations

It was assumed that the pore size distribution in water-swollen gel membranes can be described by the Gaussian distribution function with a mean pore radius r_m and standard deviation σ. The function was applied to the Renkin capillary model based on solute diffusion measurements through membranes. The numerical analysis showed that the problem does not have a unique solution but a family of solutions approximated by the function r_m = Aσ² + r_Renkin, with the pore radius, r_Renkin, obtained on the assumption of uniform radii, being the largest of all r_m obtained with the distribution. The uncertainty of the solution remained also after modification of the experimental data with a molecular probe of permeability coefficient equal to zero, and after cutting the tails of the Gaussian pore size distribution.     

Vibrational force fields and amplitudes,and zero-point average structures of (CH3)3Y molecules (Y = N,P, As,Sb, Bi): A Combination of electron-diffraction and spectroscopic data

Following the development of methods for placing electron-diffraction and spectroscopic geometrical parameters on a common basis, available data on (CH₃)₃Y molecules (Y = N, P, As, Sb, Bi) have been used to derive force fields, r.m.s. amplitudes of vibration u along the internuclear vectors, and perpendicular amplitude correction coefficients K for these molecules. For trimethylamine, the amplitudes are similar whether or not off-diagonal elements are included in the force field; hence, only diagonal elements are considered for the other molecules. Among the interesting trends, as group V is descended, is that the C-Y r.m.s. amplitudes increase only from 0.049 to 0.058 Å, whereas the C-Y stretching force constant decreases by over 60% from 5.3 to 1.8 mdyn Å^?1. There is evidence for an increasing tendency for torsional motion of methyl groups, as group V is descended.For each of the molecules, the amplitude data were used to derive zero-point average (r^o_α) structures and to make estimates of a partial equilibrium (r_e) structure. For trimethylamine the results suggest a systematic error in the electron-beam wavelength of the literature study, and the structural parameters were appropriately revised. The r^o_α lengths of the C-Y bonds in the five molecules are 1.458 ± 0.002, 1.844 ± 0.003, 1.979 ± 0.010, 2.169 ± 0.010 and 2.263 ± 0.004 Å, respectively. The estimated r_e parameters for the bonds in trimethylamine agree well with the microwave r_s structure.     

Local lattice structures,random spatial processes and molecular correlations in liquids

Structural and molecular correlations in a liquid are treated by a set of Fokker—Planck type equations for the spatial evolution of the probability density P(sr) of fluctuating local structure parameters s. The equations are generalizations of the “structural diffusion” equations. including in addition to second order terms also first order terms in the derivatives of P(sr) with respect to the components of s. A proper choice of the coefficients in these terms leads to an apparent shift of the peaks of the local quasi-lattice and to an improved radial distribution function g(r)- Comparison with g(r) data for argon was made for several different lattices. showing a best fit of r²[g(r)-1] with the bcc quasi-lattice.     

Electric birefringence and conformation of polychlorohexylisocyanate in solutions

Electric birefringence was investigated for solutions of polychlorohexylisocyanate fractions for molecular weights 30·6 × 10⁴–1·2 × 10⁴ in tetrachloromethane.Experimentally found dispersion of the Kerr effect is used for estimating the coefficients of rotatory diffusion D_r of molecules. A comparison of rotatory diffusion D_r values with molecular weights M and intrinsic viscosities [η] of fractions shows that the value of D_rM[η] decreases with M. This illustrates the change in the conformation of molecules from a random coil to a rod.On the basis of experimental dependences of D_r and the Kerr constants K on M, the main structural parameters of the polymer investigated were determined: the number of monomer units in a segment, the projection of the length of the monomer unit on the axis of the molecule, the value of the dipole moment μ₀ of the monomer unit and the angle formed by μ₀ and the chain direction.     

Solvatochromism of heteroaromatic compounds: XXVIII. Factors affecting the nonspecific solvatochromic effect in the UV spectra of aromatic nitro compounds in aprotic protophilic solvents

Examination of the UV spectra of a large series of solvatochromic indicators of the general formula 1-X-4-NO₂-C₆H₄ in aprotic solvents confirmed the proportionality between the dipole moments of these compounds in the ground (μ_g) and first electronically excited (¹ A ₁, μ_e) states: μ_e = r _μμ_g. The coefficient r _μ was determined by applying the equation of the Bakhshiev-Bilot-Kawski solvatochromism theory both to nonspecifically solvated molecules and to their H complexes with aprotic protophilic solvents. An anisotropy of the electron redistribution was revealed for low-symmetry 1-substituted 2,4-dinitrobenzenes. The r _μ value obtained allowed the calculation of the Kamlet-Taft empirical solvatochromic parameter π* on the basis of generalized characteristics of the solvent.     

Influence of the linking chain length on the recombination kinetics of covalently bonded triplet radical pairs and magnetic field effects

Nanosecond laser flash photolysis technique is used to study the formation and decay kinetics of covalently linked triplet radical pairs (RP) formed after photoinduced electron transfer in the series of 21 zinc porphyrin—chain—viologen (Pph—Sp_n—Vi²⁺) dyads, where the number of atoms (n) in the chain increases from 2 to 138. In poorly viscous polar solvents (acetone, CHCl₃—CH₃OH (1 : 1) mixture), the dependence of the rate constant of RP formation on n can be described by the equation k _e = k _e ⁰ n ^–a at k _e ⁰ = 2.95·10⁸ s^–1 anda = 0.8. In the zero magnetic field, the RP recombination rate constant (k _r(B = 0)) is significantly lower than k _e and ranges from 0.7·10⁶ to 8·10⁶ s^–1. The dependence of k _r(B = 0) on n is extreme. The dependence k _r(B = 0) reaches a maximum at n = 20. In the strong magnetic field (B = 0.21 T), the significant retardation of triplet RP recombination is observed. The chain length has an insignificant effect on k _r(B = 0.21 T), which ranges from 0.3·10⁶ to 0.9·10⁶ s^–1. The regularities found are discussed in terms of the interplay of molecular and spin dynamics.     

Mutual and self-diffusion of charged porphyrines in aqueous solutions

We have investigated the diffusion properties for an ionic porphyrin in water. Specifically, for the {tetrasodium tetraphenylporphyrintetrasulfonate (Na₄TPPS) + water} binary system, the self-diffusion coefficients of TPPS⁴⁻ and Na⁺, and the mutual diffusion coefficients were experimentally determined as a function of Na₄TPPS concentration from (0 to 4) · 10⁻³ mol · dm⁻³ at T = 298.15 K. Absorption spectra for this system were obtained over the same concentration range. Molecular mechanics were used to compute size and shape of the TPPS⁴⁻ porphyrin. We have found that, at low solute concentrations (<0.5 · 10⁻³ mol · dm⁻³), the mutual diffusion coefficient sharply decreases as the concentration increases. This can be related to both the ionic nature of the porphyrin and complex associative processes in solution. Our experimental results are discussed on the basis of the Nernst equation, Onsager–Fuoss theory and porphyrin metal ion association. In addition, self-diffusion of TPPS⁴⁻ was used, together with the Stokes–Einstein equation, to determine the equivalent hydrodynamic radius of TPPS⁴⁻. By approximating this porphyrin to a disk, we have estimated structural parameters of TPPS⁴⁻. These were found to be in good agreement with those obtained using molecular mechanics. Our work shows how the self-diffusion coefficient of an ionic porphyrin in water is substantially different from the corresponding mutual-diffusion coefficient in both magnitude and concentration dependence. This aspect should be taken into account when diffusion-based transport is modelled for in vitro and in vivo applications of pharmaceutical relevance.     

Low Energy Electron Attachment by Some Chlorosilanes

In this paper, the rate coefficients (k) and activation energies (E_a) for SiCl₄, SiHCl₃, and Si(CH₃)₂(CH₂Cl)Cl molecules in the gas phase were measured using the pulsed Townsend technique. The experiment was performed in the temperature range of 298–378 K, and carbon dioxide was used as a buffer gas. The obtained k depended on temperature in accordance with the Arrhenius equation. From the fit to the experimental data points with function described by the Arrhenius equation, the activation energies (E_a) were determined. The obtained k values at 298 K are equal to (5.18 ± 0.22) × 10⁻¹⁰ cm³·s⁻¹, (3.98 ± 1.8) × 10⁻⁹ cm³·s⁻¹ and (8.46 ± 0.23) × 10⁻¹¹ cm³·s⁻¹ and E_a values were equal to 0.25 ± 0.01 eV, 0.20 ± 0.01 eV, and 0.27 ± 0.01 eV for SiHCl₃, SiCl₄, and Si(CH₃)₂(CH₂Cl)Cl, respectively. The linear relation between rate coefficients and activation energies for chlorosilanes was demonstrated. The DFT/B3LYP level coupled with the 6-31G(d) basis sets method was used for calculations of the geometry change associated with negative ion formation for simple chlorosilanes. The relationship between these changes and the polarizability of the attaching center (α_centre) was found. Additionally, the calculated adiabatic electron affinities (AEA) are related to the α_centre.     

A neutron scattering perspective on the structure,softness and dynamics of the ligand shell of PbS nanocrystals in solution

Small-angle neutron and X-ray scattering, neutron backscattering and neutron time-of-flight spectroscopy are applied to reveal the structure of the ligand shell, the temperature-dependent diffusion properties and the phonon spectrum of PbS nanocrystals functionalized with oleic acid in deuterated hexane. The nanocrystals decorated with oleic acid as well as the desorbed ligand molecules exhibit simple Brownian diffusion with a Stokes–Einstein temperature-dependence and inhibited freezing. Ligand molecules desorbed from the surface show strong spatial confinement. The phonon spectrum of oleic acid adsorbed to the nanocrystal surface exhibits hybrid modes with a predominant Pb-character. Low-energy surface modes of the NCs are prominent and indicate a large mechanical softness in solution. This work provides comprehensive insights into the ligand–particle interaction of colloidal nanocrystals in solution and highlights its effect on the diffusion and vibrational properties as well as their mechanical softness.

Time-averaged and energy-resolved neutron and X-ray scattering reveal the structure of the ligand shell, temperature-dependent diffusion and the phonon spectrum of PbS nanocrystals functionalized with oleic acid in solution.