Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part IV. D(C)/D0=1+(αC)−β(αC)

Using the specific functional form D(C)/D₀=1+(αC)−β(αC)² an investigation has been made of (isothermal) transport through a slab membrane under ‘simple’ boundary conditions and governed by a diffusion coefficient, D(C), which, with increasing concentration, at first increases, passes through a maximum value and finally decreases. The flux, integral diffusion coefficient and concentration profile characteristic of steady-state permeation have been evaluated; special attention has been paid to the positions of such profiles in relation to the corresponding linear distribution associated with a constant diffusion coefficient.The corresponding transient-state transport has been studied within a framework of the time-lag ‘early-time’ and ‘ ’ procedures. Expressions for the ‘adsorption’ and ‘desorption’ time-lags are given. The concentration-dependence of these time-lags, of the (four) integral diffusion coefficients derived from them and of the arithmetic-mean time-lag ratios have been considered in some detail. The ‘early-time’ and ‘ ’ finite-difference procedures have likewise been employed to derive four further integral diffusion coefficients, so enabling a comparison to be made of the nine integral coefficients pertaining to established experimental techniques.Particular interest attaches to the situation for which n≡β(αC₀)=1 (where C₀ is the ingoing or upstream concentration of diffusant) resulting in D(C₀) being symmetrical about C₀/2. Some consideration has been given, in general, to features of transient-state transport when governed by a symmetrical D(C).     

The effect of polymers on the phase behavior of balanced microemulsions: diblock-copolymer and comb-polymers

The effect of some amphipilic diblock-copolymers and comb-polymers on a balanced Winsor III microemulsion system is investigated with the quaternary system n-octyl-β-d-glucoside/1-octanol/n-octane/D₂O as basis system. The diblock-copolymers are polyethyleneoxide-co-polydodecenoxide (PEO _x PEDODO _y ) and polyethyleneoxide-co-polybutyleneoxide (PEO _x PEBU _y ), constituted of a straight chain hydrophilic part and a bulky hydrophobic part. Addition of the diblock-copolymer leads to an enhancement of the swelling of the middle phase by uptake of water and oil; a maximum boosting factor of 6 was obtained for PEO₁₁₁PEDODO₂₅. Nuclear magnetic resonance diffusometry yields the self-diffusion coefficients of all the components in the system. The diffusion experiments provide information on how the microstructure of the bicontinuous microemulsion changes upon addition of the polymers. The reduced self-diffusion coefficients of water and oil are sensitive to the type of polymer that is incorporated in the film. For the diblock-copolymers, as mainly used here, the reduced self-diffusion coefficient of oil and water will respond to how the polymer bends the film. When the film bends away from water, the reduced self-diffusion of the water will increase, whereas the oil diffusion will decrease due to the film acting as a barrier, hindering free diffusion. The self-diffusion coefficient of the polymer and surfactant are similar in magnitude and both decrease slightly with increasing polymer concentration.     

Low-Dimensional Architectures in Isomeric cis-PtCl2{Ph2PCH2N(Ar)CH2PPh2} Complexes Using Regioselective-N(Aryl)-Group Manipulation

The solid-state behaviour of two series of isomeric, phenol-substituted, aminomethylphosphines, as the free ligands and bound to Pt^II, have been extensively studied using single crystal X-ray crystallography. In the first library, isomeric diphosphines of the type Ph₂PCH₂N(Ar)CH₂PPh₂ [1a–e; Ar = C₆H₃(Me)(OH)] and, in the second library, amide-functionalised, isomeric ligands Ph₂PCH₂N{CH₂C(O)NH(Ar)}CH₂PPh₂ [2a–e; Ar = C₆H₃(Me)(OH)], were synthesised by reaction of Ph₂PCH₂OH and the appropriate amine in CH₃OH, and isolated as colourless solids or oils in good yield. The non-methyl, substituted diphosphines Ph₂PCH₂N{CH₂C(O)NH(Ar)}CH₂PPh₂ [2f, Ar = 3-C₆H₄(OH); 2g, Ar = 4-C₆H₄(OH)] and Ph₂PCH₂N(Ar)CH₂PPh₂ [3, Ar = 3-C₆H₄(OH)] were also prepared for comparative purposes. Reactions of 1a–e, 2a–g, or 3 with PtCl₂(η⁴-cod) afforded the corresponding square-planar complexes 4a–e, 5a–g, and 6 in good to high isolated yields. All new compounds were characterised using a range of spectroscopic (¹H, ³¹P{¹H}, FT–IR) and analytical techniques. Single crystal X-ray structures have been determined for 1a, 1b∙CH₃OH, 2f∙CH₃OH, 2g, 3, 4b∙(CH₃)₂SO, 4c∙CHCl₃, 4d∙½Et₂O, 4e∙½CHCl₃∙½CH₃OH, 5a∙½Et₂O, 5b, 5c∙¼H₂O, 5d∙Et₂O, and 6∙(CH₃)₂SO. The free phenolic group in 1b∙CH₃OH, 2f∙CH₃OH_, 2g, 4b∙(CH₃)₂SO, 5a∙½Et₂O, 5c∙¼H₂O, and 6∙(CH₃)₂SO exhibits various intra- or intermolecular O–H∙∙∙X (X = O, N, P, Cl) hydrogen contacts leading to different packing arrangements.     

Reversible PtII–CH3 deuteration without methane loss: metal–ligand cooperation vs. ligand-assisted PtII-protonation

Di(2-pyridyl)ketone dimethylplatinum(ii), (dpk)Pt^II(CH₃)₂, reacts with CD₃OD at 25 °C to undergo complete deuteration of Pt–CH₃ fragments in ∼5 h without loss of methane to form (dpk)Pt^II(CD₃)₂ in virtually quantitative yield. The deuteration can be reversed by dissolution in CH₃OH or CD₃OH. Kinetic analysis and isotope effects, together with support from density functional theory calculations indicate a metal–ligand cooperative mechanism wherein DPK enables Pt–CH₃ deuteration by allowing non-rate-limiting protonation of Pt^II by CD₃OD. In contrast, other model di(2-pyridyl) ligands enable rate-limiting protonation of Pt^II, resulting in non-rate-limiting C–H(D) reductive coupling. Owing to its electron-poor nature, following complete deuteration, DPK can be dissociated from the Pt^II-centre, furnishing [(CD₃)₂Pt^II(μ-SMe₂)]₂ as the perdeutero analogue of [(CH₃)₂Pt^II(μ-SMe₂)]₂, a commonly used Pt^II-precursor.

Di(2-pyridyl)ketone dimethylplatinum(ii), (dpk)Pt^II(CH₃)₂, reacts with CD₃OD at 25 °C to undergo complete deuteration of Pt–CH₃ fragments in ∼5 h without loss of methane to form (dpk)Pt^II(CD₃)₂ in virtually quantitative yield.     

Transport properties of alkyltrimethylammonium bromide surfactants in aqueous solutions

Differential mutual diffusion coefficients of n-alkyltrimethylammonium bromides [CH₃(CH₂)_n–1N(CH₃)₃Br, C_nTAB] (n=10, 12, 14, 16) have been measured in aqueous solutions at 298.15 K using a conductimetric cell and an automatic apparatus to follow diffusion. The cell is based on an open-ended capillary, and the technique follows the diffusion process by measuring the resistance of a solution inside the capillaries at various times. The electrical conductances of those solutions have also been measured to calculate the critical micellar concentration (cmc). Thermodynamic analysis of the data suggests that the free ion concentration decreases at concentrations above the cmc, in agreement with theoretical predictions. The obtained values of the micellization parameters were used to model the mutual diffusion coefficients of C_nTAB aqueous solutions.     

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.     

The effect of pressure and temperature of self-diffusion coefficients in several concentrated deuterium oxide diamagnetic electrolyte solutions

The pressure dependences of the self-diffusion coefficients of deuterium oxide in 4.5m solutions of LiCl–D₂O and CsCl–D₂O (also 7m) and 3.06m CaCl₂–D₂O have been measured by the NMR spin-echo method at 30°C, 60°C, and 90°C. Shear viscosities and densities of these solutions have also been determined over the same range of experimental conditions. The experimental data show that the diffusion constantD decreases with the increasing structure-making ability of the electrolyte cation Ca⁺²>Li⁺. In contrast, the diffusion coefficient for D₂O in the 4.5 and 7m CsCl solutions is equal to that for pure D₂O at 30°C but lower at 60°C and 90°C. It has been found that the Stokes-Einstein equation relates well the diffusion coefficients to shear viscosity in these concentrated electrolyte solutions.     

Viscosity of aqueous NH4Cl and tracer diffusion coefficients of ions,water and non-electrolytes in aqueous NH4Cl,KI, and MgCl2 at 25°C

Viscosities for aqueous NH₄Cl and tracer diffusion coefficients for²²Na⁺,³⁶Cl^–, HTO, and CH₃OH, acetone and dimethylformamide (all¹⁴C-labelled) in NH₄Cl supporting electrolyte are reported for 25°, together with tracer diffusion coefficients for²²Na⁺,³⁶Cl^–, and¹⁴CH₃OH in 1M KI, and for¹⁴CH₃OH in 1M MgCl₂. The diffusion coefficient of HTO in NH₄Cl solutions is slightly larger, for most of the concentration range investigated (0.05 to 4.5 M), than the value for pure water and is almost unaffected by the supporting electrolyte up to about 4M. Similar behavior is shown by CH₃OH, acetone and dimethylformamide in NH₄Cl solutions. Onsager limiting law behavior is approached by Cl^– at NH₄Cl concentrations in the 0.05–0.1M region but at much lower concentrations by Na⁺.     

Molecular dynamics study of anisotropic translational and rotational diffusion in liquid benzene

Equilibrium NPT and NVT molecular dynamics simulations were performed on liquid benzene over an extended range of temperature (from 260 to 360 K) using the COMPASS force field. Densities and enthalpies of vaporization (from cohesive energy densities) were within 1% of experiment at all temperatures. tumbling and spinning rotational diffusion coefficients, D(perpendicular) and D(parallel), computed as a function of temperature, agreed qualitatively with the results of earlier reported experimental and computational investigations. Generally, it was found that D(parallel)/D(perpendicular) approximately 1.4-2.5 and the activation energy for tumbling was significantly greater than for spinning about the C6 axis [Ea(D(perpendicular)) = 8.1 kJ mol(-1) and Ea(D(parallel)) = 4.5 kJ mol(-1)]. Calculated translational diffusion coefficients were found to be in quantitative agreement with experimental values at all temperatures [deviations were less than the scatter between different reported measurements]. In addition, translational diffusion coefficients were computed in the molecule-fixed frame to yield values for Dxy (diffusion in the plane of the molecule) and Dz (diffusion perpendicular to the plane). It was found that the ratio Dxy/Dz approximately 2.0, and that the two coefficients have roughly equal activation energies. This represents the first atomistic molecular dynamics study of translational diffusion in the molecular frame.     

Molecular Modeling to Estimate the Diffusion Coefficients of Drugs and Other Small Molecules

Diffusion is a spontaneous process and one of the physicochemical phenomena responsible for molecular transport, the rate of which is governed mainly by the diffusion coefficient; however, few coefficients are available because the measurement of diffusion rates is not straightforward. The translational diffusion coefficient is related by the Stokes–Einstein equation to the approximate radius of the diffusing molecule. Therefore, the stable conformations of small molecules were first calculated by molecular modeling. A simple radius r_s and an effective radius r_e were then proposed and estimated using the stable conformers with the van der Waals radii of atoms. The diffusion coefficients were finally calculated with the Stokes–Einstein equation. The results showed that, for the molecules with strong hydration ability, the diffusion coefficients are best given by r_e and for other compounds, r_s provided the best coefficients, with a reasonably small deviation of ~0.3 × 10⁻⁶ cm²/s from the experimental data. This demonstrates the effectiveness of the theoretical estimation approach, suggesting that diffusion coefficients have potential use as an additional molecular property in drug screening.     

Binary fluids in planar nanopores: Adsorptive selectivity, heat capacity and self-diffusivity

Monte Carlo and molecular dynamics simulations are performed to study fluid adsorption of a two component fluid in slit pores of nanoscopic dimensions. The slit pores are immersed in a binary fluid bath, which is comprised of spherical molecules having a size ratio of 1.43, at constant temperature and composition. Pore width is varied to determine how the heat capacity and self-diffusion coefficient are linked to the composition and structure of the adsorbed fluid. In pores where the fluid structure is most pronounced, we observe: perfect (or near perfect) exclusion of one component by the other component, a heat capacity that rapidly oscillates and is of greater magnitude than in the fluid bath, and self-diffusion coefficients on the order of 10^–8 cm²/s. The behavior of the heat capacity and diffusion coefficients appears to arise from a near solid-like layering of OMCTS that occurs at certain favorable pore widths.     

Thermodynamic and Dynamic Properties of Micellar Aggregates of Nonionic Surfactants with Short Hydrophobic Tails

The densities and viscosities of binary aqueous mixtures of poly(ethylenoxide)hexanols [C₆H₁₃(OCH₂CH₂)_mOH, C₆E_m] (m= 3, 4, and 5) have been studied in the micellar composition range. For the same surfactants the self-diffusion coefficients in mixtures with heavy water have been determined by the spin-echo pulsed field gradient method. The volumetric data are interpreted by means of the phase separation model, and values of the CMC, volume change, and standard free energy change of micellization are obtained. From the viscosity data the hydration numbers of the surfactant hydrophilic head in the micellar state are computed; they are in agreement with those obtained from HDO self-diffusion data. The surfactant self-diffusion data are used to calculate the apparent micelle radius and the aggregation number. The micellization parameters obtained for the different surfactants are compared and discussed.     

New Bifunctional Bis(azairidacycle) with Axial Chirality via Double Cyclometalation of 2,2′-Bis(aminomethyl)-1,1′-binaphthyl

As a candidate for bifunctional asymmetric catalysts containing a half-sandwich C–N chelating Ir(III) framework (azairidacycle), a dinuclear Ir complex with an axially chiral linkage is newly designed. An expedient synthesis of chiral 2,2′-bis(aminomethyl)-1,1′-binaphthyl (1) from 1,1-bi-2-naphthol (BINOL) was accomplished by a three-step process involving nickel-catalyzed cyanation and subsequent reduction with Raney-Ni and KBH₄. The reaction of (S)-1 with an equimolar amount of [IrCl₂Cp*]₂ (Cp* = η⁵–C₅(CH₃)₅) in the presence of sodium acetate in acetonitrile at 80 °C gave a diastereomeric mixture of new dinuclear dichloridodiiridium complexes (5) through the double C–H bond cleavage, as confirmed by ¹H NMR spectroscopy. A loss of the central chirality on the Ir centers of 5 was demonstrated by treatment with KOC(CH₃)₃ to generate the corresponding 16e amidoiridium complex 6. The following hydrogen transfer from 2-propanol to 6 provided diastereomers of hydrido(amine)iridium retaining the bis(azairidacycle) architecture. The dinuclear chlorido(amine)iridium 5 can serve as a catalyst precursor for the asymmetric transfer hydrogenation of acetophenone with a substrate to a catalyst ratio of 200 in the presence of KOC(CH₃)₃ in 2-propanol, leading to (S)-1-phenylethanol with up to an enantiomeric excess (ee) of 67%.     

Effect of introduction of heterocyclic moieties into polymer backbone on gas transport properties of fluorinated poly(ether imide) membranes

The effects of incorporation of heterocyclic moieties into fluorinated poly(ether imide) membranes on their gas transport properties were investigated. Four novel fluorinated poly(ether imide) (PEI) membranes were prepared from four different bis(ether amine)s namely, 4,4-bis[3′-trifluromethyl-4′(4′′-aminobenzoxy)bezyl]biphenyl (BAQP); 1,4-bis[3′-trifluromethyl-4′(4′′-aminobenzoxy)bezyl] benzene (BATP); 2,6-bis[3′-trifluromethyl-4′(4′′-aminobenzoxy)bezyl]pyridine (BAPy) and 2,5-bis[3′-trifluromethyl-4′(4′′-aminobenzoxy)bezyl]thiophene (BATh), and a fluorinated dianhydride, 2,2-bis(3,4-dicarboxyphenyl)hexafluoropropane (6FDA) as a common dianhydride. Gas transport properties of these membranes were measured to investigate the effect of chemical structure on gas permeation and diffusion processes over four different gases (e.g., CH₄, N₂, O₂ and CO₂) at different temperatures (e.g., 35, 45 and 55 °C) at an applied pressure of 3.5 bar. It has been found that at 35 °C the permselectivities of BAPy and BATh based polymeric membranes (6.4 and 6.6, respectively) toward O₂ relative to N₂ are higher in comparison to BAQP and BATP (5.5 and 5.3, respectively) containing PEI membranes. The permeability coefficient of CO₂ for BAPy and BATh (51.92 and 45.31, respectively at 35 °C) based PEI membranes were observed to be much higher than BAQP and BATP based membranes (36.61 and 33.51, respectively at 35 °C) with comparable selectivity values of CO₂ relative to CH₄. All these membranes exhibit higher CO₂/CH₄ selectivity than those of common glassy polymers e.g., cellulose acetate, polysulfone and polycarbonate. The order of permeability of these gases was found as CO₂ > O₂ > N₂ > CH₄. The temperature dependency of permeation and diffusion processes enables to calculate the activation energies of the permeation and diffusion processes for these four different gases through four PEI membranes.     

Structural Diversity of Silver Fluorinated β-Diketonates: Effect of the Terminal Substituent and Solvent

In order to demonstrate the role of the fluorination and some solvents in the structural organization of the Ag(I) coordination polymers with β-diketonate ligands (R¹C(O)C_αHC(O)R²)⁻ we synthesized a series of the compounds containing tfac- (R₁ = CH₃, R² = CF₃) and pfpac- (R₁ = CH₃, R² = C₂F₅) anions. Solvent-free [Ag(L)]_∞ (L = tfac 1, pfpac 2) compounds and the corresponding acetonitrile and toluene adducts have been characterized by elemental analysis and/or NMR, IR and single-crystal XRD. This series includes five new coordination polymers. Compound 1 is a 3D coordination framework based on Ag–O_{chelate/bridge}, Ag–C_α bonds, and argentophilic interactions. An increase in the fluorinated group leads to a chain coordination polymer 2 of an unusual structural organization. These chains can be represented as a “DNA-type”, where two intertwined helices based on Ag–O_chelate and Ag–C_α bonds are connected through Ag–O_bridge ones. Two structural types of chain coordination polymers, [Ag(tfac)(CH₃CN)] and [Ag₂(L)₂(solvent)], have been revealed for the adducts. The latter structural type differs significantly from the previously studied toluene and acetonitrile adducts of fluorinated Ag(I) β-diketonates of the same stoichiometry. Thermal analysis in helium showed that both 1 and 2 decompose to metallic silver with the compound of pfpac-ligand being slightly more stable.     

Silylating Agents Grafted onto Silica Derived from Leached Chrysotile

Silica from leached chrysotile fibers (SILO) was silanized with trialkoxyaminosilanes to yield inorganic–organic hybrids designated SILx (x=1–3). The greatest amounts of the immobilized agents were quantified as 2.14, 1.90, and 2.18 mmol g⁻¹ on SIL1, SIL2, and SIL3 for –(CH₂)₃NH₂,–(CH₂)₃NH(CH₂)₂NH₂, and –(CH₂)₃NH(CH₂)₂NH(CH₂)₂NH₂ groups attached to the inorganic support. The infrared spectra for all modified silicas showed the absence of the Si–OH deformation mode, originally found at 950 cm⁻¹, and the appearance of asymmetric and symmetric C–H stretching bands at 2950 and 2840 cm⁻¹. Other important bands associated with the organic moieties were assigned to ν_as(NH) at 3478 and ν_sym(NH) at 3418 cm⁻¹. The NMR spectrum of the solid precursor material suggested two different kinds of silicon atoms: silanol and siloxane groups, between −90 and 110 ppm; however, additional species of silicon that contain the organic moieties bonded to silicon at −58 and −66 ppm appeared after chemical modification. These modified silicas showed a high adsorption capacity for cobalt and copper cations in aqueous solution, in contrast to the original SILO matrix, confirming the unequivocal anchoring of silylating agents on the silica surface.     

Binuclear ruthenium complexes of fluorous phosphine ligands: Synthesis, properties, and biphasic catalytic activity. Crystal structure of [Ru(μ-O2CMe)(CO)2P(CH2CH2(CF2)5CF3)3]2

The fluorocarbon soluble, binuclear ruthenium(I) complexes [Ru(μ-O₂CMe)(CO)₂L^F]₂, where L^F is the perfluoroalkyl substituted tertiary phosphine, P(C₆H₄-4-CH₂CH₂(CF₂)₇CF₃)₃, or P(CH₂CH₂(CF₂)₅CF₃)₃, were synthesized and partition coefficients for the complexes in fluorocarbon/hydrocarbon biphases were determined. Catalytic hydrogenation of acetophenone to 1-phenylethanol in benzotrifluoride at 105 °C occured in the presence of either [Ru(μ-O₂CMe)(CO)₂P(C₆H₄-4-CH₂CH₂(CF₂)₇CF₃)₃]₂ (1) or [Ru(μ-O₂CMe)(CO)₂P(CH₂CH₂(CF₂)₅CF₃)₃]₂ (2). The X-ray crystal structure of [Ru(μ-O₂CMe)(CO)₂P(CH₂CH₂(CF₂)₅CF₃)₃]₂ was determined. The compound exhibited discrete regions of fluorous and non-fluorous packing.     

Kinetics of Heterogeneous Isotopic Exchange Reaction in Finite Bath

A general method to find the rate constant and particle self-diffusion coefficient is suggested for a heterogeneous isotopic exchange reaction which is controlled by surface mass reaction or controlled by a combination of surface mass reaction and intraparticle diffusion. The values of the kinetic parameter, ξ₁ (ratio of the forward surface mass reaction rate to the intraparticle diffusion rate), particle self-diffusion coefficient D and rate constant k are obtained by the proposed method for the isotopic exchange reaction systems CaCO₃(s)/Ca²⁺(aq) and CaC₂O₄(s)/Ca²⁺(aq).     

PGSE-NMR studies of solvent diffusion in poly(N-isopropylacrylamide) colloidal microgels

The solvent self-diffusion coefficient has been studied in thermoshrinking poly(N-isopropyl acrylamide) microgel dispersions by the pulsed-gradient spin-echo PGSE-NMR technique, as a function of temperature and mass fraction. After suitable corrections for the temperature, the H₂O/D₂O ratio and the relative volume fractions, all the self-diffusion data obtained over a temperature range of approximately 40 °C and mass fraction (2–12 % wt/wt) could be superimposed with the volume fraction as the universal factor. The observed reduction in the solvent self-diffusion coefficient with volume fraction was greater than that predicted by simple obstruction theory. After correction for-, and the subsequent removal of the obstruction effect, the diffusion of the solvent through the core of the particle is elucidated. As found for other polymer-solvent systems, there were no specific binding effects. The diffusion of the solvent in these dispersions over such temperature and mass fraction ranges could be rationalised assuming a constant solvent self-diffusion coefficient in the core of the particles.