Diffusion of water in solutions of alkali metal bromides,tetraalkylammonium bromides and ammonium bromide

The diffusion coefficient of water D _w in aqueous solutions of the alkali metal bromides, tetraalkylammonium bromides (methyl, ethyl, n-propyl, and n-butyl) and ammonium bromide at 25°C is reported for concentrations up to 2 mol-dm^–3. In addition, values for D _w in 2 mol-dm^–3 solutions of CsBr, KBr, NaBr, LiBr, and fully deuterated methanol, acetonitrile, and acetone have been measured for temperatures in the range 5 to 50°C. The concentration dependence of the relative water diffusion coefficient D _w /D _o , where D _o is the self-diffusion coefficient of water, has been analyzed in terms of an equation analogous to the Jones-Dole equation for relative viscosity. The B-coefficient for diffusion is well correlated with the viscosity B-coefficient. For the structure-breaking electrolytes CsBr and KBr, D _w /D _o decreases rapidly with increasing temperature, whereas for the structure-makers NaBr and LiBr, the temperature dependence of D _w /D _o has the same sign but is much smaller in magnitude. For the nonelectrolyte solutions, the structure-making effect decreases with increasing temperature and the temperature coefficient of D _w /D _o is positive. It is apparent that, when diffusion of the solvent is being considered, the temperature must be taken into account in the classification of an electrolyte as a structure-breaker or structure-maker.     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

Transient permeation of organic vapors through elastomeric membranes

The permeation of benzene and acetone vapors through sulfur-cured natural rubber was studied by the time-lag method. The experimental results were analyzed by a method suggested by Meares. The zero concentration diffusion coefficient D₀ was obtained by the early-time method. The Frisch time-lag equation was utilized to estimate both the solubility coefficient s and the additional parameter b required to define the concentration dependence of the diffusion coefficient: D(c) = D₀ exp {bc}. This form of concentration dependence was manifested by the corresponding permeability coefficient values. At low entering penetrant pressure, where the transport coefficients are constant, indirect evidence was obtained that D₀ is the mechanistically correct diffusion coefficient. The solubility coefficient values calculated for benzene vapor in natural rubber are in reasonable agreement with published equilibrium sorption data for a similar rubber compound. At higher entering penetrant pressures, average diffusion coefficients obtained at steady state tended to be larger than the corresponding average diffusion coefficients derived from the time lags. This same effect has been detected by other experimental approaches. Permeation experiments designed for this rapid method of analysis appear capable of yielding information consistent with that obtained by more time-consuming traditional methods.     

Sorption and diffusion of toluene in isotropic and oriented linear polyethylene

Sorption and diffusion of toluene vapor in linear polyethylene with mass-fraction crystallinity between 0.48 and 0.82 and draw ratios λ up to 10 have been studied at 30°C. The sorbed concentration in the amorphous phase C_a is little affected by crystallinity, indicating that the free-volume fraction is roughly the same for all isotropic samples. However, the diffusion path becomes more tortuous with increasing crystalline content, thereby leading to a sixfold drop in the zero-concentration diffusion coefficient D₀. Drawing has more drastic effects, reducing C_a and D₀ by factors of 4 and 60, respectively, as λ increases to 10. These large changes result from the transformation of the initially spherulitic material into a fibrous structure, which is composed of aligned microfibrils with taut tie molecules lying on the outer boundaries. The effects of crystallinity and orientation on the concentration dependence of the diffusion coefficient are also discussed.     

Electron-spin magnetic moments of the 2Σ+ ions Li2+, Li2−, and Be2+: An ab initio ROHF study

For the ²Σ⁺ ground states of the ions Li₂⁺, Li₂⁻, and Be₂⁺, the dependence of the magnetic moment (parametrized by g-shifts) on the bond length R was studied at the ROHF level. The Δ g-values were calculated via a perturbative approach (complete to second order in Breit-Pauli interactions) using quadruple-zeta AO basis sets augmented by semidiffuse and polarization functions. All Δ g-values in these systems are negative. The parallel component Δ g_∥ generally changes little with R, remaining close to the g-shift of the corresponding ²S atomic dissociation product. For Li₂⁺ and Be₂⁺, the perpendicular component Δ g _⟂ is more sensitive to geometry than is Δ g_∥, mainly because of the second-order magnetic coupling with excited ²Π states. For Li₂⁻, Δ g _⟂ and Δ g_∥ are similar due to the large size of the 2σ_u, SOMO, resulting in g-values close to that of a free electron. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 511–521, 1997     

Physical aging and dye diffusion in polysulfone below the glass transition temperature

The effect of physical aging on the tracer diffusion coefficient D of camphorquinone in polysulfone is investigated. It is shown that if the sample is sufficiently annealed and physical aging is nearly complete, the temperature dependence of D will reflect the primary α-relaxation process of the host polymer. In the temperature range between T_g (=185°C) and 165°C, D is found to be a function of time, and the time dependence of D is given by D = At^?μ, with μ approximately equal to unity. © 1994 John Wiley & Sons, Inc.     

Molecular orientational motion in discotic liquid crystals

Abstract

The spectral densities of motion for the aromatic and chain deuterons of the discotic mesogen hexahexyoxytriphenylene (THE6) have been reported in the literature for a frequency of 46 MHz. Most spectral densities J_p (pω₀, 90°) have been obtained from samples consisting of a planar distribution of domains in which the directors were perpendicular to the magnetic field Limited data J_p (pω₀) have also been available from single-domain samples with the director aligned parallel to the magnetic field. We have applied the small-step rotational diffusion model of Nordio et al. to the data from the aromatic deuterons of THE6-ard in its uniaxial columnar D_ho phase, to describe the spinning (D _∥, rotational diffusion constant about the planar normal to the disc) and the tumbling (D?, rotational diffusion constant of the planar normal) motions of the molecular core. Although this model has been successfully used for rod-like nematic liquid crystals, its use has not been attempted for discotic liquid crystals. The model seems to indicate that molecular reorientation has slowed down in the D_ho phase, giving frequency dependence to the spectral densities. This can be explained by the high orientational order of the molecules. We are able to account for the four spectral densities J ₁ (ω₀), J ₁ (ω₀, 90°), J ₂ (2ω₀) and J ₂(2ω₀, 90°) with a calculated ratio D∥/D? of about 1. This is quite different from that of rodlike liquid crystals.     

Diffusion Mechanism of As‐spun Polyacrylonitrile Fiber in a Dimethyl Sulfoxide‐Water Coagulation Bath

In this paper, the diffusion mechanism of as‐spun PAN fiber was investigated in dimethyl sulfoxide‐water by determining the dynamic compositions of the fibers and the diffusion coefficients of solvent and nonsolvent during coagulation. The diffusion process could be divided into two stages. Results showed that the first stage of the diffusion process was the most important during the whole process, which was fundamental to further study on the formation mechanism. Also, compared with wet spinning, the dry‐jet wet spinning method had the advantage of mild coagulating at a high jet‐stretch. At high concentrations, the diffusion coefficients increased and the ratio of solvent diffusion coefficient to nonsolvent diffusion coefficient decreased; an increasing temperature resulted in the increase of both diffusion coefficients with a decrease in their ratios. To some extent, for the PAN‐DMSO‐water system, the more the ratios D_s*/D_n* tended to 1, the more the cross‐section shapes of as‐spun PAN fiber tended to be circular.     

Mutual diffusion and thermodynamics in the blends of polystyrene and tetramethylbisphenol-A polycarbonate

A study was made of miscible polymer blends of deuterated polystyrene (d-PS) and tetramethylbisphenol-A polycarbonate (TMPC). The Flory interaction parameter χ was obtained from the relation between mutual and tracer diffusion coefficients, D? and D^*, which were measured by forward recoil spectrometry. The temperature dependence of diffusion at PS weight fractions ω of 0.25 and 0.5, and the composition dependence at temperatures 45°C above the glass transition temperature, T_g, were investigated. A stronger dependence of χ on both temperature (at ω = 0.5) and composition was observed in comparison with other miscible binary polymer blends involving PS. Analysis using the generalized lattice-fluid model of Sanchez and Balazs¹ showed that the incorporation of a significant specific interaction is needed to explain the temperature dependence of χ. The diffusion coefficients obtained in the one-phase region were extrapolated to the two-phase region, and these were compared with the effective diffusion coefficient extracted from phase separation dynamics measured by light scattering.² A significant discrepancy between the extrapolated and effective diffusion coefficients was observed. © 1995 John Wiley & Sons, Inc.     

Water-absorption properties of an acetal copolymer

The kinetics of sorption from the liquid phase to equilibrium and desorption were studied over the temperature range 0–80°C. Equilibrium uptake was found to increase linearly with concentration in this range. Sorption-desorption kinetics showed the diffusion coefficients to decrease with increasing concentration, although the extent of this dependence did not appear in itself to be temperature-dependent. The apparent diffusion coefficient obeyed the law D = D₀ exp {? E/RT} over the temperature range studied, giving E = 9.9 kcal./mole and D₀ = 0.45 cm.² sec.^?1. These values are compared with corresponding values for other polymers.     

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.     

The electronic g-tensor of MgF: A comparison of ROHF and MRD?CI level results

Despite their importance in the characterization of molecular magnetism, electronic g-tensors have received rather little theoretical attention. In this work, however, the ground-state g-tensor of MgF is computed at both the ROHF and multireference CI levels. The calculations are expanded complete to second order in appropriate Breit-Pauli terms and the contributions of all important magnetically coupled excited states are accounted for. Both the CI- and ROHF-level Δg_∥-values (-59 and -55 ppm, respectively) are in agreement with experiment (-319 ± 500 ppm) within the range of experimental uncertainty. For Δg_⟂, however, the ROHF treatment yields a value (-659 ppm) in substantial disagreement with experiment (-1319 ± 500 ppm). Fortunately, this discrepancy is alleviated by CI level treatment (Δg_⟂ = -1447 ppm). © 1996 John Wiley & Sons, Inc.     

Thermal conductivity of oriented crystalline polymers

Thermal conductivities of six oriented semicrystalline polymers which range from 0.37 to 0.63 in crystallinity and 1 to 5 in draw ratio λ (up to about 15 for two polymers) have been measured between 100 and 340 K. It was found that for increasing λ the conductivity K_∥ (along the draw direction n?) increases rapidly while K_⊥ (normal to n?) decreases slightly; K_∥ also increases with temperature, but K_⊥ shows no simple pattern in temperature dependence. These general features can be reproduced reasonably well at low draw ratio (λ < 5) by the modified Maxwell model, and the discrepancy in details may be attributed to the fact that the model does not take into account the possible anisotropy of the amorphous phase of the oriented polymers. At high draw ratio the intercrystalline bridge effect becomes important, and one must resort to the Takayanagi model, but the lack of corroborating x-ray data has rendered a detailed comparison impossible.     

HTO as a conservative tracer used for characterization of contaminant migration in porous rock environment

Methodology for diffusion coefficient determination was applied on sandstone samples, using conservative non sorbing tracer. The results proved that methodology, through-diffusion cell design and GoldSim diffusion module can be used for sandstone samples in order to determine important migration parameters, necessary for transport model input. However, rock heterogeneity factor has to be taken into account in any case as it can potentially change rock properties, even within centimeter scale. Effective diffusion coefficient D _e for rock samples was determined. The values fell into the range of 1.0–6.17 × 10⁻¹⁰ m² s⁻¹. Discrepancies in measured and simulated porosity were observed. Statistical analyses revealed that values of diffusion coefficient D _e were in close interrelation to primary mineral (quartz) and cement forming minerals (kaolinite and organic matter).     

羧化聚苯醚与聚苯乙烯共混体系相分离初期分子量影响的光散射研究

 本文用激光光散射方法研究了具有特殊相行为[(低临界溶解温度(LCST),高临界溶解温度(UCST)共存]共混体系羧化聚苯醚和聚苯乙烯在UCST域内的不稳相分离初期分子量对动力学参数的影响。结果表明:相分离初期动力学过程与Cahn理论吻合;随着分子量增加,表现扩散系数D_app明显减小;该体系的表现扩散系数为10^-14 cm²s^-1数量级。deGennes管子模型可很好地描述不稳相分离初期大分子扩散行为。     

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).     

Lipophilic counterion effect on aggregation and adsorption behavior of quaternary ammonium surfactants

The obvious different aggregation and adsorption behavior of six newly quaternary ammonium surfactants with different lipophilic counterions has been discoverd by measurements of equilibrium and dynamic surface tension, fluorescence and conductivity. Interestingly, the critical micelle concentration (CMC) and its surface tension γ_CMC decrease with the increasing counterion chain length. However, three methods have confirmed that an exception of CMC increases slightly from C₁₆NC₁ to C₁₆NC₂. According to experimental results, a balanced mechanism between hydrophobicity and electrostatic of counterion is proposed. Besides, the dynamic surface tension results show the diffusion coefficient increases with the increasing counterion length both at a short time (D_t?→?0) and long time (D_t?→?∞), which indicates a faster adsorption process. Unlike the inorganic counterion, the diffusion coefficient decreases with the increase of hydrophobic chain length. This is attributed to the strong electrostatic interactions between counterions and cationic headgroups.     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Transitions between the B2 phase and more usual smectic phases in binary systems of banana-shaped with calamitic mesogens

Deuterium NMR spectroscopy is used to study a ring-deuteriated chiral liquid crystal 4-(2-methylbutyl)oxycarbonylphenyl 4-(10-undecenyloxy)benzoate. The quadrupolar and proton-deuteron dipolar splittings, and deuteron quadrupolar and Zeeman spin-lattice relaxation times were measured as a function of temperature in the smectic A phase at two different Larmor frequencies. The derived spectral densities of motion at different temperatures were analysed simultaneously using a rotational diffusion model which also includes internal ring rotations. Motional parameters (D _⊥, D _∥, D _R) and order parameter tensors (S_zz , S_xx -S_yy ) were obtained. Although the present data seem insufficient to draw a definitive conclusion, we believe that it is possible for this particular chiral molecule to have D_⊥ >D_∥ , which is different from non-chiral rod-like liquid crystals.     

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.