NMR study of diffusion of butane in linear polyethylene

The diffusion coefficient of butane in linear polyethylene at room temperature as a function of the vapor pressure of butane was measured by the spin-echo method with a pulsed magnetic field gradient. For the Special morphology of randomly oriented stacks of parallel lamellas the detour factor is 1/3. As long as the blocking factor and migration through the lamellas can be neglected, the local diffusion coefficient D_a of the small molecules through the amorphous layers in the direction parallel to the lamellas is three times the apparent diffusion coefficient D derived from the decay of the amplitude of the spin echo under the assumption of an infinitely extended homogeneous medium. The diffusion coefficient and the spin–spin relaxation time both increase exponentially with increasing pressure, i.e., butane concentration in the polymer, while the spin-lattice relaxation time is pressure independent and seems to be determined by interaction with the amorphous polyethylene matrix.     

Differential permeation — Part I: A method for the study of solvent diffusion through membranes

We describe the differential permeation method for the study of the diffusion of solvents from a liquid (or liquid mixture) through flat or tubular membranes. This method consists of measuring the transient permeation rates through the membrane when one of its faces is suddenly put into contact with the liquid medium. The change in the transient rate with time is analyzed by numerical best fitting methods to determine the Fickian diffusion coefficient. A simplified equation is proposed for the fitting of the response of a tubular membrane. Deviations from the Fickian transport mechanism with concentration-independent diffusion coefficient can be evidenced and eventually analyzed by using other mechanistic models.     

Permeation of carbon dioxide through homogeneous dense and asymmetric cellulose acetate membranes

Sorption isotherms for carbon dioxide in a homogeneous dense cellulose acetate membrane were measured by the pressure decay method at three temperatures between 20 and 40°C and gas pressures up to 1.7 MPa. Steady-state permeation rates for the same system at three temperatures between 24 and 40°C and gas pressures up to 2.2 MPa were measured by the variable volume method. The equilibrium sorption was described well in terms of the dual-mode sorption model. The pressure dependence of the mean permeability coefficient was interpreted by the total immobilization model, i.e., a limiting case of the dual-mode mobility model, where the diffusion coefficient for the Henry's law mode is not assumed to be constant but depends upon gas pressure via a modified free-volume theory. The observed pressure dependence of the mean permeability coefficient through an asymmetric cellulose acetate membrane was very similar to that through a homogeneous dense membrane. The thin skin layer in the asymmetric membrane can be simulated by a homogeneous dense membrane from the point of view of gas sorption and diffusion.     

Evaluation of sorption and diffusion behavior of selenium in crushed granite by through-diffusion column tests

Distribution coefficients (K _d), apparent diffusion coefficients (D _a) and retardation factor (Rf) in this work obtained by batch and through-diffusion experiments have been performed, respectively. The accumulative concentration method developed by Crank (The mathematics of diffusion, 12) was applied to realize apparent and effective diffusion coefficient (D _a and D _e) of Se. Besides, a non-reactive radionuclide, HTO, was initially conducted in through-diffusion experiment for assessing the ability of radionuclide retardation. The distribution coefficients (K _d) obtained by batch tests in 14 days under aerobic and anaerobic systems were 6.98 ± 0.35 and 5.21 ± 0.25 mL/g. Moreover, Rf^cal and K _d ^cal of Se obtained from accumulative concentration’s method in through-diffusion test showed an obvious discrepancy with the increase of length/diameter (L/D) ratio. However, it presented an agreement of Rf^H/Se and K _d ^H/Se in a various L/D ratio by comparison of apparent diffusion coefficient’s (D _a) between HTO and Se. It appears that the Rf^H/Se and K _d ^H/Se obtained from the through-diffusion experiments are lower than those derived from the batch experiments. Therefore, it demonstrates that reliable Rf and K _d of Se by through-diffusion experiments could be achieved at a non-reactive radiotracer (HTO) prior to tests and will be more confident in long-term performance assessment of disposal repository.     

Development of a method to determine the SFC in the fat phase of emulsions using TD-NMR FID-CPMG deconvolution

Fat crystallisation in emulsions is a complex process. One of the important parameters is the solid fat content (SFC). Up to now, there is no standardised method to measure the SFC in emulsions, let alone to determine the SFC of the fat inside droplets, thus avoiding the signal of the aqueous phase. This work evaluates the capabilities of deconvolution of the free induction decay (FID)-Carr–Purcell–Meiboom–Gill (CPMG) signal of emulsions. Three models were evaluated. The first model was a combination of a Gaussian function and a bi-exponential function (GBE model). The second model combined a Gaussian function with multiple exponential functions (GME model). The last model contained multiple Gaussian functions and multiple exponential functions (MGME model). The latter two models used a simplified CONTIN analysis. Based on the analysis of the determination coefficient R², the calculated water content and the estimated SFC of nonemulsified two-phase systems, the GBE model was selected to analyse the FID-CPMG signal of emulsified systems. However, the results obtained with the other models did not differ substantially, and hence, they could be used to obtain a full relaxation time distribution. When the GBE model was applied on different emulsion systems, no significant differences in estimated SFC of the fat phase were found, thus indicating that the emulsion formulation (i.e. water-in-oil [W/O], oil-in-water [O/W] or water-in-oil-in-water [W/O/W]) only had a minor effect on the SFC in the systems considered here.     

Analytic energy derivatives for coupled-cluster methods describing excited states: General formulas and comparison of computational costs

It is possible to derive energy derivatives for nonvariational (e.g., coupled-cluster) methods invoking the generalized Hellmann–Feynman theorem. In such a procedure, one constructs a functional which, besides the usual wave-function parameters, contains new ones. One set of stationary conditions will reproduce exactly the original equations of the method, while the others will determine the value of the new parameters. We applied this straightforward procedure to derive analytic energy derivatives for several coupled-cluster (CC ) methods applicable to excited states such as the Hilbert-space CC method, two-determinetal (TD ) CC method, Fock-space CC method, and equation-of-motion–CC (EOM –CC ) method. Finally, we compared the computational requirements for the different methods. © 1995 John Wiley & Sons, Inc.     

Sorption and diffusion of HTO and cesium in crushed granite compacted to different lengths

In this study, batch and through-diffusion experiments have been performed in order to determine the distribution coefficients (K _d ), apparent diffusion coefficients (D _a ) and retardation factor (Rf), respectively. Both apparent and effective diffusion coefficient (D _a and D _e ) of Cs were obtained by accumulative concentration method developed by Crank (1975). In addition, a non-reactive radionuclide, HTO, was initially conducted in through-diffusion experiment for assessing the ability of radionuclide retardation. The distribution coefficients (K _d ) obtained by batch tests in 14 days under aerobic and anaerobic systems were 2.06 and 3.52 ml/g. Moreover, it is found in through-diffusion test that Rf = 4.12 and 4.40 and K _d = 0.97 and 1.06 of Cs did not have an obvious discrepancy in a length/diameter/ (L/D) ratio of 0.44 and 1.78. However, Rf and K _d revealed a larger difference in an L/D ratio closing to 1 due to the geometric change of one-dimension diffusive hypothesis. Therefore, it demonstrates that Rf and K _d obtained by through-diffusion experiments only could be achieved at a lower or larger L/D ratio and would be reliable for long-term performance assessment.     

Grand canonical-like molecular dynamics simulations: application to anisotropic mass diffusion in a nanoporous medium

In this work, we describe two grand canonical-like molecular dynamics approaches to investigate mass diffusion phenomenon of a simple Lennard-Jones fluid confined between solid surfaces and in direct contact with reservoirs. In the first method, the density is used as the control variable in the reservoir whereas it is the pressure in the second method. Both methods provide consistent results, however, the constant density approach is the most efficient with respect to the computational time and implementation. Then, employing the constant density approach, we have studied the transient behavior of the diffusion process associated with the migration of one fluid into another one confined between parallel solid walls. Results have shown that the evolution of molar fraction of the invading fluid follows roughly a 1D diffusion model when the solid phase is weakly or moderately adsorbent with a characteristic time increasing when the pore width decreases. However, when the adsorption is high and the pore width small (i.e., below ten molecular sizes), the apparent mass diffusion in the adsorbed layer is reduced compared to that in the center of the slit pore. Hence, this mass diffusion process becomes a two-dimension phenomenon that must take into account an effective mass diffusion coefficient varying locally.     

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).     

A NEW MODEL FOR ESTIMATION OF DIFFUSION COEFFICIENT OF PHENOL DESORPTION WITHIN POLYMERIC RESIN UNDER ULTRASOUND

1. INTRODUCTION Ultrasound is a kind of mechanical wave whose frequency is more than 20 kilohertz. It can enhance the mass transfer, increase the rate and conversion of chemical reaction, change the reaction pathway [1,2] and accelerate the conversion of…     

Refining of nonionic surfactant micellization theory based on the law of mass action

Two approaches to determining critical micelle concentration (CMC) are assessed, i.e., from the inflection point in the curve for the concentration dependence of the degree of micellization and as K^1/(1–n), where K is the constant of the law of mass action and n is the aggregation number. The latter approach makes the theory simpler, while the former explicitly expresses the critical degree of micellization via the aggregation number. The concentrations of monomers and micelles are analyzed as functions of the overall concentration of a surfactant in a micellar solution. These functions look much simpler in the graphical form as compared with their complex exact analytical representation. This has resulted in derivation of simple analytical approximations for these functions, with these approximations being useful for calculations. The concentration dependence of the surfactant diffusion coefficient has been considered based on these approximations. It turned out that this dependence not only provides the known method for determining the diffusion coefficient of micelles, but also gives the possibility in principle to determine the aggregation number from the slope of the dependence of the diffusion coefficient on the inverse concentration (counted from the CMC in the CMC units). This new method for determining the aggregation number has been tested using the literature data on the diffusion coefficient of penta(ethylene glycol)-1-hexyl ether in an aqueous solution.     

Interpretation of diffusion measurements in cholesterics

An interpretation of the pitch and time dependence of diffusion in the cholesteric liquid crystalline phase is proposed. Experimental results on nematics twisted by chiral dopands are discussed. The model predicts a decay of the translational diffusion coefficient D_p in the helix direction with the observation time and a decrease of D_p with shorter pitch length P_o, in accord with experiment. From comparison with experimental data it is concluded that rotational diffusion in these samples is a collective phenomenon.     

Simulating critical dynamics in liquid mixtures: short-range and long-range contributions

Recently, Das et al. [J. Chem. Phys. 125, 024506 (2006)] established that computer simulations of critical dynamics in a binary Lennard-Jones mixture are consistent with the predicted Stokes-Einstein behavior of the asymptotic decay rate of the order-parameter fluctuations near criticality. Here, we show that the noncritical or "background" contributions to the computed diffusion coefficient are also in agreement with both theory and experiment, thus further validating the feasibility of molecular dynamics simulations for studying dynamic critical behavior.     

Diffusion coefficient of Brownian particle in rough micro-channel

This study examines the feasibility of using of the lattice Boltzmann method to determine how the surface roughness of a quadrate channel affects the diffusion coefficient of Brownian particle(s). The surface was represented by a regular array of spheres. Surface roughness reduced the diffusion coefficient of the Brownian particle(s) because of a change in the velocity autocorrelation function decay and in pressure. Additionally, the neighboring particles increased the diffusion coefficient of Brownian particle.     

Hydrogen uptake mechanism of a silicone‐rubber DEB getter mixture

The kinetics of the hydrogen getter 1,4‐bis(phenylethynyl)benzene (DEB) blended with carbon‐supported Pd (DEB‐Pd/C) dispersed uniformly in silicone [DEB‐Pd/C‐poly(dimethyl siloxane)] were studied with a thermogravimetric method as a function of the hydrogen pressure and temperature. A diffusion‐controlled reaction model was developed to explain the experimental results. The diffusion coefficient, solubility coefficient, and permeability of hydrogen through silicone rubber were determined. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 425–431, 2001     

Diffusion deposition of aerosol nanoparticles in model granular filters

The diffusion deposition of point aerosol particles from a flow in model granular (grained) filters, i.e., separate layers composed of parallel chains of spherical granules, has been studied at small Reynolds numbers. Numerical solution of the Stokes and convective diffusion equations has been employed to determine the drag forces and granule collection efficiencies as depending on the Peclet diffusion number in a range Pe = 0.02–2 × 10⁴ and the ratio between the granule diameter and the distance between chain axes. Layers of closed chains with square and hexagonal packings have been considered. Approximation formulas have been derived for calculation of nanoparticle penetration in model granular filters.     

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.     

Interaction of simple acids with nylon. Part 2: Diffusion of simple acids

The paper deals with the diffusion of two mineral acids, hydrobromic and sulfuric acids, and two simple dye acids, NOG (C. I. Acid Orange 7) and SY (C.I. Food Yellow 3), in water-swollen nylon 66. Anion self-diffusion coefficients were obtained by radiotracer techniques. The bromide ion and the SY anion self-diffusion coefficients show very little variation with concentration in the amino-dyeing region, whereas the H₂SO₄ and NOG anion diffusion coefficients are concentration-dependent. The variation of the H₂SO₄ anion diffusion coefficient with concentration is consistent with the formation of small quantities of the highly mobile bisulfate ion. The low SO₄ diffusion coefficient may be explained by the interaction of this ion with single, fixed sites in the polymer. The variation of the NOG anion diffusion coefficient with concentration does not follow a simple D = D₀[1/(1 ? θ)] relationship at intermediate concentrations but the rapid increase observed as the available sites became saturated, i.e., as θ → 1, is consistent with a site saturation model.     

一种新的标定体积排除色谱（SEC）的方法

基于体积排除色谱中测得的淋出体积和动态激光光散射中测得的平动扩散系数都直接依赖于高分子的流体力学体积这一事实，本文在理论上提出了一种把淋出体积分布和平动扩散系数分布二者结合起来标定体积排除色谱的新方法，并且在实验上通过对宽分布的聚苯乙烯标准样品的测试证实了该方法的可行性．