Diffusion coefficients in a halocarbon–polybutene system

The diffusion coefficient of 1,1,2-trichlorotrifluoroethane (TTE) in a liquid polybutene was determined at 25°C. as a function of concentration over the range 1.0–19.5 g. TTE/100 cc. The diffusion coefficient increase with increasing TTE concentration, rising continuously from 3 × 10^?8 cm.²/sec. at the lowest concentration to 15 × 10^?8 cm.²/sec. at the highest. The magnitudes of the diffusion coefficients indicate that the diffusion mechanism for small molecules in polymeric media must afford vastly greater opportunities for diffusion than the Stokes-Einstein relation allows. Similarly, self-diffusion coefficients for the liquid polymer are much lower than the observed mutual diffusion coefficients. An explanation for this behavior is presented.     

超临界L-J流体混合物互扩散性质的分子动力学模拟

采用分子动力学方法计算了超临界Lennard-Jones(L-J)流体混合物的扩散性质, 分析了超临界条件下二元L-J混合流体(Ar-Kr体系)中各组分的自扩散系数及Maxwell-Stefan互扩散系数随组分的变化情况. 结果表明, 与Darken公式能很好地应用于常规条件下的Ar-Kr体系不同, 超临界条件下的Maxwell-Stefan扩散系数明显大于Darken公式的预测值, 不同原子间的速度互相关函数不可忽略且为正相关.     

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.     

Diffusion study of a polymer–diluent system using the optical mass transport method

Thermotropic polymers and low-molecular-weight mesogens share many common textural features. This circumstance is exploited to determine diffusion coefficents in a system consisting of a cholesteric polymer and a low-molecular-weight nematogen using the recently developed optical mass transport method. The self-diffusion coefficient and its concentration dependence were determined by using a distance–time approach, whereas the time dependence of the mutual diffusion coefficient was evaluated by a conventional concentration–distance analysis of the diffusion profile. Comparison with literature data indicates satisfactory agreement. The coefficient of the scaling law relating the self-diffusion coefficient and concentration is in accord with the value predicted by de Gennes for semidilute polymer solutions.     

Mass transport in a chiral nematic/nematic liquid crystal system

The optical microscopic mass transport technique has been used to study diffusion phenomenon in a chiral nematic/nematic solute/solvent mixture. Analysis of the concentration-distance, concentration-time and distance-time of the diffusion profile gave the diffusion coefficient of the system as a function of time, distance and concentration, respectively. The mutual diffusion coefficient of the system was independent of the distance and time, showing an average value of 2.65 × 10^-7 cm² s^-1. In non-steady state diffusion, the diffusion coefficient was dependent on both distance and time. The diffusion coefficient exhibited an inverse relation with the local concentration of the chiral solute. The self-diffusion coefficient of the nematic solvent gave a value of 3.4 × 10^-7 cm² s^-1 via extrapolation to zero concentration of the solute.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

Correlation between thermal diffusion and solvent self-diffusion in semidilute and concentrated polymer solutions

We have performed measurements of thermal diffusion coefficients DT and solvent self-diffusion coefficients Dss in semidilute to concentrated polymer solutions. Solutes of different glass transition temperatures and solvents of different solvent qualities have been used. The investigated systems are in detail: poly(dimethyl-siloxane) in toluene, tristyrene in toluene, polystyrene in toluene, polystyrene in tetrahydrofuran, polystyrene in benzene, and polystyrene in cyclohexane. The thermal diffusion data are compared to our data and literature data for solvent self-diffusion coefficients. In all systems the concentration dependence of DT closely parallels the one of Dss which may be viewed as a local probe for friction on a length scale of the size of one polymer segment. This identifies local friction as the dominating parameter determining the concentration dependence of DT. Solvent quality, in contrast, has no influence on DT.     

Cooperative phenomena in semi-dilute solutions of poly(oxyethylene)

The concentration dependence of the cooperative diffusion coefficient (D) and the cooperative sedimentation coefficient (s) in semi-dilute aqueous solutions of a sharp fraction of poly(oxyethylene) have been studied. It was found that D varies as C^{0.60 ± 0.02} and s as C^{?0.66 ± 0.02}. The results indicate that one should distinguish between a static and an effective dynamical correlation length in order to obtain a consistent overall picture. Furthermore, the data seem to indicate that the POE chains are flexible.     

Mass dependence of mutual diffusion coefficient: computer simulation study

Molecular dynamic computer simulations are performed to study the mass dependence of mutual diffusion coefficient in an isotopic, equimolar binary system. The particles of the system are assumed to be interacting via Lennard-Jones potential. The self- and mutual diffusion coefficients are calculated from the time dependence of the mean square displacement and from the velocity correlation function using the Green–Kubo formula. The study has been carried out at different densities and temperatures. Like the self-diffusion coefficient, the mutual diffusion coefficient is also found to be weakly dependent on the mass ratio. Our study also shows that the temperature of the system has a negligible effect on the mass dependence of the diffusion coefficients.     

Colloidal forms of radionuclides and their separation from water solution

Colloidal properties of¹⁴⁴Ce(III),¹⁴⁷Pm(III),⁹¹Y(III), and other, radionuclides were determined from the course of their self-diffusion. A reduced self-diffusion indicated the formation of colloidal radionuclides. The decrease in the self-diffusion coefficient began from a certain value of pH, and a pH region of slowest self-diffusion existed for each of the radionuclides studies. The maximum formation of colloidal radionuclides may be assumed to lie in the range of these pH values. An increase in the rate of self-diffusion was observed with radionuclides in colloidal forms under the effect of gamma-radiation. The possibility of mutual interaction between radionuclides was also inferred from the course their self-diffusion. High effective sorption of¹⁴⁷Pm(III) was attained on hydrated ferric oxide in the pH range were hydrolytic products and colloidal forms of¹⁴⁷Pm(III) were formad to a large extent.     

Self-diffusion and sedimentation of dextran in concentrated solutions

Frictional coefficients for dextran in water have been evaluated from (i) self-diffusion coefficients determined by pulsed-field-gradient NMR, and (ii) sedimentation coefficients in concentrated solutions. The results show that these frictional coefficients are only equal at infinite dilution and that f_s increases more rapidly than f_D^* as the concentration increases.     

Velocity sedimentation transport properties in dilute and concentrated solutions of hydroxypropyl cellulose in water at different temperatures up to phase separation

Velocity sedimentation measurements have been performed for the system hydroxypropyl cellulose in water in both dilute and concentrated solutions (0–100 kg m^?3) and at temperatures remote from as well as close to θ-conditions (25–40°). In dilute solutions, the experimentally determined concentration dependence of the sedimentation coefficient was compared with that calculated from the theory of Yamakawa; fairly good agreement was obtained. The difference between the sedimentation behaviour under good and poor solvent conditions is also discussed. Furthermore, the frictional properties are discussed and compared with those deduced from diffusion measurements.     

On the mutual diffusion properties of ethanol-water mixtures

The structural organization, the number of hydrogen bonds (H bond), and the self- and mutual diffusion coefficients of ethanol-water mixtures were studied by molecular dynamics simulation. It was found that both the numbers of H bonds per water and per ethanol decrease as the mole fraction of ethanol increases. The composition dependences and the relationships between the self- and the mutual diffusion coefficients were further discussed. The self-diffusion coefficient of water has a large drop as the concentration of ethanol increases from 0 to 0.3 and then it nearly keeps constant, while that of ethanol has a minimum around ethanol mole fraction of 0.5. The mutual diffusion coefficient could be divided into two parts, the kinematic factor and the thermodynamic factor. Both the kinematic and thermodynamic factors for ethanol-water mixtures were calculated. It was found that the change trend of mutual diffusion coefficients with the composition is mainly dependent on the thermodynamic factors.     

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).     

NMR self-diffusion measurements in inverse micellar cubic phases

Abstract

We have measured self-diffusion coefficients of amphiphile and water molecules in novel inverse micellar lyotropic cubic phases using the pulsed field gradient NMR technique. We investigated two different ternary lyotropic systems: oleic acid/sodium oleate/water, and dioleoylglycerol/dioleoylphosphatidylcholine/water. Both of these systems have previously been shown by one of us to form a cubic phase of space group Fd3m, whose structure is a complex packing of two types of disconnected quasi-spherical inverse micelles embedded in a 3D hydrocarbon matrix. The amphiphile translational diffusion coefficients determined for the first time by ¹H NMR in both systems are surprisingly large. Thus the self diffusion coefficients of amphiphiles may not provide a reliable way of distinguising inverse micellar from inverse bicontinuous phases. The water self-diffusion coefficient has been determined to have a value of 2·4 × 10^?12 m² s^?1, a value which is more than two orders of magnitude lower than that typically observed for inverse bicontinuous cubic phases. This confirms unambiguously the inverse micellar topology of the Fd3m cubic phase, and indicates that the value of the water diffusion coefficient should permit inverse micellar and inverse bicontinuous structures to be reliably distinguished, even for systems where the structure has not been previously determined by diffraction.     

Chemical diffusion in intermediate phases in the lithium-tin system

The compositional variation of the chemical diffusion coefficient in the six intermediate phases LiSn, Li₇Sn₃, Li₅Sn₂, Li₁₃Sn₅, Li₇Sn₂, and Li₂₂Sn₅ of the lithium-tin system at 415°C has been measured. Among these intermediate phases, the phase Li₁₃Sn₅ has the highest chemical diffusion coefficient, varying with composition from 5.01 × 10^?5 to 7.59 × 10^?4 cm²/sec at that temperature. Combining this information with coulometric titration curves (emf versus composition), the self-diffusion coefficient of lithium has also been determined in the various intermetallic phases as a function of composition under the assumption that the tin atoms do not move appreciably compared with the lithium atoms. The lithium self-diffusion coefficient in the phase LiSn is lower than those in the more lithium-rich phases by one order of magnitude. This result is discussed in terms of the difference between the crystal structures of LiSn and the other lithium-rich phases in the lithium-tin system.     

A self-diffusion study of poly(ethylene-oxide) alkyl alcohols

The self-diffusion coefficients of HDO and some surfactants in aqueous mixtures at different concentrations, below the critical micelle concentration, have been determined by means of the NMR, spin-echo pulsed field gradient method. The surfactant solutes chosen were ethylene glycol-pentyl alcohol (diethylene glycolpentylalcohol, ethylene glycol-hexyalcohol, diethylene glycol-hexyl alcohol, triethylene glycol-hexyl alcohol, tetraethylene glycol-hexyl alcohol, pentaethylene glycol-hexyl alcohol). The interactions in solution are studied by analyzing the solute self-diffusion coefficients extrapolated to infinite dilution. These values are compared with those of 1-alkanols. The slope of the self diffusion coefficientsvs. the solute concentration are correlated with the microscopic friction coefficients. A model for interpreting the experimental data is suggested.     

The mutual diffusion coefficient for (meth)acrylate monomers as determined with a nuclear microprobe

The value of the mutual diffusion coefficient DV of two acrylic monomers is determined with nuclear microprobe measurements on a set of polymer films. These films have been prepared by allowing the monomers to diffuse into each other for a certain time and subsequently applying fast ultraviolet photo-polymerization, which freezes the concentration profile. The monomer diffusion profiles are studied with a scanning 2.1 MeV proton microprobe. Each monomer contains a marker element, e.g., Cl and Si, which are easily detected with proton induced x-ray emission. From the diffusion profiles, it is possible to determine the mutual diffusion coefficient. The mutual diffusion coefficient is dependent of concentration, which is concluded from the asymmetry in the Cl- and Si-profiles. A linear dependence of the mutual diffusion coefficient on the composition is used as a first order approximation. The best fits are obtained for a value of b=(0.38+/-0.15), which is the ratio of the diffusion coefficient of 1,3-bis(3-methacryloxypropyl)-1, 1,3,3-tetramethyldisiloxane in pure 2-chloroethyl acrylate and the diffusion coefficient of 2-chloroethyl acrylate in pure 1,3-bis(3-methacryloxypropyl)-1,1,3,3-tetramethyldisiloxane. Under the assumption of a linear dependence of the mutual diffusion coefficient DV on monomer composition, it follows that DV = (2.9+/-0.6)10(-10) m(2)/s at a 1:1 monomer ratio. With Flory-Huggins expressions for the monomer chemical potentials, one can derive approximate values for the individual monomer diffusion coefficients.     

Diffusion and partitioning of cations in an agarose hydrogel

Self- and mutual diffusion were measured in a low-melt 1.5% agarose hydrogel as a function of ionic strength (0.1-100 mM) and pH (3-7) for Cd(2+) and a charged rhodamine derivative. Self-diffusion was measured by fluorescence correlation spectroscopy, whereas mutual diffusion was evaluated using a diffusion cell. In contrast to the results observed for the diffusion cell, self-diffusion of rhodamine 6G increased from 50 to 90% of that found in water as the ionic strength increased from 0.1 to 100 mM (pH = 6). The combined observations of decreasing diffusive flux in parallel with an increasing diffusion coefficient were attributed to the gel's Donnan potential. Donnan potentials obtained voltammetrically using a Au amalgam microelectrode varied from -30 to 0 mV as the ionic strength increased from 0.1 to 100 mM (pH = 6). At the low ionic strengths, Donnan potentials of this magnitude accounted for a 13× enhancement of Cd(2+) concentrations in the hydrogel, which was consistent with measurements obtained by a nitric acid extraction of the gel (15×) and able to explain the apparent discrepancy between mutual and self-diffusion measurements. The overall diffusion of the positively charged substrates decreased as the pH was decreased from 12 to 3.     

Temperature control algorithms in dual control volume grand canonical molecular dynamics simulations of hydrogen diffusion in palladium

The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.