Diffusion Coefficients Of Components Research Articles

Time Variation of Insulating Properties of Closed Cell Foam Insulation

Heat is transferred through closed-cell foam insulation by conduc tion through the solid polymer making up the cell structure, conduction through the low conductivity gas (blowing agent) inside the cells, and radiation. The effective thermal conductivity of closed-cell foam panels changes with the foam age due to diffusion of air components into the foam and diffusion of the blow ing agent out from the foam. The change in the composition and thermal conductiv ity of the gas mixture was modeled as a function of the aging time. The change in the composition is computed by solving the transient diffusion equations for each gas species in the foam. The thermal conductivity of the gas mixture is computed from an empirical correlation proposed by Lindsay and Bromley. A computer program was developed to numerically solve the governing equations. The effective diffusion coefficients of the air components and the blowing agent are the main code inputs. The numerical prediction of the change of the effective con ductivity of foam panels for a given age is within 6% or better of the conductivity obtamed in long-term tests under three different thermal environments.

Mechanisms of component diffusion in mercury cadmium telluride

The component diffusion coefficients for the Hg0.8Cd0.2Te (MCT) system are measured using radioactive tracers. Multiple branches are observed in the tracer diffusion profiles which are related to fast and slow-diffusing components. Diffusion models for each component are proposed based on the defect chemistry of MCT, a calculation of the thermodynamic factor, and the relationship between component diffusion coefficients and the interdiffusion coefficients for pseudobinary systems. The model provides insight into the thermodynamic properties of the system, the mechanisms for diffusion, and the practical application of tracer diffusion data to interdiffusion and p-to-n conversion by Hg annealing.

Fast macromolecules control mutual diffusion in polymer blends

The tracer diffusion coefficient D* of small concentrations of tagged linear polymers seems well understood on the basis of the reptation model1–6, but the mutual diffusion coefficient D which characterizes diffusion at higher concentrations remains controversial7–17. Such diffusion is important in blends of miscible, yet chemically dissimilar, polymers where it controls the kinetics of phase separation and the welding of polymer interfaces. The controversy centres on predicting D from the D*s of the components of the blend. While the 'slow theory'7,8 predicts that D is controlled by the diffusion of the slower-moving component, 'fast theory'9,10 says it is controlled by the diffusion of the faster-moving one. Here we report experiments in which we measure the mutual diffusion coefficient as we increase the tracer diffusion coefficient of the faster-moving component in the blend by decreasing its molecular weight. The strong increase in D we observe demonstrates that the 'fast theory' prediction is correct.

Singularities in determination of the diffusion coefficients of components in melts of AIIIBV systems

A critical analysis is performed of the mathematical expressions used to compute the diffusion coefficients of components on the basis of data on the growth rate or dissolution of crystals of AIIIBV compounds. It is shown that neglect of high-order terms of the series that are the solution of the mass transport differential equations will result in substantial errors during processing of the experimental results. To simplify the computations and eliminate mathematical inaccuracy, it is proposed to use the analytic solution of the diffusion mass transport equations in the approximation of a semi-infinite medium. The diffusion coefficient of arsenic in liquid indium in the 550–750‡C temperature range is computed on the basis of experimental results on the rate of InAs dissolution in an unsaturated In-As melt by using the method proposed.

Application of non-equilibrium thermodynamics to surfactant diffusion

Surfactant diffusion is studied using non-equilibrium thermodynamics. Equations for the phenomenological coefficients, the main diffusion coefficient of the surfactant component and the cross diffusion coefficients are derived. The estimated D values of the surfactant component agree reasonably well with the experimental data provided that the concentrations are not too high. At zero salt the decrease and sudden increase in D near the CMC is predicted. The equations obtained for the cross phenomenological coefficients of the neutral components satisfy Onsager's reciprocal relations.

Adsorption of gaseous hydrocarbons on activated carbon: Characteristic kinetic curve

AbstractThe internal diffusion coefficients, Di, of pure methane, ethane and ethylene as well as some of their binary and ternary mixtures, have been calculated at 20°C for solid particles of a commercial activated carbon. It has been observed that the contribution of the surface migration mechanism to the global mass transfer process inside the adsorbent particles can be as much as 70–80%. Values for the surface migration coefficient Ds have also been calculated from the relation Di = Dg + KDs, where K is a dimensionless mean slope factor. Values found for both coefficients are of the same order of magnitude as those reported in the literature for similar systems.All the values for the internal diffusion coefficients of these pure components and their mixtures fit into a single correlation curve, the characteristic kinetic curve of the adsorbent.

Mobility of fluorescent derivatives of cytochrome c in mitochondria.

Motion of cytochrome c bound to giant (2-10-micron diam) mitochondria isolated from the waterbug Lethocerus indicus was examined using the technique of fluorescence recovery after photobleaching. Fluorescent cytochrome c was exchanged for native cytochrome c through partly damaged outer membrane. Recovery profiles were not statistically different when the fluorescence from iron-free cytochrome c or fluorescein-labeled cytochrome c was used and were essentially the same in the presence or absence of an uncoupler. In the presence of excess porphyrin cytochrome c, the apparent diffusion coefficient was 6 X 10(-11) cm2/s in 0.3 M sucrose-mannitol-EDTA and 3 X 10(-10) cm2/s in 0.10 M KCl/0.10 M sucrose. At concentrations of porphyrin cytochrome c that are stoichiometric with cytochrome c oxidase and for mitochondria in which excess cytochrome c was washed away, two components were observed in the recovery profile. The diffusion coefficient of the fast component was 1 X 10(-10) cm2/s. The second component showed no recovery during the time scale of measurement (D less than 10(-12) cm2/s). We speculate on the origin of the immobile fraction.

Electrochemical investigations on the kinetics of the growth of PbO 2 layers on lead

Potentiostatic polarization measurements of the growth of lead dioxide layers on lead electrodes in sulfuric acid solutions have been made. During an initial period a closed PbO 2 layer is formed anodically on the lead surface. Subsequent growth takes place according to a parabolic rate law with a “parabolic tarnishing constant”, k PbO 2 , in the order of magnitude of 10 −11 cm 2 s −1. This is in agreement with the assumption that the rate-determining step of the growth reaction is the diffusion of oxygen (O 2− ions and electrons) through the oxide layer from the PbO 2/electrolyte interface, where oxygen is incorporated anodically into the solid phase, to the internal phase boundary, where the reaction with lead takes place. Using the fact that the chemical potentials of oxygen in the PbO 2 layer at the phase boundaries are fixed by the electrode potential and by the equilibrium with the internal neighbouring phase, respectively, a mean component diffusion coefficient, D o 2− (PbO 2), of oxygen ions in lead dioxide has been calculated from k PbO 2. D o 2− (PbO 2) is in the order of magnitude of 10 −13 cm 2s −1.

Diffusion in dilute aqueous solutions of phosphoric acid. Verification of the limiting law for diffusion of weak electrolytes

The diffusion coefficient of aqueous phosphoric acid has been measured by a conductimetric technique at 25 °C over the concentration range from 0.0012 to 0.0826 mol dm–3. Below 0.01 mol dm–3 dissociation of neutral H3PO4 molecules to H+ and H2PO–4 produces a sharp increase in the diffusion coefficient of the phosphoric acid component. When a small correction is included to allow for the association reaction H3PO4+ H2PO–4⇌H5P2O–8, the results are in good agreement with predictions based on the limiting law for diffusion of a weak electrolyte. Analysis of the data gives (0.87 ± 0.01)× 10–9 m2 s–1 for the limiting diffusion coefficient of the aqueous phosphoric acid molecule. Within experimental error this value is identical to the limiting diffusion coefficient of H2PO–4.

AN EXPERIMENTAL STUDY OF POLYMER DIFFUSION IN CONCENTRATED SOLUTION: IMPLICATIONS FOR DIFFUSION IN POLYMERIZATION

Abstract The Trommsdorf or gel effect in free radical polymerization is due to the fact that the termination reaction becomes strongly diffusion controlled above a critical concentration associated with the onset of molecular entanglements. Therefore, an understanding of polymer self-diffusion in entangled systems becomes essential to understanding the Trommsdorf effect. Our group has previously proposed a molecular model for the gel effect which uses a specific theory for polymer diffusion (reptution). The present work represents an experimental attack on the same problem Experimental studies of polymer self-diffusion in entangled systems are scarce. Quasielastic light scattering from ternary systems composed of solvent(l)-polymer(2)-polymer(3), in which species (3) is isorefractive to the solvent (i.e. 0n/0c 3 = 0), offers an attractive way to study the tracer diffusion coefficient of species (2) in a binary mixture of composition c 3. In regimes of low momentum transfer (qR G < 1,) where q is the scattered wave vector and R G is the polymer radius of gyration, we have shown that the correlation function of the scattered electric field should decay with a single exponential decay time, given by (D22 q 2)−1 where D 22(c 2, c 3) is the main ternary diffusion coefficient of component (2). Extrapolation to zero concentration of 2) at fixed concentration of (3) yields the tracer diffusion coefficient of (2) in the binary mixture of (1) and (3). The systems toluene(l)-polystyrene(2)-polymethylmethacrylate(3) (0n/0c 3 ≈ 0.007 at 25°C) and toluene(l)-polystyrene(2)-polyvinylmethylether (3) (0n/0c 3 ≈ 0.012 at 60°C) very nearly satisfy the above criteria. In both systems, we have found that the tracer diffusion coefficient of the polystyrene decreases with increasing concentration of the isorefractive polymer. Further studies have focused upon the dependence of the tracer diffusion coefficient upon polystyrene molecular weight, and upon the effect of incomplete index matching.

The chemical diffusion coefficient in (low temperature)α-Ag 2S determined by an electrochemical relaxation method

An electrochemically probed relaxation method has been used to determine the chemical diffusion coefficient, D̃, of α-Ag 2+δS. The experiments were performed at 168°C and span the homogeneity range of this phase, which at this temperature is of the order of 10 -5 in δ. D̃ is found to have values between 0.02 and 0.15 cm 2 s -1 and, as a function of nonstoichiometry, to reflect correctly the composition dependence of the thermodynamic factor, d ln a Ag/d ln c Ag. Using previously determined data for the thermodynamic factor, the component diffusion coefficient of Ag + at 168°C is found to be D Ag + =(5.4 ± 0.4) × 10 -8 cm 2 s -1.

Dissipative Structures in 1D and 2D Chemically Reacting Systems

Abstract A transient analysis of the 1D and 2D reaction-diffusion equations associated with the model reaction of Prigogine and Lefever (Brusselator model), including diffusion of the initial (sub-strate) component, has been performed. For low system lengths and for fixed boundary conditions, the steady state low amplitude solutions are unstable. For zero flux boundary conditions a multiplicity of symmetric solutions with the same wave number may exist, the majority of them being unstable. The diffuion of initial components induce relaxation oscillations in space both for fixed as well as zero flux boundary conditions. The amplitude of the oscillation increases as the diffusion coefficient of the initial component decreases. For conditions of relaxation oscillations the spatial profiles result in single or multiple propagating fronts. High system lengths (or low diffusion coefficient of intermediate components), for both zero flux and periodic boundary conditions, may give rise to a multipeak incoherent wave pattern. For periodic boundary conditions a multiplicity of waves has been observed. Numerical simulation of the 2D-spatial structures reveal certain similarities between the 1D and 2D cases.

Diffusion in mantle liquids: Ion dynamics

New calculations by ion dynamics computer simulation methods suggest that the component diffusion coefficients of many silicate liquids show anomalous pressure dependences. At high pressures of several hundred kilobars the viscosities of certain silicate melts decrease strongly and the ion diffusivities of their components increase sharply.Formerly, the question of diffusion coefficients in silicate liquids in the earth was answered easily: there was little or, essentially, no diffusion. Stirring, mixing, and density‐driven upwelling processes were thought to be effective in transporting ions in silicate liquids, but the excess of free energy provided by temperature or compositional gradients in magmatic‐liquids were considered to be insufficient to drive ionic diffusional processes within appropriate time scales. In laboratory experiments, for example, if two chemically miscible silicate liquids of differing composition are placed in contact along a plane surface, they remain essentially unchanged. After hundreds of hours of contact there is no more than microscale chemical diffusion observed

Pressure Enhancement of Ion Mobilities in Liquid Silicates from Computer Simulation Studies to 800 Kilobars

Ion dynamics computer simulation methods show that for many liquid silicates, like silica itself, the component diffusion coefficients show anomalous pressure dependences. This implies that their viscosities have negative pressure dependences. Overall, there is an interesting degree of analogy between the fundamental binary solutions of geochemistry and the aqueous solutions of common experience; however, due to the stronger bonding in silicate systems, the anomalies are much more persistent. Diffusivity maxima occur at pressures of 200 to 300 kilobars and are correlated with a prevalence of fivefold coordination of silicon ions. The relevance of these findings to planetary dynamics and thermophysical modeling problems is briefly considered.

Lateral mobility in membranes as detected by fluorescence recovery after photobleaching

The evaluation of lateral diffusion coefficients of membrane components by the technique of fluorescence recovery after photobleaching (FRAP) is often complicated by uncertainties in the values of the intensities F(O), immediately after bleaching, and F(infinity), after full recovery. These uncertainties arise from instrumental settling time immediately after bleaching and from cell, tissue, microscope, or laser beam movements at the long times required to measure F(infinity). We have developed a method for precise analysis of FRAP data that minimizes these problems. The method is based on the observation that a plot of the reciprocal function R(tau) = F(infinity)/[F(infinity)-F(tau)] is linear over a large time range when (a) the laser beam has a Gaussian profile, (b) recovery involves a single diffusion coefficient, and (c) there is no membrane flow. Moreover, the ratio of intercept to slope of the linear plot is equal to tau 1/2, the time required for the bleached fluorescence to rise to 50% of the full recovery value, F(infinity). The lateral diffusion coefficient D is related to tau 1/2 by tau 1/2 = beta w2/4D where beta is a defined parameter and w is the effective radius of the focused laser beam. These results are shown to indicate that the recovery of fluorescence F(tau) can be represented over a large range of percent bleach, and recovery time tau by the relatively simple expression F(tau) = [ F(o) + F(infinity) (tau/tau 1/2)]/[1 + tau/tau 1/2)]. FRAP data can therefore be easily evaluated by a nonlinear regression analysis with this equation or by a linear fit to the reciprocal function R(tau). It is shown that any error in F(infinity) can be easily detected in a plot of R(tau) vs. tau which deviates significantly from a straight line when F(infinity) is in error by as little as 5%. A scheme for evaluating D by linear analysis is presented. It is also shown that the linear reciprocal plot provides a simple method for detecting flow or multiple diffusion coefficients and for establishing conditions (data precision, differences in multiple diffusion coefficients, magnitude of flow rate compared to lateral diffusion) under which flow or multiple diffusion coefficients can be detected. These aspects are discussed in some detail.

Mobility of cytoplasmic and membrane-associated actin in living cells.

We have combined fluorescent analogue cytochemistry with fluorescence photobleaching recovery to measure the mobility of fluorescently labeled actin and other labeled test proteins microinjected into living amoebae. Bovine serum albumin, ovalbumin, and ribonuclease A have a cytoplasmic mobility, expressed as a diffusion coefficient, that is 1/2 to 1/3 of that observed in aqueous solution; 90% of the actin has a mobility 1/2 to 1/8 of that of G-actin in aqueous solution, and approximately equal to 10% of the actin has a mobility comparable to that of F-actin in aqueous solution. Therefore, no more than 10% of the actin in the cytoplasm of amoebae can exist as static filaments. Microinjection of phalloidin decreases the diffusion coefficient of the mobile component of cytoplasmic actin, and it also increases the low-mobility fraction to 50% but has no effect on the mobility of labeled ovalbumin. By comparing the mobility of actin in different parts of amoebae and by separating cytoplasm from plasmalemma-ectoplasm, we found the low-mobility fraction of actin to be enriched in the tail, along the plasmalemma-ectoplasm, and in contracted cytoplasm.

On the statistical independence of various column contributions to band broadening. Part 3: Independent treatment of longitudinal diffusion in the plate model

AbstractIt is shown theorectically that the classical formula for calculating the theoretical plate number from squared first central moment, t, and second central moment, σ2, according to ntheor = t/σ2 is valid only when the capacity ratio, k approaches infinity. The general relation between the classical experimental HETP value, H = L/nmtheor, and the underlying true theoretical plate height, ΔL, is found to be when (σ′)2 is the total column contribution to band broadening, L is the column length, Dm is the average diffusion coefficient of the sample component in the mobile phase, Ds is its value in the stationary phase, and u is the average linear velocity of the mobile phase. The mobile phase displacement, as well as the mass exchange process, is assumed to be continuous, but the application of the plate concept conditions leads to a mass balance equation that can be interpreted as belonging to a modified discontinuous plate model. The contributions 2Dm/u and k 2 Ds/u from longitudinal sample diffusion in the mobile and stationary phases, respectively, are consistent with the assumption that the processes are statistically independent, although the common solution technique of the differential equations does not take full account of this independence.

A Method for the Determination of Diffusion Coefficients of Food Components in Low‐ and Intermediate Moisture Systems

ABSTRACTA simple set‐up to measure translational diffusion of components in low moisture systems is described. The tracer technique was tested on the diffusion of 14C‐labeled tripalmitin and palmitic acid in a model system containing paraffin oil, microcrystalline cellulose and gum arabic. Different methods to evaluate the apparent diffusion coefficients from the experimental diffusion curve were compared. Good results were obtained using a curve‐fitting procedure based on the sum of least squares. The technique appears to be suitable for measuring diffusion coefficients up to 10−9 cm2/sec. The procedure offers the possibility to quantify the mobility of chemical components in dried foodstuffs in order to elucidate the mechanisms and kinetics of reactions occurring during storage.

Application of A‐C Techniques to the Study of Lithium Diffusion in Tungsten Trioxide Thin Films

The small signal a‐c impedance of the cellhas been measured at room temperature as a function of frequency from to at various open‐circuit voltages. The diffusion equations have been solved for the appropriate finite boundary conditions, and analysis of the impedance data by the complex plane method yields values for the chemical diffusion coefficient, the component diffusion coefficient, the partial ionic conductivity of lithium, and the thermodynamic enhancement factor for as a function of . The films of were prepared by vacuum evaporation and were largely amorphous to x‐rays. The chemical diffusion coefficient has a value of at , increasing to at . At short times the interfacial charge transfer reaction is important, but at longer times the rate of lithium injection is determined by the diffusion kinetics.

Diffusion Coefficients of the 45S and 50S States of the Large Ribosomal Subunit of E. coli by Quasielastic Light Scattering.

The translational diffusion coefficients of the 45S and 50S states of the large ribosomal subunit of E. coli were determined from the spectral distributions of quasielastically scattered light with a 5 mW He-Ne laser as the source. The spectral analysis was performed by directly Fourier transforming the photocurrent and fitting to double-Lorentzian profile via a non-linear regression routine. A small amount (about 1%) of strongly scattering contaminants required the double-Lorentzian profile in order to extract the diffusion coefficients of the principal components. The results are: D20°, w(45S) = (1.79 ± 0.12) × 10-7cm2/sec, and D20°, w(50S) = (1.91 ± 0.06) × 10-7cm2/sec, the latter being in accord with those reported in the literature. The transition from the 50S state to the 45S state is not attended by a change in its molecular weight if the partial specific volumes are assumed to be the same.