Relative Diffusion Rates Research Articles

Dissolution in molten silicates: effects of solid solution

The effects of solid solution and solid state diffusion on crystal dissolution in a multicomponent liquid was examined by studying exact and approximate solutions to equations governing isothermal-isobaric diffusive dissolution of a crystalline solid solution in binary and ternary liquids. The dissolution rate is proportional to the square root of time in diffusive dissolution. The effect of solid state diffusion is to change the dissolved crystal composition from that in the interior of the crystal to that at the crystal-melt interface, which depends on the relative rate of diffusion in the solid to the rate of dissolution. If the dissolution rate is much faster than the diffusive exchange rate in the solid, the dissolved crystal will retain its interior or far-field composition that has not been affected by diffusion (referred to as Regime I dissolution). The dissolution rate is proportional to the diffusion rate in the liquid, independent of the crystallographic orientation of the dissolving crystal. If the dissolution rate is much slower than the rate of diffusion in the solid, the dissolved crystal will have its solidus composition at the crystal-melt interface (termed Regime II dissolution). The dissolution rate is proportional to the diffusion rate in the solid and hence dependent of the crystallographic orientation of the dissolving crystal if the degree of undersaturation is extremely small (i.e., <0.5% difference in concentrations in the liquid). Regime I dissolution is important when the diffusion rate in the liquid is more than four to six orders of magnitude faster than the diffusion rate in the solid. Convection in liquid facilitates crystal dissolution and further diminishes the role of diffusive exchange in crystal. Given the large disparities between diffusion rates in silicate crystals and diffusion rates in silicate melts (typically greater than 10 4), dissolution of practically all silicate xenocrysts and xenoliths in natural molten silicates are characterized by Regime I dissolution. Regime II dissolution is important when the dissolving crystal and melt are in near chemical equilibrium.

Cell growth and differentiation on feeder layers is predicted to be influenced by bioreactor geometry

Tissue function is comprised of a complex interplay between biological and physicochemical rate processes. The design of bioreactors for tissue engineering must account for these processes simultaneously in order to obtain a bioreactor that provides a uniform environment for tissue growth and development. In the present study we consider the effects of fluid flow and mass transfer on the growth of a tissue in a parallel-plate bioreactor configuration. The parenchymal cells grow on a preformed stromal (feeder) layer that secretes a growth factor that stimulates parenchymal stem cell replication and differentiation. The biological dynamics are described by a unilineage model that describes the replication and differentiation of the tissue stem cell. The physicochemical rates are described by the Navier-Stokes and convective-diffusion equations. The model equations are solved by a finite element method. Two dimensionless groups govern the behavior of the solution. One is the Graetz number (Gz) that describes the relative rates of convection and diffusion, and the other a new dimensionless ratio (designated by P) that describes the interplay of the growth factor production, diffusion, and stimulation. Four geometries (slab, gondola, diamond, and radial shapes) for the parallel-plate bioreactor are analyzed. The uniformity of cell growth is measured by a two-dimensional coefficient of variance. The concentration distribution of the stroma-derived growth factor was computed first based on fluid flow and bioreactor geometry. Then the concomitant cell density distribution was obtained by integrating the calculated growth factor concentration with the parenchymal cell growth and unilineage differentiation process. The spatiotemporal cell growth patterns in four different bioreactor configurations were investigated under a variety of combinations of Gz (10(-1), 10(0), and 10(1)) and P(10(-2), 10(-1), 10(0), 10(1), and 10(2)). The results indicate high cell density and uniformity can be achieved for parameter values of P = 0.01, ..., 0.1 and Gz = 0.1, ..., 1.0. Among the four geometries investigated the radial-flow-type bioreactor provides the most uniform environment in which parenchymal cells can grow and differentiate ex vivo due to the absence of walls that are parallel to the flow paths creating slow flowing regions.

Hydrogen and carbon kinetic isotope effects during soil uptake of atmospheric methane

The hydrogen and carbon kinetic isotope effects (KJEs) occurring during uptake of atmospheric methane (CH4) by soils were measured using in situ static flux chambers in a native grassland and a temperate forest in Washington State. The hydrogen KIE was αDsoil =k(CH4)/k(CH3D) = 1.099 ± 0.030 and 1.066 ± 0.007 for the grassland and forest, respectively. The carbon KIE of αCsoil =k(12CH4)/k(13CH4) = 1.0173 ± 0.0010 and 1.0181 ± 0.0004 for the grassland and forest, respectively, compares well to previous determinations in other ecosystems. Local spatial variability in αsoil was as large as the between‐ecosystem variability. The dependence of αsoil on αox and the KIE during diffusion is described. The apparent KIE associated with microbial oxidation, αox, was determined from αsoil and the relative rates of CH4 oxidation and diffusion in the soil column, derived from observed steady state profiles of soil air CH4 concentration. The apparent αox ranged from 1.094 to 1.209 for αDox and from 1.0121 to 1.0183 for αCox. These are the first determinations of the hydrogen KIEs during soil uptake of atmospheric CH4 and during aerobic microbial oxidation of CH4 at or below atmospheric concentrations. The KIE during uptake of atmospheric CH4 by soils is significantly different than the KIEs associated with the other sinks of atmospheric CH4. The interhemispheric asymmetry in the strength of the soil sink of atmospheric CH4 suggests a difference of ∼6‰ between the overall hydrogen KIEs in the two hemispheres. Modeling studies of the global atmospheric CH4 budget using deuterium as a tracer must therefore include αDsoil.

The Role of Carbon and Vacancies in Determining the Hardness of FeAl Intermetallic in the Quenched and the Aged States

ABSTRACTThe role of quenched-in vacancies in FeAl intermetallics on producing considerable hardening is well known, as is the softening on annealing as vacancies are annihilated. The present study examines quench hardening and anneal softening by quenched-in vacancies and interstitial carbon solute in Fe-40Al-C. Interstitial carbon is seen to be a more potent hardening agent than the vacancy, while the co-annihilation of vacancies and carbon atoms from solution during annealing leads to dislocation loop debris, and equiaxed or plate-like carbide precipitation, according to the annealing conditions. The processes occurring have been followed by detailed TEM studies, and are discussed in terms of the relative solubilities and diffusion rates of vacancies and carbon. The relevance of such interstitial solute hardening to the behaviour of other FeAl intermetallics is also briefly considered.

Studies on Glucose Biosensors Based on Nonmediated and Mediated Electrochemical Oxidation of Reduced Glucose Oxidase Encapsulated Within Organically Modified Sol-Gel Glasses

A new, organically modified sol-gel glass electrode is reported using 3-aminopropyltriethoxy silane and 2-(3,4-epoxycyclohexyl)-ethyltrimethoxy silane as sol-gel precursors for the construction of electrochemical biosensors. Four different systems of new sol-gel glass modified glucose electrodes are made in acidic medium having common sol-gel precursors and: 1) glucose oxidase, 2) glucose oxidase along with polyethylene glycol, 3) glucose oxidase and graphite powder, and 4) glucose oxidase along with polyethylene glycol and graphite powder. Both nonmediated and mediated electrochemical regeneration of immobilized glucose oxidase within sol-gel glasses are studied in these four systems. The nonmediated regeneration is achieved in the presence of oxygen as electron donor whereas mediated regeneration involves soluble ferrocene monocarboxylic acid as electron donor in each system. The electrochemical performance of sol-gel glass based biosensors is compared on the basis of cyclic voltammetry and amperometry. This leads to the observations: i) all four systems reach a diffusion limited condition associated with the transport of soluble ferrocene monocarboxylic acid as well as for dissolved oxygen within the sol-gel matrix, ii) the relative rate of diffusion of these analytes increases from system 1 to system 4, iii) both nonmediated and mediated amperometric responses at suitable potentials are based on the oxidation of H2O2 and enzymatically reduced soluble ferrocene with relatively amplified electrochemical signal of system 4. Data on the reduction of oxygen at conventional graphite disk electrode and at typical sol-gel glass modified electrode are reported.

Isotopic fractionation accompanying helium diffusion in basaltic glass

The relative rates of 3He and 4He diffusion in basaltic glass set limits on the extent to which diffusive loss can alter initial magmatic 3He/4He ratios. Typically a value of 1.15 for the isotopic diffusivity ratio, D3He/D4He, has been assumed, because this corresponds to the inverse square-root of the masses ratio, (m4/m3)1/2. Measurements of the isotopic compositions of sequential releases of He from mid-ocean-ridge and seamount basalt glasses heated in-vacuo reveal this to be an overestimate. The observed isotopic diffusivity ratio ranges from 1.06 at room temperature to 1.10 at 500°C. Assuming Arrhenius temperature dependence and extrapolating suggests that insignificant He isotopic fractionation will occur at seafloor temperatures (D3He/D4He=1.02±0.03), with more pronounced fractionation at magmatic temperatures (e.g. 1.12±0.02 at 1100°C). These low values mean that significantly larger He losses are required to alter initial 3He/4He ratios than was previously assumed, and these larger losses require much longer loss times. For example, lowering an initial 3He/4He ratio by 10% requires 65% gas loss for D3He/D4He equal to 1.15, but 80% loss for D3He/D4He of 1.08, which requires twice as long to occur.Consideration of solid-state diffusion theory, and comparison to cation and other noble gas diffusivities, suggests that the low values and positive temperature dependence of the D3He/D4He ratio result from the relatively widely spaced vibrational energy levels of the He atoms in the silicate glass structure. Temperature dependent diffusive He isotopic fractionation is likely in other geologic materials.

Crosslinking vs. interdiffusion rates in melamine-formaldehyde cured latex coatings: A model for waterborne automotive basecoat

Designing optimal formulations for automotive waterborne basecoats can be fairly complex, often requiring knowledge of events that occur at the molecular level. The ultimate performance of the coating can depend upon the success with which this knowledge is applied. We examine a system in which an aqueous dispersion of an acrylic latex with -OH functionality reacts with a melamine derivative when heated. We use fluorescence-labeling and energy transfer measurements to obtain information on the relative rates of crosslinking and interparticle polymer diffusion in these films. We show that temperature and particle morphology play an important role in the development of film properties. Finally, these energy transfer experiments provide information on the location of the melamine-formaldehyde resin in the dry film before the onset of crosslinking. This system can serve as a model for waterborne basecoat development in many automotive applications.

Modelling thin film growth: Monte-Carlo models of fullerite films

Two-dimensional Monte-Carlo computer simulations have been implemented to help explain some of the mechanisms responsible for structures observed during the deposition of fullerite (C 60) films on mica and glass over a temperature range from 20 to 300 °C. The crystal structures grown by thermal evaporation were investigated by Scanning Force Microscopy and direct comparisons were made between the experimental results and the simulations. A model is presented which is a modification of diffusion-limited aggregation but which allows for diffusion of particles within a cluster as well as cluster diffusion over the surface. The number of islands which form at different coverage, are given by the relative speed of diffusion of clusters of different sizes over the surface and the shape of the islands by the relative rate of diffusion of the molecules within a cluster. Dynamic computer visualization of the growth models assist in the understanding of the processes involved.

Complex zoning in apatite from the Idaho Batholith; a record of magma mixing and intracrystalline trace element diffusion

Apatite crystals in a sample of biotite granodiorite from the Idaho batholith display complex chemical zoning, characterized by abrupt changes in REE+Y+Si content, more subtle variations in S, Na, La/Yb, and Mn contents, and petrographic evidence for multiple episodes of partial resorption. The zoning is attributed to changes in melt composition, resulting from magma mixing and differentiation, although the possibility that some rounded cores may be inherited cannot be disproved. High S contents in apatite cores and the presence of an included anhydrite grain indicate crystallization from an oxidized host magma. Divalent cations that occupy the apatite Ca sites (Sr, Mn, Fe) show evidence of having been redistributed between zones by intracrystalline diffusion, whereas cations that participate in coupled substitutions involving the tetrahedral site (Si, Y, REE, Na, S) were not readily redistributed. The main REE substitution in this case is REE3+ + Si4+ ↔ Ca2+ + P5+, and REE diffusion is rate-limited by slow Si diffusion. However, exchange of LREE (e.g., LaSm-1) on the Ca sites does not involve Si and proceeds more rapidly, resulting in homogenization of La/Sm between zones within individual crystals. Relative diffusion rates inferred from zoning profiles in this study are: Mn, Sr, Fe, and LaSm-1 are faster than Na, S, and LaYb-1, which are faster than Si. These data imply that REE patterns can be decoupled from REE abundances during diffusion, and that even apatite zones or cores that appear sharply bounded in backscattered electron images may not retain their original chemical or Sr-Nd isotopic traits.

Dynamic hologram recording characteristics in DuPont photopolymers

Hologram formation and diffusion reactions in photopolymer films are examined at different stages of exposure and at different spatial frequencies. Different properties of the grating formation process are evaluated from efficiency data, including the relative rates of diffusion and photoinitiated polymerization, dye absorption, and residual efficiency enhancement after UV curing. It was also found that gratings with larger periods (approximately 1.4 microm) are susceptible to erasure effects with postexposure laser illumination. In addition, crossed gratings were found to have an extended dynamic range. This effect can have a significant impact on the number of holograms formed with rotational or peristrophic multiplexing.

Reactions between La1−x CaxMnO3 and CaO-stabilized ZrO2 Part II Diffusion couples

The chemical stability of diffusion couples and coarse grain powder mixtures of calcium substituted lanthanum manganite and cubic calcia stabilized zirconia have been studied. The aim was to investigate the chemical stability of these materials as a model system for respectively the cathode and the electrolyte in solid oxide fuel cells. With increasing amount of Ca in lanthanum manganite, the major secondary phase was shifted from La2Zr2O7 to CaZrO3, and the thickness of the reaction layers of secondary phases was increasing with increasing heat treatment time. Precipitation of La2O3 had taken place in the perovskite containing low amounts of Ca (0 and 20 mol %). The transport mechanisms of the cations were strongly dependent on the interface geometry. La0.7Ca0.3MnO3 was observed to give the most stable interface to zirconia both in air and in reducing atmosphere (pO ∼ 10−6 atm). A-site deficiency of LaMnO3 was also observed to increase the stability. However, we conclude that a thin film of an electrode material consisting of lanthanum manganite on a zirconia substrate is unstable, regardless of A-site deficiency, because the solubility limit of Mn in the zirconia is not reached. From the experimental data, a reaction mechanism has been proposed, based on observations of relative diffusion rates.

Lamellar modelling of reaction, diffusion and mixing in a two-dimensional flow

We present a one-dimensional model of reaction, diffusion and mixing in a two-dimensional flow. The model assumes that initially segregated reactants are stretched and folded into a lamellar structure. Reaction and diffusion are simulated within this one-dimensional lamellar array. The lamellae are assumed to have a uniform thickness. Mixing is included as a single parameter i.e. the average stretch rate of the flow. Results are compared with full two-dimensional simulations of the concentration fields. Given the very simple nature of the one-dimensional model and the complexity of the full system, remarkably good agreement is obtained with a considerable saving in computational effort. For a competitive–consecutive reaction the predicted yields agree to within 6%. A typical one-dimensional simulation on a Silicon Graphics R5000 workstation takes around 1 min compared to 25 h on a 1024-node nCUBE 2 parallel computer for the concentration field simulations. The one-dimensional lamellar simulations are not limited by the relative rates of diffusion, reaction and advection, and are generally applicable to complex two-dimensional and, in principle, three-dimensional flows.

Competitive Adsorption of Poly(ethylene oxide) Chains with and without Charged End Groups

Competitive adsorption between species of the same backbone chemistry and chain length, but differing in their end groups, has been studied employing the model system of fluorescein dianion terminated PEO (F-PEO) and the corresponding native PEO [poly(ethylene oxide)] onto negatively charged silica glass. Here, one end of each F-PEO chain is electrostatically repelled from the surface. Kinetic and equilibrium measurements in gentle shearing flow were accomplished with a combination of total internal reflectance fluorescence and optical reflectivity. Pure samples of F-PEO and native PEO exhibited identical transport-limited adsorption kinetics and high-affinity isotherms, but remarkable differences became apparent during competitive adsorption from mixtures of the two. The surface selectivity, which favored adsorption of native PEO, was screened as the ionic strength was increased. The selectivity was also reduced for chains of high molecular weight, though the molecular weight effect was not as intense as the influence of ionic strength. Coadsorption kinetics over a variety of bulk solution concentrations were in excellent agreement with predictions from a binary mixture treatment that involved Langmuir isotherms for each species and allowed the relative rates of adsorption and diffusion from solution to be varied. Comparison of theory and experiment revealed that the entire competitive adsorption process including the initial coadsorption and late-stage exchange was completely controlled by the diffusion rate of the chains to the surface.

Transformations of heavy metals added to soil — application of a new sequential extraction procedure

A sequential extraction procedure, used to remove the heavy metals in specifically adsorbed and easily reducible manganese (Mn) oxide fractions, was used to study the transformation of heavy metals added to an alkaline soil. Most of the endogenous Cu (86%) and Pb (79%) were found in the residual fraction (RES) which was considered to be mainly highly crystalline Fe oxides and silicate minerals. The recently added Cu, Pb and Cd existed mainly on the surfaces of the soil particles as reactive fractions (water-soluble plus exchangeable and NaCaHEDTA-extractable fractions) and as highly stable forms (RES fraction). There was a particularly high affinity of Pb for Mn oxides. The concentrations of metals in the reactive fractions were in the order: Cd>Cu>Pb. When water-soluble heavy metals are added to the soil, they are rapidly retained by the soil. The reactive forms then slowly transform into highly stable forms. The processes associated with the transformation of added Cu and Pb can be described by a diffusion equation. The processes may be attributed mainly to the diffusion of the surface species into micropores and the entrapment in microporous solids. Unlike Cu and Pb, most of the exchangeable Cd transformed to the forms extracted with NaCaHEDTA and to residual forms. The slow processes of the transformation of Cd added to soil may be attributed to inner-sphere surface complexation via partial or complete dehydration of surface species. The relative diffusion rate coefficients ( D/ r 2) were found to be of the order of 10 −10 to 10 −11 s −1. Addition of CaCO 3 decreased the reactivity or extractability of added heavy metals through the increase in pH.

Roughness of thermal oxide layers grown on ion implanted silicon wafers

We have studied by atomic force microscopy (AFM) the surface morphology of SiO2 layers grown by thermal oxidation of silicon wafers implanted with As, B, Ge, or Si ions. In order to grow oxides having comparable thickness at different temperatures, we have employed both dry and wet processes. Roughness values up to 0.4 nm have been measured on the surface of these oxides. Surface morphology is not influenced by the oxidation ambient, while temperature-related effects are predominant. For low temperature oxidation (920 °C), the predominating effects are due to the behavior of the implanted species, and mainly consist in segregation phenomena, that are the result of a complex competition among different factors, including the segregation coefficient, the relative diffusion rates in the oxide and silicon, and the oxidation rate. At higher temperature (1100 °C), impurity segregation is inhibited or considerably reduced by the increased diffusivity, and defects formation, due to the evolution of the radiation damage, becomes the main effect. Finally, the comparison among AFM, Rutherford backscattering spectrometry, and transmission electron microscopy data has allowed to demonstrate that the morphologies of the SiO2 surfaces are tightly related to the corresponding SiO2/Si interfaces.

The study of diffusion of solvents from the coating films during the curing process by bulk acoustic wave admittance analysis

The diffusion of solvents from a coating layer and their evaporation at the surface of the coating film during the curing process of the coating are investigated by bulk acoustic wave (BAW) admittance analysis and can be expressed as change in the relative diffusion rate (J). The porosity and permeability of the coating film are related to the curing degree (η). The changes in J and the values of J s (the relative diffusion rate at the surface dry time, t s , Δt p (the time difference between the surface dry time t s and the turning point time t p when the diffusion behaviour changes), and η can provide much useful information on selecting solvents and optimizing coating ingredients in the preparation of coatings. The effects of the coating film thickness, solvent content of the coating liquid, and the volatility of the solvent on the diffusion of solvent from the film are also discussed.

Numerical simulation of mass transfer in porous media of blood vessel walls.

The tunica media of a blood vessel wall is modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells and a continuous interstitial fluid phase of proteoglycan and collagen fibers. By applying Brinkman's model to describe the behavior of the interstitial flow, we obtain an analytical solution for the transmural flow field through the periodic array of smooth muscle cells in the form of a power series, making it possible to compute the convection of solutes in the interstitial phase. With reaction of solutes at the surface of smooth muscle cell membranes being treated as boundary conditions and the diffusion of species being limited to the interstitial fluid phase only, mass transfer in the media of blood vessel walls is simulated numerically using Cray supercomputers. It is found that the Sherwood number (the dimensionless mass-transfer coefficient) is not only constant for all interior smooth muscle cells but also minimally sensitive to changes of parameters controlling the relative rates of diffusion and convection in the interstitial fluid phase and the reaction on the smooth muscle cell surface. In addition, the Sherwood number is not very sensitive to changes in the volume fraction of smooth muscle cells. A homogeneous, one-dimensional model (effective-medium model) is also developed to predict the bulk concentration profile in the media, based on the equivalent properties of the effective medium derived from the heterogeneous medium. A comparison of results from the one-dimensional model and two-dimensional simulation is quite satisfactory for all practical ranges of parameters. It is also determined that, for a small molecule such as ATP, the mass transfer to the surface of smooth muscle cells is "reaction limited" as assumed previously in the literature, whereas, for a large molecule such as low-density lipoprotein, the mass transfer might not be reaction limited.

Adsorption kinetics of zinc in a calcareous soil as affected by pH and temperature

Sorption of zinc (Zn) in a calcareous soil was studied using a miscible displacement procedure. Sorption of Zn in soil can be described by a second‐order equation and by a diffusion equation based on the overall higher value of correlation coefficient and the lower value of standard error. The results show that the sorption of Zn in soil was increased by elevated temperature and pH. The maximum of Zn sorbed in soil increased, but the rate coefficient decreased with increasing pH. The maximum of sorbed Zn and rate coefficient tended to increase with elevated temperature. The value of activation energy (Ea) estimated with different kinetic equations was found to be variable and in the range of 5.0–17 kJ.mol‐1. The relative diffusion rate coefficient (D/r2), estimated using a diffusion equation, was found to be in the order of 10‐6 sec‐1. The intra‐aggregate diffusion and/or film diffusion of Zn may be a rate‐limiting process in the sorption of Zn in soils.

Lattice defect/grain boundary interactions related to IASCC

Radiation-induced segregation (RIS) of major alloying elements to grain boundaries in austenitic stainless steels has emerged as a critical aspect of irradiation-assisted stress corrosion cracking (IASCC). Discriminating interactions between individual solute species and vacancy and interstitial defects as they migrate to grain boundaries result in redistribution of solute. Measurements of grain boundary Ni enrichment and Cr depletion indicate that RIS of major alloying elements is in reasonable agreement with the inverse-Kirkendall mechanism. The discriminating interactions for inverse-Kirkendal segregation are the relative rates of solute diffusion by vacancy exchange. Mechanistically, the ternary composition path, defined by change in Cr relative to Ni, depends on relative diffusivities. The absolute change in the composition, that is, extent along the composition path, depends on the kinetics of vacancy formation and migration. The composition path approach is used to quantify diffusional characteristics at low temperatures. Lastly, model predictions suggest a significant influence of grain boundary defect characteristics in addition to matrix defect characteristics. These grain-boundary sensitive characteristics may influence IASCC.

Simulation study of phase separation caused by polymerization

We study phase separation in a polymerizing system by means of Monte Carlo simulation on a triangular lattice. This serves as a model for the processes occurring in the formation of polymer-dispersed liquid crystals (PDLCs). The resulting structures are dependent not only on temperature and concentration but also on the relative rates of polymerization and diffusion. The effective phase diagrams observed in the simulations can be approximated by Flory—Huggins theory when the degree of polymerization is treated as an adjustable parameter. The time-resolved structure factor is less well approximated by an expression of the Lifshitz—Slyozov type.