Diffusion-limited Model Research Articles

Direct simulation of effective conductivity of porous silicon: Fourier treatments

The effective thermal conductivity of anisotropic porous-silicon layers is predicted using the simulated pore structure from a two-dimensional, diffusion-limited model along with the Fourier conduction. The low-dimensionality effect due to the phonon boundary scattering is included through an available modified solid conductivity. It is shown that for the highly branched columnar structure, the effective conductivity across the layer is small and yet much larger than that along the layer. Good agreement is found with available experimental results. It is predicted that the combination of a small pore size and a high porosity leads to a very small effective conductivity. This makes porous-silicon layer an attractive insulator and readily integrable in silicon-based microstructures. In a following paper, the low-dimensionality effect is directly included in a Boltzmann treatment of phonon transport.

Formation of 〈001〉-aligned nano-scale pores on (001) n-InP surfaces by photoelectrochemical anodization in HCl

〈001〉-oriented nanometer sized straight pores without branches were formed for the first time on (001) n-type InP surfaces by photoelectrochemical anodic reaction in HCl. The pore diameter, wall thickness and pore length could be changed in the ranges of 110–250 nm, 16–50 nm and 17–80 μm, respectively, by changing the anodizing overpotential and time. Based on the diffusion limited model for porous Si formation, the formation of 〈001〉-aligned straight pores without branches on n-type InP was explained in terms of the short lifetime of holes combined with the presence of a strong electric field at the pore tip. Contrary to the expectation of blue-shifted photoluminescence (PL) emission due to quantum confinement at pore walls, porous (001) InP samples exhibited intense red-shifted PL peaks. This was explained by formation of a set of well defined new surface state levels on the anodized wall surfaces of pores.

Experimental and theoretical study of one- and two-component droplet vaporization in a high pressure environment

A new experimental set-up is introduced where the evaporation of free falling, non-interacting droplets is investigated. Detailed measurements with one- and two-component droplets are presented for different pressures ( p → 40 bar) and gas temperatures ( T → 650 K). The experimental results are compared with numerical calculations based on the Conduction Limit model and the Diffusion Limit model.

Influence of Structural Heterogeneity on Selectivity in Fractal Catalyst Structures

In the past Monte-Carlo simulations have been used to study the influence of morphological properties of fractal surfaces on the selectivity between competing three-step catalytic reactions. These simulations were conducted using abstract two-dimensional diffusion-limited aggregate models. In an attempt to identify the appropriate properties of a real material that should be represented in a model this previous work has been extended to consider three-dimensional models (cluster-cluster aggregates and the Menger sponge), in order to correlate selectivity with model characteristics which may be related to input from experimental characterisation data, such as that from magnetic resonance imaging. The simulations on three-dimensional models have shown that both the porosity and the mass fractal dimension of the models are important to accurately represent a real porous material; a finding not explicit in previous work in two dimensions.

Compositional variation in AlGaAs crystals grown by LPE under microgravity and terrestrial conditions

We grew AlGaAs crystals on GaAs substrates from solutions aboard the Japanese free-flying satellite SFU, using low temperature range type isothermal heating furnaces. Six GaAs substrates forming a cube eliminate the free surface from the solution, which causes surface tension-driven convection. The samples were heated to 850°C to make Al–Ga–As solutions by dissolving the GaAs substrate surfaces into the Al–Ga solutions. Then the furnace temperature was reduced gradually to grow crystals from the supersaturated solution. The space experiments were carried out as planned, and AlGaAs crystals were grown under convectionless conditions. The surface morphology of the μ-g sample was much smoother than that of the 1-g sample. The growth thickness difference in the six substrates used in the μ-g experiments was much less than that of those used in the 1-g experiments. These facts prove that convectionless growth was achieved. The Al composition in the crystal decreases as the distance from the growth interface increases. This decrease in the μ-g sample is more gradual than that in the 1-g sample. Our calculational results using a theoretical model maintaining phase-equilibrium together with the constancy of diffusion flux at the growth interface at the same time showed the same tendency, while conventional diffusion-limited model results in opposite tendency. These results prove that our model for calculating compositional variation in ternary LPE layers correctly expresses diffusion-limited growth conditions.

Theoretical study of sorption‐induced bending of polypyrrole films

Polypyrrole films containing perchlorate were electrochemically synthesized and the bending and recovery motion of the films obtained has been investigated. It was found that the thickness of the film and ambient relative humidity (RH) were crucial to the motion of film: An increase of the film thickness decreased the displacement of the bending but increased the bending stress. On the other hand, an increase of the ambient RH decreased both functions. The motion of film was caused by the difference of expansion on both sides of the film owing to anisotropic sorption of water vapor, which could be expressed by the diffusion-limited bending model. The diffusion coefficients calculated from the bending and recovery motion at 25°C, RH 50% were 12.2 × 10−8 cm2 s−1 and 3.5 × 10−8 cm2 s−1, respectively. The maximum expansion of the film surface calculated from the bending curve was about 0.36%. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2237–2246, 1998

Theoretical study of sorption‐induced bending of polypyrrole films

Polypyrrole films containing perchlorate were electrochemically synthesized and the bending and recovery motion of the films obtained has been investigated. It was found that the thickness of the film and ambient relative humidity (RH) were crucial to the motion of film: An increase of the film thickness decreased the displacement of the bending but increased the bending stress. On the other hand, an increase of the ambient RH decreased both functions. The motion of film was caused by the difference of expansion on both sides of the film owing to anisotropic sorption of water vapor, which could be expressed by the diffusion-limited bending model. The diffusion coefficients calculated from the bending and recovery motion at 25°C, RH 50% were 12.2 × 10 -8 cm 2 s -1 and 3.5 × 10 -8 cm 2 s -1 , respectively. The maximum expansion of the film surface calculated from the bending curve was about 0.36%.

Molecular-beam epitaxial growth of HgCdTe infrared focal-plane arrays on silicon substrates for midwave infrared applications

Molecular beam epitaxy has been employed to deposit HgCdTe infrared detector structures on Si(112) substrates with performance at 125K that is equivalent to detectors grown on conventional CdZnTe substrates. The detector structures are grown on Si via CdTe(112)B buffer layers, whose structural properties include x-ray rocking curve full width at half maximum of 63 arc-sec and near-surface etch pit density of 3–5 × 105 cm−2 for 9 µm thick CdTe films. HgCdTe p+-on-n device structures were grown by molecular beam epitaxy (MBE) on both bulk CdZnTe and Si with 125K cutoff wavelengths ranging from 3.5 to 5 µm. External quantum efficiencies of 70%, limited only by reflection loss at the uncoated Si-vacuum interface, were achieved for detectors on Si. The current-voltage (I-V) characteristics of MBE-grown detectors on CdZnTe and Si were found to be equivalent, with reverse breakdown voltages well in excess of 700 mV. The temperature dependences of the I-V characteristics of MBE-grown diodes on CdZnTe and Si were found to be essentially identical and in agreement with a diffusion-limited current model for temperatures down to 110K. The performance of MBE-grown diodes on Si is also equivalent to that of typical liquid phase epitaxy-grown devices on CdZnTe with R0A products in the 106–107 Θ-cm2 range for 3.6 µm cutoff at 125K and R0A products in the 104–105 Θ-cm2 range for 4.7 µm cutoff at 125K.

Thermal generation of vacancies in high-quality aluminium crystals

Abstract The dislocation density in high-purity (99.9999%) aluminium has been decreased to 105–107 m−2 by cyclic annealing. In such a crystal, there are only a few sources for vacancy generation, so that it is expected to take a long time to attain the thermal equilibrium concentration of vacancies. In order to study the generation rate of vacancies, the electrical resistance has been measured accurately at high temperatures. It is found that it takes at least several hours to attain the thermal equilibrium concentration. For comparison, generation profiles from pre-existing dislocations and interstitial-type dislocation loops are estimated with a diffusion-limited model. It is concluded that, even in a high-quality aluminium crystal, most vacancies are generated from pre-existing dislocations, and only a small fraction is generated by the growth of interstitial-type dislocation loops. The surface oxidizes at a rate of about an atom layer per an hour and is not effective for the generation of vacancies.

Diffusion-limited model for a lithium/polymer battery

A simple diffusion-limited model is presented to explain the capacity limitations of an actual 3 volt rechargeable lithium/polymer electrolyte/lithium manganese dioxide cell at low to moderate discharge rates. Chemical diffusion coefficients of lithium in lithium manganese dioxide on the order of 10 −12–10 −14 cm 2/sec were determined for the temperature range of −10–40°C.

In situ transmission electron microscopy of AlN growth by nitridation of (0001) α-Al2O3

Using a novel ultrahigh vacuum transmission electron microscope (TEM) with in situ reactive molecular beam epitaxy system, we report the successful synthesis of epitaxial AlN on the (0001) sapphire surface upon exposure to ammonia. The substrate, an electron transparent sapphire foil, was annealed in oxygen at high temperature to eliminate damage induced during preparation and to create large atomically flat regions. The sample was then held at 950 °C in flowing ammonia inside the microscope for 2 h during which periodic observations of microstructural development were made. We report direct observation of the formation of epitaxial AlN with the orientation relationship (0001)AlN//(0001)sub, [1̄010]AlN//[1̄1̄20]sub and present both TEM and atomic force microscope images of the sample before and after nitridation. The results are consistent with a diffusion-limited reaction model involving transport of oxygen and nitrogen ions through the growing AlN epilayer between the free surface and the unreacted α-Al2O3.

Diffusion-limited, but not perfusion-limited, compartmental models describe cerebral nitrous oxide kinetics at high and low cerebral blood flows.

This study aimed to evaluate the relative importance of diffusion-limited vs. perfusion-limited mechanisms in compartmental models of blood-tissue inert gas exchange in the brain. Nitrous oxide concentrations in arterial and brain efferent blood were determined using gas chromatographic analysis during and after 15 min of nitrous oxide inhalation, at separate low and high steady states of cerebral blood flow (CBF) in five sheep under halothane anesthesia. Parameters and model selection criteria of various perfusion- or diffusion-limited structural models of the brain were estimated by simultaneous fitting of the models to the mean observed brain effluent nitrous oxide concentration for both blood flow states. Perfusion-limited models returned precise, credible estimates of apparent brain volume but fit the low CBF data poorly. Diffusion-limited models provided better overall fit of the data, which was best described by exchange of nitrous oxide between a perfusion-limited brain compartment and an unperfused compartment. In individual animals, during the low CBF state, nitrous oxide kinetics displayed either fast, perfusion-limited behavior or slow, diffusion-limited behavior. This variability was exemplified in the different parameter estimates of the diffusion limited models fitted to the individual animal data sets. Results suggest that a diffusion limitation contributes to cerebral nitrous oxide kinetics.

Selective Metal Ion Sorption and Transport Using Polymer Inclusion Membranes Containing Dicyclohexano-18-crown-6

A novel polymer material composed of cellulose triacetate as support, o-ni-trophenyl octyl ether as plasticizer (solvent), and dicyclohexano-18-crown-6 as carrier was investigated as a solid extractant for metal ion sorption and as a membrane material for ion transport. Selective extraction and transport of Pb(II), Ga(III), and Fe(III) were observed. The influence of the source solution counterion on sorption and transport processes was investigated. The transport mechanism is discussed in terms of diffusion coefficients (D) and extraction constants (K 1). A diffusion-limited transport model has been found to accurately describe metal ion transport by dicyclohexano-18-crown-6 in these systems. The membranes are easy to prepare in the laboratory, and they may be useful in separation and concentration procedures.

Scaling Relationships in Agglomeration and Annihilation Models

A relation between two exponents characterizing the scaling behavior of random agglomeration models with particle injection is proposed and verified by numerical simulations. This relation, and a link between diffusion-limited agglomeration models with and without injection combined with an exact solution of the latter, leads to a solution of the former in arbitrary dimensionality.

A Kinetic Analysis of the Effects of β-Phenylethylamine on the Concentrations of Dopamine and Its Metabolites in the Rat Striatum

The purpose of this investigation was to determine whether the increase in the dopamine (DA) concentration in the rat striatum after a rapid iv injection of β-phenylethylamine (PEA) can be quantitatively explained by the alteration of the striatum PEA concentration using a constructed DA metabolism model and to examine whether the time courses of the striatum DA metabolites 3,4-dihydroxyphenylacetic acid (DOPAC) and homovanillic acid (HVA) concentration can be described by this DA metabolism model. The time courses of PEA concentration in plasma and the striatum were determined by gas chromatography–mass spectrometry. The plasma PEA concentration was described by a two-compartment model with nonlinear elimination kinetics. The striatum PEA concentration was about 10 times higher than the plasma PEA concentration. The time course of the striatum PEA concentration was described by a diffusion-limited model including a Michaelis–Menten type transport system from plasma to the striatum and nonlinear elimination from the striatum. The DA concentration in the striatum increased immediately after PEA injection. In contrast, the DOPAC concentration in the striatum decreased immediately. HVA concentration in the striatum increased gradually. Assuming that the enhancement of DA concentration in the striatum after PEA injection is caused by the competitive inhibition of PEA on the reuptake of DA into DA neuronal terminals (and the metabolism from DA to DOPAC is then competitively inhibited by PEA in the DA neuronal terminals), the relationship between the enhancement of DA concentration and PEA concentration in the striatum was analyzed using a constructed DA metabolism model. The enhancement of the DA concentration in the striatum was described quantitatively by this model. Thus, it was clarified that a quantitative relationship between PEA concentration and the enhancement of DA concentration in the striatum is present after PEA injection. However, the time courses of the striatum DOPAC (lower dose) and HVA (time delay) concentrations could not be described by this model. These results indicated that other factors might be necessary to explain the time courses of the DOPAC and HVA concentrations in the striatum after PEA injection, such as the separate evaluation of the effect of PEA on the reuptake of DA into DA neuronal terminals and on the monoamine oxidase-B (MAO-B) activity in the DA neuronal terminals, and the metabolic pathway from DOPAC to HVA.

A Comparative Study of Flow-Limited and Diffusion-Limited Physiological Models for Fentanyl

This paper reports on a comparative study of two different approaches for modelling and simulation of fentanyl pharmacokinetics in humans; one being based on a flow-limited assumption, whereas the other assumes a diffusion-limited model. Under these two assumptions, the study shows that this leads to different values of predicted peak concentrations within various tissues considered, and stresses the need for a more detailed approach, if more accurate predictions are needed, especially during the first few seconds following drug administration

EXPERIMENTAL STUDY OF PURE AND MULTICOMPONENT FUEL DROPLET EVAPORATION IN A HEATED AIR FLOW

The dynamics and vaporization of both pure and multicomponent fuel droplets in a laminar-flow field are investigated. Extensive data are obtained on the velocity and size history of a fuel droplet injected into a well-characterized hot laminar flow. Fuels considered are n-hexane, n-decane, and a bicomponent mixture of equal amounts of hexane and decane. The droplet velocity and size histories are measured by phase Doppler particle analyzer, and compared with the predictions from three different liquid-phase models, the infinite-diffusion, diffusion-limit, and thin-skin models. Predicted results generally show good agreement with measured data. For the conditions of this study, it is shown that the use of a solid-sphere, steady-state drag law adequately reproduces the measured velocity history for small to moderate droplet accelerations, provided the variable-property effects are included in the model. However, the quasi-steady drag equation is not able to capture either the large deceleration experienced by the droplet near the injection location, nor the measured inflection point, where the droplet acceleration changes sign, underscoring the importance of unsteady effects on droplet motion. The comparison of vaporization history indicates that, under relatively low-temperature conditions, the predictions of both the infinite-diffusion and the diffusion-limit models are in close agreement with experiments. However, the thin-skin model overpredicts the vaporization rate, and shows significant differences with experiments, especially for less volatile (n-decane) and multicomponent fuel droplets. The comparison also indicates that the thermophysical properties of the gas film surrounding the droplet should be calculated accurately; in particular, the effect of fuel vapor should be considered.

Numerical simulation of diffusion-limited PSA process models by finite difference methods

A numerical method based on finite differences is proposed for simulating pressure swing adsorption processes with intraparticle diffusion controlling. The problem has two important spatial coordinates: the axial position in the bed and the location within a particle. The method proposed keeps the two coordinate scales separate. Diffusion equations with variable main- and cross-term diffusivities are solved implicitly for the particles at each time step and the solution is expressed in terms of the bed-scale variables. The material balances on the bed can then be solved with the bed-scale variables as the only unknowns. The method is computationally efficient and validated by comparison with an exact solution derived under conditions of plug flow, constant total pressure, and with a binary Langmuir isotherm. As a full example, we treat the kinetic separation of air to produce nitrogen using a fixed bed of carbon molecular sieve. Characteristics of the specific implementation are incorporation of variable-step grids with identical volumes for the intraparticle diffusion equations and the use of the third-order QUICK scheme to discretize the convection terms in the material balances for the bed.

Reply to ‘‘Comment on ‘Evidence of enhanced epitaxial crystallization at low temperature by inelastic electronic scattering of mega-electron-volt heavy-ion-beam irradiation’ ’’ [J. Appl. Phys. 80, 4235 (1996)

Enhanced epitaxial crystallization by mega-electron-volt (MeV) heavy-ion-beam irradiation cannot be explained only by the diffusion-limited model. The validity of data showing the absence of dose rate effect on MeV ion-beam-induced epitaxial crystallization (IBIEC) rate is examined in relation to the self-ion-beam annealing effect in MeV As+-ion-beam irradiation in the crystalline Si substrate. The reliability of the experimental results showing the critical thickness dependence in the diffusion-limited model is discussed in detail. It is pointed out that there is room to question the existence of critical thickness. Two guidelines for constructing an accurate IBIEC model are proposed.

Growth of Wetting Layers from Liquid Mixtures

We have examined the growth with time $t$ of the thickness $l$ of wetting layers from thin films of binary fluid mixtures, using real-space composition-depth profiling based on nuclear reaction analysis. We find over a wide range of parameters that the observed growth behavior has a power law form $l\ensuremath{\propto}{t}^{\ensuremath{\kappa}}$, where $\ensuremath{\kappa}$ is the range 0.2--0.3. Comparison with the predictions of a diffusion-limited wetting model shows that growth of the wetting layers is driven primarily by long-ranged surface fields.