Actual Concentration Profiles Research Articles

The influence of dissociative adsorption on effectiveness factors of porous catalysts

AbstractThe actual concentration profile of a reacting fluid inside a porous catalyst is something of a mystery. However, there are powerful models to predict the concentration distribution, and effectiveness factor as a function of the Thiele modulus. This work provides a model for the porous catalyst particle considering heterogeneous kinetics for steady‐state Langmuir‐Hinshelwood rate expressions, including the cases when adsorption stoichiometry is other than 1:1, as for dissociative adsorption (1:2), which have not been covered by the preceding literature. The isothermal and the non‐isothermal particles are considered. Numerical solutions for the concentration profile of a limiting reactant were calculated by three methods: finite differences with Newton‐Raphson recursion, Chebyshev orthogonal collocation, and integration by Adams method as done by Weisz and Hicks. The Weisz‐Hicks method outperformed the other two. Plots show the results for specific cases, which are briefly discussed. Adsorption stoichiometry and pellet geometry are of paramount importance for the assessment of effectiveness factors. The results demonstrate that the effectiveness of a catalyst pellet with prevalent dissociative adsorption of a reactant is always inferior to the effectiveness with prevalent simple adsorption.

Modeling Drug Dissolution in 3-Dimensional Space.

The purpose of the study is to present a mathematical model capable of describing drug particle dissolution in 3-dimensional (3D) space, and to provide experimental model verification. Through this study, we also aim to elaborate limitations of the classic, 1D-based Nernst-Brunner formalism in dissolution modeling. The 3D dissolution model was derived by treating the dissolution of a spherical particle as a diffusion-driven process, and by solving Fick's 2nd law of diffusion in spherical coordinates using numerical methods. The resulting model was experimentally verified through analyzing the dissolution behavior of single succinic acid particles in un-stirred water droplet under polarized light microscopy, in combination with image segmentation techniques. A set of working equations was developed to describe drug particle dissolution in 3D space. The predicted dissolution time and profile are in good agreement with the experimental results. The model clearly shows that the concentration gradient within the diffusion layer, in realistic 3D condition, must not be a constant value as implicated in the Nernst-Brunner formalism. The actual concentration profile is a hyperbola, and the concentration gradient at the surface of the particle can be significantly higher than the classic 1D-based dissolution model. The study demonstrates that the classic, 1D-based dissolution models may lead to significant under-estimation of drug dissolution rates. In contrast, modeling dissolution in 3D space yields more reliable results. This study merits further development of comprehensive 3D drug dissolution models, by considering polydispersed particle ensemble and imposing the changes of diffusion layer thickness during dissolution.

Evolution of helium bubbles in nickel-based alloy by post-implantation annealing* *Project supported by the Special Funds for the Key Research and Development Program of the Ministry of Science and Technology of China (Grant Nos. 2017YFB0702201 and 2020YFB1901800) and the National Natural Science Foundation of China (Grant Nos. 11975135 and 12005017).

Nickel-based alloys have been considered as candidate structural materials used in generation IV nuclear reactors serving at high temperatures. In the present study, alloy 617 was irradiated with 180-keV helium ions to a fluence of 3.6 × 1017 ions/cm2 at room temperature. Throughout the cross-section transmission electron microscopy (TEM) image, numerous over-pressurized helium bubbles in spherical shape are observed with the actual concentration profile a little deeper than the SRIM predicted result. Post-implantation annealing was conducted at 700 °C for 2 h to investigate the bubble evolution. The long-range migration of helium bubbles occurred during the annealing process, which makes the bubbles of the peak region transform into a faceted shape as well. Then the coarsening mechanism of helium bubbles at different depths is discussed and related to the migration and coalescence (MC) mechanism. With the diffusion of nickel atoms slowed down by the alloy elements, the migration and coalescence of bubbles are suppressed in alloy 617, leading to a better helium irradiation resistance.

Contribution of elastic photoelectron scattering to the shape of the measured XPS intensity in‐depth profile

The in‐depth profiles obtained from Auger electron spectroscopy or X‐ray photoelectron spectroscopy (XPS) experiments are known to differ from an actual concentration profiles due to limitations of surface‐sensitive techniques, e.g. finite sampling depth, or atomic mixing during sputtering. However, the monitored signal intensities are also affected by elastic scattering of signal electrons. Calculations performed for idealized multilayer structures indicate that elastic scattering of photoelectrons may significantly influence the in‐depth signal intensity. In the present work, an attempt is made to evaluate the contribution of elastic photoelectron scattering to measured signal intensity profile for samples with diffused interfaces. The in‐depth profile measured for the 5x(Au/Ni)/Si multilayer structure has been submitted to this analysis. A relatively simple procedure to evaluate the contribution of elastic scattering to the profile shape has been proposed. The effect of elastic scattering is found to be a reduction of the XPS intensity by 5–10% in the investigated cases. Copyright © 2014 John Wiley & Sons, Ltd.

Investigation of the specificity of Raman spectroscopy in non-invasive blood glucose measurements

Although several in vivo blood glucose measurement studies have been performed by different research groups using near-infrared (NIR) absorption and Raman spectroscopic techniques, prospective prediction has proven to be a challenging problem. An important issue in this case is the demonstration of causality of glucose concentration to the spectral information, especially as the intrinsic glucose signal is smaller compared with that of the other analytes in the blood-tissue matrix. Furthermore, time-dependent physiological processes make the relation between glucose concentration and spectral data more complex. In this article, chance correlations in Raman spectroscopy-based calibration model for glucose measurements are investigated for both in vitro (physical tissue models) and in vivo (animal model and human subject) cases. Different spurious glucose concentration profiles are assigned to the Raman spectra acquired from physical tissue models, where the glucose concentration is intentionally held constant. Analogous concentration profiles, in addition to the true concentration profile, are also assigned to the datasets acquired from an animal model during a glucose clamping study as well as a human subject during an oral glucose tolerance test. We demonstrate that the spurious concentration profile-based calibration models are unable to provide prospective predictions, in contrast to those based on actual concentration profiles, especially for the physical tissue models. We also show that chance correlations incorporated by the calibration models are significantly less in Raman as compared to NIR absorption spectroscopy, even for the in vivo studies. Finally, our results suggest that the incorporation of chance correlations for in vivo cases can be largely attributed to the uncontrolled physiological sources of variations. Such uncontrolled physiological variations could either be intrinsic to the subject or stem from changes in the measurement conditions.

Particulate sulfur species in the water column of the Cariaco Basin

The biogeochemistry of iron sulfide minerals in the water column of the Cariaco Basin was investigated in November 2007 (non-upwelling season) and May 2008 (upwelling season) as part of the on-going CARIACO (CArbon Retention In A Colored Ocean) time series project. The concentrations of particulate sulfur species, specifically acid volatile sulfur (AVS), greigite, pyrite, and particulate elemental sulfur, were determined at high resolution near the O 2/H 2S interface. In November 2007, AVS was low throughout the water column, with the highest concentration at the depth where sulfide was first detected (260 m) and with a second peak at 500 m. Greigite, pyrite, and particulate elemental sulfur showed distinct concentration maxima near the interface. In May 2008, AVS was not detected in the water column. Maxima for greigite, pyrite, and particulate elemental sulfur were again observed near the interface. We also studied the iron sulfide flux using sediment trap materials collected at the Cariaco station. Pyrite comprised 0.2–0.4% of the total particulate flux in the anoxic water column, with a flux of 0.5–1.6 mg S m −2 d −1. Consistent with the water column concentration profiles for iron sulfide minerals, the sulfur isotope composition of particulate sulfur found in deep anoxic traps was similar to that of dissolved sulfide near the O 2/H 2S interface. We conclude that pyrite is formed mainly within the redoxcline where sulfur cycling imparts a distinct isotopic signature compared to dissolved sulfide in the deep anoxic water. This conclusion is consistent with our previous study of sulfur species and chemoautotrophic production, which suggests that reaction of sulfide with reactive iron is an important pathway for sulfide oxidation and sulfur intermediate formation near the interface. Pyrite and elemental sulfur distributions favor a pathway of pyrite formation via the reaction of FeS with polysulfides or particulate elemental sulfur near the interface. A comparison of thermodynamic predictions with actual concentration profiles for iron sulfides leads us to argue that microbes may mediate this precipitation.

Probing Zeta Potential in Flat Nanochannels

Measuring zeta potentials in nanometer-deep channels (nanochannels) is challenging but critical in modeling mass transport through these channels. To our knowledge, there are no reliable methods available to determine these potentials, presumably due to the fact that zeta potential changes with channel depth in nanochannels. In this work, we describe a novel approach to address this issue. The approach includes four steps: (1) a series of potential curves is calculated at various zeta potentials using an established model; (2) a set of corresponding concentration profiles of a selected ion is obtained according to the Boltzmann equation, and an average concentration is calculated from each of the profiles; (3) the average concentration of the selected ion in a nanochannel is experimentally measured; and (4) the actual concentration profile is identified by matching the measured concentration with the calculated results. Once the concentration profile is unveiled, the zeta potential is determined. To demo...

Calibration of a detector for nonlinear responses

A calibration curve is often needed to derive from the record of the detector signal the actual concentration profile of the eluate in many studies of the thermodynamic and kinetic of adsorption by chromatography. The calibration task is complicated in the frequent cases in which the detector response is nonlinear. The simplest approach consists in preparing a series of solutions of known concentrations, in flushing them successively through the detector cell, and in recording the height of the plateau response obtained. However, this method requires relatively large amounts of the pure solutes studied. These are not always available, may be most costly, and could be applied to better uses. An alternative procedure consists of deriving this calibration curve from a series of peaks recorded upon the injection of increasingly large pulses of the studied compound. We validated this new method in HPLC with a UV detector. Questions concerning the reproducibility and accuracy of the method are discussed.

Calibration of a detector for nonlinear chromatography

In many studies of nonlinear or preparative chromatography, chromatographic signals must be recorded for relatively concentrated solutions and the detectors, that are designed for analytical applications and are highly sensitive, must be used under such experimental conditions that their responses are often nonlinear. Then, a calibration curve is needed to derive the actual concentration profiles of the eluates from the measured detector response. It becomes necessary to derive a relationship between the concentration of the eluent and the detector signal at any given time. The simplest approach consists in preparing a series of solutions of known concentrations and in flushing them successively through the detector cell, recording the height of the plateau response obtained. However, this method requires relatively large amounts of the pure solutes being studied and these are not always available or they may be most costly, although these solutions can be recovered. We describe and validate an alternative procedure providing this calibration from a series of peaks recorded upon the injection of increasingly large pulses of the studied compound.

皮膚拡散モデルに基づく皮膚中薬物濃度勾配の評価

This study was carried out to determine the possibility of estimating drug concentration profiles in skin via a diffusion model. In an in vitro permeation study using butylparaben as model drug, percent of drug permeated amounted to approximately 57% and 76% for intact and stripped skin respectively, suggesting that the drug itself highly permeated through the stratum carneum. On the other hand, in vivo absorption study revealed that concentration of butylparaben decreased with skin depth where the maximum was achieved at approximately 30 rain and thereafter decreased gradually with time. In order to analyze both in vitro and in vivo percutaneous drug absorptions, Laplace transformed equations were derived based on four different kinds of hypothetical diffusion models. Initially, diffusion and partition parameters for butylparaben was calculated by curve-fitting using nonlinear regression program combined with a fast Laplace transform algorithm (MULTI(FILT)). Using these parameters, further simulation studies of in vivo drug concentration profiles were carried out. When washout process due to blood flow was not taken into consideration, the decline of drug concentration profiles could hardly be stimulated. However, when model considering washout process to have occurred at the specific range in the dermis (50-200 μm from the stratum carneum/dermis boundary), this could fit the actual concentration profiles of butylparaben in skin well. Thus, this study demonstrated that the diffusion model enables us to evaluate the in vivo behavior of drug in skin.

A new method for the simultaneous condensation of complete ternary alloy systems under ultrahigh vacuum conditions

An ultrahigh vacuum apparatus is described for the simultaneous condensation of complete ternary alloy systems. Three singly controlled electron beam evaporation sources provide a constant evaporation rate of the different elements. A specially designed rotating mask guarantees a concentration gradient on the substrate according to a ternary phase diagram. The conversion of the actual concentration profile into a standard ternary phase diagram is done by simple computer calculations. They involve corrections for the beam characteristics of the evaporation sources and for the rotating mask. As an example, measurements for the Zr–Cu–Co system are given. The concentration range for the amorphous phase is compared with thermodynamic predictions using Miedema’s parameter.

Historical fluxes of particle-bound pollutants from deconvolved sedimentary records

A deconvolution method to extract the historical input records of particle-associated pollutants from their sedimentary profiles, influenced by mixing, is developed. The method operates in the time domain and requires that an equal number n of time and depth intervals be appropriately chosen. An n X n matrix E of pollutant concentrations as a function of time and depth for unit influx is generated by forward programs, and the historical influxes are calculated by inverting E and multiplying with the actual concentration profile of the pollutant. Application of the method to Pb, Zn, and Cd in several Lake Michigan sediment cores shows that pollution with these metals started around 1894 in the southern part of the lake and 15-30 years later further north. A maximum was obtained during 1954-1969 for Pb and Zn and during 1939-1954 for Cd, while current levels have declined 45-35% relative to these maxima in accordance with available atmospheric loading data (Pb) and US consumption figures (Zn and Cd). 24 references, 9 figures, 5 tables.

Fate of a tritiated Ekofisk crude oil in a controlled ecosystem experiment with North Sea plankton

Flexible plastic enclosures were employed with the main intent of determining the fate of an Ekofisk crude oil exposed to North Sea spring conditions. By use of a tritium-labeled Ekofisk crude oil, a dynamic model was developed that allowed calculation of vertical mass fluxes with depth based on actual concentration profiles and measured sedimentation rates. It has been concluded that adsorption and subsequent sedimentation of plankton and organic detritus may cause a rapid sinking of petroleum hydrocarbons. Microbial mineralization seemed to be insignificant on a short-term scale.

Theory of departure from local equilibrium at the interface of a two-phase diffusion couple

A simple model is developed to calculate the departure from local equilibrium at a moving two-phase interface in a binary diffusion couple. The model is based on the solution of a generalized diffusion equation derived by assuming that the diffusion flux of a species is proportional to the gradient of the functional derivative, with respect to concentration, of the total Helmholtz free energy. This total free energy is composed of the integral of two terms, a coarse-grained free energy per unit volume that reflects the bulk thermodynamic properties of the material and an energy density proportional to the square of the concentration gradient. Final results are conveniently represented by replacing the actual concentration profile with another having a jump discontinuity at a plane whose position is judiciously chosen within the region of high concentration gradient; values of composition and its derivative at the discontinuity are chosen such that the bulk solutions, when extrapolated to these values, are the same as for the complete profile. The composition deviations from thermodynamic equilibrium in each phase at the interface are found to be proportional to an assumed large interfacial resistivity; they contain a term proportional to the interface velocity and a second independent term proportional to the flux of one atomic species through the interface. Fluxes of A and B atoms, measured in the interface frame, are found to be related linearly to differences in chemical potential across the interface by a symmetric matrix which guarantees a decrease of net free energy but allows a given species to move contrary to its chemical potential gradient, thus giving rise to trapping in some circumstances.

Mass transfer driving forces in packed and fluidized beds

AbstractThe evaporation of n‐decane into air from the surface of Celite particles, has been used for the establishment of mass transfer factors for both packed and fluidized bed systems. For these calculations log mean partial pressure differences were used. Actual concentration profiles of the transferable component were also experimentally measured by monitoring, at different bed heights, the concentration of n‐decane vapor present in air used as the carrier gas. This was made possible through the use of an extremely sensitive hydrocarbon analyzer. The resulting profiles were used to obtain, by graphical integration, the actual driving force prevailing for each run. A nearly one‐to‐one correspondence was found to exist between the actual driving force and the corresponding log‐mean value for both packed and fluidized bed runs.

Concentration Profile of Superparamagnetic Precipitates

According to previous work the temperature variation of the initial susceptibility, χ0, of superparamagnetic Cu–Fe–Ni alloys deviates from Curie's law, Ms2/χ0 = CT (Ms = spontaneous magnetization). After tentatively correcting for magnetostatic interaction effects with the first order Debye term, the data could be analyzed quantitatively in terms of a temperature-dependent ferromagnetic particle volume which follows from a gradual concentration transition (interface) between precipitates and matrix. Based on this analysis the interface thickness, Δρ, was determined on 74Cu2Fe24Ni for the aging temperature Θ≡TA/TS≃0.95 (TS = critical temperature of the precipitation); Δρ≃12 Å. In this work the variation of Δρ with TA was studied. For 71Cu3Fe26Ni, Δρ decreases from 17A for Θ = 0.97 to 6.5 A for Θ = 0.915, following the theoretical relation Δρ ∝ (TS−TA)−1/2. For Θ = 0.85, Ms2/χ0 nearly follows Curie's law. This explains why no interface effect was detected on other alloys for Θ < 0.6. Furthermore, it is shown that the Debye interaction correction is applicable in all of the above mentioned work. Finally, it is indicated how the actual concentration profile of precipitates may be determined from experimental data of χ0(T).

Donor Concentration at the Surface of a Diffused N‐type Layer on P‐type Germanium

Four methods of evaluating the donor concentration at the surface of a diffused N‐type layer on P‐type germanium have been investigated. All methods assumed a complementary error function (erfc) distribution in the diffused layer. The methods required the use of experimental data for junction depth and sheet resistivity, and of published data for diffusion coefficients of group V elements and electron mobilities in germanium. The methods were applied to calculate the donor concentrations at the surfaces of a number of diffused samples. Under diffusion conditions, which were expected to result in an erfc impurity distribution, the actual concentration profile in the vicinity of the junction was shown to deviate from the erfc law. Due to this deviation, one of the methods of calculating the surface concentration was ruled out. With the other three methods, calculated surface concentrations agreed within a factor of 2 or 3. The disagreement is mainly caused by lack of precise information in respect to the electron mobilities in the diffused layer. Therefore, all the methods represent approximations only.