Additional Correction Factor Research Articles

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Omega_0' found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97+/-0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U,V,W)o=(9.28,20.35,7.36)+/-(0.05,0.07,0.05) km s^{-1}, the angular velocity of Galactic rotation Omega0=27.24+/-0.30 km s^{-1} kpc^{-1}, and its first derivative Omega_0'=-3.77+/-0.06 km s^{-1} kpc^{-2}; here, the circular rotation velocity of the Sun around the Galactic center is V_0=218+/-6 km s^{-1} kpc (for the adopted distance R_0=8.0+/-0.2 kpc), while the Oort constants are A=15.07+/-0.25 km s^{-1} kpc^{-1} and B=-12.17+/-0.39 km s^{-1} kpc^{-1}, p=0.98+/-0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz-Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Omega_0"=0.864+/-0.021 km s^{-1} kpc^{-3} is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide–nitrogen gas system and five porous media with permeability coefficients ranging from 10−13 to 10−11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection–diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Parameterization of Nuclear Hulthén Potential for Nucleus-Nucleus Elastic Scattering

In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulthén type interaction is considered to describe the α-α, α-3He and α-3H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELab = 100 MeV for the α-α system and ELab = 15 MeV for α-3He and α-3H systems. The S-wave phase shift δ0 for the α-α system tends to 2π and δ3/2− for the α-3He system tends to π, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2− states of α-3He and α-3H systems. With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2− states. We have also compared our results with the convenient Born approximations.

Abstract ID: 13 Monte Carlo simulations for the beam quality factors of a parallel-plate ion-chamber in the presence of magnetic field

Magnetic resonance imaging-guided radiotherapy provides real-time imaging with a superior soft-tissue contrast without radiation exposure. Recently, several groups have been developing such a new technology. Strong magnetic fields can influence trajectories of the secondary electrons by the Lorentz force. The reference dosimetry using an ion-chamber in magnetic fields needs additional correction factors [1]. In this study, we calculated magnetic field correction factors by the Monte Carlo method for the reference dosimetry using a parallel-plate ion-chamber. The EGSnrc user code, egs_chamber was used to simulate an ion-chamber. The full head and spectral source models of Varian therapeutic linear accelerator of 6 MV, 10 MV, and 15 MV photon beam have been simulated by BEAMnrc and beamdp. A parallel-plate ion-chamber (NACP-02 model) was positioned in the water phantom (30 × 30 × 30 cm3) at a depth of 10 cm (5 cm for Co-60 beam). The beam quality factors (KQ) and magnetic field correction factors (KQ,B) were calculated. The absorbed dose of a parallel-plate ion-chamber was scored with and without a 1.5 T of magnetic field. The KQ of 6 MV, 10 MV, and 15 MV were 0.994, 0.980, and 0.976, respectively. These values were compatible to the previous published data (<0.3%) [2]. In a 1.5 T of magnetic field, the KQ,B of 6, 10, and 15 MV were 0.935, 0.985, and 0.994, respectively, compared to 0.975, 0.983, and 0.983 in a 0.35 T of magnetic field. All of simulation uncertainties were within 0.2%. When photon energy increases, KQ,B is also increased, but KQ,B in high strength of a magnetic field are not always smaller than those in low strength of a magnetic field. The magnetic field correction factors of a parallel-plate ion-chamber were successfully calculated by the Monte Carlo method. The parallel-plate ion-chambers need several percent of correction factors when measuring doses in the presence of a magnetic field.

A Study of Sandstone Permeability Anisotropy Through Fractal Concept

Most correlation equations of rock permeability are usually based on the Euclidean geometry concept. Pore geometry and structure of most porous rocks are very complex, therefore non-Euclidean geometry concept, e.g. fractal theory, is needed to handle such a complexity. This paper presents a new equation for sandstone permeability involving other properties and fractal dimensions of pore space and surface. The equation is derived by combining Newton’s Law of viscosity, Darcy equation, and fractal geometry concept. It is shown that parameters such as tortuosity, internal surface area, and shape factor can be replaced by fractal dimensions. As natural porous media are mostly anisotropic, this study enables us to identify factors that affect the anisotropy. Eighteen sandstone samples with porosity and permeability range from 21 to 37% and 2.76 to 3,644 millidarcies, were employed in this study. The pore space and surface fractal dimensions for each orthogonal direction for each sample was determined by box counting method. The results of this study demonstrate that calculated directional permeability of the high permeability samples is very close to the measured one after corrections were made for pore sizes of less than one micron. This finding suggests that micropores of the samples may be a major factor not contributing to fluid flow. For the low and medium permeability samples, however, an additional pore geometrical correction is needed. The additional correction factor is considerably different for different directions of fluid flow, indicating that the anisotropy is due to the difference in directional pore structural characteristics.

Features of calculations of the limit cost of high-rise constructions for housing and civil purposes with the use of consolidated standards

When determining the cost of capital construction objects, for purposes of pre-investment workings out and purposes of initial maximum initial price determination on tenders, construction price norms are used (CPNs). Modern CPNs are not designed to determine the value of high-rise buildings. It is necessary to adapt modern CPNs to get opportunity for the possibility to take into account special cost factors in determining the cost of high-rise buildings. The main ways can be: selection of new representative objects or application of additional correction factors.

Formation of costs of high-rise objects of housing and civil purpose based on enlarged norms

When determining the cost of capital construction objects, for purposes of pre-design workings out and purposes of initial maximum initial price determination on tenders, construction price norms are used (CPNs). Modern CPNs are not designed to determine the value of high-rise buildings. It is necessary to adapt modern CPNs to get opportunity for the possibility to take into account special cost factors in determining the cost of high-rise buildings. The main ways can be: selection of new representative objects or application of additional correction factors.

Line broadening of SO2 and CO2 volcanic activity gases in the Earth’s atmosphere

Calculations of the CO2-broadening coefficients of sulfur oxide lines by the semi-empirical method [Mol. Phys. 102 (2004) 1653] and averaged energy difference method [Atmosph. Ocean. Optics 28 (2015) 403] are presented. In this work, 41 lines are considered, the rotational quantum number J varies from 14 to 51. Calculations of the line widths are carried out for room temperature (296 K), and also for the temperature range typical for the Ears atmosphere. There is good agreement with the literature data. The carbon dioxide lines broadening coefficients induced by nitrogen, nitrogen oxide, carbon monoxide and carbon dioxide at room temperature (T = 296 K) are obtained for a wide range of the rotational quantum number J (up to 100). The temperature exponents are calculated for every line widths. The calculations were performed by a semi-empirical method, based on the semiclassical impact theory of line broadening and modified by introducing additional correction factor whose parameters can be determined by fitting the broadening or shifting coefficients to the experimental data.

Measurement and modeling of out-of-field doses from various advanced post-mastectomy radiotherapy techniques

More and more advanced radiotherapy techniques have been adopted for post-mastectomy radiotherapies (PMRT). Patient dose reconstruction is challenging for these advanced techniques because they increase the low out-of-field dose area while the accuracy of out-of-field dose calculations by current commercial treatment planning systems (TPSs) is poor. We aim to measure and model the out-of-field radiation doses from various advanced PMRT techniques. PMRT treatment plans for an anthropomorphic phantom were generated, including volumetric modulated arc therapy with standard and flattening-filter-free photon beams, mixed beam therapy, 4-field intensity modulated radiation therapy (IMRT), and tomotherapy. We measured doses in the phantom where the TPS calculated doses were lower than 5% of the prescription dose using thermoluminescent dosimeters (TLD). The TLD measurements were corrected by two additional energy correction factors, namely out-of-beam out-of-field (OBOF) correction factor KOBOF and in-beam out-of-field (IBOF) correction factor KIBOF, which were determined by separate measurements using an ion chamber and TLD. A simple analytical model was developed to predict out-of-field dose as a function of distance from the field edge for each PMRT technique. The root mean square discrepancies between measured and calculated out-of-field doses were within 0.66 cGy Gy−1 for all techniques. The IBOF doses were highly scattered and should be evaluated case by case. One can easily combine the measured out-of-field dose here with the in-field dose calculated by the local TPS to reconstruct organ doses for a specific PMRT patient if the same treatment apparatus and technique were used.

A Radio-to-mm Census of Star-forming Galaxies in Protocluster 4C23.56 at Z = 2.5: Gas Mass and Its Fraction Revealed with ALMA

Abstract We investigate gas contents of star-forming galaxies associated with protocluster 4C23.56 at z = 2.49 by using the redshifted CO (3–2) and 1.1 mm dust continuum with the Atacama Large Millimeter/submillimeter Array. The observations unveil seven CO detections out of 22 targeted Hα emitters (HAEs) and four out of 19 in 1.1 mm dust continuum. They have high stellar mass ( M ⊙) and exhibit a specific star-formation rate typical of main-sequence star-forming galaxies at . Different gas-mass estimators from CO (3–2) and 1.1 mm yield consistent values for simultaneous detections. The gas mass ( ) and gas fraction ( ) are comparable to those of field galaxies, with )) , where is the CO-to-H2 conversion factor and A(Z) is the additional correction factor for the metallicity dependence of , and from CO (3–2). Our measurements place a constraint on the cosmic gas density of high-z protoclusters, indicating that the protocluster is characterized by a gas density higher than that of the general fields by an order of magnitude. We found with the CO(3–2) detections. The five ALMA CO detections occur in the region of highest galaxy surface density, where the density positively correlates with global star-forming efficiency (SFE) and stellar mass. Such correlations possibly indicate a critical role of the environment on early galaxy evolution at high-z protoclusters, though future observations are necessary for confirmation.

Feasibility of dosimetry with optically stimulated luminescence detectors in magnetic fields

The objective of this study was to analyze the applicability of optically stimulated luminescence detectors (OSLDs) for dosimetry in magnetic resonance (MR) guided radiation therapy devices with focus on dose dependence and angular dependence on the magnetic field strength.Precise detectors for dosimetry in high magnetic fields for such devices are still subject to research. In contrast to ionization chambers, OSLDs contain no air cavities, such that only minor changes in detector response with increasing magnetic field strengths are expected.To study the behavior of OSLDs in magnetic fields, Al2O3:C detector packages were irradiated at a 6 MV linac in a water phantom, while magnetic fields between 0.0 T and 1.0 T were applied. In order to study the angular dependence, the OSLD packages were rotated around the vertical axis for three different magnetic field strengths (0.0 T, 0.5 T, 1.0 T). Additionally, the angular dependence was measured at a clinical 0.3 T 60Co device. The OSLDs were read out using a portable OSL reader and an automated Risø TL/OSL-DA-15 reader.Readout with the portable reader yielded package standard deviations of 1–2% and revealed no significant relation between dose response and magnetic field strength, while readout with the Risø reader resulted in standard deviations of only 1% and a significant decrease in response of −1.3% per T (95%-confidence interval: −1.9% to −0.7%). The angular dependence was not significantly influenced by the magnetic field. The small decrease in dose response supports the applicability of the OSL technique in MR-guided radiation therapy devices. We expect that no additional magnetic field correction factor has to be used when a calibration of the detectors in the magnetic field of such a device is performed.

A high‐performance belief propagation decoding algorithm for codes with short cycles

SummaryThe simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.

Interest of Integrating Spaceborne LiDAR Data to Improve the Estimation of Biomass in High Biomass Forested Areas

Mapping forest AGB (Above Ground Biomass) is of crucial importance to estimate the carbon emissions associated with tropical deforestation. This study proposes a method to overcome the saturation at high AGB values of existing AGB map (Vieilledent’s AGB map) by using a map of correction factors generated from GLAS (Geoscience Laser Altimeter System) spaceborne LiDAR data. The Vieilledent’s AGB map of Madagascar was established using optical images, with parameters calculated from the SRTM Digital Elevation Model, climatic variables, and field inventories. In the present study, first, GLAS LiDAR data were used to obtain a spatially distributed (GLAS footprints geolocation) estimation of AGB (GLAS AGB) covering Madagascar forested areas, with a density of 0.52 footprint/km2. Second, the difference between the AGB from the Vieilledent’s AGB map and GLAS AGB at each GLAS footprint location was calculated, and additional spatially distributed correction factors were obtained. Third, an ordinary kriging interpolation was thus performed by taking into account the spatial structure of these additional correction factors to provide a continuous correction factor map. Finally, the existing and the correction factor maps were summed to improve the Vieilledent’s AGB map. The results showed that the integration of GLAS data improves the precision of Vieilledent’s AGB map by approximately 7 t/ha. By integrating GLAS data, the RMSE on AGB estimates decreases from 81 t/ha (R2 = 0.62) to 74.1 t/ha (R2 = 0.71). Most importantly, we showed that this approach using LiDAR data avoids underestimating high biomass values (new maximum AGB of 650 t/ha compared to 550 t/ha with the first approach).

Modification and laboratory evaluation of a TSI ultrafine condensation particle counter (Model 3776) for airborne measurements

ABSTRACTA butanol-type ultrafine condensation particle counter (UCPC, Model 3776, TSI, Inc., Shoreview, MN, USA), which can achieve a 50% detection efficiency diameter (d50) of 2.5 nm using a capillary-sheath structure, was modified and tested in the laboratory for airborne measurements. The aerosol flow rate through the capillary is a key factor affecting the quantification of aerosol particle number concentrations. A pressure-dependent correction factor for the aerosol flow rate was determined using a newly added mass flow meter for the sheath flow and the external calibration system. The effect of particle coincidence in the optical sensing volume was evaluated using an aerosol electrometer (AE, Model 3068B, TSI, Inc.) as a reference. An additional correction factor for the coincidence effect was derived to improve the quantification accuracy at higher concentrations. The particle detection efficiency relative to the AE was measured for mobility diameters of 3.1–50 nm and inlet absolute pressures of 10...

High-resolution gamma ray attenuation density measurements on mining exploration drill cores, including cut cores

Physical property measurements are increasingly important in mining exploration. For density determinations on rocks, one method applicable on exploration drill cores relies on gamma ray attenuation. This non-destructive method is ideal because each measurement takes only 10s, making it suitable for high-resolution logging. However calibration has been problematic. In this paper we present new empirical, site-specific correction equations for whole NQ and BQ cores. The corrections force back the gamma densities to the “true” values established by the immersion method. For the NQ core caliber, the density range extends to high values (massive pyrite, ~5g/cm3) and the correction is thought to be very robust. We also present additional empirical correction factors for cut cores which take into account the missing material. These “cut core correction factors”, which are not site-specific, were established by making gamma density measurements on truncated aluminum cylinders of various residual thicknesses. Finally we show two examples of application for the Abitibi Greenstone Belt in Canada. The gamma ray attenuation measurement system is part of a multi-sensor core logger which also determines magnetic susceptibility, geochemistry and mineralogy on rock cores, and performs line-scan imaging.

Airborne sound insulation evaluation and flanking path prediction of coupled room

One of the parameters to review the acoustic comfort is based on the value of the insulation partition in the classroom. The insulation value can be expressed by the sound transmission loss which converted into a single value as weighted sound reduction index (Rw, DnTw) and also have an additional sound correction factor in low frequency (C, Ctr) .In this study, the measurements were performed in two positions at each point using BSWA microphone and dodecahedron speaker as the sound source. The results of field measurements indicate the acoustic insulation values (DnT w + C) is 19.6 dB. It is noted that the partition wall not according to the standard which the DnTw + C> 51 dB. Hence the partition wall need to be redesign to improve acoustic insulation in the classroom. The design used gypsum board, plasterboard, cement board, and PVC as the replacement material. Based on the results, all the material is simulated in accordance with established standards. Best insulation is cement board with the insulation value is 69dB, the thickness of 12.5 mm on each side and the absorber material is 50 mm. Many factors lead to increase the value of acoustic insulation, such as the thickness of the panel, the addition of absorber material, density, and Poisson's ratio of a material. The prediction of flanking path can be estimated from noise reduction values at each measurement point in the class room. Based on data obtained, there is no significant change in noise reduction from each point so that the pathway of flanking is not affect the sound transmission in the classroom.

Diagnostic reference level: an important tool for reducing radiation doses in adult and pediatric nuclear medicine procedures in Brazil.

This study aimed to establish a concise method for determining a diagnostic reference level (DRL) for adult and pediatric nuclear medicine patients on the basis of diagnostic procedures and administered radioisotope as a means of controlling medical exposure. A screening was carried out in all Brazilian Nuclear Medicine Service (NMS) establishments to support this study by collecting the average activities administered during adult diagnostic procedures and the rules applied to adjust these according to the patient's age and body mass. Percentile 75 was used in all the activities administered as a means of establishing DRL for adult patients, with additional correction factors for pediatric patients. Radiation doses from nuclear medicine procedures on the basis of average administered activity were calculated for all diagnostic exams. A total of 107 NMSs in Brazil agreed to participate in the project. From the 64 nuclear medicine procedures studied, bone, kidney, and parathyroid scans were found to be used in more than 85% of all the NMSs analyzed. There was a large disparity among the activities administered, when applying the same procedures, this reaching, in some cases, more than 20 times between the lowest and the highest. Diagnostic exams based on Ga, Tl, and I radioisotopes proved to be the major exams administering radiation doses to patients. On introducing the DRL concept into clinical routine, the minimum reduction in radiation doses received by patients was about 15%, the maximum was 95%, and the average was 50% compared with the previously reported administered activities. Variability in the available diagnostic procedures as well as in the amount of activities administered within the same procedure was appreciable not only in Brazil, but worldwide. Global efforts are needed to establish a concise DRL that can be applied in adult and pediatric nuclear medicine procedures as the application of DRL in clinical routine has been proven to be an important tool for controlling and reducing radiation doses received by patients in medical exposure.

Predicting the bioaccumulation of polyaromatic hydrocarbons and polychlorinated biphenyls in benthic animals in sediments

There were two main objectives in this study. The first was to compare the accuracy of different prediction methods for the chemical concentrations of polyaromatic hydrocarbons (PAHs) and polychlorinated biphenyls (PCBs) in the organism, based on the measured chemical concentrations existing in sediment dry matter or pore water. The predicted tissue concentrations were compared to the measured ones after 28-day laboratory test using oligochaeta worms (Lumbriculus variegatus). The second objective was to compare the bioaccumulation of PAHs and PCBs in the laboratory test with the in situ bioaccumulation of these compounds. Using the traditional organic carbon-water partitioning model, tissue concentrations were greatly overestimated, based on the concentrations in the sediment dry matter. Use of an additional correction factor for black carbon with a two-carbon model, significantly improved the bioaccumulation predictions, thus confirming that black carbon was important in binding the chemicals and reducing their accumulation. The predicted PAH tissue concentrations were, however, high compared to the observed values. The chemical concentrations were most accurately predicted from their freely dissolved pore water concentrations, determined using equilibrium passive sampling. The patterns of PCB and PAH accumulation in sediments for laboratory-exposed L. variegatus were similar to those in field-collected Lumbriculidae worms. Field-collected benthic invertebrates and L. variegatus accumulated less PAHs than PCBs with similar lipophilicity. The biota to sediment accumulation factors of PAHs tended to decrease with increasing sediment organic carbon normalized concentrations. The presented data yields bioconcentration factors (BCF) describing the chemical water-lipid partition, which were found to be higher than the octanol-water partition coefficients, but on a similar level with BCFs drawn from relevant literature. In conclusion, using the two-carbon model method, or the measured freely dissolved pore water concentrations method is recommended for predicting the bioaccumulation of PAHs and PCBs.

A rate‐dependent constitutive model of high damping rubber bearings: modeling and experimental verification

SummaryIn this study, a constitutive model of high damping rubber bearings (HDRBs) is developed that allows the accurate representation of the force–displacement relationship including rate‐dependence for shear deformation. The proposed constitutive model consists of two hyperelastic springs and a nonlinear dashpot element and expresses the finite deformation viscoelasticity laws based on the classical Zener model. The Fletcher–Gent effect, manifested as high horizontal stiffness at small strains and caused by the carbon fillers in HDRBs, is accurately expressed through an additional stiffness correction factor α in the novel strain energy function. Several material parameters are used to simulate the responses of high damping rubber at various strain levels, and a nonlinear viscosity coefficient η is introduced to characterize the rate‐dependent property. A parameter identification scheme is applied to the results of the multi‐step relaxation tests and the cyclic shear tests, and a three‐dimensional function of the nonlinear viscosity coefficient η with respect to the strain, and strain rate is thus obtained. Finally, to investigate the accuracy and feasibility of the proposed model for application to the seismic response assessment of bridges equipped with HDRBs, an improved real‐time hybrid simulation (RTHS) test system based on the velocity loading method is developed. A single‐column bridge was used as a test bed and HDRBs was physically tested. Comparing the numerical and RTHS results, advantage of the proposed model in the accuracy of the predicted seismic response over comparable hysteretic models is demonstrated. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Accounting for the concentration dependence of electrolyte diffusion coefficient in the Sand and the Peers equations

The equations for calculating the diffusion limiting current, ilim, in steady-state voltammetry (known as the Peers equation in membrane science) and the transition time, τ, in chronopotentiometry (the Sand equation) are broadly used in electrode and membrane electrochemistry. The applicability of these equations is limited because they are deduced under the assumption of a constant diffusion coefficient. However, within the diffusion boundary layer, the diffusion coefficient, D, varies between the values corresponding to the bulk solution (Db), and the infinitely dilute solution (D0) near the electrode or membrane surface. In this paper, we explore two models, which account for the concentration dependence D(c) in order to generalise the above fundamental equations. We show that the correct value of ilim can be found via solution of a 2D model, while to find τ, a 1D non-stationary model is sufficient. Generally, the dependence of ilim on the bulk concentration deviates from the proportionality. The similar situation occurs with the proportionality of τ to the squared concentration in the Sand equation. We show that the numerical solutions for ilim and τ can be presented in the forms analogous to the Peers and the Sand equations, respectively, but with an additional correction factor. In particular, an effective diffusion coefficient, Def (an average between Db and D0) has to be introduced in the case of Sand equation. Comparison of our theoretical prediction with experimental chronopotentiograms confirms the necessity of taking into account the D(с) dependence.