Regression analysis of electrocapillary curves of mercury electrode in solutions of secondary butyl alcohol

A regression technique is used for analyzing electrocapillary curves (ECC) in secondary butanol solutions, which were published earlier. It was shown that, in contrast to similar analysis of electrocapillary curves for a number of other compounds, if we want to describe the adsorption of 2-BuOH within the framework of the model of two parallel capacitors, the linear dependence of the parameter of intermolecular interaction on the electrode potential should be taken into account. This result stems from the very high accuracy of interface tension measurements in the system under study. It is found that, in terms of the Frumkin isotherm and the model of two parallel capacitors, the interpretation of data on the adsorption of 2-BuOH has a much simpler physical meaning as compared with the strictly thermodynamic approach used earlier.     

Equilibrium differential capacitance and electrocapillary curves within the framework of a generalized model of the surface layer

Equations that describe the equilibrium differential capacitance C and the interface tension of an electrode subjected to the adsorption of organic molecules under the conditions where this adsorption strictly follows a generalized model of the surface layer are derived. Using the developed programs, the dependences of C on the electrode potential φ are calculated at different concentrations of the organic substance. Based on these C vs. φ curves, a set of effective parameters is obtained. With these parameters, the capacitance curves can best be described by the model of two parallel capacitors combined with the Frumkin isotherm.     

Adsorption parameters in solutions of ethyl esters of aliphatic acids

Based on the regression analysis of electrocapillary curves (ECC) in solutions of ethyl esters of aliphatic acids (from acetic to valeric), it is shown that the adsorption of these compounds on a mercury electrode from aqueous solutions corresponds in the first approximation to the model of two parallel capacitors. Moreover, to describe experimental ECC, the knowledge of only five main parameters of this model is necessary. The dependence of the adsorption parameters found on the number of carbon atoms in an ester molecule is analyzed.__________Translated from Elektrokhimiya, Vol. 41, No. 4, 2005, pp. 406–411.Original Russian Text Copyright © 2005 by Damaskin.     

Regression Analysis of Two Dimensional Pressure Isotherms for Individual Adsorption of Surface Active Molecules and Ions

A new version of the regressive technique is proposed for calculating adsorption parameters from two-dimensional pressure isotherms. The method assumes that the Frumkin isotherm is applicable to individual adsorption of surface-active neutral molecules and single-charged ions. Based on literature data, the adsorption parameters are assessed for tetraethylammonium, tetrapropylammonium, and tetrabutylammonium cations and for saccharose molecules for their adsorption from aqueous solutions on the uncharged mercury surface.     

Temperature dependence of adsorption parameters of n-butanol and n-valeric acid at their adsorption on mercury electrode from aqueous solutions

Adsorption parameters that enter into the Frumkin isotherm and the model of two parallel capacitors are calculated based on the data of the regression analysis of differential capacitance curves of a mercury electrode in solutions of n-butanol and n-valeric acid at 25, 50, and 75°C. The analysis of the temperature dependences of these parameters allowed free energies, entropies, and enthalpies of adsorption to be found. It is shown that the hydrophobic effect, which is associated with the increase in the enthalpy of liquid water when adsorbate molecules leave it, makes a substantial contribution into the adsorption free energy of studied compounds.     

Prediction of breakthrough curves for multicomponent adsorption in a fixed-bed column using logistic and Gompertz functions

In order to facilely predict the multicomponent breakthrough curves and avoid the complicated numerical solution, this work proposes two empirical models based on the logistic and Gompertz functions. The S-shaped and bell-like curves correspond to the adsorption and displacement processes respectively. The equilibrium loading of each component can be calculated by integration of the measured breakthrough curves. The effects of the model parameters on the breakthrough curves are investigated. The applicability of the two empirical models is validated by three binary and four ternary adsorption systems, including the gas–solid and liquid–solid adsorption. The residual plot and coefficient of determination (R²) are used to evaluate their fitting quality. The results indicate that the fitting curves agree well with the experimental data and all of the residuals are distributed randomly. The five model parameters (k, τ, k*, τ* and c) are easily obtained by the nonlinear regression. For example, the fitting results are k = 1.37 × 10^?2 min^?1, τ = 292 min, k* = 1.25 × 10^?2 min^?1, τ* = 453 min and c = 85.3 for adsorption of n-butyl acetate and p-xylene on granular activated carbon. On the whole, the Gompertz model is superior to the logistic model in terms of the fitting accuracy. The significance of this work is to provide a simple and practical method for prediction of the multicomponent breakthrough curves.     

Refining adsorption parameters of n-butyl alcohol at the interface of mercury electrode with aqueous NaF and Na2SO4 solutions by correcting the adsorbate concentration

As an adjunct to the regression analysis of differential capacitance curves, which allows refining the adsorption parameters, a program, which takes into account possible errors in volume concentrations of organic substances, is developed. Using this procedure, the earlier data on the differential capacitance of a mercury electrode in aqueous solutions of normal butanol (1-BuOH) containing either 0.1 M NaF or 0.05 and 0.5 M Na₂SO₄ as the supporting electrolyte are analyzed. This allows obtaining the most accurate values of adsorption parameters for the systems mentioned above within the framework of the model of two parallel capacitors and the Frumkin isotherm. It is shown that, when a linear dependence of the intermolecular interaction parameter on the electrode potential is taken into account, the standard deviation of experimental capacitance values from those calculated using the mentioned model is 6.8–8.8%, which points to very high accuracy of this phenomenological model.     

New Analysis of Data on the Differential Capacitance of a Mercury Electrode during the Adsorption of tert-Butanol

A regression analysis of data on the differential capacitance of a mercury electrode in aqueous solutions of tert-butanol, which were published previously, is performed. It is shown that, in contradistinction to an analogous analysis of electrocapillary curves (ECC), in order to describe the adsorption of this compound in the framework of a model of two parallel capacitors, it is necessary to take into account the linear dependence of the parameter of an intermolecular interaction on the electrode potential. It is established on the basis of modeling calculations that, in order to obtain the same result in the case of a regression analysis of ECC, the relative accuracy of measurements of the interfacial tension must be two orders of magnitude the relative accuracy of measurements of the differential capacitance.     

Three-dimensional bond-charge models for potential curves of diatomic molecules

Several simple three-dimensional Fermi-gas models for potential energy curves of diatomic molecules are suggested. Bond-charge parameters close to those predicted by the earlier point bondcharge model of Borkman, Simons and Parr [J. Chem. Phys. 49, 1055 (1968); 50, 58 (1969)] are obtained for models assuming uniform spherical or elliptical electron distributions in the bond region.Aided by a research grant to The Johns Hopkins University from the National Science Foundation.     

Correspondence between the Frumkin and Alekseev-Popov-Kolotyrkin models at the adsorption of neutral organic molecules

By the example of a system Hg/(H₂O + xM NaF + yM n-C₄H₉OH) for four x values (0.01, 0.03, 0.1, and 0.3) in combination with six different y values (in a range from 0.05 to 0.8), an assumption on the simultaneous fulfillment of the classical model of the diffuse layer and the model of two parallel capacitors supplemented by the Frumkin isotherm is analyzed. It is shown that the classical theory of the diffuse layer agrees with experimental data on the capacitance in this system and also on the adsorption of secondary butanol not only near the zero-charge potential but also in the vicinity of adsorption-desorption peaks where the electrode charge reaches absolute values of 6–10 μC/cm². At the same time, the experimental differential capacitance curves in this system are well described by the model of two parallel capacitors supplemented by the Frumkin isotherm (the Frumkin model) for all supporting-electrolyte concentrations. However, this model is far less accurate in describing the calculated curves of the dense-layer differential capacitance, which contradicts the straightforward physical basis of the Alekseev-Popov-Kolotyrkin model. To resolve this contradiction, further studies with the use of molecular models are necessary.     

一类用于多元光度分析的小波基主成分回归法

通过将变尺度小波分解滤噪与特征信息提取相结合,提出一类新的多元光度分析算法－小波基主成分回归（ＰＣＲＷ）方法。该法可有效地减小主成分向量残留噪声所引 误差显著提高多元校正准确性。将其用于分析氯霉素、醋酸对塞米松、尼泊金乙脂体系、得到满意的回收率,与ＰＣＲ法相比,分析结果的总平均相对误差从３．３８％降低到０．８３％。     

Ensemble Regression Coefficient Analysis for Application to Near-Infrared Spectroscopy

A new variable selection method called ensemble regression coefficient analysis is reported on the basis of model population analysis. In order to construct ensemble regression coefficients, many subsets of variables are randomly selected to calibrate corresponding partial least square models. Based on ensemble theory, the mean of regression coefficients of the models is set as the ensemble regression coefficient. Subsequently, the absolute value of the ensemble regression coefficient can be applied as an informative vector for variable selection. The performance of ensemble regression coefficient analysis was assessed by four near infrared datasets: two simulated datasets, one wheat dataset, and one tobacco dataset. The results showed that this approach can select important variables to obtain fewer errors compared with regression coefficient analysis and Monte Carlo uninformative variable elimination.     

Adsorption parameters of cyclobutane carboxylic acid at the interface of a mercury electrode with aqueous solutions of 0.4 M Na2SO4 + 0.1 M H2SO4

Based on the results of the regression analysis of differential capacitance curves of a mercury electrode in solutions of cyclobutane carboxylic acid (CBCA) at 25, 50, and 75°C, the adsorption parameters that enter into both the Frumkin isotherm and the model of two parallel capacitors are estimated. The free energies of adsorption found from the analysis of the temperature dependence of these parameters are incorrect due to the partial blowing out of CBCA during the deaeration of the solutions. The corresponding adsorption parameters are corrected under the assumption that the hydrophobic effect associated with the increase in the liquid-water entropy at the removal from it of CBCA molecules is the same as for n-valeric acid. The physical meaning of the squeezing-out effect is revised.     

也谈计算机在测试数据统计处理中的应用——与秦建侯等同志商榷

本文对多元回归分析及其计算机程序进行了进一步研究.指出了《分析试验室》1989年第3期所载回归程序疏漏之处,并指出该程序采用回归系数简化计算法具有局限性。为此提出了另一种逐步回归程序,对一些经典数据进行回归分析,得到满意结果。     

Estimation of parameters characterizing the adsorption of sodium,potassium, and rubidium cryptates at the mercury electrode/solution interface

The adsorption of complexes formed by sodium, potassium, and rubidium cations with macrobicyclic ligand (kryptofix 222 with C₁₈H₃₆N₂O₆ composition) is studied as a function of the ligand concentration on a stationary mercury drop in 0.1 M solutions of corresponding sulfates and chlorides by using the differential capacitance technique. Based on the model of two parallel capacitors supplemented by the Frumkin isotherm, the adsorption parameters of studied cryptates are estimated by using the regression analysis technique. Differential capacitance curves calculated with the parameters found are compared with experimental data. The comparison of the found adsorption parameters makes it possible to reveal the effects of the nature of included cations and specifically adsorbed supporting-electrolyte anions on the adsorption behavior of cryptates under study.__________Translated from Elektrokhimiya, Vol. 41, No. 4, 2005, pp. 475–481.Original Russian Text Copyright © 2005 by Stenina, Sviridova.     

Adsorption of the lanthanum and thorium cryptates at mercury electrode

The adsorption behavior of cryptates of La³⁺ and Th⁴⁺ cations at the Hg/aqueous solution interface is studied by using the electrochemical impedance spectroscopy method. It was shown that the studied complexes have high surface activity at the interface. The lanthanum cryptate adsorption parameters are found using the regression analysis based on the two parallel capacitor model supplemented by the Frumkin adsorption isotherm. The differential capacitance curves calculated by using these parameters agree satisfactorily with the experimental ones. The more complicated adsorption behavior of lanthanum cryptate, as compared with the complexes of lower valence cations, is interpreted with taking into consideration the strong interaction of the La³⁺ cation contained in the [2.2.2.] cryptand intramolecular cavity with the supporting electrolyte anions.     

Enthalpy Relaxation in Glasses: Regression analysis of integral DSC data

A new method of calculation of parameters of enthalpy relaxation models is proposed. Regression analysis treatment compares the experimental and calculated values of relaxation enthalpy. The experimental values of relaxation enthalpy are obtained by numerical integration of the difference between the two DSC curves. Contrary to the overall shape of the DSC curve the integral values are not affected by particular heat flow conditions during the DSC experiment. The Narayanaswamy's numerical model based on the Kohlrausch—William—Watts relaxation function was used to calculate the theoretical values of relaxation enthalpy. The application of the proposed method on the DSC experimental data of enthalpy relaxation of As₂Se₃ is shown.This revised version was published online in November 2005 with corrections to the Cover Date.     

快速多模型回归分析方法的研究

逐步回归[1]是变量选择的常用方法．由逐步回归法得到的数学表达式不一定是最优数学模型，所以有其局限性．假如有m个变量x；，x。，……，x。，我们希望得到分别包含1个变量、2个变量、……、直至m个变量的最优回归方程，可以采用组合算法C：，对每个子集的所有组合进行回归分析，然后从C：个回归方程中选出最优的数学模型．由于随着变量个数m的增加，总的回归次数以2”的形式倍增，运算量大，时间长．此时可采用快速多模型（LeaPsandbounds）回归分析［‘j．此法为一种快速多模型回归，据此可以得到一组含有不同变量个数的最优方程．该…