Conductance theory of concentrated electrolytes in an MSA-type approximation

A closed system of equations for the nonequilibrium pair-distribution function is given which corresponds to the mean spherical approximation (MSA) in equilibrium. The electrophoretic contribution to the conductance is calculated exactly in the framework of the MSA. For the calculation of the remaining contributions the equilibrium distribution function due to Henderson and Smith was used. The final expressions for the conductance are given in analytic terms using the restricted primitive model. The calculated curves are in good agreement with experimental data for 1-1 electrolytes up to about 1 M and qualitatively show the right behaviour up to rather high concentrations.     

Determination of component concentrations in mixtures of weak and strong acids and bases by linear algebraic methods

A general expression for transforming potentiometric titration curves of mixtures of weak acids into a system of linear equations is derived. The solution of the linear equations gives directly the concentrations of the components. This linear transformation method is illustrated by the analysis of mixtures of weak acids with overlapping dissociation equilibria. The possible presence of a strong acid or strong base in the mixture can also be detected and its concentration simultaneously determined. The method can also be used for analysis of an ampholyte and solutions containing a weak acid and its conjugate base. For example a mixture of hydroxyacetic acid (pK approximately 3.6), acetic acid (pK approximately 4.6) and hydroxylamine hydrochloride (pK approximately 6) was analysed in the presence of strong acid with an average relative error of approximately 2%.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 24: Experimental kinetics of aldehyde and carboxylic acid formation

The experimental kinetics for carboxylic acids shows more complexity than that for ketones. The fitting of the experimental results for the initial stages to the equation consisting of a linear and a quadratic term in processing time accounts well for the ketone data but not for the acid data. Instead of that, the data for the acids show fair fit to an equation containing a linear term and another term that is cubic in processing time. In the temperature range of the experiments the linear term is practically constant. The cubic term increases strongly with temperature. The combination of a linear and a quadratic term can account for the advanced stages of processing. The corresponding quadratic term shows strong increase if the processing temperature passes from 150 to 160 °C. However, for higher processing temperatures it remains constant within experimental error. The difference carbonyl absorbance measured after treatment of the polyethylene films with ammonia corresponds to the sum of the acids and aldehydes. It shows similarly complex kinetics. Some of the difficulties encountered with the experimental kinetics cannot be resolved with the data available. It is only the comparison with the formal kinetics based on potential mechanisms of product formation that allows for better understanding of the experimental results.     

Linearity of calibration curves: use and misuse of the correlation coefficient

The correlation coefficient is commonly used to evaluate the degree of linear association between two variables. However, it can be shown that a correlation coefficient very close to one might also be obtained for a clear curved relationship. Other statistical tests, like the Lack-of-fit and Mandel’s fitting test thus appear more suitable for the validation of the linear calibration model. A number of cadmium calibration curves from atomic absorption spectroscopy were assessed for their linearity. All the investigated calibration curves were characterized by a high correlation coefficient (r >0.997) and low quality coefficient (QC <5%), but the straight-line model was systematically rejected at the 95% confidence level on the basis of the Lack-of-fit and Mandel’s fitting test. Furthermore, significantly different results were achieved between a linear regression model (LRM) and a quadratic regression (QRM) model in forecasting values for mid-scale calibration standards. The results obtained with the QRM did not differ significantly from the theoretically expected value, while those obtained with the LRM were systematically biased. It was concluded that a straight-line model with a high correlation coefficient, but with a lack-of-fit, yields significantly less accurate results than its curvilinear alternative. Received: 15 January 2002 Accepted: 18 April 2002     

Calibration in atomic spectrometry: A tutorial review dealing with quality criteria,weighting procedures and possible curvatures

Calibration is required to obtain analyte concentrations in atomic spectrometry. To take full benefit of it, the adequacy of the coefficient of determination r² is discussed, and its use is compared with the uncertainty due to the prediction bands of the regression. Also discussed from a tutorial point of view are the influence of the weighting procedure and of different weighting factors, and the comparison between linear and quadratic regression to cope with curvatures. They are illustrated with examples based on the use of ICP-AES with nebulization and laser ablation, and of LIBS. Use of a calibration graph over several orders of magnitude may be problematic as well as the use of a quadratic regression to cope with possible curvatures. Instrument softwares that allow reprocessing of the calibration by selecting standards around the expected analyte concentration are convenient for optimizing the calibration procedure.     

Series approach to modeling ion size effects for asymmetric electrolytes in the diffuse double layer

The theory of the diffuse layer for asymmetric electrolytes is reconsidered with emphasis on the effects of ion size on the diffuse layer potential drop and differential capacity. For asymmetric 2:1 and 1:2 electrolytes, this potential drop is expressed in terms of a polynomial with a linear, quadratic, and cubic term in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 2:1 electrolytes are provided by least-squares regression of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. These coefficients are then expressed as simple functions of the parameters commonly associated with the mean spherical approximation. The series approach accurately describes potential drops and differential capacities of the diffuse layer for 2:1 and 1:2 electrolytes for the chosen assumptions.     

The uncertainty of a result from a linear calibration

The standard error of a result obtained from a straight line calibration is given by a well known ISO-endorsed expression. Its derivation and use are explained and the approach is extended for any function that is linear in the coefficients, with an example of a weighted quadratic calibration in ICPAES. When calculating the standard error of an estimate, if QC data is available it is recommended to use the repeatability of the instrumental response, rather than the standard error of the regression, in the equation.     

Optimale Strategie zur Ermittlung von Eichkurven, dargestellt am Beispiel der AAS

Summary Accuracy of the determination of concentrations depends under calibration conditions on experimental factors as well as the mathematical treatment of the calibration data matrix. An advantageous strategy for computation of calibration curves which considers all relevant information including standard measuring error as well as standard errors of concentrations in the estimation procedure is presented here.The example of atomic absorption spectrometry (AAS) given shows that the connection of the developed strategy with application of non-linear regression functions yields remarkable improvements of the detection power.     

Electrolyte diodes with weak acids and bases. II. Numerical model calculations and experiments

This is the second part of our work dealing with electrolyte diodes with weak acids and bases. In the first part an approximative analytical solution was derived for the steady-state current-voltage characteristic (CVC) of a reverse-biased diode (a quasi-one-dimensional gel connecting an acidic and an alkaline reservoir), applying either strong or weak electrolytes. An approximative analytical solution is compared here with a numerical solution free of any approximations and with CVCs measured experimentally with both strong and weak electrolytes. It is shown that the deviations between the numerical and analytical solutions are mostly due to assumptions made for the fixed charge concentration profiles. The concept of optimal analytical solution is introduced which does not use such assumptions and applies only the quasielectroneutrality and quasiequilibrium approximations. It is proven that the slope of the CVC based on the optimum analytical solution can be calculated without the complicated derivation of that solution itself. The calculation of that slope is based on the fact that in the optimum analytical solution all currents are inversely proportional to the length if the boundary conditions are held constant and realizing that in the middle part of the gel the only mobile counterions of the fixed ionized groups are hydrogen ions. In the experimental part the apparatus and the preparation of the gel are described together with the CVCs measured with strong and weak electrolytes. From these CVCs the fixed ion concentration in the middle part of the gel can be determined. That fixed ion concentration is 1.96 x 10(-4)M measured with weak electrolytes and 3.48 x 10(-4)M measured with strong electrolytes. The deviation indicates that the strong base causes some hydrolysis of the gel. Finally, possible applications of weak acid-weak base diodes are discussed.     

Comparison of linear and non-linear equations for univariate calibration

Univariate data accumulated for the purpose of calibration of chromatographic and spectroscopic methods often exhibit slight but definite curvature. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = a + bx(m), (m not equal to 1) is compared with the commonly used linear equation, y = a + bx, as well as the quadratic equation, y = a + bx + cx2. All equations were applied to high quality HPLC calibration data using unweighted least squares. Parameter estimates and their standard errors were calculated for each equation. Standard errors and 95% prediction intervals in analyte concentrations were estimated with the aid of the fitted equations and their respective covariance matrices. Results indicate that the non-linear and quadratic equations each provide a better fit than the linear equation to the data considered here, as judged by the Akaikes information criterion (AIC), the adjusted coefficient of multiple determination, the magnitude and scatter of residuals, standard errors in estimated analyte concentrations and lack of fit analysis of variance (ANOVA). While the difference between the equations y = a + bx + cx2 and y = a + bx(m) as judged by the same criteria is more marginal, this work suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low noise calibration data which exhibit slight curvature.     

The learning machine in quantitative chemical analysis: Part 2. Potentiometric titrations of mixtures of three bases

Computer-calculated curves for the titration of mixtures of one strong base and two weak bases are used in the training and testing of a linear learning machine. The results indicate that multicategory classifiers can be calculated from a computer-generated training set of titration curves in which a random error of ±0.01 unit in the pH values is introduced. The relative error in the predictions for concentrations of bases not included in the training set was of the orderof ± 1% for concentration ratios up to 10:1 when δpK_b for the weak bases exceeded 1 pK unit and for K_b1 ? 5 × 10^-4 and K_b2 ? 10^-9. Calculation of the first derivative of the volume of titrant versus pH curves as a preprocessing step was necessary to obtain this accuracy for the weak bases, whereas the volume of titrant versus pH curves had to be used directly in the determination of the strong base. Predictions of concentrations of actual samples were in agreement with the computer-calculated results.     

Standard systems for measurement of pKs and ionic mobilities. 1. Univalent weak acids

Determination of pK values of weak bases and acids by CZE has already attracted big attention in current practice and proved to offer the advantage of being applicable for mixtures of analytes. The method is based on the measurement of mobility curves plotting the effective mobility vs. the pH of the background electrolyte, and following computer-assisted regression involving corrections for ionic strength and temperature. To cover the necessary range of pH for a given case, both buffering weak acids and bases are used in one set of measurements, which requires implementing computations of individual ionic strength corrections for each pH value. It is also well known that some components of frequently used background electrolytes may interact with the analytes measured, on forming associates or complexes. This obviously deteriorates the reliability of the resulting data. This contribution brings a rational approach to this problem and establishes a standard system of anionic buffers for measurements of pKs and mobilities of weak acids, where the only counter cation present (besides H(+)) is Na(+). In this way, the risk of formation of complexes or associates of analytes with counter ions is strongly reduced. Moreover, the standard system of anionic buffers is selected in such a way that it provides, for an entire set of measurements, constant and accurately known ionic strength and the operational conditions are selected so that they provide constant Joule heating. Due to these precautions only one correction for ionic strength and temperature is needed for the obtained set of experimental data. This considerably facilitates their evaluation and regression analysis as the corrections need not be implemented in the computation software. The reliability and the advantages of the proposed system are well documented by experiments, where the known problematic group of phenol derivatives was measured with high accuracy and without any notice of anomalous behaviour.     

Electrolyte diodes with weak acids and bases. I. Theory and an approximate analytical solution

Until now acid-base diodes and transistors applied strong mineral acids and bases exclusively. In this work properties of electrolyte diodes with weak electrolytes are studied and compared with those of diodes with strong ones to show the advantages of weak acids and bases in these applications. The theoretical model is a one dimensional piece of gel containing fixed ionizable groups and connecting reservoirs of an acid and a base. The electric current flowing through the gel is measured as a function of the applied voltage. The steady-state current-voltage characteristic (CVC) of such a gel looks like that of a diode under these conditions. Results of our theoretical, numerical, and experimental investigations are reported in two parts. In this first, theoretical part governing equations necessary to calculate the steady-state CVC of a reverse-biased electrolyte diode are presented together with an approximate analytical solution of this reaction-diffusion-ionic migration problem. The applied approximations are quasielectroneutrality and quasiequilibrium. It is shown that the gel can be divided into an alkaline and an acidic zone separated by a middle weakly acidic region. As a further approximation it is assumed that the ionization of the fixed acidic groups is complete in the alkaline zone and that it is completely suppressed in the acidic one. The general solution given here describes the CVC and the potential and ionic concentration profiles of diodes applying either strong or weak electrolytes. It is proven that previous formulas valid for a strong acid-strong base diode can be regarded as a special case of the more general formulas presented here.     

Different approaches to multivariate calibration of nonlinear sensor data

In this study, different approaches to the multivariate calibration of the vapors of two refrigerants are reported. As the relationships between the time-resolved sensor signals and the concentrations of the analytes are nonlinear, the widely used partial least-squares regression (PLS) fails. Therefore, different methods are used, which are known to be able to deal with nonlinearities present in data. First, the Box–Cox transformation, which transforms the dependent variables nonlinearly, was applied. The second approach, the implicit nonlinear PLS regression, tries to account for nonlinearities by introducing squared terms of the independent variables to the original independent variables. The third approach, quadratic PLS (QPLS), uses a nonlinear quadratic inner relationship for the model instead of a linear relationship such as PLS. Tree algorithms are also used, which split a nonlinear problem into smaller subproblems, which are modeled using linear methods or discrete values. Finally, neural networks are applied, which are able to model any relationship. Different special implementations, like genetic algorithms with neural networks and growing neural networks, are also used to prevent an overfitting. Among the fast and simpler algorithms, QPLS shows good results. Different implementations of neural networks show excellent results. Among the different implementations, the most sophisticated and computing-intensive algorithms (growing neural networks) show the best results. Thus, the optimal method for the data set presented is a compromise between quality of calibration and complexity of the algorithm.Electronic Supplementary Material Supplementary material is available for this article at     

ICP—AES分析的线性回归校准曲线

本文对ICP-AES分析中2种线性回归方法的校准曲线作了比较和讨论。对大多数元素而言,用加权法得到的校准曲线的斜率比不加权校准曲线的斜率略大,减小3校准曲线在低浓度部分的弯曲,曲线明显优于不加权校准曲线。将2种方法得到的校准曲线进行比较时,应将剩余标准偏差(或剩余变差平方和)及曲线截距等加以综合考虑。用含零标的标准系列制作校准曲线可使曲线的截距更接近原点,有利于提高在低浓度部分校准分析的准确性。     

Optimal speed as a function of system performance for continuous flow analyzers

The limitation to high rates of sample throughput with continuous flow automated analyzers is unacceptably high sample-to-sample carry-over. Previous programs for carry-over correction have involved relatively large computer capacities. Here, the simple expression derived for carry-over can be easily programmed in BASIC for a Commodore PET operating in real time. The program includes peak picking and calculation of the calibration graph and sample concentrations. At 240 samples per hour, the results obtained for total protein (linear calibration graph) and haptoglobin (non-linear calibration plot) showed acceptable precision and recovery and correlated well with the same determination conducted at normal operating speeds. Standard Auto Analyzer equipment was used througout. A parameter which monitors the instrument function is also calculated; this replaces the conventional visual examination of the curve for function monitoring. At high sample rates with degraded curves, visual curve examination is not effective.     

2-methoxyethanol as a solvent for conductometric acid-base titrations

Conductometric titrations of a series of organic acids in 2-methoxyethanol were performed with 1,3-diphenylguanidine (DPG) as titrant. For benzoic, p-chlorobenzoic and picric acids, phenylphenol and barbital, excellent recoveries were obtained from well-defined conductance vs. volume plots. Results for the dicarboxylic phthalic and adipic acids were also good. However, the titration curves for the difunctional salicylic and p-hydroxybenzoic acids were not clearly defined. The results are discussed and compared with cnductometric titrations of acids in other non-aqueous solvents. Several determinations of electrolyte conductance as a function of concentration revealed that, as expected, the selected substances are weak electrolytes in methoxyethanol.     

Use of factorial experimental design for the rapid evaluation of main and interactive factors affecting linearity in calibration curves for sulfate analysis by ion chromatography

Analytical results of anion determination by suppressed ion chromatography are significantly affected by calibration curve calculation. In this paper, as expected, eluent pK_a is shown to influence calibration linearity in the range 1–20 mg/l sulfate, with A carbonate-hydrogencarbonate mixture producing a larger non-linearity than NaOH. Evidence is given for very large errors (about 30–40%) in estimating sample sulfate concentration when linear regression is used instead of a quadratic calibration curve. This study was performed following a 2⁴ run full factorial experimental design, including eluent pK_a, counterion type, solution composition and current level for background suppression as main variables.     

多元线性回归同时单点pH滴定法研究

本文将多元线性回归分析用于单点ＰＨ滴定中，同时测定极弱酸或碱混合物含量。对 十个五元 极弱碱混合样进行了测定，获得满意结果。     

Application of global kinetic models to HMX beta-delta transition and cookoff processes

The reduction of the number of reactions in kinetic models for both the HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) beta-delta phase transition and thermal cookoff provides an attractive alternative to traditional multi-stage kinetic models due to reduced calibration effort requirements. In this study, we use the LLNL code ALE3D to provide calibrated kinetic parameters for a two-reaction bidirectional beta-delta HMX phase transition model based on Sandia instrumented thermal ignition (SITI) and scaled thermal explosion (STEX) temperature history curves, and a Prout-Tompkins cookoff model based on one-dimensional time to explosion (ODTX) data. Results show that the two-reaction bidirectional beta-delta transition model presented here agrees as well with STEX and SITI temperature history curves as a reversible four-reaction Arrhenius model yet requires an order of magnitude less computational effort. In addition, a single-reaction Prout-Tompkins model calibrated to ODTX data provides better agreement with ODTX data than a traditional multistep Arrhenius model and can contain up to 90% fewer chemistry-limited time steps for low-temperature ODTX simulations. Manual calibration methods for the Prout-Tompkins kinetics provide much better agreement with ODTX experimental data than parameters derived from differential scanning calorimetry (DSC) measurements at atmospheric pressure. The predicted surface temperature at explosion for STEX cookoff simulations is a weak function of the cookoff model used, and a reduction of up to 15% of chemistry-limited time steps can be achieved by neglecting the beta-delta transition for this type of simulation. Finally, the inclusion of the beta-delta transition model in the overall kinetics model can affect the predicted time to explosion by 1% for the traditional multistep Arrhenius approach, and up to 11% using a Prout-Tompkins cookoff model.