Nonlinear Calibration Curve Research Articles

Calibration Curve for Quantitative Analysis of the Monoclinic-Tetragonal ZrO2System by X-Ray Diffraction

A nonlinear calibration curve for volume fraction vs integrated intensity ratio was obtained for the monoclinic-tetragonal ZrO2 system by using X-ray powder pattern-fitting and pattern-decomposition techniques. The empirical equation agrees well with the theoretical one. By using this equation, the deviation from linearity (6.8% maximum) resulting from the intensity difference of corresponding reflections of the two phases can be estimated quite accurately.

Calibration and curve fitting for extended range AAS

Several curve fitting methods, including linear, quadratic, and rational least squares fits and linear, cubic spline, and Stineman interpolations, are evaluated for their ability to fit highly nonlinear atomic absorption analytical calibration curves. In addition, the number of standards required to effectively calibrate a dynamic range covering 3 orders of magnitude of concentration is determined. Finally, the concentration ranges providing minimum relative concentration precision (RCP) are identified and the slopes of the calibration curves in these ranges are noted. Concentration ranges of minimum RCP also provide minimum curve fitting errors and generally have log-log slopes of approximately 0.5 indicating that linearity alone is not a sufficient criterion for choosing suitable calibration and curve fitting concentration ranges.

Ein verfahren zur eichung der gelchromatographie (GPC) mit präparaten beliebiger, bekannter molekulargewichtsverteilung

If, in GPC calibration, the mean elution volume (or centre of gravity volume) of the elution curves obtained with monomolecular samples is used, the mean elution volume of a polymolecular mixture is a weight-average. According to the calibration curve, a molecular weight average can be attributed to the mean elution volume. For the special case of a logarithmic-linear calibration curve, this is the geometric (weight) mean of the molecular weight. Thus one can perform broad-standard calibration of GPC without interference by column dispersion. The potential application for non-linear calibration curves is discussed. It is considered how calibration functions for the higher moments of the monomolecular elution curves could be determined and how universal calibration should be performed if the standards are polydisperse relative to hydrodynamic volume. Absolute determination of polydispersity becomes possible with an additional z-detector.

Determination of free chlorine in water by chemiluminescence reaction with hydrogen peroxide

The analytical utility of the hydrogen peroxide—hypochlorite singlet oxygen chemiluminescence reaction for the determination of hypochlorite in water is investigated. Effects of pH and hydrogen peroxide concentration are discussed and interference data for over 35 species in the absence and presence of hypochlorite are provided. The limit of detection is 4 μg l -1 with a usable non-linear calibration curve up to about 200 μg l -1. The new method is shown to be relatively free from interferences and to give results for tap water comparable to a standard colorimetric method based on a reaction with N, N-diethyl- p-phenylenediamine.

Standard addition for strongly non-linear calibration curves

An iterative procedure has been applied to standard addition in order to overcome limitations so far involved with the standard addition technique. Using a FORTRAN-program even strongly nonlinear calibration functions could be evaluated. Moreover, in contrast to linear standard addition techniques remaining background absorption does hardly influence the result.

Determination and Use of Cumulants of the Peak Broadening Function in Steric Exclusion Chromatography

Abstract A procedure is developed which allows to deduce from recycle measurements the central moments and cumulants of the molecular mass distribution of polymers and the broadening function by the use of properties of statistical distributions. Results of an experimental application of the method are presented. Equations for the calculation of true molecular mass averages from the elution curve are extended for the cases of nonlinear calibration curves and nonlinear broadening.

Molecular weight estimation using sodium dodecyl sulfate-pore gradient electrophoresis

Pore gradient electrophoresis (PGE) in the presence of sodium dodecyl sulfate (SDS) provides a means for high resolution fractionation of multicomponent protein systems and permits estimation of molecular weights for macromolecules ranging from 10 3 to 10 6. We have evaluated the performance of several methods used to construct calibration curves for estimation of molecular weights using SDS-PGE. A linear relationship between the logarithm of molecular weight, log ( M r), and the logarithm of the relative mobility, log ( R l ), can be obtained for a 30-fold range of molecular weights. However, this range of linearity depends on the choice of the concentration gradient, the degree of crosslinking of the gel, and on the nature of the underlying relationship between the retardation coefficient, K R , and the molecular weight. An empirical relationship, first introduced by Lambin et al. (1976, Anal. Biochem. 74, 567) between log ( M r) and the logarithm of the gel concentration at the position reached by the protein, log (% T), provides better linearity over a wider molecular weight range than does the use of log ( R l ). We have compared these relatienships by experimental analysis of 10 standard proteins and by a theoretical analysis of an idealized model system. A computer program has been developed which provides appropriate statistical estimation of the molecular weight for an unknown protein, together with its standard error and 95% confidence limits. A new method has also been developed for analysis of nonlinear calibration curves in terms of molecular weight versus distance migrated, based on a theoretically justifiable, physical-chemical model. This model implies that either the relationship between log ( M r) and log ( R l ) or the one between log ( M r) and log (% T) will become nonlinear as the range of molecular weight is extended. We suggest that the use of a nonlinear least-squares curve-fitting procedure provides an optimal method for molecular weight estimation when sufficient data are available. Based on these findings, a general strategy is presented for estimation of molecular weights by polyacrylamide gel electrophoresis.

The Application of Robust Calibration to Radioimmunoassay

The minute concentrations of many biochemically and clinically important substances are currently estimated by radioimmunoassay (RIA). Traditionally, the most popular approaches to the statistical analysis of RIA data have been to linearize the data through transformation and fit the calibration curve using least squares or to directly fit a nonlinear calibration curve using least squares. Estimates of the hormone concentration in patients are then obtained using this curve. Unfortunately, the transformation is frequently unsuccessful in linearizing the data. Furthermore, the least squares fit can lead to erroneous results in both approaches since the many sources of error which exist in the RIA process often result in outlier observations. In this paper, an approach to the analysis of RIA data which incorporates robust estimation methods is described. An algorithm is presented for obtaining the M-estimates of nonlinear calibration curves. The curves to be fitted are modified hyperbolae based on 12 to 16 observations. A procedure, based on the application of the Bonferroni Inequality, is presented for obtaining tolerance-like interval estimates of the concentration of the hormone of interest in the patients. Results of simulations are cited to support the method of construction of confidence bands for the fitted calibration curve. Data obtained from the Veteran's Hospital, Buffalo, New York are used to illustrate the application of the algorithm which is presented.

Chromatography of Suspensions - Analytical Corrections for Axial Dispersion

Abstract An analytical method is proposed to correct the signal from a turbidity detector for axial dispersion in the chromatography of particle suspensions. An earlier analytical method due to Hamielec and Singh [1] is limited to light scattering in the Rayleigh regime. The solution reported herein is derived using the more general Mie light scattering theory and enables the correction of various moments of the particle diameter frequency distribution function. The axial dispersion phenomenon is described by the well known integral equation where the instrumental spreading function is assumed Gaussian. The solution is applicable for both linear and nonlinear particle diameter-retention volume calibration curves.

Nonlinear calibration curves

Nonlinear calibration curves

Difficulties with determining the detection limit with nonlinear calibration curves in spectrometry

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDifficulties with determining the detection limit with nonlinear calibration curves in spectrometryJ. D. Ingle and R. L. WilsonCite this: Anal. Chem. 1976, 48, 11, 1641–1642Publication Date (Print):September 1, 1976Publication History Published online1 May 2002Published inissue 1 September 1976https://doi.org/10.1021/ac50005a057RIGHTS & PERMISSIONSArticle Views383Altmetric-Citations31LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (259 KB) Get e-Alerts Get e-Alerts

Some methods for nonlinear regression using desk-top calculators with an application to the Lowry Protein method

An iterative method of calculation has been used to fit exponential and logarithmic models to data by the method of least squares. The nonlinear calibration curve of the Lowry Protein assay was used as an example of this method. With these data, exponential or logarithmic models yield improvement over second degree polynomials, and the necessary calculations can be easily accomplished with a small programmable calculator.

The blank correction in case of non-linear calibration curves

It is shown that in case of non-linear calibration curves the application of a correction for the blank will lead in most cases to incorrect results. Generally, the best procedure is to omit any correction and to make a calibration curve by treating the standard sample in exactly the same way as the sample to be analysed.

The instrument spreading correction in GPC. III. The general shape function using singular value decomposition with a nonlinear calibration curve

AbstractThe Gram‐Charlier series was suggested as an empirical instrument spreading function in the first paper (part I) of this series. In the second paper (part II) of this series, the Fourier transform method was used together with the suggested series to solve Tung's integral equation. In this paper, an alternate method for solving Tung's equation is proposed which eliminates some of the limitations of the Fourier transform method. In the approach used in this study, Tung's integral equation is approximated by a set of linear equations. Since no unique least‐squares solution can be computed, a closely related problem whose solution closely approximates the original problem is formulated and solved using singular value decomposition. By avoiding the use of the smallest singular values and forcing the equality of the areas of the corrected and the uncorrected chromatograms, an approximate solution to the original problem is obtained in which the oscillations inherently present due to the ill‐posed nature of the problem are filtered out. The performance of the method with the experimental data given in Part II is indicated.

Spectrophotometric measurement of ferric ion concentration in the ferrous sulphate (Fricke) dosemeter

A systematic error in the spectrophotometric measurement of ferric ion concentrations in the ferrous sulphate dosemeter may be made by an incorrect evaluation of a non-linear spectrophotometric calibration curve. Methods are discussed for determining the radiation-produced change in molarity from the actual calibration curve, and a method of normalization of measured absorbances is suggested. Normalization factors, converting measured absorbances into normalized values, can either be calculated by choosing a reference value of the molar extinction coefficient, or can be determined by comparative absorbance measurements on two spectrophotometers, one of them to be a precision instrument. Normalized absorbances are proportional to molarity and may be considered to be free of errors due to instrumental parameters and inaccuracies in acidity and temperature of solutions, and of errors in molarity if derived by comparative measurements.

The Instrument Spreading Correction in GPC. II. The General Shape Function Using the Fourier Transform Method with a Nonlinear Calibration Curve

Abstract The instrument spreading function suggested in Part I of this series is investigated for use with the Fourier transform method for generating corrected elution volume chromatograms. The instrument spreading parameters are obtained using linear theory on narrow molecular weight distribution standards, as indicated in Part I. The corrected chromatogram is then combined with a nonlinear molecular weight calibration curve which was fit with a function suggested by Yau and Malone to generate true values of the number- and weight-average molecular weights. The instrument spreading function is shown to qualitatively and quantitatively describe the dispersion, skewing, and flattening effects ordinarily found in GPC chromatograms due to imperfect resolution by the GPC columns. The Yau-Malone function is shown to be a very useful function for fitting nonlinear molecular weight vs elution volume calibration data. Although the Fourier transform method is shown to work well with analytically generated data, i...

Polymer reactors and molecular weight distribution. VIII. A method of interpreting skewed GPC chromatograms

AbstractA new‐method of interpreting GPC chromatograms which accounts for skewing and symmetrical axial dispersion has been developed. General relationships for a symmetrical axial dispersion correction and for a skewing correction are derived.The method has been verified experimentally for unimodal chromatograms and linear calibration curves over a wide range of GPC operating conditions, polymer molecular weights and polydispersities. Measurements of h and skewing factors were obtained by a once‐through technique. The need for performing reverse flow experiments has been eliminated. Artificial oscillations in the corrected chromatogram due to step size (Method of Pierce‐Armonas), and to number of terms in a polynomial expansion (Method of Tung and Method of Smith) are eliminated.The method has yet to be evaluated for nonlinear calibration curves and multi‐modal distributions. However, suggestions for its application in these circumstances are presented.

Elektronisches rechnen in der analytischen chemie—IV : Algol-prozedur für ausgleichsfunktionen mit zwei konstanten

Optimal functions to interpret the relationship between different series of experimental data measured for similar objects or processes can be found by least squares adjustments of systematically varied functions. The mathematical structure of a universally applicable equation with two constants has been developed, and also two reduced equations with only one constant each. A calculation procedure, named AUSGL 2, is given for it in the problem-oriented language ALGOL for electronic computing. This procedure is a cybernetic “black box” and is used as a closed block within a simple frame programme for special problems. Its practical use presupposes only a little mathematical knowledge. By means of briefly outlined examples of the application of the function to bi-, ter- and multivalent adjustment of corresponding series of analytical results, a partially novel approach to a rational test and evaluation technique is shown. In a comprehensive example a functional analysis is made of two flame-photometric test series for Na and K in concentration ranges which result-through self-absorption and self-reversal-in non-linear calibration curves. By a simple frame programme a total of 8 (2 × 4) functions can be electronically evaluated in less than 17 min, whereas the time needed for conventional calculation is more than 170 times as long.

Serum Lactic Dehydrogenase Activity: An Analytical Assessment of Current Assays

Abstract Serum LDH activities assayed spectrophotometrically by the "forward" (lactate + DPN to pyruvate + DPNH + H) method have linear reaction rates, activity proportional to the amount of serum added, and a reproducibility of 1.3%. The reagent mixture can be stored frozen for 6 months and in the lyophilized state indefinitely. Poor separation of normal from abnormal serum LDH activities results from the nonlinear calibration curves and decreasing reaction rates of the "backward" spectro-photometric assay. The dinitrophenylhydrazine colorimetric assay is deemed unsuitable for clinical use because large variations in activity result from minor variations in the reagent calibration curve, and because colorimetric activities are inaccurate as compared to activities obtained with the "forward" spectrophotometric assay.

オキシン抽出吸光光度法によるセリウムと共存する微量のトリウムの定量

A small amount of Th in the presence of large amount of Ce could be extracted quantitatively at pH 5 by oxine in benzene solution (1 g oxine/100 ml benzene). The extracted Th and free oxine in the benzene phase were then re- extracted by 0.6N HCl. A 0.1% aqueous solution of thorin was added to the acid extract and its absorbance at 545 m mu was measured using 1-cm cell. A slightly nonlinear but reproducible calibration curve was obtained. Samples containing more than 0.1% Th can be determined by this method. (H.H.D.)