Correction method for quantitative area determination of overlapping chromatographic peaks based on the exponentially modified Gaussian (EMG) model

A simple method is presented for peak area correction of overlapping peaks. This correction is necessary for the normal approach of dealing with overlapping peaks by a vertical line at the valley point. The relative area errors caused by this vertical line are calculated as the correction factors in three dimensions of peak separation, peak ratio, and peak tailing skew. The calculation is based on the exponentially modified Gaussian asymmetric peak model.     

Spline wavelet in the resolution of overlapping voltammetric peaks

Spline wavelet transform is used to resolve overlapping voltammetric peaks. A suitable resolving factor is chosen to multiply the filters of spline wavelet and make it a peak resoluter. Simulated overlapping voltammetric peaks are processed by the peak resoluter and satisfactory results are obtained. Base-line separation can be achieved, the relative errors of peak position are less than 3.0%, and the relative errors of peak area are less than 5.0%. The effect of different resolving factors and spline wavelet basis are discussed. To test the procedure, two systems, cadmium (Ⅱ)-indium (Ⅲ) and lead (Ⅱ)-thallium (Ⅰ), are used.     

Automated resolution of overlapping peaks in chromatographic data

Parallel factor analysis 2 (PARAFAC2) has been shown to be a powerful tool for resolution of complex overlapping peaks in chromatographic analyses. It is particularly useful because of its ability to handle shifts in the elution time mode and peak shape changes. Like all curve resolution techniques, PARAFAC2 will only find chemically meaningful parameters (elution time profiles and mass spectra) if the correct number of factors are determined. So far, the primary way to determine an appropriate number of factors, when using PARAFAC2, is to calculate models with different number of factors and then inspect the models manually. This approach is time consuming, and the result may be biased because of the manual assessment of the model quality, making PARAFAC2 inaccessible for analytical chemists in general. Here, we develop a method that can determine an appropriate number of factors in an automated way. The automation is based on a number of model diagnostics (quality criteria) collected from models with different numbers of factors. Combining these diagnostics, it is possible to assess what the appropriate number of components is. In this work, only gas chromatography–mass spectrometry data are considered. However, it will most likely be fairly straightforward to expand the work to also cover liquid chromatography data (with a multivariate detector). Automating the model quality evaluation of the PARAFAC2 model enables both the inexperienced and trained user to perform comprehensive and advanced analysis of chromatographic data with a minimum of manual work. © 2013 The Authors. Journal of Chemometrics Published by John Wiley & Sons Ltd.     

Extending the power transform approach for recovering areas of overlapping peaks

Power functions, , are embedded in some modern chromatography detectors and software which not only alter the linear dynamic range of such detectors but also improve the cosmetic aspects of the chromatograms. These aspects include a reduction in baseline noise, improved peak symmetry, and better resolution. However, after raising the electronic output of a detector to a selected power (n > 1), the original peak area information is lost as are very small peaks. Recent advances in the peak processing protocol allow us to recover peak areas from overlapping peak areas, even in noisy environments using power functions. One of the primary protocol requirements of this approach was to have resolution factors ≥0.9. An increasing positive bias in the recovered area was observed as the resolution factors decreased below 0.9. In this work, we extend the capabilities of power function to lower resolution values. This bias is addressed by considering the increasing contributions in peak height coming from adjacent peaks. It is shown that the power function can now be used as long as the peak maxima are visible, making  = 0.5, the lower treatable resolution factor for two peaks of similar areas.     

Cross-sections of spectrochromatograms for the resolution of overlapping peaks in diode-array high-performance liquid-chromatography

Multi-wavelength detectors offer improved detection capabilities for liquid chromatographic methods, but require multivariate approaches to utilise all the available information. The photodiode-array detector in high-performance liquid chromatography (HPLC) generates a three-dimensional data matrix, which is conventionally presented as an isometric projection or a contour plot. In this work, a new graphical technique is described for improving the quantitative results obtained from HPLC, using the available spectrochromatographic information in both the time and wavelength domains. The technique consists of performing cross-sections through the data matrix to obtain the maximum analytical information for each of the analytes. Hence, the resolution of overlapping peaks and the sensitivity in the determination are optimised. In order to demonstrate the validity and simplicity of the approach, the method has been applied to the resolution of synthetic mixtures of iprodione, procymidone and chlorothalonil. Also, the method has been satisfactorily applied to the simultaneous determination of the pesticides in environmental groundwater samples.     

Evaluation of the error in values of interatomic distances obtained by the method of radial distribution

Summary The maximum error in values of interatomic distances obtained with radial distribution curves can be calculated in each concrete case if the maximum error in the evaluation of the intensities of the reflections is known.     

Electrochemical determination of standard thermodynamic parameters characterizing resolvation of Cu2+ cations in water-acetone mixtures

Standard thermodynamic parameters characterizing the resolvation of the Cu²⁺ ions and the surface potential at the gas-phase/acetone interface, Δχ^Me ₂ ^CO, are determined on the basis of the results of measuring compensating voltages of the Volta circuits by the Kenrick method at 298.15 K and the value of the surface potential at the nonaqueous-solvent/gas phase interface, Δχ _H2O ^S , which was obtained earlier. A comparison of thermodynamic parameters characterizing the resolvation of the copper ions with similar quantities for the calcium and cadmium ions is performed. Specific features pertaining to the solvation of copper ions in a mixed water-acetone solvent are elucidated and the effect of the composition and nature of the mixed solvent on the quantities obtained is determined. A dependence of variations in the thermodynamic parameters characterizing the resolvation of cations on their charge and crystallographic radius is established. The dependence corresponds to the series K⁺, Ca²⁺, Cd²⁺, Cu²⁺.     

The separation of overlapping peaks in cyclic voltammetry by means of semi-differential transformation

A method for extracting single peaks from complex linear sweep and cyclic voltamperograms is presented. Voltamperograms are transformed by means of semidifferentiation, then all undesired peaks are removed from the semiderivative curve and replaced by calculated baselines. The resulting curve is semiintegrated back, giving a voltamperogram with one peak only. Baselines in the semiderivative domain are determined by the least-squares curve-fitting of datapoints from peak border regions, using the equation that describes the semiderivative peak of a reversible electrode process. With this procedure peaks can be removed without assumptions about the mechanism of the underlying electrode reaction. Due to its design, the algorithm presented is suitable for the fully automatic processing of cyclic and linear sweep voltamperograms. Performance of the procedure was checked with generated reversible voltamperograms as well as in real experiments with both reversible and irreversible systems. The smallest distance between two peaks of equal height, for which the described method can yield correct results, has been found to be 110 mV for a reversible one-electron process at 298 K. This procedure can also be applied to the elimination of the cathodic current from the cyclic voltamperogram of a single component in order to get a pure anodic current value, free from cathodic contribution, or vice versa.     

Quality assurance in the determination of overlapping peak areas

The ability of different computer programs to yield accurate peak areas in statistical control in the case of partially overlapping photopeaks has been tested by the Analysis of Precision. A modified Covell method, two commercially available peak-fitting programs from Nuclear Data and Ortec, and the SAMPO80 program were used to evaluate the 843.8 keV peak area in the 843.8/846.6 keV doublet of²⁷Mg and⁵⁶Mn produced by thermal neutron activation of a candidate biological reference material to be certified for magnesium. The best performance was given by the Ortec program, but a modified SAMPO80 performed almost as well. The modified Covell program gave reliable results, but with poorer precision.     

The investigation of the resolution enhancement transformation and the analysis of complex overlapping peaks in gamma-ray spectra

A method is proposed for the resolution enhancement transformation (RET) of the γ-ray spectrum, which is not only a simple convolution operation but also have a definite analytical significance because of the introduction of the parameter ω representing the degree of the resolution enhancement. We apply the RET to the peak detection method for complex overlapping peaks. The validity of this method is ascertained by the analysis of X-ray overlapping peaks.     

Measurement of voltammetric peak area and resolution of overlapping peaks in the simultaneous determination of copper, lead, cadmium, and nickel in environmental matrixes

Peak area was used for the simultaneous determination of copper(II), lead(II), cadmium(II), and nickel(II) in environmental matrixes by differential pulse voltammetry. The voltammetric measurements were performed with a conventional 3-electrode cell and an ammonia-ammonium chloride buffer, pH 9.1, as the supporting electrolyte. The analytical procedure was verified first in aqueous reference solutions and later by analysis of the standard reference materials Estuarine Sediment BCR-CRM 277 and River Sediment BCR-CRM 320. The precision and accuracy of the method, expressed as the relative standard deviation and the relative error, respectively, were <5% in all cases; the detection limit for each element under the experimental conditions used was in the range 1-5 microg/L. In the case of mutual interference between neighboring elements, an analytical procedure is proposed that is based on the standard additions technique, which allows the resolution of the overlapping voltammetric peaks.     

Accurate determination of pyridine-poly(amidoamine) dendrimer absolute binding constants with the OPLS-AA force field and direct integration of radial distribution functions

OPLS-AA force field and direct integration of intermolecular radial distribution functions (RDF) were employed to calculate absolute binding constants of pyridine molecules to amino group (NH2) and amide group hydrogen atoms in and first generation poly(amidoamine) dendrimers in chloroform. The average errors in the absolute and relative association constants, as predicted with the calculations, are 14.1% and 10.8%, respectively, which translate into ca. 0.08 and 0.06 kcal/mol errors in the absolute and relative binding free energies. We believe that this level of accuracy proves the applicability of the OPLS-AA, force field, in combination with the direct RDF integration, to reproducing and predicting absolute intermolecular association constants of low magnitudes (ca. 0.2-2.0 range).     

Mass analysis of overlapping ion kinetic energy peaks arising from charge separation in dications

A triple-sector instrument of reversed geometry, BEQQ, has been employed to resolve overlapping ion kinetic energy peaks arising from charge separation of metastable dications. Separation was achieved through mass resolution of the dication in the magnetic sector and of the singly charged product ion of greater mass in the quadrupole mass filter accompanied by energy resolution with the electric sector; the electric sector was scanned to cover the complete range of each charge separation peak. Two overlapping ion kinetic energy peaks arising from charge separation of the diphenylenimine dication and up to four overlapping ion kinetic peaks arising from charge separations of dications arising from benzene-1,3,5-d₃ have been resolved. The kinetic energy releases have been calculated in each case. Enhanced z-discrimination is observed with the final stage of mass analysis.     

Determination of ebrotidine metabolites in overlapping peaks from capillary zone electrophoresis using chemometric methods

This paper illustrates the possibilities of chemometric methods in the resolution and quantification of various compounds in overlapping peaks from capillary electrophoresis. Ebrotidine and most of its metabolites were efficiently separated by capillary zone electrophoresis (CZE) in a fused-silica capillary. However, the procedure was not suitable for the physical separation of the three less ionizable metabolites, which comigrated and overlapped with the electroosmotic flow signal. Multivariate curve resolution based on an alternating least squares procedure was used for their mathematical resolution. For such a purpose, data obtained in the CZE system with a diode array detector, which consisted of UV spectra registered over time, were analyzed. The ebrotidine metabolites were successfully resolved and quantified in synthetic mixtures and urine samples.     

Use of a data treatment software for the resolution of overlapping differential pulse polarographic peaks

Summary A procedure based on the use of the Beckman Data Leader Software is proposed for resolving binary mixtures of electroactive analytes when their differential pulse polarographic peaks are overlapping without any separation step. The resolution is made by measuring in the selected zero-crossings of the first derivative differential pulse polarograms. For testing the procedure, two well-known systems were used, cadmium (II)-indium (III) and thallium (I)-lead (II) mixtures. The four metallic ions can be determined in diverse ratios with quantification limits lower than 10^–7 mol/l.