Modeling of analytical peaks: peaks properties and basic peak functions

The general approach to the detailed characterizing of peak properties based on the use of characteristic points on a peak contour located at the certain levels is proposed. Three basic functions of peaks have been chosen which are submitted in normalized form on height and width. The ability to characterize a peaks shape of a certain analytical series is shown by an example of series of analytical peaks of thallium obtained by stripping voltammetry at linear and step potential sweep. Also the proposed shape parameters are studied for groups of stripping voltammetry and chromatographic peaks.     

Mathematical functions for the representation of chromatographic peaks.

About ninety empirical functions for the representation of chromatographic peaks have been collected and tabulated. The table, based on almost 200 references, reports for every function: (1) the most used name; (2) the most convenient equation, with the existence intervals for the adjustable parameters and for the independent variable; (3) the applications; (4) the mathematical properties, in relation to the possible applications. The list includes also equations originally proposed to represent peaks obtained in other analytical techniques (e.g. in spectroscopy), which in many instances have proved useful in representing chromatographic peaks as well; the built-in functions employed in some commercial peak-fitting software packages were included, too. Some of the most important chromatographic functions, i.e. the Exponentially Modified Gaussian, the Poisson, the Log-normal, the Edgeworth/Cramér series and the Gram/Charlier series, have been reviewed and commented in more detail.     

Three-dimensional representation of metastable peaks at high mass resolution

Isobaric daughter ions formed from a common metastable ion have been analysed at high mass resolution. A three-dimensional representation is used to summarize the data for competitive CO and C₂H₄ losses and competitive CHO˙ and C₂H₅˙ losses from metastable molecular ions of cyclohexanone.     

New approaches to the calculation and interpretation of asymmetry factors of chromatographic peaks

The suitability of the determination of the asymmetry factor of chromatographic peaks by the ratio of areas of two components separated by a perpendicular dropped from the maximum of the peak to the base-line, A _s * = S _b /S _a , where symbol a corresponds to the leading edge of the peak and b is for its tailing slope, is discussed. It is demonstrated that this method enables the estimation of the asymmetry of even partially separated chromatographic signals, including those eluted “in the tail” of intense peaks of solvents. The concepts of the asymmetry index I(A _s *) and its increment ΔI(A _s *) = (A _s *)–I(A _s *) are introduced, which ensures the characterization of the asymmetry of peaks of polar analytes with respect to the asymmetry of nonpolar reference components, that is, the separation of the effects of the polarity of analytes and their quantities injected into the chromatographic column on this parameter. For the first time we revealed a correlation of the asymmetry factors of compounds of different chemical nature with such a characteristic of their polarity as the difference in chromatographic separation temperature and the normal boiling point of analytes.     

A three-dimensional representation of metastable peaks from double focusing mass spectrometers

The ion current transmitted by the collector slit of a double focusing mass spectrometer is considered as a function of two variables which independently reflect the effects of the instrument's electric and magnetic sectors. The ionic products of reactions occurring in the source and in various regions of the flight tube give rise to peaks or ridges with distinctive shapes and positions in the surface so derived. Volumes under peaks are proportional to abundances of ions. The surface provides a unified view of the alternative methods of scanning and facilitates understanding of the contrasting perspectives of metastable peaks which they reveal. The method, which may be applied with instruments of either conventional or reversed geometry, is illustrated for the former by reference to that part of the surface for toluene which relates to the loss of H from the molecular ion.     

A new and consistent parameter for measuring the quality of multivariate analytical methods: Generalized analytical sensitivity

Generalized analytical sensitivity (γ) is proposed as a new figure of merit, which can be estimated from a multivariate calibration data set. It can be confidently applied to compare different calibration methodologies, and helps to solve literature inconsistencies on the relationship between classical sensitivity and prediction error. In contrast to the classical plain sensitivity, γ incorporates the noise properties in its definition, and its inverse is well correlated with root mean square errors of prediction in the presence of general noise structures. The proposal is supported by studying simulated and experimental first-order multivariate calibration systems with various models, namely multiple linear regression, principal component regression (PCR) and maximum likelihood PCR (MLPCR). The simulations included instrumental noise of different types: independently and identically distributed (iid), correlated (pink) and proportional noise, while the experimental data carried noise which is clearly non-iid.     

Design and characterization of a direct current glow discharge lamp for analytical applications

This paper describes a compact, small volume direct current glow discharge lamp operating at low wattage for atomic emission spectrometric analysis and its process optimization for copper and brass solid samples. The design aspects, fundamental characteristics and analytical performance are described in detail. The discharge is observed end-on, with water-cooled cathode surface parallel to the spectroscopic entrance slit. The anode diameter is 7 mm and the minimum sample diameter required is 20 mm. The sample is located outside the lamp for easy access and interchangeability. The lamp is powered by a dc power supply capable of delivering 300 mA (max.) and 1500 V. The studies of fundamental characteristics include the current-voltage relationship and their dependence on pressure and the emission intensity of copper spectral line (324.7 nm). The studies were made in the pressure range of 2-7 mbar. Long-term stability of optical emission spectra was also recorded to be within ±0.75%. The performance of the lamp is quite linear in the pressure range 3.5-7 mbar at an applied voltage of about 450 V.     

Orbital electronegativity and analytical representation of atom valence state energy

An analytical representation of atom valence state energy (E(n_j), j = 1,…?4; E(n_j) is a nonlinear function of orbital occupancy numbers n_j) is proposed and explicitly derived for H? Ar; the values of electronegativity calculated based on E(n_j) agree within truncation error with those of Hinze and Jaffe. However, in our representation, orbital electronegativity χ and hardness parameters η of a given orbital always include nonlinear contributions from other orbitals, hence accounting for their influence on χ and η. An atomic charge calculation procedure based on E(n_j) is also described and shown to perform well.     

The laser as an analytical probe in glow discharge mass spectrometry

A pulsed dye laser was used alone and in combination with an auxiliary glow discharge for diagnostic studies. We have compared the mass ablation rate and ion signal in high vacuum and in the presence of an ambient buffer gas. Laser pulse energy and repetition rate were studied over the analytical range of the system. The effect of ambient gas pressure on redeposition was determined for three different gases: helium, neon, and argon. The laser/auxiliary discharge system was also shown to have analytical utility for the analysis of nonconducting samples. Spectra are included to illustrate the enhancement of the laser atomization/discharge ionization scheme over laser atomization/ionization.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria     

The use of matrix-specific calibrations for oxygen in analytical glow discharge spectrometry

The performance of glow discharge optical emission spectroscopy and mass spectrometry for oxygen determination is investigated using a set of new conductive samples containing oxygen in the percent range in three different matrices (Al, Mg, and Cu) prepared by a sintering process. The sputtering rate corrected calibrations obtained at standard conditions for the 4 mm anode (700 V, 20 mA) in GD-OES are matrix independent for Mg and Al but not for Cu. The importance of a “blue shifted” line of oxygen at 130.22 nm (first reported by Köster) for quantitative analyses by GD-OES is confirmed. Matrix-specific calibrations for oxygen in GD-MS are presented. Two source concepts—fast flow (ELEMENT GD) and low gas flow (VG9000)—are evaluated obtaining higher sensitivity with the static flow source. Additional experiments using Ar-He mixtures or μs pulsed GD are carried out in ELEMENT GD aiming to improve the oxygen sensitivity.     

Comparison of Ar and Ne as working gases in analytical glow discharge mass spectrometry

Summary Glow discharge mass spectrometry shows promising analytical performance, in particular low detection limits. Its application is impeded by problems with molecular interferences, a major group of which is made up by argides. Problems of this type can be eliminated effectively by use of alternative working gases. Investigations have been made concerning the application of Ne as alternative working gas in comparison with the commonly used Ar. Differences in spectral interferences are discussed with the example of spectra of a very pure Fe standard sample. Influence of pressure and power variation on elemental sensitivities and analytical figures of merit has been studied. Nearly equal values of the electrical parameters with similar analytical performance can be realized with both gases if a correspondingly lower pressure is chosen for Ar. Pressure dependence enables two different analytical operation modes: one to give highest detection power and precision, and the other to give better accuracy in case of a semiquantitative analysis which does not require standards or knowledge of sensitivity factors.

---

Vergleich von Ne und Ar als Arbeitsgase in der analytischen Glimmentladungs-Massenspektrometrie

---

Dedicated to Prof. Dr. Günther Tölg on the occasion of his 60th birthday     

Systematic study of elementary models of analytical signals in the form of peaks and waves

An analytical signal represented as a symmetrical peak or a corresponding integral curve (wave) was described using three elementary functions: Gaussian function, derivative of a logistic function, and Cauchy function. The shape and geometric properties of such an analytic peak were characterized by a triangular frame formed by the tangents at the inflection points and the asymptotes to peak branches. In the case of a wave, a frame formed by the tangent at the inflection point of the wave and the asymptotes to its lower and upper branches was used for the same purpose. The use of the shape of differential curves as increments for physicochemical calculations was discussed.     

An accurate analytical representation for the electron screening function

The screening function Φ [ = V_ee(R) - V_ee(∞)], a key quantity in the theory of isoelectronic molecules, has been given an accurate analytical representation for a large number of states of the species Na₂, Na₂⁺ Li₂ and Li₂⁺. The election-electron repulsion V_ee at various internuclear distances has been obtained from high-quality MC SCF/SCF wavefunctions.     

Electronic tongues and their analytical application

Electronic tongues for liquid analysis, based on the organizational principles of biological sensory systems, developed rapidly during the last decade. A brief historical overview of the research and development in the field of electronic tongue systems is presented. Current achievements of scientific groups working in this field are outlined and critically reviewed. The performance of electronic tongues in quantitative analysis and in classification of multicomponent media is considered. The exciting possibility of establishing a correlation between the output from an electronic tongue and human sensory assessment of food flavour, thereby enabling quantification of taste and flavour, is described. Application areas of electronic tongue systems including foodstuffs, clinical, industrial, and environmental analysis are discussed in depth. Prospective research and development in the field of electronic tongues is discussed.     

System peaks and their positive and negative aspects in chromatographic techniques

Whenever a mobile phase contains more than one component, additional signals commonly called system peaks can appear. The origin of these signals is explained through loss of equilibrium in the separation column caused by injection of analyte dissolved in a different solvent than the mobile phase. The system peaks are then generated by a relaxation process started by the non-equilibrium state. An overview of the theory and applications of the system peaks in separation methods, mainly in liquid chromatography, is presented in this paper. Only a brief theoretical discussion of the system peak origin is given as the theoretical aspects of system peak formation have already been published in many papers. The main focus of this review is to summarize applications, in which system peaks were used to measure physical or physicochemical data. Signals of system peaks are often misinterpreted but they offer valuable information about thermodynamics and kinetics of the separation process that takes place in chromatographic column.     

Present and future of glow discharge — Time of flight mass spectrometry in analytical chemistry

The coupling of glow discharges (GDs) as ion sources for time of flight mass spectrometry (TOFMS) chemical analysis has been extensively investigated during the last two decades. However, important instrumental advances in GD-TOFMS as well as demonstration of unique analytical applications (particularly quasi-simultaneous production of elemental, structural and molecular information from organics in gas phase, multielemental depth profile analysis with high depth resolution of layered materials, direct speciation in solid samples and identification of polymers) are rocketing in the last years.In the present review, instrumental developments and recent applications of GD-TOFMS are presented, both for the elemental and molecular direct solid analyses of materials and for analytes in gaseous phase (including permanent gases, vaporized compounds and GD-TOFMS uses as detector for gas chromatography). Also, GD-TOFMS analytical potential in important fields of modern research is critically discussed.     

Influence of the anode material on the characteristics of an analytical glow discharge cell

The energy transfer to the discharge gas due to various collision processes in the plasma and the heating of the sample are widely known effects in glow discharge (GD) spectroscopy. Despite of the considerable thermal effects and their serious influence on the performance of GD devices, measurements of the discharge gas and sample temperatures are not common at all. The gas temperature depends on the power absorption of the discharge as well as on the temperature of boundaries (sample and anode). In this work the influence of different anode materials in a Grimm-type source on the voltage–current characteristics, crater shapes and GD spectra is investigated. Anodes made of titanium and copper alloys, graphite, and steel with thermal conductivities covering a wide range of values are used. For a fixed voltage and pressure a decrease of the measured current is observed for bad thermal conductive anodes. Cooling of the sample results in an increase of the measured current. Both observations can be explained by changes of the discharge gas temperature. The temperature of the sample is measured from the back side and compared for different anodes. Further, it is found that the choice of the anode material (i) has no significant influence on the crater shape, (ii) results in slightly different sputtering rates and (iii) strong differences of the GD spectra.