The peak width of nearly Gaussian peaks

Summary In chromatography the peak shape is often described by the method of statistical moments and therefore the second central moment is considered as the correct measure of peak width. Using the exponentially modified Gaussian peak model as an example and a criterion more related to chromatography, the extent of separation, it is shown that for nearly Gaussian peaks the width measured at 1/8 of the peak height is a more meaningful width parameter to evaluate the efficiency of chromatography and the resolution. The second central moment gives too much weight to the remote parts of the tail of the usual, somewhat skewed, peak.     

Temporally convoluted Gaussian equations for chromatographic peaks

Both spatial and temporal peaks that are produced by the discrete parcel model can be mathematically approximated by Gaussian functions, but the transformation from a spatial pattern to a temporal image requires a convolution treatment. A first-order convolution is given for temporal peaks under a linear isotherm, whereas a second-order convolution is proposed for those under non-linear isotherms. Numerical tests show that the peak shapes generated by the proposed temporally convoluted Gaussian equations (TCG) match perfectly with those obtained by the discrete parcel model. Although the full TCG equation may be quite complicated, it can be made easier by a recursion calculation technique, and a group of peak curves can be plotted simultaneously on computer worksheet. The results also suggest that the temporal distortion effect should be predominately considered, in addition to those known-to-exist spatial effects, for explaining the peak asymmetry.     

Investigation of peak compression effects in packed column supercritical fluid chromatography using chemometrics

Summary In this paper chemometrics have been used to study and characterize peak compression phenomena in packed column SFC. A carbon dioxide/2-methyl-1-propanol mobile phase was used in the experimental design (modifier concentration, temperature and pressure) and modelling part of the investigation. A cubic interaction term was needed in the model to obtain a reasonable fit, suggesting that all three parameters are of significance in terms of controlling peak compression. At the optimum conditions derived from the model a narrow peak was obtained as predicted.     

Factors affecting peak shape in comprehensive two-dimensional gas chromatography with non-focusing modulation

In the case of a non-focusing modulator for comprehensive two-dimensional gas chromatography (GC × GC), the systematic distortions introduced when the modulator loads the second-dimension column give rise to a characteristic peak shape. Depending on the operating conditions this systematic distortion can be the dominant component of the second-dimension elution profiles in the GC × GC peak. The present investigation involved a systematic investigation of peak shape in pulsed-flow modulation (PFM)–GC × GC. It is shown that low flow ratio can lead to significant peak skewing and increasing the flow ratio reduces the magnitude of peak skewing. Validation of the peak shape model is made by comparison with experimental data. The residuals from the fitting process (normalised to the maximum detector response) vary between –1.5% and +2.6% for an isothermal model and between –1.0% and +3.0% for a temperature-programmed model.     

The analytical and chemometric procedures used to profile illicit drug seizures

Over the last 20 years there has been an increasing interest in the development of robust systems, both analytical and statistical, to enable the linkage of seizures of illicit drug to each other. Much of this work has concentrated on the analysis of synthetic drugs, such as amphetamine and its analogues. In recent years, the analysis of both organic and elemental impurities as well as isotope ratios has advanced the usefulness of the techniques available. The application of specific chemometric methods to the derived analytical data has begun to provide the possibility of robust methods by which the resultant information can be interrogated.     

Testing the capability of a polynomial‐modified gaussian model in the description and simulation of chromatographic peaks of amlodipine and its impurity in ion‐interaction chromatography

In this paper, the capability of a polynomial‐modified Gaussian model to relate the peak shape of basic analytes, amlodipine, and its impurity A, with the change of chromatographic conditions was tested. For the accurate simulation of real chromatographic peaks the authors proposed the three‐step procedure based on indirect modeling of peak width at 10% of peak height (W_0.1), individual values of left‐half width (A) and right‐half width (B), number of theoretical plates (N), and tailing factor (Tf). The values of retention factors corresponding to the peak beginning (k_B), peak apex (k_A), peak ending (k_E), and peak heights (H₀) of the analytes were directly modeled. Then, the investigated experimental domain was divided to acquire a grid of appropriate density, which allowed the subsequent calculation of W_0.1, A, B, N, and Tf. On the basis of the predicted results for Tf and N, as well as the defined criteria for the simulation the following conditions were selected: 33% acetonitrile/67% aqueous phase (55 mM perchloric acid, pH 2.2) at 40°C column temperature. Perfect agreement between predicted and experimental values was obtained confirming the ability of polynomial modified Gaussian model and three‐step procedure to successfully simulate the real chromatograms in ion‐interaction chromatography.     

Study of peak shape and efficiency in butyl acrylate-based monolithic columns for capillary electrochromatography

The study and modelling peak shape of in capillary electrochromatography (CEC), obtained using butyl acrylate (BA)-based monolithic columns, is described in this article. A modified-Gaussian model, which is a function of conventional experimental parameters: retention time (t_R), peak height (H₀) and standard deviation (σ₀) at the peak maximum, and left (A) and right (B) halfwidths, was used to describe the peaks of thiourea and several polyaromatic hydrocarbons compounds, which were eluted under several applied voltages. A mean relative error below 2% in the prediction of peak shape is obtained. Based on peak parameters, an easy and reliable estimation of global chromatographic performance, efficiency and peak capacity of BA-based monoliths was also considered. A comparison in terms of chromatographic performance of BA-based monoliths in CEC with CE mode and RPLC microparticulate columns was also performed.     

Recognizing chromatographic peaks with pattern recognition methods III. Application of the algorithm for peak recognition in trace analysis

Summary The application of a newly developed peak recognition algorithm is shown. This algorith is based on the KNN method, one of the pattern recognition methods. It is shown that peaks with a S/N-ratio down to one can be safely recognized. This is also possible if the baseline has not only detector noise, but has other disturbances, e.g., noise signals which are generated by a reaction detector. The recognition ability of the algorithm is demonstrated by a standard chromatogram with three different concentrations and with two different sampling rates. The improvement against the classical algorithm is demonstrated. Some properties of the algorithm are discussed.     

Effect of injected sample amount on the shape of chromatographic peaks under condition of linear partition isotherm

In a previous paper a model function was tested in order to approximate the peak shape obtained on non-polar column by injecting different compounds. The simulation of the symmetrical or non-symmetrical shape of gas chromatographic peaks was satisfactory. In this paper, the influence of the amount of injected substance was investigated at different values of inlet pressure and carrier gas velocity, in order to evaluate the relative contribution to the total peak area and shape of the symmetrical distribution due to partition phenomena and of the non-symmetrical and tailing distribution due to adsorption-desorption kinetics. The effect of the molecular mass and of the chain length of compounds belonging to the homologous series of 1-alcohols and n-alkanes on the adsorption phenomena was evaluated.     

Influence of solvent properties on separation and detection performance in non-aqueous capillary electrophoresis-mass spectrometry of basic analytes

The versatility of non-aqueous capillary electrophoresis (NACE) results mainly from the variety of physico-chemical properties of the different solvents. They provide solubility for a wide range of analytes, enable to control electrophoretic selectivity, but affect in some cases UV absorbance detection. The coupling of NACE to electrospray mass spectrometry (ESI-MS) allows to cope with the high UV cut-off of some CE relevant solvents (e.g., formamides). In this paper the pure organic solvents methanol, acetonitrile, dimethylsulfoxide, formamide, N-methylformamide and N,N-dimethylformamide are evaluated against water for the preparation of ammonium acetate electrolytes to separate the basic model substances 2-aminobenzimidazole, procaine, propranolol and quinine with NACE-MS. MS coupling is assisted with the sheath liquid water-isopropanol (1:4, v/v) with 0.1% formic acid. The goal of the paper is to assess the influence of the solvent on selectivity, separation speed, and peak efficiency for a given set of model compounds on a simple empirical basis. It should give the user an idea how the separation quality is changed when nothing but the running solvent is altered. The obtained efficiency results were discussed with respect to physico-chemical models described in literature (assuming longitudinal diffusion as the only source of band broadening), but no satisfying correlations with solvent properties could be traced. The feasibility of all six organic solvents for MS coupling was demonstrated and the influence of the separation solvent on the MS detection performance was compared. In the seven different solvents, the shortest run time was obtained with acetonitrile, the best peak resolution with the amphiprotic solvents (especially methanol) best peak efficiency with methanol and formamide, and the most sensitive ESI-MS detection with acetonitrile and methanol, but with only slight advantage to water.     

Automated methods for the location of the boundaries of chromatographic peaks

Several simple techniques are presented for the identification of the boundaries of chromatographic peaks. These methods provide a significant reduction in the time needed to perform the rapid, automatic calculation of the central peak moments and to evaluate the quality of a separation while improving the accuracy of the measurements of column efficiencies. It was found that the identification of the peak boundaries as functions of the peak widths and the examination of the slope of the signal to noise versus time plot are viable alternatives to a manual determination.     

Multivariate data analysis approach to understand magnetic properties of perovskite manganese oxides

Here we apply statistical multivariate data analysis techniques to obtain some insights into the complex structure-property relations in antiferromagnetic (AFM) and ferromagnetic (FM) manganese perovskite systems, AMnO₃. The 131 samples included in the present analyses are described by 21 crystal-structure or crystal-chemical (CS/CC) parameters. Principal component analysis (PCA), carried out separately for the AFM and FM compounds, is used to model and evaluate the various relationships among the magnetic properties and the various CS/CC parameters. Moreover, for the AFM compounds, PLS (partial least squares projections to latent structures) analysis is performed so as to predict the magnitude of the Néel temperature on the bases of the CS/CC parameters. Finally, so-called PLS-DA (PLS discriminant analysis) method is employed to find out the most influential/characteristic CS/CC parameters that differentiate the two classes of compounds from each other.     

Peak half-width plots to study the effect of organic solvents on the peak performance of basic drugs in micellar liquid chromatography

The addition of the anionic surfactant sodium dodecyl sulphate (SDS) to hydro-organic mixtures of methanol, ethanol, propanol or acetonitrile with water yielded enhanced peak shape (i.e. increased efficiencies and symmetrical peaks) for a group of basic drugs (β-blockers) chromatographed with a Kromasil C18 column. The effect can be explained by the thin layer of surfactant associated to the hydrocarbon chain on the stationary phase in the presence of the organic solvents, which covers the free silanols on the siliceous support avoiding their interaction with the cationic basic drugs. These instead interact with the anionic head of the surfactant increasing their retention and allowing a more facile mass transfer. The peak shape behaviour with the four organic solvents (methanol, ethanol, propanol and acetonitrile) was checked in the presence and absence of SDS. The changes in peak broadening rate and symmetry inside the chromatographic column were assessed through the construction of peak half-width plots (linear relationships between the left and right half-widths at 10% peak height versus the retention time). The examination of the behaviour for a wide range of compositions indicated that the effect of acetonitrile in the presence of SDS is different from ethanol and propanol, which behave similarly. Acetonitrile seems to be superior to the alcohols in terms of peak shape, which can be interpreted by the larger reduction in the adsorbed surfactant layer on the C18 column. However, the decreased efficiencies observed at increasing surfactant concentration in the mobile phase should be explained by the reduction in retention times, more than by a change in the stationary phase nature.     

The role of the theoretical plate concept and gamma density functions in studies on mass transport and mass loadability of chromatographic columns

Summary The validity of the use of the plate theory in transport processes with non-Gaussian peak shapes is discussed. It is shown that the application of the plate theory implies the assumption of a peak with a gamma density shape which, however, converges rapidly to symmetrical Gaussian shape for large plate numbers. A proposal for an extension of the plate theory, based on a gamma density function is given. This approach results in an extra parameter which characterizes the asymmetry of a peak. Use of the suggested fitting function permits an estimate of the moments of the peak, even without the use of a computer. The proposed model can be used to determine a transfer function for the chromatographic system, allowing a system theoretical approach to determine the influence of, for example, amplifiers, filters and detectors on the peak shape. The exponentially modified Gauss (EMG) is one of the possible peak shapes included in the model.     

Influence of the peak height distribution on separation performances: Discrimination factor and effective peak capacity

Summary A new index of performance of the chromatographic separation between two adjacent peaks, the discrimination factor, d₀, is defined. It is normalized between 0 and 1 and is directly and easily determined from the chromatogram. It does not depend on any assumption regarding peak shape, except that the peak profiles of individual sample components have a single mode. Its value depends on the relative heights of the two peaks as well as on their separation. The separation power of a chromatographic system is classically measured by its peak capacity, defined on the basis of constant resolution between adjacent peaks. A previously developed statistical theory of the composition of mixtures makes it possible to extend the concept of peak capacity by taking into account the peak height distribution in typical average chromatograms. A new parameter, the effective peak capacity, is defined for this purpose on the basis of a constant discrimination factor between adjacent peaks. It allows to take into account the distribution of peak heights in statistical theories of the evaluation of complex chromatograms and in the measurement of the limit of determination in quantitative analysis. The characteristics of the two new parameters, the discrimination factor and effective peak capacity, are discussed and compared with those of their classical homologs, resolution and peak capacity, in the case of gaussian component peaks of equal widths.     

Modeling mechanical properties of polyhydroxyalkanoate during degradation in animal tissue

Polyhydroxyalkanoates (PHAs) are a family of biodegradable and biocompatible polymers produced by several species microorganisms that possess favorable mechanical properties (e.g. strength and elongation properties). Different types of PHA polymers have been used in medical applications. However, in order to better understand the use of this polymer in the different applications, a thorough understanding of the kinetics of in vivo degradation is one of the major requirements. In this study, poly(3‐hydroxybutyrate) (PHB) was subcutaneously implanted in mice and incubated for 2, 4, 8, or 16 weeks. After removal from the animal, the strength, elongation, mass loss, and enthalpy of the PHB were tested for each time point. From these data, a mathematical model was generated by Rayleigh's method of dimensional analysis, where polymer strength over tissue contact time could be predicted. To prove the model, previous data obtained by our group were used: poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate) [P(HB‐co‐HHx)] incubation in the presence of human embryonic kidney cells (HEK). It was found that the developed model was aligned with experimental results, could predict the strength of the polymer when in contact with cells, and the predicted strength follows the trend of the experimental data. Also, the dimensionless constant (K) value associated with the model is different for both experiments, where this constant, produced via experimental data, is used for construction of a homogeneous equation. Copyright © 2017 John Wiley & Sons, Ltd.     

Advanced ceramics and their basic products: A challenge to the analytical sciences

The analytical characterization required in the development and in the quality control of new ceramics is discussed. For the basic substances, the problems encountered in the development of routine techniques for a direct and reliable analysis of Al₂O₃, AlN, Si₃N₄, SiC, and ZrO₂ powders are reported. Among the atomic spectrometric methods, especially slurry atomization ICP-spectrometry is described. Also the problems encountered in the development of combined procedures as required for the characterization of reference samples are presented. Methods for the direct bulk analysis of ceramics and microdistributional analysis, as they are now under development with laser-based techniques and various probe techniques, are described as well.     

Broadening of peaks eluted before the solvent in capillary GC Part II: The role of phase soaking

Summary Phase soaking is a solvent effect which tends to reconcentrate peaks eluted after and to broaden peaks eluted before the solvent. The principles of the phase soaking effect on peaks eluted before the solvent are discussed. The broadening effect is distinguished from the broadening effect occurring in the flooded column inlet by partial solvent trapping. It was found that in most cases broadening by partial solvent trapping strongly predominated over broadening by phase soaking. Phase soaking was noticeable only in the neighbourhood of the solvent peak.Phase soaking does not broaden peaks eluted before the solvent as much as it re-concentrates those eluted after it. The two phase soaking effects on the front and the rear of the solvent band (that is, of the soaked zone) differ strongly from each other.Peak broadening by phase soaking is negligible for non-trapped components, because such solutes start their chromatography before a significant quantity of solvent enters the column. Phase soaking only broadens solute bands which were retained by the solvent in the column inlet, that is, bands already broadened by partial solvent trapping.     

Mutual peak matching in a series of HPLC–DAD mixture analyses

One of the largest challenges in high performance liquid chromatography (HPLC) method development is the necessity for tracking the movement of peaks as separation conditions are changed. Peak increments are then used to build a mathematical model capable of minimizing the number of experiments in an optimization circuit. Method optimization for an unknown mixture is, moreover, complicated by the absence of any a priori information on component properties and retention times when direct signal assignment is not possible. On the contrary, achievement of the maximum separation becomes an important factor for successful identification or quantitation. In this case, the optimization may be based on assigning peaks of the same component chosen from different experiments to each other. In other words, mutual peak matching between the HPLC runs is required.

A new method for mutual peak matching in a series of HPLC with diode array detector (HPLC–DAD) analyses of the same unknown mixture acquired at varying separation conditions has been developed. This approach, called mutual automated peak matching (MAP), does not require any prior knowledge of the mixture composition. Applying abstract factor analysis (AFA) and iterative key set factor analysis (IKSFA) on the augmented data matrix, the algorithm detects the number of mixture components and calculates the retention times of every individual compound in each of the input chromatograms. Every candidate component is then validated by target testing for presence in each HPLC run to provide quantitative criteria for the detection of “missing” peaks and non-analyte components as well as confirming successful matches. The matching algorithm by itself does not perform full curve resolution. However, its output may serve as a good initial estimate for further modeling. A common set of UV-Vis spectra of pure components can be obtained, as well as their corresponding concentration profiles in separate runs, by means of alternating least-square multivariate curve resolution (ALS MCR), resulting in reconstruction of overlapped peaks.

The algorithms were programmed in MATLAB^® and tested on a number of sets of simulated data. Possible ways to improve the stability of results, reduce calculation time, and minimize operator interaction are discussed. The technique can be used to optimize HPLC analysis of a complex mixture without preliminary identification of its components.