Quantitative impurity profiling by principal component analysis of high-performance liquid chromatography-diode array detection data

Related organic impurities generally have approximately similar molar absorption coefficients (epsilon) due to their structural similarities. On the assumption that all peaks in an impurity profiling chromatogram have approximately the same maximum molar absorption coefficients (epsilon(max)) and the chromatogram contains one major peak and several much smaller ones, all of which are completely separated, integration of the summed score vectors from the principal component analysis (PCA) decomposition of high-performance liquid chromatography-diode array detection (HPLC-DAD) data will give areas that are quantitatively proportional to the actual content of the compounds. Due to the sequential nature of PCA, the first principal component (PC) will primarily be related to the main compound and all peaks showing a similar spectrum, while the second PC will be related to the impurities with a spectrum different from the main peak. Summing the two score vectors thus makes it possible to take account of different spectra in the score chromatogram, which make the method proposed give better quantitative estimates of the impurities than any single wavelength chromatogram. Multivariate curve resolution alternating least squares (MCR-ALS) is used for comparison. The results are presented for two examples of simulated HPLC-DAD data as well as for three examples of real HPLC-DAD data from impurity profiling. The results show that integration of the score chromatograms can handle differences in the unknown epsilon(max) of the peaks and take account of the different spectra of the impurity peaks, giving quantitative estimates of the content of the impurities that closely correspond to the reference values. The results obtained are also better than integration with the best possible separate wavelength. The method could be a straightforward approach to impurity profiling in order to obtain a good estimate of the content or relative response factors of small chromatographic impurity peaks without knowledge of their molar absorption coefficients and without any precalibration.     

Recycling Technique in Preparative Liquid Chromatography

Abstract

A theoretical and practical study of recycling technique is developped for preparative liquid chromatography. The optimal cycle number, n_opt, is determined for the separation of two solutes in such a way that the resolution between the second peak of cycle (n-1) and the first one of cycle n is equal to the resolution between the peaks of cycle n. A simple relationship is propounded to determine n_opt which only depends on retention volumes and external volume, but it does not depend on band spreading. With this recycling technique it is shown that the maximum injection volume under optimal recycling conditions is greater than n_opt times the maximum injection volume for one cycle. So the use of recycling can be opportune and beneficial to increase the throughput in preparative liquid chromatography.     

Characterization of polymer-based monolithic capillary columns by inverse size-exclusion chromatography and mercury-intrusion porosimetry

Comprehensive two-dimensional gas chromatography (GCxGC) offers favourable resolution and sensitivity compared with conventional one-dimensional gas chromatography (1D-GC), as reported in many studies. These characteristics are of major interest when analytes are in trace concentration, and are present in complex mixtures, as is the case of polycyclic aromatic hydrocarbons (PAHs) in atmospheric particulate samples. Whilst GCxGC has been widely applied to identification of different types of analytes in several matrices, less seldom has it been used for quantification of these analytes. Although several quantitative methods have been proposed, they may be tedious and/or require considerable user development. Whereas quantification in 1D-GC is a routine and well-established procedure, in GCxGC, it is not so straightforward, especially where novel or untested procedures have yet to be incorporated into software packages. In the present study, it is proposed that a subset of the modulated peaks generated for each solute may be summed, based on the specific target ion mass of each compound present in a certified standard reference material (SRM) 1649a (urban dust). The ratio between a PAH and its corresponding deuterated (PAH-d) form showed that there is no statistical loss of sensitivity when this ratio is calculated based on whether the total sum of modulated peaks, or if only the two or the three most intense modulated peaks, are employed. Manual integration may be required, and here was found to give more acceptable values than automatic integration. Automated integration has been shown here to underestimate the modulated peak responses when low concentrations of PAHs were analyzed. Although for most PAHs good agreement with the certified values were observed, the analytical method needs to be further optimized for some of the other PAH, as can be see with those PAH with high variability in the range of urban dust analyzed.     

A novel approach to the qualitative and quantitative assay of HPTLC plates: Second and fourth derivative recording of spectrophotodensitograms

One of the limitations due to lack of resolution for a given pair of analytes in TLC or HPTLC is the need to optimize the system. In Practice this requires time, rerunning of the sample in different developing solvents, and a great deal of expertise on the part of the analyst. In our experience, application of first and second derivative recording techniques to HPTLC facilitates and speeds the whole process, permitting qualitative and quantitative assay of most unresolved spots. Consequently, we have now extended our instrumental capabilities to fourth derivative measurements. For this purpose, we have added a homemade electronic unit in series with the one previously used for first and second order derivatives. Thus, we have been able to evaluate the potential advantages of higher order derivatives for HPTLC analysis of unresolved components in various pharmaceutical products. A comparison of second and fourth order derivative measurements of seriously overlapping HPTLC components in a sample of preservatives used in the pharmaceutical industry suggests that the lower order derivatives might be a better choice in view of the higher accuracy and precision of the corresponding data. This is supported by the results of other applications, such as the assay of a commercial colorant, and a syrup formulation. The observed lack of precision of fourth order measurements stems from the fact that although the second and higher order derivatives produce narrower bandwidths, thus contributing to improved resolution, the signal to noise ratio decreases and satellite peak interactions increase, thus rendering correct discrimination of the fine structural detail of overlapping components more difficult.     

基于积分渐进展开的气相色谱重叠峰快速解析法

论文提出用积分渐进展开解析气相色谱重叠峰,该方法有3个主要步骤：首先将谷峰或肩峰分成两个积分区域,得到一个子区域的积分方程和一个重叠峰面积的代数方程;然后用数值积分求出这两个方程计算中所需要的峰面积,再用积分渐进公式将积分方程展开成代数方程;最后,将这两个方程与峰高约束方程联立后,得到一个非线性代数方程组,用Gauss-Seidel迭代可以快速求解方程组,方程收敛的最大迭代次数不超过20次。仿真和实验结果表明,解析的峰高和峰面积误差均很小,峰面积最大误差低于6.44%,峰高的最大误差约为6.80%。由于该算法精度高,效率高,所以这个方法可以用于气相色谱重叠峰和一般色谱峰的实时在线解析。     

Considerations on the modelling and optimisation of resolution of ionisable compounds in extended pH-range columns

The problems associated to the modelling and optimisation of the chromatographic resolution of mixtures involving ionisable solutes at varying pH and acetonitrile content are discussed. Several retention models that separate the contributions of solute, column and stationary phase, were used. The retention was predicted with low errors in large pH domains (2-12), which was an essential requirement to face the optimisation of resolution. The selected mixture was particularly problematic under the viewpoint of resolution, owing to the excessively diverse acid-base behaviour of solutes. This variety led to sudden drops in retention at different pH for each solute, yielding numerous peak crossing, which made finding shared regions of high resolution especially difficult. Conventional resolution diagrams for these situations are scarcely informative, since both the overall and the worst elementary resolutions drop to zero if at least two compounds remain overlapped, even when all the others are baseline resolved. A new chromatographic objective function is proposed to address this drawback. This function, called "limiting peak count", is based on the limiting peak purity concept, and measures the success in the resolution focusing on the resolved solutes, in contrast to conventional resolution assessments that attend mainly to the least resolved solutes. Limiting peak count yields the same result as conventional assessments when full resolution is possible, but it is also able to discriminate the maximal resolving power in low-resolution situations. It offers a different perspective to that given by the complementary mobile phases approach, and the computation is far simpler.     

Optimizing separations in reversed-phase liquid chromatography by varying pH and solvent composition

Summary An interpretive optimization procedure in which pH can be one of the variables is presented with the emphasis on optimizing separations. When varying the pH in reversed-phase liquid chromatography the retention of ionogenic solutes will change. Thus, the selectivity between ionogenic and neutral solutes or between ionogenic solutes mutually can be optimized. However, pH also greatly affects the efficiency (plate count) and peak shape (asymmetry). Optimum selectivity (i.e. large differences in retention times) may be observed under conditions where peaks are broad and asymmetrical. Thus, it is essential to simultaneously consider retention, peak width and peak shape and their effects on separation (effective resolution) in pH-optimization studies. A procedure in which this is done is presented and applied to optimizing the separation of a synthetic mixture of selected pharmaceuticals. After initial experiments to establish the parameter space (boundaries for pH and binary methanol — water composition), twelve experiments are performed according to a 3×4 experimental design. At each loaction the retention, peak height, peak area and peak symmetry are recorded for each solute. These data are then used to build models for each of the four characteristics and for each solute. From this set of models the response surface, describing the quality of separation as a function of pH and composition, can be calculated. A variety of optimization criteria (quantifying quality of separation) can be used. The optimum corresponds to the highest point on the response surface.     

Quantitative Conformational Studies on Poly(vinyl Chloride)

Although curve fitting provides a method for obtaining intensity data for the individual components of overlapping band systems, the number of configurational and conformational bands in the C-Cl stretching region of the vibrational spectrum of poly(vinyl chloride) is such that many parameters have to be optimized. It is therefore desirable to impose constraints in the calculations, and prior knowledge of the number of component bands would be valuable. The potential of derivative spectroscopy for obtaining this information has been examined. It is shown that the superior resolution of second and fourth derivative spectra is partially offset by their inferior signal-to-noise ratio, a discriminatory effect against broader bands, and interference by subsidiary derivative peaks. The method has been used to examine the CH₂ deformation and C-Cl stretching modes of three PVC samples of different tacticity. With the former the overlapping system proves to be more complex than hitherto realized; hence, tacticity determinations based on the intensity ratio of two peaks only at 1428 and 1434 cm^?1 must be suspect. With the C-Cl stretching bands second derivatives are more useful than fourth derivatives, and the number and positions of the located bands are in broad agreement with the results from curve fitting, so providing confirmatory evidence for the correctness of the latter.     

Preserving the chromatographic integrity of high-speed supercritical fluid chromatography separations using time-of-flight mass spectrometry

The advantage of high-speed time-of-flight-mass spectrometry (TOF-MS) detection for ultrafast qualitative supercritical fluid chromatography/mass spectrometry (SFC/MS) applications allows the superior resolving power of SFC to be exploited in high-throughput analysis. A chromatographic comparison of quadrupole MS and TOF-MS shows high-speed TOF total ion current data point sampling to be more indicative of fast SFC separations and corresponding short (1-2 s) baseline peak widths. Results shown for analysis of a six-compound mixture with two peaks eluting at 0.86 and 0.89 min exhibit >50% resolution by high-speed TOF data sampling, whereas the same peaks appear to coelute using quadrupole MS data sampling. Additionally, a marked improvement in the peak baseline widths is afforded by fast TOF data acquisition of 0.1 s/spectrum, resulting in a reduction in the baseline width, 1.6 s, of sulfanilamide in a four-compound mixture that is more than 2-fold greater than that achieved at the slower data acquisition of 0.5 s/spectrum. The resulting increase in resolution and improved peak shapes allow automatic integration routines to perform more effectively. For most classes of compounds amenable to high performance liquid chromatography, including druglike species, steroids, and polymers, the union of SFC with TOF-MS provides the maximum density of chemical information per unit time available with any high-speed chromatographic/mass spectrometric method.     

离子色谱不对称色谱峰的处理

介绍了通过微分处理分辨离子色谱中不对称峰的方法。实验将Ｆ＾－、Ｃｌ＾－、Ａｃ＾－、ＮＯ２＾－、ＮＯ３＾－、ＰｈＣＯＯ＾－、ＳＣＮ＾－、柠檬酸根、水杨酸根、山梨酸根和葡萄糖酸根等常见离子按一定比例配合混合液,对出现的不对称峰进行微分处理,得到的导数谱图可进行峰高定量,收到了较好的效果。     

Comparison of mass resolution criteria in mass spectrometry

For a single peak, mass spectral resolution can be expressed in terms of peak width or ratio of peak position to peak width. Alternatively, for two equally intense peaks of equal width, resolution can be defined as the minimum peak separation such that the height of the valley between the combined peaks is less than a specified ratio (1%, 10%, 50%, 100%) of the individual (or combined) peak maximum. All these definitions depend on peak shape. Conversion formulae between various mass resolution criteria are presented for each of eight spectral peak shapes: Gaussian, triangular, trapezoidal, Lorentzian (absorption-mode, magnitude-mode, and sine-apodized magnitude-mode), and sinc (absorption-mode and magnitude-mode). From these formulae, mass resolutions based upon different criteria are readily compared for the same or different line shapes.     

A study of the practical limitations of principal components analysis and the labelling of unresolved HPLC peaks

Summary The method of iterative target transformation factor analysis (ITTFA) used in conjunction with second derivative peak finding has shown to be a practical method for the peak deconvolution and reconstruction of HPLC chromatograms and spectra. The second derivative method of peak finding is acceptable for resolutions above 0.5 for peaks of similar heights. Above 0.5 resolution the labelling gives correct results where the spectra are substantially different and also when reasonably similar. Below this value the peak labelling was still accurate where the spectra were different. Solvent effects on the spectra of the compounds studied are small and do not hinder the peak labelling process. Thus small “local” libraries are feasible. Presented at the 17th International Symposium on Chromatography, September 25–30, 1988. Vienna, Austria.     

Development of a resolution metric for comprehensive two-dimensional chromatography

A new resolution metric for two-dimensional chromatography is proposed and tested. This resolution measurement is based on the concept of the (one-dimensional) valley-to-peak ratio, which has been adapted and modified for two-dimensional chromatography. Two questions are considered related to the computation of the resolution of a given (two-dimensional) peak. First, the concept of peak neighbourhood is revised, since it changes drastically from one- to two-dimensional chromatography. In a chromatogram resulting from a two-dimensional analysis, one peak may be surrounded by more than two neighbouring peaks. However, the neighbouring peaks can be remote from the peak or some interfering peaks may be in between. In these cases, it is not meaningful to compute the resolution between them. A method is proposed to determine whether a resolution measurement between two two-dimensional peaks is reasonable. Second, a measurement of the valley-to-peak ratio in two-dimensional chromatography is proposed. The measurement is based on the concept of the saddle point (which is defined for two-dimensional surface plots). A study of the correlation of the valley-to-peak ratio with the error obtained for quantification is presented. The new metric can be used as an estimator of the quantification errors. Also, valley-to-peak ratios can be calculated for one or more target peak(s) to estimate the separation quality of the entire chromatogram. This makes the proposed measurement suitable for optimisation purposes. Although the algorithm was developed for GC x GC, preliminary studies suggested that its application to other two-dimensional separation methods (e.g. LC x LC) should only require minor modification (if any).     

正交投影用于一维重叠色谱峰分辨及背景扣除

对于两组份色谱重叠峰体系,当以小组份色谱峰作为干扰时,本文利用正交投影方法,通过构造正交投影矩阵,利用原始信号及其投影与背景之间的内在关系来确定真实背景,从而将背景干扰予以扣除,使含背景干扰的一维重叠色谱峰得以分辨。模拟研究表明,对于两组份色谱峰重叠体系当以小色谱峰为干扰时本文方法具有很好的分辨效果,对于完全重叠峰,即使其峰分离度为零能得到满意的结果。     

Practical limitations of capillary gas chromatography

Glass capillary gas chromatography is a high resolution separation method which allows the qualitative and quantitative analysis of even complex mixtures, which may contain many components–also isomeric–in a wide range of volatilities, polarities and concentrations. The principal limitation of gas chromatographic application is given by an insufficient volatility of the species to be separated. Elevated temperatures have to be applied if the application range is to be extended and to achieve steep peak profiles, i.e. low detection limits at high resolution. The use of elevated temperatures is limited, of course, by the temperature stability of both the solvent (stationary liquid and support) and the solutes. The problems of trace analysis for low volatility compounds at high resolution and its limitational parameters regarding sampling, separation and detection are discussed. The applicability of glass capillary columns in this field is influenced by the following parameters: tailing behaviour; irreversible adsorption of polar and decomposition of unstable solutes; thermal stability of stationary liquid (including the support deactivation); separation efficiency and sample capacity (film thickness). Multidimensional gas chromatography using capillary columns coupled either with a packed or another capilllary column for preseparations may be applied with advantage in the analysis of complex mixtures.     

Exact expressions for ensemble functionals from particle number dependence

Some properties of exact ensemble density functionals can be determined by examining the particle number dependence of ground state ensemble density matrices for systems where the integer ground state energies satisfy a convexity condition. The results include the observation that the integral of the product of the functional derivative and Fukui function of functionals that can be expressed as the trace of an operator is particle number independent for particle numbers between successive integers and the integral itself is equal to the difference between functionals evaluated at successive integer particle numbers. Expressions that must be satisfied by 2nd and higher order functional derivatives are formulated and equations that must be satisfied point by point in space are derived. Using the analytic Hooke's atom model, it is shown that commonly used correlation functional approximations do not bear any resemblance to a spatially dependent expression derived from the exact second order functional derivative of the correlation functional. It is also shown that two expressions for the mutual Coulomb energy are not equal when approximate exchange and correlation functionals are used.     

Thermal analyses of mono- and divalent montmorillonite cationic derivatives

DTA and TG analyses were carried out for mono- and divalent cationic derivatives of Jelsovy-Potok montmorillonite. A certain relation between the charge density and the highest dehydration DTA peak was established for both series, since the two variables are a function of the magnitude of binding the hydrated water molecules. According to the charge density levels the cationic derivatives can be classified into three categories: (i) the single peak group falls in the range of charge density lower than 1 C m^?2; (ii) the double peak group falls between 1 and about 2 C m^?2; and (iii) for the higher charge densities three peaks are observed. The Ba derivative presents the only exception in this series. As the charge density increases, not only the number of dehydration peaks increases, but also the isolation between them becomes better, i.e., the overlapping of these peaks decreases in the order Ca > Li > Mg.The slopes of the TG curves in the temperature range 200–500°C increase with increase in charge density on the cationic derivative. This indicates that the rate of dehydration differs by changing the exchangeable cation of the surface, whereas the rate of dehydroxylation for all derivatives is the same since they all have the same origin.     

Fast, comprehensive online two-dimensional high performance liquid chromatography through the use of high temperature ultra-fast gradient elution reversed-phase liquid chromatography

A new approach to high speed, comprehensive online dual gradient elution 2DLC (LCxLC) based on the use of ultra-fast, high temperature gradient elution reversed phase chromatography is described. Entirely conventional gradient elution instrumentation and columns are assembled in a system which develops a total peak capacity of about 900 in 25 min; this is equivalent to roughly one peak/2 s. Each second dimension gradient is done in a cycle time of 21 s and the peak retention times measured for a set of twenty six indole-3-acetic acid (IAA) derivatives are reproducible to 0.2 s. Each peak eluting from the first dimension column is sampled at least twice across its width, as the corresponding peaks on the second dimension column appear in two or three consecutive second dimension chromatograms, clearly indicating that there is little loss in the resolution gained in the first dimension separation. Application to the separation of the low molecular weight components of wild-type and mutant maize seedlings indicates the presence of about 100 peaks on a timescale of 25 min. Compelling illustrations of the analytical potential of fast, high temperature 2DLC are evident in the clear presence of nine distinct peaks in a single second dimension chromatogram from a single quite narrow first dimension peak, and the great power of 2DLC to solve the "analytic dynamic range" problem inherent in the measurement of small peaks that are neighbors to a gigantic peak.     

The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Modern chromatographic data acquisition softwares often behave as black boxes where the researchers have little control over the raw data processing. One of the significant interests of separation scientists is to extract physico‐chemical information from chromatographic experiments and peak parameters. In addition, column developers need the total peak shape analysis to characterize the flow profile in chromatographic beds. Statistical moments offer a robust approach for providing detailed information for peaks in terms of area, its center of gravity, variance, resolution, and its skew without assuming any peak model or shape. Despite their utility and theoretical significance, statistical moments are rarely incorporated as they often provide underestimated or overestimated results because of inappropriate choice of the integration method and selection of integration limits. The Gaussian model is universally used in most chromatography softwares to assess efficiency, resolution, and peak position. Herein we present a user‐friendly, and accessible approach for calculating the zeroth, first, second, and third moments through more accurate numerical integration techniques (Trapezoidal and Simpson's rule) which provide an accurate estimate of peak parameters as compared to rectangular integration. An Excel template is also provided which can calculate the four moments in three steps with or without baseline correction.     

Resolution of the Embedded Chromatographic Peaks by Modified Orthogonal Projection Resolution and Entropy Maximization Method

ABSTRACT

The embedded chromatographic peaks usually can not be completely resolved by conventional multivariate resolution methods. The resolution condition of a certain component in two-way data is first reviewed. A modified orthogonal projection resolution (OPR) algorithm and new entropy maximization (EM) method are then proposed to resolve embedded chromatographic peaks in this paper. The modified OPR algorithm performs more precisely than conventional orthogonal projection resolution algorithm in resolving the chromatography of minor peak. The entropy criterion defined on the differential chromatography could obtain an approximate solution in resolution of the major chromatographic peak. Simulated and real data show that the modified OPR and entropy maximization (EM) methods perform well in solving the embedded problem.