三元重叠色谱峰面积的定量方法

本从色谱峰的ＥＭＧ模型出发，通过对重叠色谱峰的模拟和回归分析，提出了一种三元重叠色谱峰的面积的定量方法，三元重叠色谱峰的每一个峰面积可以由峰面积比和总面积求得，此法所需的数据都由实验色谱图上测得，峰面积计算结果的相对误差小于±５％，适用于相对峰谷为５０％－９５％的三元重叠色谱峰面积的定量。     

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.     

Exponentially Modified Gaussian functions—A good model for chromatographic peaks in isocratic HPLC?

Summary The Exponentially Modified Gaussian (EMG) function is fitted to a variety of typical peaks from isocratic HPLC, to assess its validity for peak characterization. This model has previously been applied, but with simplifying assumptions, allowing estimation of peak parameters from simple front and rear half-width measurements. The full EMG function is employed in this work. The results of the simplified approach have been compared to the EMG fitted results. Comparison is also made to fitted Gaussian functions. Results show that the EMG function is a good model for typical LC peaks, under a range of conditions, and that the simplified approaches give close correlation for a range of peak assymetries.     

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.     

A new mathematical function for describing electrophoretic peaks

A new model is proposed for characterizing skewed electrophoretic peaks, which is a combination of leading and trailing edge functions, empirically modified to get a rapid recovery of the baseline. The peak model is a sum of square roots and is called thereby "combined square roots (CSR) model". The flexibility of the model was checked on theoretical and experimental peaks with asymmetries in the range of 0-10 (expressed as the ratio of the distance between the center and the trailing edge, and the center and the leading edge of the chromatographic peak, measured at 10% of peak height). Excellent fits were found in all cases. The new model was compared with other three models that have shown good performance in modelling chromatographic peaks: the empirically transformed Gaussian, the parabolic Lorentzian-modified Gaussian, and the Haarhoff-van der Linde function. The latter model was proposed recently to describe electrophoretic peaks. The CSR model offered the highest flexibility to describe electrophoretic peak profiles, even those extremely asymmetrical with long tails. The new function has the advantage of using measurable parameters that allow the direct estimation of peak areas, which is useful for quantitative purposes.     

A Study on the Peak Type of Flow Injection Analysis

Abstract

Two equations for justifying whether a FIA peak is a gamma peak or an exponentially modified Gaussian (EMG) peak or neither of them have been presented. From these two equations, the peaks of flow injection extraction and FIA with single-line and two-line manifolds obtained in this paper are gamma peaks.     

A linear modulation-based stochastic resonance algorithm applied to the detection of weak chromatographic peaks

A simple stochastic resonance algorithm based on linear modulation was developed to amplify and detect weak chromatographic peaks. The output chromatographic peak is often distorted when using the traditional stochastic resonance algorithm due to the presence of high levels of noise. In the new algorithm, a linear modulated double-well potential is introduced to correct for the distortion of the output peak. Method parameter selection is convenient and intuitive for linear modulation. In order to achieve a better signal-to-noise ratio for the output signal, the performance of two-layer stochastic resonance was evaluated by comparing it with wavelet-based stochastic resonance. The proposed algorithm was applied to the quantitative analysis of dimethyl sulfide and the determination of chloramphenicol residues in milk, and the good linearity of the method demonstrated that it is an effective tool for detecting weak chromatographic peaks. Figure The linear modulation-based stochastic resonance algorithm (LSRA) improved the output chromatographic peak of chloramphenicol     

严重重叠的色谱峰对的解析

本文根据指数修正的高斯函数模型(EMG),并利用回归分析提出了一种解析严重重叠的色谱峰对的方法。此法可适用于相对峰谷在50％～95％的严重重叠的色谱峰对的解析。     

Estimation of the band broadening parameters in single detection size-exclusion chromatography: a comparative study of various column combinations

Alternative approaches for the determination of band broadening in size-exclusion chromatography based on the use of exponentially modified Gaussian (EMG) functions were used to experimentally investigate the performance of two different column sets. In both cases, the columns were combined in order to cover the complete fractionation range (from 10³ to 5 × 10⁶ g mol⁻¹), which is of interest in many applications. When analyzing experimental chromatograms the question of proper data treatment (especially the necessary smoothing routines) became obvious and is discussed accordingly. First results indicate that the exponential decay time of the EMG decreases and the standard deviation of its Gaussian component slightly increases (or remains almost constant) with increasing retention volumes. As a consequence, the total variance and the asymmetry of the EMG both decrease with the retention volume. A favorable agreement with independent experimental results (obtained by other researchers on the basis of analyzing ultra narrow standards) was found. Additionally, the skew was also investigated as a function of the retention volume and the trend was found to be in concordance with the predictions of theoretical models. The comparison with theoretical models is also discussed.     

Exponentially modified Gaussian relevance to the distributions of translocation events in nanopore-based single molecule detection

Nanopore technique plays an important role in single molecule detection, which illuminates the properties of an individual molecule by analyzing the blockage durations and currents. However, the traditional exponential function is lack of efficiency to describe the distributions of blockage durations in nanopore experiments. Herein, we introduced an exponentially modified Gaussian （EMG） function to fit the duration histograms of both simulated events and experimental events. In comparison with the traditional exponential function, our results demonstrated that the EMG provides a better fit while covers the entire range of the distributions. In particular, the fitted parameters of EMG could be directly used to discriminate the sequence length of the oligonucleotides at single molecule level.     

The use of derivatives for establishing integration limits of chromatographic peaks

Summary The paper deals with composite peaks in which the resolution is not sufficient to allow simple area determinations with conventional integrator procedures. It is proposed to use the second derivatives of composite peaks, since the derivatives accentuate envelope perturbations due to overlapped peaks. In particular, when there are two solutes in the composite, and when the peak separation is between 2 and 4σ, the second derivative of the composite has two minima and three maxima. The second maximum is indicative of the cross point of the two solutes. This point can be used to initiate and/or terminate the integration of the components in the composite. Similarly, the second minimum occurs at a point close to the true maximum of the second peak in the composite. This point can also be used for the quantitative determination of the second component in the composite. The second derivative traces can also be integrated, but their utility in quantitative analysis of the peaks is questionable. An inversion procedure is given in which the second derivative trace is inverted to yield a trace similar to the conventional chromatograms but with better apparent resolution. In special circumstances, the inverted derivatives can be used for integration purposes.     

The stochastic resonance algorithm with the direct current signal as external force and its application to the detection of weak chromatographic peaks

As a potential tool for amplifying weak chromatographic peaks, the stochastic resonance algorithm was developed based upon a counterintuitive physical phenomenon. Therefore, the essential step, parameter optimization, was perplexing and difficult for analysts. In order to avoid optimizing the system parameters on a case‐by‐case basis, an improved algorithm was proposed by introducing a constant or direct current signal into the signal to be measured as the external force. The weak chromatographic peak can be amplified and detected by the new algorithm using the same set of parameters. Two sets of our previous experimental data were reanalyzed by using the developed algorithm and the results were satisfactory. A generalized solution was expected to come into being on account of the new algorithm.     

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.     

A study of thermal peak splitting in capillary GC

Fluctuating thermal gradients are recognized as a distinct source of peak splitting in capillary column gas chromatography. In this study, the influence of analyte signal level, temperature oscillation amplitude, and oscillation frequency on splitting are quantitatively examined. Stable gradients are also considered. A simple, effective method is proposed for virtually eliminating thermal peak splitting in isothermal capillary GC analysis.     

Additivity of statistical moments in the exponentially modified Gaussian model of chromatography

A homologous series of saturated fatty acids ranging from C₁₀ to C₂₂ was separated by reversed-phase capillary liquid chromatography. The resultant zone profiles were found to be fit best by an exponentially modified Gaussian (EMG) function. To compare the EMG function and statistical moments for the analysis of the experimental zone profiles, a series of simulated profiles was generated by using fixed values for retention time and different values for the symmetrical (σ) and asymmetrical (τ) contributions to the variance. The simulated profiles were modified with respect to the integration limits, the number of points, and the signal-to-noise ratio. After modification, each profile was analyzed by using statistical moments and an iteratively fit EMG equation. These data indicate that the statistical moment method is much more susceptible to error when the degree of asymmetry is large, when the integration limits are inappropriately chosen, when the number of points is small, and when the signal-to-noise ratio is small. The experimental zone profiles were then analyzed by using the statistical moment and EMG methods. Although care was taken to minimize the sources of error discussed above, significant differences were found between the two methods. The differences in the second moment suggest that the symmetrical and asymmetrical contributions to broadening in the experimental zone profiles are not independent. As a consequence, the second moment is not equal to the sum of σ² and τ², as is commonly assumed. This observation has important implications for the elucidation of thermodynamic and kinetic information from chromatographic zone profiles.     

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.     

一种变压器油色谱峰识别算法的设计

在变压器油色谱峰识别领域,传统的一阶导数法需要斜率阈值来实现色谱峰识别,因此自动化程度低及容易失真。针对这些缺点,本文在一阶导数法的基础上进行了改进,将迭代移动平均及归一化分析技术应用到色谱峰识别中,通过对信号曲线及方波曲线多次迭代移动平均确定最优的归一化识峰参数,结合色谱峰的绝对保留时间及识峰窗口实现对色谱峰的准确识别。实验结果表明：该算法可以准确识别色谱峰,对噪声、色谱峰的峰宽及峰形变化不敏感,具有很强的自适应性,满足变压器油中气体在线监测装置的现场使用要求。     

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.     

A spin-coupled study of the Claisen rearrangement of allyl vinyl ether

The spin-coupled (SC) form of modern valence bond (VB) theory is utilised to examine the electronic structure of the transition state (TS) and the electronic reaction mechanism of the Claisen rearrangement of allyl vinyl ether. The differences between the spin-coupling patterns and orbital overlap integrals at the optimised TS geometries obtained using B3LYP/6-31G^*, MP2/6-31G^* and MP4(SDQ)/6-31G^* wavefunctions are minimal, and the SC picture suggests that the TS is non-aromatic. SC calculations along the intrinsic reaction coordinates computed at these three levels of theory also produce near identical results. The SC wavefunctions at different stages of the reaction provide easily interpretable orbital diagrams which, in combination with the changes in the orbital overlap integrals, indicate an electronic reaction mechanism involving concerted, though not entirely synchronous, bond breaking and bond formation processes. The evolution of the active space spin-coupling pattern, which is closely related to the classical VB concept of resonance, combined with the changes in the orbital overlap integrals, show that the reaction path involves a region in which the electronic structure of the reacting system becomes similar to that of benzene. This suggests that during the Claisen rearrangement the reacting system can attain moderately aromatic character but that this does not necessarily happen at the TS. The results of the SC analysis indicate that the most appropriate schematic representation of the Claisen rearrangement is furnished by a homolytic mechanism in which six harpoons describe the changes in the bonding pattern from reactant to product