Parcel model for peak shapes in chromatography numerical verification of the temporal distortion effect to peak asymmetry

The traditional plate concept has been reassessed and improved to a parcel matrix model, which can be used to imitate the chromatographic behavior of a hypothetic column on a computer worksheet. Under programmed conditions, various peak shapes (nearly Gaussian, and with prolonged or fronting tails) are generated. The peak tailing has been separated into two major fractions: spatial and temporal. The former fraction is caused by the retention nature of a column, whereas the latter is induced by the observer's relative position and the changing of the zone broadening rate. The temporal distortion effect can be identified qualitatively and quantitatively through a normalized peak-overlapping process. In general, a chromatographic peak may carry a prolonged (or normal type) tail under linear isotherms, while both prolonged and fronting tails will appear under non-linear conditions. The temporal distortion is proved to be significant, and may be regarded as the major cause of peak asymmetry in most cases. This is in contrast to the conclusions of many previous studies. The model is also eligible to simulate chromatographic peaks for various injection sizes.     

Origin of peak asymmetry and isotherm nonlinearity in micellar electrokinetic chromatography: variation of peak shape with buffer concentration

The diffuse fronts and sharp rears of peaks of nitrobenzene (nbz) solubilized at high concentrations in 50 mM SDS and 2.5, 25, and 50 mM sodium tetraborate buffers were modeled in MEKC by measurements of, and fits to, concave upward isotherms, and by numerical solution of the continuity equation. The isotherms varied with buffer concentration, with the smallest limiting slope and largest curvature found for the 50 mM tetraborate buffer. The Brunauer, Emmett, and Teller isotherm described the peak profiles in all buffers, with symmetrical peaks observed at sub- and low-mM levels of nbz, anti-Langmuirian peaks observed at 10-20 mM levels, and aquiline peaks resembling curved noses observed at 20-30 mM levels. The variation of the partition coefficient with nbz and buffer concentrations was shown to result from nonideal thermodynamics. High-buffer concentrations salt out nbz from the mobile phase, as quantified by a mobile-phase activity coefficient related to the Setchenov constant of nbz in sodium tetraborate. The activity coefficient of nbz in SDS micelles was shown to resemble that measured by other researchers for benzene in micelles of sodium octyl sulfate, i.e. it decreases with increasing solute concentration and increases with electrolyte concentration. Many examples from the literature are discussed, in which the variation of the intramicellar activity coefficient with solute mole fraction is consistent with peaks having diffuse fronts and sharp rears.     

Determination of the thermodynamic contribution to peak asymmetry of basic solutes in reversed-phase liquid chromatography

To this day packing materials manufacturers are still trying to develop reversed-phase stationary phases that have silica more completely reacted with bonding ligands to afford more homogeneous particle surfaces. Incomplete bonding causes inhomogeneous effects that are readily observed when separating basic solutes because of the acidic silanols that are unreacted. However, it is still not understood exactly what types of silanol sites are unreacted or if metal impurities are contributing to the resulting peak asymmetry observed. A method is presented which utilizes (1) the frontal analysis method of chromatography to obtain adsorption/partition isotherms, (2) a heterogeneous Langmuir distribution model for the resulting isotherm, (3) an expectation-maximization numerical procedure to solve the mathematical problem to yield the most probable distribution of adsorption parameters, and (4) the equilibrium-dispersive model of chromatography incorporating the fitted isotherm model to check the validity of the sorption model with experimental observations. Correlation of packing materials characterization parameters with results obtained by this procedure will indicate what type of silanols or other sites are responsible for observed tailing behavior. Developers and manufacturers will then be able to more efficiently target their synthetic designs for "base-deactivated" reversed-phase silicas.     

Automatic peak detection in chromatography

Summary A modified derivative of chromatographic signal is proposed for detection of the appearance of a new peak. The method is shown to yield peak areas of good precision even in very noisy systems.This paper is dedicated to Dr. Leslie Ettre on his 60th birthday.     

Sample peak width in gradient ion chromatography

A mathematical model is constructed for calculating peak widths and positions in gradient ion chromatography. It is shown that in high performance chromatography, the width of the chromatographic peak is completely determined by the eluant properties at the moment of peak elution from the column. Model test calculations are presented.     

Multiple peak analysis in gel permeation chromatography

Summary This paper describes the resolution of multimodal GPC chromatograms into their individual components through the use of two optimization techniques, applied sequentially. The principle of the method can be applied to any form of curve but only the mathematics for Gaussian curves is given. The method has been successfully tested against both model and real chromatograms. The model chromatograms consisted of overlapping, perfectly Gaussian, curves whilst the real chromatograms were obtained from oligomeric polyesters submitted for routine GPC analysis and contained from three to five components. These chromatograms, which would have been too complex to resolve by “pencil and ruler” techniques, were resolved by this method to a precision within experimental error.     

Semi-automated peak trapping recycle chromatography instrument for peak purity investigations

A peak trapping recycle chromatography system has been developed and optimized for peak purity assessment of active pharmaceutical ingredients analyzed by high performance liquid chromatography (HPLC). After being analyzed using a reversed phase analytical column, peaks of interest are trapped and are subsequently introduced to a recycle chromatography system. In addition to the increased effective length afforded the recycling system, the small selectivity difference between the analytical and recycling methods help separate potential impurities under the main peak. For more difficult to separate components, the increased efficiency of recycle chromatography provides the necessary resolution. Over 227,000 theoretical plates have been obtained in the recycle dimension for some compounds. The sensitivity of the system fell short of the target (0.1%), but it did show sensitivity (0.5%) comparable to other peak purity techniques commonly used in the pharmaceutical industry. The recovery and repeatability have also been shown to be adequate for peak purity assessment. The system has also been automated using a Visual Basic macro, simplifying the interface allowing it to be used as an open access instrument.     

The mechanism of peak broadening in paper chromatography

Summary The mechanism of peak broadening in paper chromatography was investigated by comparing the peak widths in paper chromatography with those caused only by diffusion in the paper for nine amino acids of widely differing R_f values.It appeared that eddy diffusion and resistance to mass transfer do not contribute to the peak broadening. By considering the peak widths as a function of R_f it could be shown that diffusion in the stationary phase cannot be neglected.

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Zusammenfassung Der Vorgang der Peak-Verbreiterung in der Papierchromatographie wurde untersucht. Dazu wurden die Peakbreiten nach Chromatographie mit den nur durch Diffusion erhaltenen verglichen. Neun Aminosäuren mit sehr unterschiedlichen R_f-Werten wurden verwendet. Wirbeldiffusion und Massentransport spielen bei der Peak-Verbreiterung keine Rolle, dagegen kann der Einfluß der Diffusion in der stationären Phase nicht vernachlässigt werden.

     

Multiplex advantage and peak resolution in correlation chromatography

The multiplex advantage in correlation chromatography not only makes the signal-to-noise ratio better than that of conventional chromatography, but also improves the peak resolution for the same signal-to-noise ratio. This property is demonstrated for the headspace analysis of components from an ethylene-propylene copolymer. The disadvantageous sample dilution in the pneumatic Deans-type switch is discussed.     

Information theory of optimization in chromatography: Optimum peak separation and dependency on peak area

Summary If a peak (j=2) moves along the time axis of a chromatogram with no change in the position ₁ of the other peak (j=1) or in areas A₁ and A₂, the optimum separation, _s, is defined as the resolution R_s which provides the maximum information, called FUMI, among all possible positions ₂ of the peak (₂₁). This paper demonstrates that optimum separation, _s, of chromatographic peaks critically depends on the peak areas. As the area ratio A₂/A₁ of overlapped peaks increases, greater separation (higher resolution R_s) is needed to obtain maximum information. The quantitative relationship between _s and A₂/A₁ is derived by computer simulation.     

Achieving high peak capacity production for gas chromatography and comprehensive two-dimensional gas chromatography by minimizing off-column peak broadening

By taking into consideration band broadening theory and using those results to select experimental conditions, and also by reducing the injection pulse width, peak capacity production (i.e., peak capacity per separation time) is substantially improved for one dimensional (1D-GC) and comprehensive two dimensional (GC×GC) gas chromatography. A theoretical framework for determining the optimal linear gas velocity (the linear gas velocity producing the minimum H), from experimental parameters provides an in-depth understanding of the potential for GC separations in the absence of extra-column band broadening. The extra-column band broadening is referred to herein as off-column band broadening since it is additional band broadening not due to the on-column separation processes. The theory provides the basis to experimentally evaluate and improve temperature programmed 1D-GC separations, but in order to do so with a commercial 1D-GC instrument platform, off-column band broadening from injection and detection needed to be significantly reduced. Specifically for injection, a resistively heated transfer line is coupled to a high-speed diaphragm valve to provide a suitable injection pulse width (referred to herein as modified injection). Additionally, flame ionization detection (FID) was modified to provide a data collection rate of 5kHz. The use of long, relatively narrow open tubular capillary columns and a 40°C/min programming rate were explored for 1D-GC, specifically a 40m, 180μm i.d. capillary column operated at or above the optimal average linear gas velocity. Injection using standard auto-injection with a 1:400 split resulted in an average peak width of ～1.5s, hence a peak capacity production of 40peaks/min. In contrast, use of modified injection produced ～500ms peak widths for 1D-GC, i.e., a peak capacity production of 120peaks/min (a 3-fold improvement over standard auto-injection). Implementation of modified injection resulted in retention time, peak width, peak height, and peak area average RSD%'s of 0.006, 0.8, 3.4, and 4.0%, respectively. Modified injection onto the first column of a GC×GC coupled with another high-speed valve injection onto the second column produced an instrument with high peak capacity production (500-800peaks/min), ～5-fold to 8-fold higher than typically reported for GC×GC.     

液相色谱梯度洗脱中的谱带压缩效应

谱带压缩效应是梯度洗脱区别于等度洗脱的重要特征。经典的范德姆特(van Deemter)理论塔板高度方程基于等度洗脱推导得到,因此不能对谱带压缩效应进行描述。在梯度洗脱中,保留因子(k)会随流动相组成(φ)的改变而发生变化,这就使得对梯度洗脱机理的研究要比等度洗脱复杂许多。该文对近10年来谱带压缩效应的研究进展,特别是溶剂强度模型(即描述ln k与φ关系的数学表达式)的非线性特征对谱带压缩因子(G)的影响进行了述评,指出为了更好地认识谱带压缩效应需要将这种非线性因素考虑在内。     

Maximizing peak capacity and separation speed in liquid chromatography

The practical effects of gradient time and flow rate on the peak capacities of a range of analytes of differing molecular weights (MWs) and physico-chemical properties have been evaluated using ultra high pressure LC instrumentation with sub-2 mum and superficially porous particle phases. Optimum peak capacity, in RP gradient LC, for small molecules, including typical pharmaceutical drugs and peptides with MWs up to 1300, was demonstrated at a maximum flow rate for a given gradient time (i.e. up to 40 min). Flow rates significantly higher than the optimum in the van Deemter plots and also higher than those typically employed by the majority of the chromatographers today are recommended for gradient LC (i.e. up to 1.0 mL/min on 50-150x2.1 mm 1.7 mum columns). This recommendation is applicable for temperatures above 40 degrees C, i.e. temperatures typically utilized for separations employing sub-2 mum particles to reduce column back pressure. Van Deemter and pseudo van Deemter plots were determined and combined with chromatographic gradient elution theory to explain our unexpected observations. The derived models exhibited good agreement between experimental and predicted peak capacities (absolute average error 4%, max. error 12%).     

An alternative approach for predicting peak width in gas chromatography

Summary The linear relationship between natural logarithm of width factor (lnp′)and natural logarithm of retention factor (lnk) is demonstrated. This relationship is then used to establish the relationship between (lnp′), absolute temperature (T), and carbon number (z), as follows: Inp′=A+bz+c/T+dz/T where A, b, c and d are thermodynamically related constants. The above equation is used to predict the unadjusted widths (w _R ) ofn-alkanes, fatty alcohols and fatty acid methyl esters (FAMEs) at various temperatures, predicted values are in good agreement with experimental values. The above equation can be used to predict the width of FAMEs from rice bran oil. The largest difference between the experimental and predicted values is 0.66 s or 6.32%.     

Chromatographic peak broadening in circulation gas chromatography on capillary columns

Conclusions Ideas about the effect of the hydrodynamic pulse broadening of Chromatographic peaks have been developed. The pulse peak broadening factor of compounds undergoing chromatography has been introduced to account for the effect of the partition ratio k, and the relationship of this new factor to one proposed earlier has been established. The physicochemical concepts developed in the course of the theoretical investigations are supported by experimental results for circulating gas chromatography on glass capillary columns.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2019–2024, September, 1986.     

Relationship between carbon number and peak width in gas chromatography

When the unadjusted width (wR) is divided into hold-up width (wM) and adjusted width (w'R), a linear relationship between the natural logarithm of the width factor (p') and the carbon number (n) is demonstrated and can be described by: In p' = a + bn where a and b are constants. The coefficients of variance (r2) for n-alkanes, fatty acid methyl esters and fatty alcohols are 0.9997, 0.9996 and 0.9998, respectively.     

Development of an algorithm for peak detection in comprehensive two-dimensional chromatography

A method for peak detection in two-dimensional chromatography is presented. The algorithm applies first the methods developed for peak detection in one-dimensional chromatography to detect peaks in one dimension. In a second step, a decision tree is applied to decide which one-dimensional peaks are originated from the same compound and have to be 'merged' into one two-dimensional peak. To this end, different features of the peaks (second-dimension peak regions and second-dimension retention times) are compared and different criteria (common peak regions, retention time differences, unimodality in the first dimension) are applied. Different options can be used, depending on the nature of the data. The user controls this decision tree by establishing several options and "switches". The algorithm was tested with GCxGC chromatograms obtained for a commercial air-freshener sample, detecting and merging the modulated peaks belonging to the same compound. Recommendations for the set of options and switches are given. A utility that calculates and sums peak areas from merged peaks is added to facilitate automated quantification. Although the algorithm was developed for GCxGC, its application to comprehensive two-dimensional liquid chromatography (LCxLC) data should at most require minor modifications.     

色谱双柱系统智能定性方法

双柱系统分析未知样品能提供交叉信息。因此, 可以提高峰定性的可靠性。如何有效地利用交叉信息, 将指定组分识别出来, 本文进行了研究。根据每支选择性不同柱子上, 色谱峰的流出次序、位置和峰面积信息, 采用模糊数学方法和领域专家的逻辑, 编制智能定性软件, 可以比较方便、快速、准确地对包括重叠峰在内的流出峰进行定性。通过空气毒物卤代烃化合物, 对双柱智能定性方法进行了验证。