PCB separation by HRGC-MS. Fourier analysis for characterizing Aroclor chromatograms

Aroclor and Aroclor mixture chromatograms obtained using temperature programmed high resolution capillary GC coupled with mass spectrometric selective detection have been investigated by Fourier analysis developed for the study of multicomponent chromatograms. The experimental autocorrelation function (EACF), i.e. peak shape and position correlation, showed a retention - structure pattern which could be associated with both the type of Aroclor and the ion used for selective ion monitoring (m/z value). In particular, o-m and m-m isomerization effects were singled out by EACF analysis. By fitting EACF with previously developed theoretical models, it was possible to characterize a specific Aroclor in terms of the number of PCB congeners present in it. The results obtained agreed closely with the typical Aroclor content. For the Aroclor mixture, the distribution of inter-distance between successive peaks was derived. The two first distribution moments obtained agreed with those derived from retention data reported in the literature. The consequences on the separation performance, i.e. the number of singlets, doublets, etc. in the chromatogram, are discussed.     

Generalized Gaussian reference curve measurement model for high‐performance liquid chromatography with diode array detector separation and its solution by multi‐target intermittent particle swarm optimization

In order to separate a high‐performance liquid chromatography with diode array detector (HPLC‐DAD) data set to chromatogram peaks and spectra for all compounds, a separation method based on the model of generalized Gaussian reference curve measurement (GGRCM) and the algorithm of multi‐target intermittent particle swarm optimization (MIPSO) is proposed in this paper. A parameter θ is constructed to generate a reference curve r(θ) for a chromatogram peak based on its physical principle. The GGRCM model is proposed to calculate the fitness ε(θ) for every θ, which indicates the possibility for the HPLC‐DAD data set to contain a chromatogram peak similar to the r(θ). The smaller the fitness is, the higher the possibility. The algorithm of MIPSO is then introduced to calculate the optimal parameters by minimizing the fitness mentioned earlier. Finally, chromatogram peaks are constructed based on these optimal parameters, and the spectra are calculated by an estimator. Through the simulations and experiments, the following conclusions are drawn: (i) the GGRCM‐MIPSO method can extract chromatogram peaks from simulation data set without knowing the number of the compounds in advance even when a severe overlap and white noise exist and (ii) the GGRCM‐MIPSO method can be applied to the real HPLC‐DAD data set. Copyright © 2014 John Wiley & Sons, Ltd.     

Multivariate Composition Distribution in Free‐Radical Multicomponent Polymerization, 1

Statistical multicomponent polymerization is a typical example of a Markovian process for which the generating function approach can be applied. Up to the present, generating functions have been used mainly to obtain analytical solutions. However, recent advances of computer software capable of handling symbolic calculations can throw new light on the old mathematical technique. After formulating the equations representing the instantaneous composition distribution of polymers for a given chain length, r, the illustrative numerical calculations are conducted by using the symbolic calculator. For a multicomponent polymerization consisting of more than two components, the second component distribution is dependent on the composition of the first component (F₁), which is represented by the conditional probability given r and F₁, . It is found that is well approximated by the Gaussian distribution with the variance following the relationship, , as in the case of the first component distribution , where A and B are the constants. With the knowledge of chain length distribution, it is now possible to conduct the full analysis of multivariate distribution of chain length and compositions for multicomponent free‐radical polymerization.

Bivariate distribution of composition F₁ and F₂ for chain length r = 100 in a three‐component system.     

Decoding complex multicomponent chromatograms by fourier analysis

Summary The present work discusses the many attributes—classified as observable, intrinsic or hidden—which can be conceived for any complex multicomponent chromatogram. Discussion ensues on how to decode such chromatograms, i.e. determining the intrinsic and/or hidden attributes from those which can be observed. There are two main steps. The first is based on Fourier Analysis (FA) and determines the intrinsic attributes: i.e., the number of single components which can be detected; their distribution over the available chromatographic space and peak capacity. The second evaluates the hidden attributes: i.e., the effects of incomplete separation, the number of peaks created by one or more single components as well as their degree of purity. The hidden attributes can be obtained by applying the theory of Statistical Degree of peak Overlapping (SDO) and the paper goes into the extent to which the SDO step depends on the FA results. In addition, the role Exponential distribution plays as a point of reference for the distribution of both single component peak position interdistances and peak heights is discussed. Finally, a simplified graphical FA procedure is presented and the main achievements in this field are reviewed. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

A Green Approach for the One‐Pot,Three‐Component Synthesis of 2‐Arylpyrroloacridin‐1(2H)‐Ones using Lactic Acid as a Bio‐based Catalyst under Solvent‐Free Conditions

A facile and benign synthetic strategy is proposed for the synthesis of 2‐arylpyrroloacridin‐1(2H )‐ones via a lactic acid‐catalyzed three‐component reaction of dimedone, various anilines, and isatins under solvent‐free conditions. Avoidance of hazardous organic solvents, the use of a one‐pot multicomponent procedure for the synthesis of 2‐arylpyrroloacridin‐1(2H )‐ones, operational simplicity, no need for column chromatography, lactic acid utilization as a bio‐based organic compound, reusability, homogeneity, and commercial availability of the catalyst, and superior synthetic performance are some important aspects of this methodology to access a series of pyrroloacridine motifs with potentially biological scaffolds.     

Algebrants in many-electron quantum mechanics: Applications of generalized determinants or matrix functions

We define the algebrant, a mathematical generalization of the determinant, the immanant, the permanent, and the Schur functions. Algebrants are classified as multilinear matrix functions or multicomponent symmetrized tensors. In applications, such as N-electron quantum mechanics, where extensive computation is required, it is vital to reduce computational effort, e.g., the well-known N-factorial problem. We derive certain mathematical properties that can be incorporated in efficient computing algorithms for algebrants. Foremost is our “elimination theorem,” which allows (in important special cases) zeros to be introduced into an algebrant in close analogy with Gaussian elimination for determinants. Savings accruing from such elimination can be substantial. We show examples from Matsen's spin-free quantum chemistry where elimination effectively removes the N-factorial problem that has hitherto stifled possible applications.     

Adsorption of organics on MSC5A in supercritical CO2, chromatographic measurements & stop & go simulation

Chromatographic measurements were made for the adsorption of benzene, toluene and m-xylene on molecular sieving carbon (MSC) in supercritical fluid CO₂ mixed with organics. Supercritical chromatograph packed with MSC was used to detect pulse responses of organics. Adsorption equilibria and adsorption dynamics parameters for organics were obtained by moment analysis of the response peaks. Dependences of adsorption equilibrium constants, K ^?, and micropore diffusivity,?D, on the amount adsorbed were examined. The dependencies of adsorption equilibrium constants, K ^?, and micropore diffusivity, D, of benzene, toluene and m-xylene, on molarity of benzene with each parameters of temperature or pressure were obtained. It was found that the values of K ^? and D for an organic substance depended on the amount adsorbed of other organics strongly. And stop & go method was used as simulation method of perturbation chromatography for investigating adsorption equilibrium and rate. Numerical solution for multicomponent chromatogram in time domain could be obtained by appropriate model equations with experimental conditions. This simulated chromatogram can be compared with experimental chromatogram to determine the adsorption equilibrium and rate parameters. In addition, molecular simulation of multicomponent adsorption equilibria was performed, and potential parameters were determined by comparing the simulation with experimental results. Simulation soft ware is Cerius2 (Version?4.2) made by MSI. The purpose of performing simulation is to elucidate an adsorption mechanism on the molecule level.     

Micro-Scale Frontal Affinity Chromatography with Mass Spectrometric Detection: A New Method for the Screening of Compound Libraries

In one run the binding constants K_d for all the active components of a ligand library at sub-microgram quantities can be determined. A mixture of ligands is continuously infused through a column of immobilized receptor, and the eluent analyzed by electrospray mass spectrometry. From the affinity chromatogram produced (see picture) the breakthrough volume of a single compound and hence its K_d value can be determined.     

Complementary Design in Multicomponent Electrocatalysts for Electrochemical Nitrogen Reduction: Beyond the Leverage in Activity and Selectivity

Electrochemical nitrogen reduction reaction (eNRR) is promising in place of the Haber–Bosch process for artificial N₂ fixation. However, the high activity and selectivity of eNRR are challenging to achieve simultaneously due to the scaling relations. Such “leverage” between activity and selectivity has severely restricted eNRR. To overcome this bottleneck, the complementary design of electronic structures in multicomponent electrocatalysts has been recently pursued, aiming to maximize the advantages of each component and optimize the multistep reactions, which has stood at the cutting edge in this aspect. Here, we present a minireview of the design, performance, and mechanism of multicomponent electrocatalysts with complementary electronic structures. We particularly emphasize the interactions between N₂ and elements from d-, p-, and s-blocks, which are essential for understanding how these electrocatalysts are beyond the “leverage” between activity and selectivity.     

HELP法在中草药分析中的应用研究-冬虫夏草的化学成分测定

基于直观推导式演进特征投影（ＨＥＬＰ）法,对冬虫夏草子座和虫体分别进行了多组分同时定性定量测定．结果表明,ＨＥＬＰ法能减少样本提取分离的步骤,降低色谱分离条件的要求,提高检测准确度．联用色谱检测与化学计量学解析法相结合将为复杂中草药分析提供一种全新手段     

Peak recognition imitating human judgement

Summary Peak integration is still a major source of error in analytical techniques such as chromatography (LC and GC), aapillary electrophoresis (CE), spectrosocpy, and electrochemistry. If the baseline is complex, e.g. because of matrix effects, or if the peak shape is irregular, e.g. because of peak tailing, the results are often not satisfactory when classical procedures are used. These shortcomings arise because of the stepwise appearance of the chromatogram. An algorithm that copies the human method of considering baseline and peaks as a whole has already been introduced. Here the use of a straight line as a baseline model led to an improvement in several instances. The baseline is, however, usually not exactly straight and rigid. A baseline model with flexible properties is more advantageous. Thus the smoothing cubic spline function is applied in this work. Here the rigidity can be controlled by use of a parameterp _k. The prediction interval of the spline is used for iterative distinction between baseline and peak regions. Afterwards straightforward optimization of the peak boundaries is applied. More than 50 series of consecutive injections of the same sample (n=40 on average) were used to test the performance of this procedure. The same raw data have been integrated by means of the algorithm described here and by use of commercially available software. The reproducibility of the main component peak are within the series was taken as a measure of integration quality. Typically the new procedure reducesRSD % by approximately 33% (e.g. from 1.5% to 1.0%). The improvement is even more impressive for difficult samples with complex matrices, e.g. blood plasma or polymer excipients. for such samples improvements of up to a factor of 6 are obtained.     

Application of Computer-Aided Spectral Deconvolution Technique in Validation of High Performance Liquid Chromatographic Peaks

Abstract

Reliable analysis with high performance liquid chromatography (HPLC) requires purity of the eluting peak. The present work has combined the advantages of the availability of full spectral data from HPLC photodiode array UV detector and computer algorithms to perform chromatographic peak purity check. A deconvolution technique based on multicomponent analysis has been applied to the UV spectra of co-eluting components. This method employs residual error (Relative-fit-error, RFE) between predicted spectrum and analyte's spectrum to detect presence of other component or contaminant. Typical RFE values for uncontaminated chromatographic peaks of norethisterone and ethynyloestradiol range between 1 and 3, while contaminated peaks have RFE values as large as 145. A systematic increase in ‘relative-fit error’ from 1.10 to 145 was observed for peaks of norethisterone when contaminated to varied extent with ethynyloestradiol. Extent of peak overlap in chromatogram was also mapped out with this technique. The co-prescribed oral contraceptive, norethisterone and ethynyloestradiol were used as model in this work. An advantage of the method is its applicability when the contaminant's spectrum is unavailable. The method, unlike several earlier techniques, is also applicable to chromatograms with concidental elution time for the components.     

Correlation and Calculation of Multicomponent Adsorption Equilibria Data Using a Generalized Adsorption Isotherm

Enhanced by the need for reliable and accurate data of multicomponent gas adsorption equilibria on porous solids like activated carbons or zeolites, a new method to measure and correlate coadsorption equilibria has been developed. This method is a combination of gravimetric or volumetric measurements of the total load of pure or multicomponent adsorbates (Staudt, 1994; Gregg and Sing, 1982) and a correlation and calculation procedure using a new adsorption isotherm (AI) (Keller, 1990). This AI is thermodynamically consistent and describes adsorbates with fractal dimension for single- or multicomponent systems and load dependent adsorption energies. This method allows calculation of partial loads of multicomponent coadsorption equilibria from pure component data and the total loads of the mixture adsorption equilibria. This will be demonstrated for binary and ternary adsorption equilibria of CH₄, C₂H₄ and C₂H₆ on activated carbon (Reich et al., 1980).     

A novel thin layer chromatography–flame ionization detection method for saturated,asphaltenes, resins,and asphaltenes group-type composition analysis with reverse order of chromatogram development

The methodologies of asphaltenes-containing petroleum materials: saturated, aromatics, resins, asphaltenes group-type composition analysis are performed with the use of column adsorption-desorption or thin layer chromatography (TLC)-flame ionization detection under normal phase conditions with silica gel as the adsorbent. In a three-step procedure, the TLC chromatogram is developed within a decreasing distance by the mobile phase with increasing elution strength (polarity). The n-alkane used in the first step does not dissolve asphaltenes, which leads to the occlusion effect and an underestimation of the percentage of saturated hydrocarbons. In this article, the reverse order of the subsequent elution steps was proposed: the solvent polarity is simultaneously reduced and the chromatogram development distance is increased in the order dichloromethane:methanol 95:5 v/v, 3 cm; toluene, 6 cm; and n-hexane, 10 cm. It was also intentional to reduce the weight of the applied sample to 5 μg for bitumen and 2 μg for asphaltene purity testing. It should be the rule that in stepwise TLC chromatogram development, the first mobile phase is a good solvent for all testing components. The IP 469 procedure should be corrected.     

Green chromatographic fingerprinting: An environmentally friendly approach for the development of separation methods for fingerprinting complex matrices

A chromatographic fingerprint is a comprehensive method that reveals the distinctive pattern of peaks across the chromatogram for a given sample. It is considered an effective strategy to assess the identity and quality of herbal materials, as well as for the control of the quality of their derived products. HPLC is the most employed technique for these purposes and it is used routinely for quality control in industry. Hence, its impact on the environment should not be neglected. This work provides a rational and generic procedure to qualitatively fingerprint complex matrices. Resource‐ and time‐saving experimental designs were selected; an alternative safer organic solvent was tested and a time‐saving and innovative response entitled the green chromatographic fingerprinting response was developed and employed. This procedure was applied in the development of chromatographic fingerprints for extracts of Bauhinia forficata and Casearia sylvestris. Moreover, the response proposed here can be combined with a complementary metric available in the literature to compare methods using different solvents. According to this, the chromatographic fingerprints developed here using ethanol as the organic solvent provided a performance better than that of reference methods in which more harmful acetonitrile or methanol were employed.     

Green Microwave‐assisted Multicomponent Route to the Formation of 5,8‐Dihydropyrido[2,3‐d]pyrimidine Skeleton in Aqueous Media

Three‐component synthesis of 5‐substituted 6‐acetyl‐2‐amino‐7‐methyl‐5,8‐dihydropyrido[2,3‐d ]pyrimidines was brought to facile energy‐efficient and environmental‐friendly conditions using multicomponent reaction, microwave field as an activation method and hot water as a solvent. A series of the target compounds was synthesized using the developed procedure.     

Criteria for judging the quality of separation in chromatograms containing solvent peaks

Summary Formal procedures used for optimizing chromatographic selectivity require objective, numerical functions to assess the quality of each chromatogram obtained during the process. Many of such optimization criteria have been suggested for chromatograms in which all or a number of well-shaped peaks need to be separated. This paper describes a method by which resolution can be measured in chromatograms in which very large, highly non-symmetrical background peaks,e.g. typical solvent peaks, are present. Using this method, various optimization criteria can be calculated. The method is evaluated using a simulation program which constructs chromatograms from the recorded profiles of individual experimental peaks. It is also demonstrated for use in an experimental optimization procedure in reversed-phase liquid chromatography.     

Green Synthesis of Imidazole Derivatives via Fe3O4‐MNPs as Reusable Catalyst

In this research, a one‐pot, efficient, and high yielding procedure for the synthesis of imidazole derivatives is investigated. The procedure was carried out via multicomponent reaction of isothiocyanate, alkyl bromides, N‐methylimidazole, and triphenylphosphine in the presence of magnetic iron oxide nanoparticles (Fe₃O₄‐MNPs) as reusable catalyst under solvent‐free conditions at 50°C. Also, Fe₃O₄‐MNPs were produced using green synthetic method by reduction of ferric chloride solution with Clover Leaf water extract. The nanoparticles generated using this procedure can potentially be important in different purposes such as organic synthesis. Easy, simple, rapid, and clean procedures for the synthesis of imidazole derivatives are the advantages of this study.     

Principal component analysis and multicomponent surface free energy theories

The same underlying mathematical structure characterizes some of the most popular multicomponent models for the prediction of surface free energies and adhesion works. After a brief illustration of the general methods for the computation of liquid and solid components in typical multicomponent theories, it is shown that both model definition and component estimate may take great advantage from application of Principal Component Analysis techniques, owing to the very peculiar structure of adhesion work equations. It is also put into evidence that a problem of scale multiplicity arises as a consequence of the symmetries involved in the model equations for adhesion work and surface free energy. A special discussion is devoted to the specific cases of van Oss–Chaudhury–Good acid–base theory, Qin–Chang model and extended Drago theory, which constitute the most common multicomponent models usually applied in the analysis of adhesion phenomena.      

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.