High-speed chromatographic analysis of high-fructose corn syrup for process monitoring

High-speed chromatography is coupled with numerical methods for analyzing unresolved chromatograms and applied to a process analysis of high-fructose corn syrup. A column selection process is demonstrated where a minimum amount of resolution is sacrificed in order to decrease analysis time from over 5 min to 25 sec. Two data analysis methods, linear least squares regression and the sequential chromatogram ratio technique coupled with sequential suppression, are compared for their ability to quantitate the poorly resolved chromatograms. Both methods fit pure component analyte chromatograms, collected on a computer, to a sample chromatogram with unknown concentrations of each analyte. For a high-fructose corn syrup sample with a nominal fructose concentration of 55%, linear least squares analysis gave a fructose concentration percentage of 57.2 +/- 0.9%. The sequential chromatogram ratio algorithm gave a fructose concentration percentage of 57.9 +/- 0.7%.     

Monolithic silica columns for high-efficiency chromatographic separations

A deconvolution methodology for overlapped chromatographic signals is proposed. Several single-wavelength chromatograms of binary mixtures, obtained in different runs at diverse concentration ratios of the individual components, were simultaneously processed (multi-batch approach), after being arranged as two-way data. The chromatograms were modelled as linear combinations of forced peak profiles according to a polynomially modified Gaussian equation. The fitting was performed with a previously reported hybrid genetic algorithm with local search, leaving all model parameters free. The approach yielded more accurate solutions than those found when each experimental chromatogram was fitted independently to the peak model (single-batch approach). The improvement was especially significant for those chromatograms where the peaks were severely affected by the tails of the preceding compounds. Peak shifts among chromatograms, which are a usual source of non-bilinearity, were modelled in a continuous domain instead of in a discrete way, which avoided some drawbacks associated with latent variable methods. An experimental design involving simulated chromatograms was applied to check the method performance. Five main factors affecting the deconvolution were examined: concentration pattern, chromatographic resolution, number of batches and replicates, and noise level, which were evaluated using first- and second-order figures of merit. The method was also tested on three real samples containing compounds showing different overlap. Four multi-batch deconvolution methods were considered differing in the nature of the processed information and kind of peak matching among chromatograms. In all cases, the multi-batch deconvolution yielded better performance than the single-batch approach.     

GC-MS in space research: decoding complex isothermal chromatograms recovered from space missions

An analytical procedure is described to study GC-MS isothermal chromatograms simulating those recovered from space missions: in fact GC plays a predominant role in space missions devoted to characterizing the chemical composition of extra-terrestrial atmospheres. SIM (selected ion monitoring) detection was used for monitoring selected chemical classes: a simplified chromatogram can be obtained giving information on the chemical composition of the complex mixture. Since only isothermal GC chromatograms are allowed by flight constraints, a time axis transformation is required to make them homogeneous: i.e., constant retention increments for CH2 additions in terms of a homologous series. The order in the linearized chromatogram can be simply singled out with a chemometric approach based on the study of the Autocovariance Function (ACVF) computed on the digitized chromatogram: the plot of the experimental autocorrelation function (EACF) shows well-shaped peaks if constant interdistances are repeated in different regions of the chromatogram. The method was applied to standard mixtures representative of planetary atmospheres--hydrocarbons, nitriles and oxygenated compounds with between 3 and 12 carbon atoms--analyzed in flight simulating conditions. The coupling of the selectivity of SIM detection with the interpretation power of the EACF procedure proves to be a powerful tool for interpreting data recovered from space missions: the chemical composition of the mixture can be identified by handling the raw SIM chromatograms.     

Decoding of complex isothermal chromatograms recovered from space missions. Identification of molecular structure

A chemometric approach, based on the study of the autocovariance function, is described to study isothermal GC chromatograms of multicomponent mixtures: isothermal GC analysis is the method of choice in space missions since it is, to date, the only method compatible with flight constraints. Isothermal GC chromatograms look inhomogeneous and disordered with peak density decreasing at higher retention times: a time axis transformation is proposed to make retention an homogeneous process so that CH2 addition in terms of an homologous series yields a constant retention increment. The time axis is transformed into a new scale based on the retention times of n-alkanes, as they are the basis of the universal Kovats indices procedure. The order introduced into the chromatogram by retention time linearization can be simply singled out by the experimental autocorrelation function (EACF) plot: if constant inter-distances are repeated in different regions of the chromatogram, well-shaped peaks are evident in the EACF plot. By comparison, with a standard mixture it is possible to identify peaks diagnostic of specific molecular structures: study of the EACF plot provides information on sample chemical composition. The procedure was applied to standard mixtures containing compounds representative of the planetary atmospheres that will be investigated in the near future: in particular, those related to Titan's atmosphere (Cassini-Huygens mission) and cometary's nucleus (Rosetta mission). The employed experimental conditions simulated those applied to GC instruments installed on space probes and landers in space missions. The method was applied to two specific investigations related to space research, i.e., a comparison of retention selectivity of different GC columns and identification of the chemical composition of an unknown mixture.     

Signal processing of GC-MS data of complex environmental samples: characterization of homologous series

Identification and characterization of homologous series by GC-MS analysis provide very relevant information on organic compounds in complex mixtures. A chemometric approach, based on the study of the autocovariance function, EACVF_tot, is described as a suitable tool for extracting molecular-structural information from the GC signal, in particular for identifying the presence of homologous series and quantifying the number of their terms. A data pre-processing procedure is introduced to transform the time axis in order to display a strictly homogenous retention pattern: n-alkanes are used as external standard to stretch or shrink the original chromatogram in order to build up a linear GC retention scale. This addition can be regarded as a further step in the direction of a signal processing procedure for achieving a systematic characterization of complex mixture from experimental chromatograms. The EACVF_tot was computed on the linearized chromatogram: if the sample presents terms of homologous series, the EACVF_tot plot shows well-defined deterministic peaks at repeated constant interdistances. By comparison with standard references, the presence of such peaks is diagnostic for the presence of the ordered series, their position can be related to the chemical structure of the compounds, their height is the basis for estimating the number of terms in the series. The power of the procedure can be magnified by studying SIM chromatograms acquired at specific m/z values characteristic of the compounds of interest: the EACVF_tot on these selective signals makes it possible to confirm the results obtained from an unknown mixture and check their reliability.The procedure was validated on standard mixtures of known composition and applied to an unknown gas oil sample. In particular, the paper focuses on the study of two specific classes of compounds: n-alkanes and oxygen-containing compounds, since their identification provides information useful for characterizing the chemical composition of many samples of different origin. The robustness of the method was tested in experimental chromatograms obtained under unfavorable conditions: chromatograms acquired in non-optimal temperature program conditions and chromatographic data affected by signal noise.     

Retention time alignment of LC/MS data by a divide-and-conquer algorithm

Liquid chromatography-mass spectrometry (LC/MS) has become the method of choice for characterizing complex mixtures. These analyses often involve quantitative comparison of components in multiple samples. To achieve automated sample comparison, the components of interest must be detected and identified, and their retention times aligned and peak areas calculated. This article describes a simple pairwise iterative retention time alignment algorithm, based on the divide-and-conquer approach, for alignment of ion features detected in LC/MS experiments. In this iterative algorithm, ion features in the sample run are first aligned with features in the reference run by applying a single constant shift of retention time. The sample chromatogram is then divided into two shorter chromatograms, which are aligned to the reference chromatogram the same way. Each shorter chromatogram is further divided into even shorter chromatograms. This process continues until each chromatogram is sufficiently narrow so that ion features within it have a similar retention time shift. In six pairwise LC/MS alignment examples containing a total of 6507 confirmed true corresponding feature pairs with retention time shifts up to five peak widths, the algorithm successfully aligned these features with an error rate of 0.2%. The alignment algorithm is demonstrated to be fast, robust, fully automatic, and superior to other algorithms. After alignment and gap-filling of detected ion features, their abundances can be tabulated for direct comparison between samples.     

HRGC separation performance evaluation by a simplified fourier analysis approach

A simple procedure is presented for determining separation performance of HRGC analysis of multicomponent mixtures. The procedure is based on the computation of Autocovariance Function (EACVF) from the digitized experimental chromatogram. Graphic inspection of the EACVF plot permits easy computation of the width value of the single component peak, σ; from the EACVF value at t=O the number of component in the mixture, m, can be simply derived. From these two basic quantities all the other chromatographic performance attributes can be calculated. The consistency of the procedure is tested for different chromatograms and compared with the more complex EACVF fitting method. Several features of the multicomponent chromatogram, overloading effects included, are directly detected.     

Mathematical algorithm for qualitative and semiquantitative analysis of petroleum hydrocarbons in solid wastes using on-line gas chromatography

Non-degradated mineral-oils like gasoline, solvent naphtha, diesel fuel, fuel and lubricating oils provide a characteristic fingerprint gas chromatogram. This visual classification, e.g. in solid wastes, is complicated due to the simultaneous presence of several mineral-oils. Therefore, a mathematical algorithm for the separation of gas chromatographic fingerprint of “single mixtures” of aliphatic hydrocarbons is developed. The technique ¶is essential for analysis of time-overlapping “single mixtures” of petroleum hydrocarbons (so-called “complex mixtures”) and it relies on the concentration-varying hydrocarbons during evaporation. It is possible to separate the data from the gas chromatogram of a “complex mixture” of hydrocarbons into the chromatograms of the pure “single mixtures” and to give their respective concentrations. A synthetic ?complex mixture” of kerosene, diesel fuel and lubricating oil is used to illustrate the method.     

Mathematical algorithm for qualitative and semiquantitative analysis of petroleum hydrocarbons in solid wastes using on-line gas chromatography

Non-degradated mineral-oils like gasoline, solvent naphtha, diesel fuel, fuel and lubricating oils provide a characteristic fingerprint gas chromatogram. This visual classification, e.g. in solid wastes, is complicated due to the simultaneous presence of several mineral-oils. Therefore, a mathematical algorithm for the separation of gas chromatographic fingerprint of "single mixtures" of aliphatic hydrocarbons is developed. The technique is essential for analysis of time-overlapping "single mixtures" of petroleum hydrocarbons (so-called "complex mixtures") and it relies on the concentration-varying hydrocarbons during evaporation. It is possible to separate the data from the gas chromatogram of a "complex mixture" of hydrocarbons into the chromatograms of the pure "single mixtures" and to give their respective concentrations. A synthetic "complex mixture" of kerosene, diesel fuel and lubricating oil is used to illustrate the method.     

Optimization of gradient profiles in ion-exchange chromatography using computer simulation programs

Optimization procedure of gradient separations in ion-exchange chromatography using simplex optimization method in combination with the computer simulation program for ion-exchange chromatography is presented. The optimization of parameters describing gradient profile for the separation in ion chromatography is based on the optimization criterion obtained from calculated chromatograms. The optimization criterion depends on the parameters used for calculations and thus exhibits the quality of gradient conditions for the separation of the analytes. Simplex method is used to calculate new gradient profiles in order to reach optimum separations for the selected set of analytes. The Simplex algorithm works stepwise, for each new combination of parameters that describe the gradient profile a new calculation is performed and from the calculated chromatogram the optimization criterion is determined. The proposed method is efficient and may reduce the time and cost of analyses of complex samples with ion-exchange chromatography.     

Gel-permeation chromatography. V. A study of “overloading effects”

In the calculation of molecular weight averages from GPC chromatograms and in the correction for zone broadening effects, it is assumed that the retention volumes of the individual species are not affected by the presence of the other components in the sample (linear fractionation process). This assumption was tested by the computer comparisons of the chromatograms of mixtures of narrow molecular weight distribution polystyrene standards and the envelopes of the individual chromatograms of the components of the mixtures. Disagreements between experimental and computer synthesized chromatograms were interpreted as non-linear fractionation effects. The investigation covered a range of molecular weights (1.8 × 10⁶ to 2100), molecular weight distributions (binary and seven component mixtures), and sample loadings (2 to 70 mg). Accurate normalizations of raw GPC chromatograms and calculations of molecular weight averages were made possible through an automated GPC apparatus using a high-speed computer for data acquisition and data reduction. It was found that some nonlinear fractionation effects (large disagreement between chromatograms of the mixture and the computed envelopes of the individual chromatograms of the components of the mixture) became more pronounced as sample loading was increased and as the molecular weight distribution of the sample narrows. The nonlinear effect was also found to be sensitive to the molecular weight of the sample.     

Mixture-mixture design for the fingerprint optimization of chromatographic mobile phases and extraction solutions for Camellia sinensis

A composite simplex centroid-simplex centroid mixture design is proposed for simultaneously optimizing two mixture systems. The complementary model is formed by multiplying special cubic models for the two systems. The design was applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Camellia sinensis Chinese tea plant. The extraction mixtures investigated contained varying proportions of ethyl acetate, ethanol and dichloromethane while the mobile phase was made up of varying proportions of methanol, acetonitrile and a methanol-acetonitrile-water (MAW) 15%:15%:70% mixture. The experiments were block randomized corresponding to a split-plot error structure to minimize laboratory work and reduce environmental impact. Coefficients of an initial saturated model were obtained using Scheffe-type equations. A cumulative probability graph was used to determine an approximate reduced model. The split-plot error structure was then introduced into the reduced model by applying generalized least square equations with variance components calculated using the restricted maximum likelihood approach. A model was developed to calculate the number of peaks observed with the chromatographic detector at 210 nm. A 20-term model contained essentially all the statistical information of the initial model and had a root mean square calibration error of 1.38. The model was used to predict the number of peaks eluted in chromatograms obtained from extraction solutions that correspond to axial points of the simplex centroid design. The significant model coefficients are interpreted in terms of interacting linear, quadratic and cubic effects of the mobile phase and extraction solution components.     

Combination of dynamic time warping and multivariate analysis for the comparison of comprehensive two-dimensional gas chromatograms: application to plant extracts

Comprehensive two-dimensional gas chromatography (GC x GC) is now recognized as the preferred technique for the detailed analysis and characterization of complex mixtures of volatile compounds. However, for comparison purposes, taking into account all the information contained in the chromatogram is far from trivial. In this paper, it is shown that the combination of peak alignment by dynamic time warping and multivariate analysis facilitated the comparison of complex chromatograms of tobacco extracts. The comparison is shown to be efficient enough to provide a clear discrimination among three types of tobacco. A tentative interpretation of loadings is presented in order to give access to the compounds which differ from one sample to another. Once located, mass spectrometry was used to identify markers of tobacco type.     

Quantification of naphthalenes in jet fuel with GC x GC/Tri-PLS and windowed rank minimization retention time alignment

Comprehensive, two-dimensional gas chromatography (GC x GC) is used in conjunction with trilinear partial least squares (Tri-PLS) to quantify the percent weight of naphthalenes (two-ring aromatic compounds) in jet fuel samples. The increased peak capacity and selectivity of GC x GC makes the technique attractive for the rapid, and possibly less tedious analysis of jet fuel. The analysis of complex mixtures by GC x GC is further enhanced through the use of chemometric techniques, including those designed for use on 2-D data such as Tri-PLS. Unfortunately, retention time variation, unless corrected, can be an impediment to chemometric analysis. Previous work has demonstrated that the effects of retention time variation can be mitigated in sub-regions of GC x GC chromatograms through the application of an objective retention time alignment algorithm based on rank minimization. Building upon this previous work, it is demonstrated here that the effects of retention time variation can be mitigated throughout an entire GC x GC chromatogram with an objective retention time alignment algorithm based on windowed rank minimization alignment. A significant decrease in calibration error is observed when the algorithm is applied to chromatograms prior to construction of Tri-PLS models. Fourteen jet fuel samples with known weight percentages of naphthalenes (ASTM D1840) were obtained. Each sample was subjected to five replicate five-minute GC x GC separations over a period of two days. A subset of nine samples spanning the range of weight percentages of naphthalenes was chosen as a calibration set and Tri-PLS calibration models were subsequently developed in order to predict the naphthalene content of the samples from the GC x GC chromatograms of the remaining five samples. Calibration models constructed from GC x GC chromatograms that were retention time corrected are shown to exhibit a root mean square error of prediction of roughly half that of calibration models constructed from uncorrected chromatograms. The error of prediction is lowered further to a value that nearly matches the uncertainty in the standard percent weight values (ca. 1% of the median percent volume value) when the aligned chromatograms are truncated to include only regions of the chromatogram populated by naphthalenes and compounds of similar polarity and boiling point.     

Micro-HPLC/TLC/FTIR

Identification problems often encountered in high performance liquid chromatography (HPLC)/Fourier transform infrared spectrometry (FTIR) can be circumvented through the use of a thin-layer chromatographic (TLC) plate as deposition and infra-red sampling medium. The combination of complementary separation modes is shown to demonstrate increased resolution of the components of complex mixtures. In this particular work, the effluent from a reversed-phase microcolumn is continuously deposited on a TLC plate with alumina stationary phase. The solute remains on the plate as a continuous record of the HPLC separation, which is then analyzed by diffuse reflectance FTIR. When the HPLC separation is inadequate for full separation of the components, the immobilized HPLC chromatogram serves as a starting point for subsequent TLC separation. A number of FTIR reconstructed chromatograms and spectra which are derived from the TLC plate aid in the interpretation.     

Peak alignment using wavelet pattern matching and differential evolution

Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).     

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.     

Gas-Chromatographic Analysis of Mixtures of Hydrogen Isotopes

A simple method is proposed for the gas-chromatographic analysis of complex gas mixtures containing hydrogen isotopes; the method is based on the substantial difference in the thermal conductivity of these isotopes. The total peak of the isotopes is recorded in a chromatogram, and the calibration is performed by pure reference gases. The concentrations of impurity gases in the analyzed mixture and in reference samples for each of the hydrogen isotopes are determined simultaneously. The fractional concentrations of protium and deuterium are calculated by the equations involving the heights of the unresolved peaks of hydrogen isotopes in chromatograms and concentrations of impurity components.     

The preopt package for pre-optimization of gradient elutions in high-performance liquid chromatography

A theoretical model is described for quick pre-optimization of binary multistep gradient elutions in liquid chromatography. This model utilizes experimental retention-time data under isocratic elution conditions for different proportions of organic modifier in the mobile phase, and simulates the position of the peaks in the chromatogram by calculation of the average velocity of the peaks through the column. Optimization is done for multistep gradients by means of the simplex algorithm. The results must then be confirmed experimentally. Results are given demonstrating the power and validity of the model in the resolution of complex mixtures. The whole process done on a micro-computer with the PREOPT package usually takes about 30 min, without requiring user participation or chromatographic instrumentation.     

Model for predicting comprehensive two-dimensional gas chromatography retention times

A model for approximating the relative retention of solutes in comprehensive two-dimensional gas chromatography (GCxGC) is presented. The model uses retention data from standard single-column temperature-programmed separations. The one-dimensional retention times are first converted into retention indices and then these indices are combined in a simple manner to generate a retention diagram. A retention diagram is an approximation of the two-dimensional chromatogram that has retention order and spacing in both dimensions similar to that found in the experimental chromatogram. If required, the retention diagram can be scaled to more closely resemble the two-dimensional chromatogram. The model has been tested by using retention time data from single-column gas chromatography-mass spectrometry and valve-based GCxGC. A total of 139 volatile organic compounds (VOCs) were examined. Approximately half of the VOCs had a single functional group and a linear alkyl chain (i.e., compounds with the structure Z-(CH(2))(n)-H). The retention diagrams had primary retention orders that were in excellent agreement with the GCxGC chromatograms. The relative secondary retention order for compounds with similar structures was also accurately predicted by the retention diagram. However, the relative secondary retention for compounds with dissimilar structures, such as acyclic alcohols and multi-substituted alkylbenzenes, were less accurately modeled. This study demonstrates how readily available single-column retention time data can be used to provide an a priori estimate of the relative retention of solutes in a GCxGC chromatogram. Such a capability is useful for screening possible combinations of stationary phases.