Monte-carlo simulation of gas chromatographic separation for the prediction of retention times and peak half widths

Summary A new method for prediction of gas chromatographic retention times and peak half widths is based on the renewal theory. The only requirements are the heats of vaporization of the compounds to be separated and one calibration measurement. With this data, retention times and peak half widths can be predicted for isothermal as well as temperature-programmed gas chromatography. For the separation of non-polar substances on non-polar stationary phases the prediction error for retention times is approx. 1–2%. First simulations of polar molecules and polar stationary phases indicate that this method is also applicable in these cases but some extension will be required.     

Thermodynamics‐based modelling of gas chromatography separations across column geometries and systems,including the prediction of peak widths

Thermodynamics‐based models have been demonstrated to be useful for predicting retention time and peak widths in gas chromatography and two‐dimensional gas chromatography separations. However, the collection of data to train the models can be time consuming, which lessens the practical utility of the method. In this contribution, a method for obtaining thermodynamic‐based data to predict peak widths in temperature‐programmed gas chromatography is presented. Experimental work to collect data for peak width prediction is identical to that required to collect data for retention time prediction using approaches that we have presented previously. Using this combined approach, chromatograms including retention times and peak widths are predicted with very high accuracy. Typical errors in retention time are < 0.5%, while errors in peak width are typically < 5% as demonstrated using polycycic aromatic hydrocarbons and a mixture containing compounds with aldehyde, ketone, alkene, alkane, alcohol, and ester functionalities.     

Interpretation on Band‐Broadening in Chromatography with Spatial Peak Profiles Obtained Using Whole‐Column Detection

Fifteen liquid chromatographic experiments were investigated using a whole‐column detection (WCD) system and a conventional post‐column UV/Vis detector. The peak widths obtained from chromatograms were found dependent on the retention factor; the larger the retention factor was the greater the peak width. However, the on‐column spatial peak widths were dependent on the locations where they were measured in the column. The peak widths monitored at 17 cm from the column inlet were found essentially the same no matter what their retention factors were. In addition, a linear relationship was found between the chromatographic peak width and the reciprocal of the average linear rate of the solute migration. The peak widths on chromatograms did not reflect how they appeared in the column; instead, the widths were determined by the solute speed passing the detector.     

Prediction of the effects of methanol and competing ion concentration on retention in the ion chromatographic separation of anionic and cationic pharmaceutically related compounds

The mixed-mode separation of a selection of anionic and cationic pharmaceutically related compounds is studied using ion-exchange columns and eluents consisting of ionic salts (potassium hydroxide or methanesulfonic acid) and an organic modifier (methanol). All separations were performed using commercially available ion-exchange columns and an ion chromatography instrument modified to allow introduction of methanol into the eluent without introducing compatibility problems with the eluent generation system. Isocratic retention prediction was undertaken over the two-dimensional space defined by the concentration of the competing ion and the percentage of organic modifier in the eluent. Various empirical models describing the observed relationships between analyte retention and both the competing ion concentration and the percentage of methanol were evaluated, with the resultant model being capable of describing the separation, including peak width, over the entire experimental space based on six initial experiments. Average errors in retention time and peak width were less than 6% and 27%, respectively, for runs taken from both inside and outside of the experimental space. Separations performed under methanol gradient conditions (while holding the competing ion concentration constant) were also modelled. The observed effect on retention of varying the methanol composition differed between analytes with several analytes exhibiting increased retention with increased percentage methanol in the eluent. An empirical model was derived based on integration of the observed t_R vs. %methanol plot for each analyte. A combination of the isocratic and gradient models allowed for the prediction of retention time using multi-step methanol gradient profiles with average errors in predicted retention times being less than 4% over 30 different 2- and 3-step gradient profiles for anions and less than 6% over 14 different 2- and 3-step gradient profiles for cations. A modified peak compression model was used to estimate peak widths under these conditions. This provided adequate width prediction with the average error between observed and predicted peak widths being less than 15% for 40 1-, 2- and 3-step gradients for anions and less than 13% over 14 1-, 2- and 3-step gradients for cations.     

Experimental designs for modeling retention patterns and separation efficiency in analysis of fatty acid methyl esters by gas chromatography-mass spectrometry

The retention behavior of components analyzed by chromatography varies with instrumental settings. Being able to predict how changes in these settings alter the elution pattern is useful, both with regards to component identification, as well as with regards to optimization of the chromatographic system. In this work, it is shown how experimental designs can be used for this purpose. Different experimental designs for response surface modeling of the separation of fatty acid methyl esters (FAME) as function of chromatographic conditions in GC have been evaluated. Full factorial, central composite, Doehlert and Box-Behnken designs were applied. A mixture of 38 FAMEs was separated on a polar cyanopropyl substituted polysilphenylene-siloxane phase capillary column. The temperature gradient, the start temperature of the gradient, and the carrier gas velocity were varied in the experiments. The modeled responses, as functions of chromatographic conditions, were retention time, retention indices, peak widths, separation efficiency and resolution between selected peak pairs. The designs that allowed inclusion of quadratic terms among the predictors performed significantly better than factorial design. Box-Behnken design provided the best results for prediction of retention, but the differences between the central composite, Doehlert and Box-Behnken designs were small. Retention indices could be modeled with much better accuracy than retention times. However, because the errors of predicted tR of closely eluting peaks were highly correlated, models of resolution (Rs) that were based on retention time had errors in the same range as corresponding models based on ECL.     

Innovative high-performance liquid chromatography method development for the screening of 19 antimalarial drugs based on a generic approach, using design of experiments, independent component analysis and design space

An innovative methodology based on design of experiments (DoE), independent component analysis (ICA) and design space (DS) was developed in previous works and was tested out with a mixture of 19 antimalarial drugs. This global LC method development methodology (i.e. DoE-ICA-DS) was used to optimize the separation of 19 antimalarial drugs to obtain a screening method. DoE-ICA-DS methodology is fully compliant with the current trend of quality by design. DoE was used to define the set of experiments to model the retention times at the beginning, the apex and the end of each peak. Furthermore, ICA was used to numerically separate coeluting peaks and estimate their unbiased retention times. Gradient time, temperature and pH were selected as the factors of a full factorial design. These retention times were modelled by stepwise multiple linear regressions. A recently introduced critical quality attribute, namely the separation criterion (S), was also used to assess the quality of separations rather than using the resolution. Furthermore, the resulting mathematical models were also studied from a chromatographic point of view to understand and investigate the chromatographic behaviour of each compound. Good adequacies were found between the mathematical models and the expected chromatographic behaviours predicted by chromatographic theory. Finally, focusing at quality risk management, the DS was computed as the multidimensional subspace where the probability for the separation criterion to lie in acceptance limits was higher than a defined quality level. The DS was computed propagating the prediction error from the modelled responses to the quality criterion using Monte Carlo simulations. DoE-ICA-DS allowed encountering optimal operating conditions to obtain a robust screening method for the 19 considered antimalarial drugs in the framework of the fight against counterfeit medicines. Moreover and only on the basis of the same data set, a dedicated method for the determination of three antimalarial compounds in a pharmaceutical formulation was optimized to demonstrate both the efficiency and flexibility of the methodology proposed in the present study.     

Estimation of chromatographic parameters on two silica-based columns connected in series under nonaqueous reversed phase liquid chromatographic conditions

Empirical equations were produced to relate important chromatographic parameters on two silica-based columns serially linked, in isocratic nonaqueous RP HPLC, to retention times and peak widths of the separated compounds on the individual columns. These equations were derived because the experimental data seemed to deviate from the values expected, applying basic chromatographic theoretical equations. The chromatographic parameters studied were retention time, peak width, resolution, number of theoretical plates, capacity factor, and separation factor. In addition, empirical linear relationships were produced for the estimation of the above mentioned parameters of the serial systems, in direct and reverse order, relating them to those obtained on each column, separately. The experimentally obtained values were in good agreement with those estimated by the derived equations.     

Theoretical study of incomplete sampling of the first dimension in comprehensive two-dimensional chromatography

The process of regularly transferring material from the primary column to the secondary column is critical in producing comprehensive two-dimensional separations. A series of calculations have been performed to determine how sampling period, duty cycle, and sampling phase affect (1) the fraction of material transferred from the primary column to the secondary column, (2) the accuracy of primary retention time determination, and (3) the effective peak width along the primary retention axis. The results demonstrate that comprehensive two-dimensional separations can be produced without a substantial loss in quantitative precision and with only a moderate loss in primary column resolution if the sampling period is less than 1.5 times the primary peak standard deviation. The quantitative precision of total peak areas (for duty cycles less than 1.0) and primary retention time determination are rapidly reduced as the sampling period is increased above 1.5 times the primary peak standard deviation.     

The application of small porous particles, high temperatures, and high pressures to generate very high resolution LC and LC/MS separations

The effect of combining sub-2 microm porous particles with elevated operating temperatures on chromatographic performance has been investigated in terms of chromatographic efficiency, productivity, peak elution order, and observed operating pressure. The use of elevated temperature in LC does not increase the obtainable performance but allows the same performance to be obtained in less time. Increasing the column temperature did allow the use of longer columns, generating column efficiencies in excess of 100,000 plates and gradient peak capacities approaching 1000. Raising the temperature increased the optimal mobile phase linear velocity, negating somewhat the pressure benefits observed by reducing the solvent viscosity. When operating at higher temperature the analyte retention is not only reduced, but the order of elution will also often change. High temperature separations allowed exotic organic modifiers such as isopropanol to be exploited for alternative selectivity and faster analysis. Finally, care must be taken when using high temperature separations to ensure that the narrow peak widths produced do not compromise the quality of data obtained from detectors such as high resolution mass spectrometers.     

Study of elution behaviour with gradient voltage in CEC using methacrylate monolithic columns

A theoretical study on the retention behaviour and chromatographic performance of neutral solutes using a lauryl methacrylate‐based monolithic column under voltage gradient mode in CEC was carried out. Through a flexible mathematical function based on a modified Gaussian model, the peak shape of compounds was firstly fitted under constant and gradient voltage. Using the peak shape parameters and retention time, the estimation of global chromatographic performance, efficiency and peak capacity under several voltage conditions was performed. The influence of voltage gradient on the separation efficiency is discussed and simple equations are presented to calculate retention and peak widths under voltage gradient conditions. A comparison in terms of chromatographic performance of a test mixture of neutral solutes under constant and gradient voltage modes was also carried out. The experiments carried out under gradient voltage showed better efficiencies (172 000 plates/m) and lower peak widths than those obtained under constant voltage (52 000 plates/m).     

The reproducible acquisition of comparative liquid chromatography/tandem mass spectrometry data from complex biological samples

An in-depth study of the reproducibility of data acquired for comparative proteomics analysis using a prototype two-stage heated laminar flow chamber fitted to a commercial high-performance liquid chromatography/tandem mass spectrometry (HPLC/MS/MS) instrument was undertaken. The study is based on 24 replicate samples from four independent membrane preparations derived from two matched breast cancer cell lines. Variation and reproducibility in the data were evaluated at several levels highlighting the relative efficiency and variability of the acquisition routines used. Specifically, variation in the number and relative intensities of chromatographic peaks eluted from the LC column, precursor ion selection and sequence identification were evaluated. On average, approximately 6500 chromatographic peaks were generated for each acquisition with a corresponding coefficient of variance (CV) of less than 20%. Precursor ion selection and sequence identification averaged 1380 and 780 events per acquisition sample, respectively, with corresponding CVs of less than 10% for each. The reproducibility in the precursor ion selection was typically better than 60% between similar replicates. Using protein and peptide internal standards, it was found that the CV in retention time across the gradient between two acquisition pairs was typically less than 5%, whereas the average intensity ratio was 1.0 (expected) with a CV approaching 20%. An evaluation of the intensity ratios calculated from endogenous peptide sequences, identified across the acquisition set, indicated a CV of approximately 30%. Similarly, the CV associated with the top 1000 peptides indicated a mean and median of 28.4 and 26.95%. For a given acquisition pair it was also found that approximately 11% of the chromatographic peaks eluting from the column were linked to a sequence or identified. For these experiments, less than 10% of the peak pairs had absolute ratios greater than 2.0 and of those only approximately 10% had sequences linked to them. For each matched acquisition set on average 406 proteins were identified with a CV of less than 10%. Of the proteins that were identified approximately 30% had at least one predicted trans-membrane domain, indicating a four-fold increase over a crude homogenate sample with only minor enrichment. During these experiments it was found that the interface did not significantly alter the relative charge state distribution of ions, nor did it introduce significant interference from background ions. The interface was capable of 24-hour acquisition cycles.     

Retention time and peak width in the combined pH/organic modifier gradient high performance liquid chromatography

The purpose of this work was to test the applicability of the current theory to predict the peak retention time and the peak width in the combined pH/organic modifier gradient reversed phase high performance liquid chromatography (RP HPLC). A series of 38 isocratic measurements have been conducted for a wide range of pH and methanol contents for ketoprofen (weak acid) and papaverine (weak base). It served to find the model describing dependence of retention factor and the height equivalent of a theoretical plate (HETP) on pH and organic modifier content. The information gathered in the isocratic mode was used to simulate retention times and peak widths for 30 various methanol gradients, 25 pH gradients, and 3 combined pH/methanol gradients. The simulations were compared with the experimental data. We also proposed a simplified version of this model that was parameterized based on 12 initial organic modifier gradients carried out for different pHs and for the 20 min and 60 min gradient development times. The full and the simplified model described the experimental data very well. In conclusion, the proposed modeling approach allowed predicting analyte retention times and peak width for various pH and organic modifier changes. Its simplified version required only 12 initial experiments and seems to be very promising in the optimization RP HPLC separations for complex samples and for conditions providing peak compression.     

Evaluation of a nitrogen-cooled, electrically heated cold trap inlet for high-speed gas chromatography

Gas chromatography has the potential to be a much faster method of separation than is usually realized. If column operating conditions are optimized for speed and injection band width is minimized, some simple separations can be completed in a few seconds. A prototype cryofocusing system for producing narrow injection bands with 0.25-mm i.d. columns is described here. The gas-cooled and electrically heated inlet produces injection bands with widths of about 10-20 ms. In the present study the system is evaluated using mixtures of common organics, including alkanes, aromatics, alcohols, ketones, and chlorinated hydrocarbons. Quantitative trapping and reinjection is achieved for all tested compounds. Coefficients of variation are less than 3% for peak area and less than 0.2% for retention time. Base-line separation of simple mixture is achieved with retention times of less than 10 s. By using the cold trap inlet with a low-dead-volume detector and a high-speed electrometer, the efficiency available from commercial capillary columns can be better utilized, and retention times for some routine separations may be reduced to a few seconds.     

Computer optimization of separation in gas-solid chromatography,optimization model and computer-modified mapping procedure

Summary This paper proposes an optimization model for gas-solid chromatographic separations in a non-linear programming form and an approximate equation of the plate height for the model. A computer-modified mapping procedure is also described for searching the optimum separation conditions. Just five experiments and about 20 minutes of the computer time are needed to establish the optima of column temperature and of the carrier gas linear velocity. The relative deviation between the predicted and the experimental values was found to be within 20% for the plate heights, and within 1.5% for the retention times.     

Methodology for porting retention prediction data from old to new columns and from conventional-scale to miniaturised ion chromatography systems

Several procedures are available for simulating and optimising separations in ion chromatography (IC), based on the application of retention models to an extensive database of analyte retention times on a wide range of columns. These procedures are subject to errors arising from batch-to-batch variability in the synthesis of stationary phases, or when using a column having a different diameter to that used when the database was acquired originally. Approaches are described in which the retention database can be recalibrated to accommodate changes in the stationary phase (ion-exchange selectivity coefficient and ion-exchange capacity) or in the column diameter which lead to changes in phase ratio. The entire database can be recalibrated for all analytes on a particular column by performing three isocratic separations with two analyte ions. The retention data so obtained are then used to derive a "porting" equation which is employed to generate the required simulated separation. Accurate prediction of retention times is demonstrated for both anions and cations on 2mm and 0.4mm diameter columns under elution conditions which consist of up to five sequential isocratic or linear gradient elution steps. The proposed approach gives average errors in retention time prediction of less than 3% and the correlation coefficient was 0.9849 between predicted and observed retention times for 344 data points comprising 33 anionic or cationic analytes, 5 column internal diameters and 8 complex elution profiles.     

A Comparative Study of Pentafluorophenyl and Octadecylsilane Columns in High‐throughput Profiling of Biological Fluids

In high‐throughput metabolomic profiling, chromatographic separation is crucial because a well‐performed chromatographic separation may reduce signal suppression from complex biological matrices and improve the discoverability of low‐abundance metabolites. We compared the performance of pentafluorophenyl (PFP )‐ and octadecylsilane (ODS )‐based columns in profiling biological fluids. Peak resolutions and consistencies were acquired using several reversed‐phase columns and were evaluated. Total and extracted ion chromatograms demonstrated that the PFP column achieved better analyte separations than the ODS column. Low relative standard deviations on peak areas and retention times (<10.2 and <0.9%, respectively) acquired using the PFP column evidenced the high reproducibility and consistency of this column. In our study, a PFP column was used for profiling metabolomes extracted from urine and serum samples. Metabolomic study revealed a metabolome difference in normal and overweight participants. In total, 26 lipid species were significantly perturbed and further identified. Choline‐containing lipids were the most abundant perturbed lipidome in overweight participants, followed by sphingolipids and various phospholipids. We recommend the use of PFP columns in high‐throughput metabolomic analysis to promote the development of basic biological and clinical research in the future.     

Optimizing the relationship between chromatographic efficiency and retention times in temperature‐programmed gas chromatography

A methodology that can maximise the chromatographic efficiency that can be achieved within a defined time frame in temperature‐programmed gas chromatography is described. The efficiency can be defined as the inverse of peak widths measured in retention index units. This parameter can be described by a model similar to the van Deemter equation, which is expanded to account for the effect of the temperature rate in addition to the effect of carrier gas velocity. The model of efficiency is found by response surface methodology, where the temperature rates and the carrier gas velocities are systematically varied in the experiments. A second model that accurately explains the retention time of the last eluting compound can be found from the same experiments, and optimal conditions are found by combining the two models. The methodology has been evaluated with four capillary columns and three carrier gases, using fatty acid methyl esters as analytes. All experiments showed that there is a fairly linear decrease in efficiency with increasing temperature rates. At any temperature rate, optimal velocity is only marginally higher than the velocity that maximises chromatographic efficiency, since the carrier gas velocity has a limited effect on the retention times.     

High-performance liquid chromatographic separation of molecular species of neutral phospholipids.

Molecular species of neutral phospholipids, phosphatidylcholine (PC) and phosphatidylethanolamine (PE), were resolved by reversed-phase high-performance liquid chromatography (HPLC) using mobile phases of acetonitrile-methanol-water containing tetraalkylammonium phosphates (TAAPs). Competitive interactions of TAAPs and analyte solutes with a reversed-phase HPLC column resulted in reduced retention of PC or PE with concomitant increase in detection sensitivity. The chromatographic data for PC and PE were distinctly different from those for negatively charged phospholipids where ion-pair retention mechanisms prevailed. While PC (or PE) components eluted at longer retention times with a larger size of TAAP, an increase in the TAAP concentration invariably caused a decrease in phospholipid retention times. Optimization of HPLC conditions by using high concentrations (25-100 mM) of tetramethylammonium phosphate in acetonitrile-methanol-water (70:22:8) facilitated elution of components with improved peak symmetry. HPLC separations of neutral phospholipids derived from animal sources were more complex than those from soybeans.     

Chemometric analysis of comprehensive two-dimensional gas chromatography data using cryogenic modulation

The two-dimensional (2D) data structure generated under a high resolution GC×GC system with a small number of samplings taken across the first dimension is evaluated for the purpose of the application of chemometric deconvolution methods. Chemometric techniques such as generalized rank annihilation method (GRAM) place high demands on the reproducibility of chromatographic experiments. For GRAM to be employed for GC×GC data interpretation, it is critical that the separation method provides data with a bilinear structure; the peak-shape and retention times on both columns must be reproducible. With a limited number of samplings across a ¹D (first dimension) peak (e.g. four to six samplings) repeatability of the pattern of the modulated peaks (controlled by the modulation phase) becomes important in producing a bilinear data structure. Reproducibility of modulation phase can be affected by both reliability of the modulation period and reproducibility of the retention time of the peak on the first column (which arises from oven temperature and carrier flow rate stability). Evaluation of within-run and run-to-run retention time reproducibility (retention time uncertainty) on both columns, and modulation phase reproducibility using a modulated cryogenic system for a pair of overlapping components (fatty acid methyl esters) was undertaken. An investigation of the quality of data to permit quantification of each component by using GRAM deconvolution, was also conducted. Less than 4% run-to-run retention time uncertainty was obtained on column 1 and less than 9% run-to-run and within-run retention time uncertainty was obtained on column 2, where these R.S.D. measures are reported normalised to peak widths on each respective dimension. The R.S.D. of duplicate quantification results by GRAM ranged from 2 to 26% although the average quantification error using GRAM was less than 5%.     

Evaluation of a reversed-phase column (supelcosil LC-ABZ) under isocratic and gradient elution conditions for estimating octanol-water partition coefficients

The solvation parameter model is used to identify suitable chromatographic models for estimating the octanol-water partition coefficient for neutral compounds of varied structure by reversed-phase liquid chromatography. The stationary phase Supelcosil LC-ABZ with methanol-water mobile phases affords a series of suitable correlation models for estimating the octanol-water partition coefficient (log KOW) under isocratic and gradient elution conditions. Isocratic separations with mobile phase compositions containing from about 25 to 40% (v/v) methanol provide the most accurate results for log KOW values in the range -0.1 to 4.0. Gradient separations programmed from 5 to 100% (v/v) methanol are suitable for faster separations of compounds with large log KOW values. The standard error in the estimate for the regression models of the predicted log KOW values against literature values are 0.135 log units for the 30% (v/v) methanol-water isocratic system and 0.263 log units for the methanol-water gradient system. Isocratic retention factors predicted from two gradient separations with gradient times of 15 and 45 min afford a poorer fit for the correlation models between log KOW and the estimated retention factors than that of either the above isocratic and gradient models. Plots of the retention factor (log k) as a function of mobile phase composition are generally non-linear. Values of log kw obtained by non-linear extrapolation to a volume fraction of 0% (v/v) methanol do not afford a useful model for estimating log KOW.