Prediction of the resolution of capillary columns in different conditions of inlet pressure and temperature

A procedure previously described for the prediction of the plate height of capillary columns operated at different inlet pressure of the carrier gas and at various column temperatures by using few retention data measured under isobaric conditions was modified and improved in order to permit the prediction of the retention times and of the peak widths at various heights. It is therefore possible to calculate the ratio, delta, between the peak width at different heights and the peak width at half height, whose value is used to predict the resolution at different height of two closely eluting peaks. It was found that the delta values do not depend on temperature and inlet pressure and are a characteristic of the used column; they can therefore be used in order to calculate the resolution in any temperature and inlet pressure condition. The method was used to predict the retention time, the peak width and the resolution of polar and non-polar compounds (alkanes, alkenes, chloroalkanes, alcohols, ketones) on capillary columns of different length and polarity by using as the starting data retention and width values measured in three isobaric runs only.     

Nonlinear variation of sorption parameters of n-alkane homologsl in temperature-programmed gas chromatography (tpgc) and new equation for calculation of retention indixces

It has been demonstated that the considaerable difference in temperature increments of sorption parameters of n-alkanes under isothermal conditions is the main reason for nonlinear dependence of sorption parameters on molecular mass of homolog in temperaturre programmed gas chromatography (TPGC). A new nonlinear 4th parameter equation has been given for calculation of the retention indices. Coefficients of the equation are calculated from n-alkanes. The equation allows extrapolation and interpolation calculations of retention indices under TPGC conditions with experimental precision. The results obtained; for fatty acidkl methyl esters demonstrate the advantage of ovr equation in comparison with van den Dool and Kratz's equation.     

Resolution prediction and optimization of temperature programme in comprehensive two-dimensional gas chromatography

A model is developed for predicting the resolution of interested component pair and calculating the optimum temperature programming condition in the comprehensive two-dimensional gas chromatography (GC x GC). Based on at least three isothermal runs, retention times and the peak widths at half-height on both dimensions are predicted for any kind of linear temperature-programmed run on the first dimension and isothermal runs on the second dimension. The calculation of the optimum temperature programming condition is based on the prediction of the resolution of "difficult-to-separate components" in a given mixture. The resolution of all the neighboring peaks on the first dimension is obtained by the predicted retention time and peak width on the first dimension, the resolution on the second dimension is calculated only for the adjacent components with un-enough resolution on the first dimension and eluted within a same modulation period on the second dimension. The optimum temperature programming condition is acquired when the resolutions of all components of interest by GC x GC separation meet the analytical requirement and the analysis time is the shortest. The validity of the model has been proven by using it to predict and optimize GC x GC temperature programming condition of an alkylpyridine mixture.     

Simulation of column efficiency in temperature programmed gas-liquid chromatography

Summary If the dependence of HETP on temperature is specified under isothermal conditions, it is possible to predict the HETP for programmed temperature elution and subsequently peak width at half-height. This requires knowledge of isothermal retention time at retention temperature, which is computed by means of a model including the variation with temperature of dead time estimated from 3 homologs with carbon number: n, (n + j), (n + jk), where n, j and k are any integers. Predicted and measured peak widths corresponded within 4–9 %.     

Simulation of column efficiency in temperature programmed gas-liquid chromatography

Summary If the dependence of HETP on temperature is specified under isothermal conditions, it is possible to predict the HETP for programmed temperature elution and subsequently peak width at half-height. This requires knowledge of isothermal retention time at retention temperature, which is computed by means of a model including the variation with temperature of dead time estimated from 3 homologs with carbon number: n, (n+j), (n+jk), where n, j and k are any integers. Predicted and measured peak widths corresponded within 4–9%.     

An alternative approach for the estimation of equivalent temperature in gas chromatography

The temperature at which the isothermal retention time (tRiso) is equal to the temperature-programmed retention time (tRTPGC) or the isothermal retention index (Iiso) is equal to the temperature-programmed retention index (ITPGC) is defined as the equivalent temperature (Teq). The Teq of one-, two-, three-, and four-step temperature-programmed gas chromatography (TPGC) of unsaturated fatty acid methyl esters (FAMEs) from Chinese mustard seed oil is calculated. All of the tR values obtained at the Teq (tRTeq) are very close to the tRTPGC. The highest difference for each chromatogram is less than 0.5%. The slight deviation may partly arrive from the difficulty in setting the desired carrier gas flow rate. Also, good agreement among equivalent chain length values determined by different methods is observed, including the graphical method at the Teq. Therefore, it is speculated that the proposed method may facilitate the GC identification of FAMEs as well as other organic compounds in TPGC by using the available isothermal retention index database.     

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.     

The prediction of the peak width at half height in HPLC

The prediction of the peak width at half height is an important aspect in the optimization of the chromatographic operating conditions. In this paper, a linear relationship, between the peak widths at half height and the retention values with various isocratic elution is observed. In gradient elution, however, the relationship between the peak widths at half height and the so-called invented retention values that correspond to the mobile phase composition by eluting the solute from the column end is developed. We believe that there is almost the same band width at half height inside the column (in unit of length) for different solutes. The peak width at half height in the chromatogram (in unit of time) is mainly determined by the capacity factor of the solute when it is eluted from the column end. The larger the capacity factor of a solute eluted from the column end, the more slowly will be the solute eluted from the column end and the wider will be the peak width at half height. It is possible to predict the peak width at half height in various isocratic and gradient elutions by using this linear relationship.     

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.     

Prediction of gas chromatographic retention times of esters of long chain alcohols and fatty acids

The linear free energy of solution (DeltaG) relationship (DeltaG=DeltaGo+zdeltaG) for compounds of different carbon atoms (z) in the same homologous series is expanded and modified to cover compounds with two different hydrocarbon side chains. The expanded equation is successfully used to predict the retention times (tR) of standard esters of long chain alcohols and fatty acids of different chain lengths in both isothermal and temperature-programmed gas chromatography (TPGC). Approximately 90% of the 125 predicted tR values have a difference of less than 1.00% from the actual tR and the highest difference is 1.26%. Two different temperature gradients in TPGC are tested. The expanded equation can be used to forecast the tR of TPGC with good accuracy. The highest difference is +/-1.40% and +/-1.00% for the temperature gradients of 2 degrees C and 4 degrees C/min, respectively. However, the increments in free energy per carbon atom (zdeltaG) of the alcohol and acid are approximately equal but have slightly different temperature sensitivities. Therefore, it is very difficult to separate esters of different acid and alcohol chain length but with the same total carbon numbers. Furthermore, the difference in temperature sensitivities for the acid and alcohol side chains renders them to be inversely eluted at different temperatures.     

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.     

Off-line optimization of the separation of 2,4-dinitrophenylhydrazones by gas chromatography using chemometric techniques

An off-line optimization technique based on soft modeling methods has been used to determine the optimum conditions for the separation of eight carbonyl-2,4-dinitrophenylhydrazones by gas chromatography equipped with a nitrogen-phosphorous detector. In this method theoretical simulations of peak retention time and peak width at base-line are coupled to a factorial design to map the chromatographic response surface. The calculated retention times from isothermal data have been used to calculate the chromatographic parameters. A full 3(3) factorial design was used to locate the optimum conditions for the temperature program, utilizing initial oven temperature, T(i), the programming rate for the first ramp, PR(1), and the programming rate for the second ramp, PR(2) as independent variables. The optimum conditions obtained for these parameters were: T(i), 140 degrees C; PR(1), 12 degrees Cmin(-1); PR(2), 8 degrees Cmin(-1). The maximum analysis times achieved by this optimum was 10.6 min.     

Novel computer-assisted approach to quick prediction and optimization of gradient separation for online enrichment-reversed phase liquid chromatography tandem system

An algorithm capable of predicting and optimizing the gradient separation of LC × LC system was developed in this paper. Two groups of structural analogues, five ginsenosides as well as eight bisphenols,which were difficult to discriminate in routine analysis, were used to verify the effectiveness of the proposed algorithm in fast separation optimization. Average errors of retention times below 1% were found in the retention prediction for all types of gradient programs, implying that the theory...     

Temperature effect on peak width and column efficiency in subcritical water chromatography

Subcritical water has been recently employed as the mobile phase to eliminate the use of organic solvents in reversed-phase liquid chromatography. Although the influence of temperature on retention in subcritical water chromatography has been reported, the temperature effect on peak width and column efficiency has not yet been quantitatively studied. In this work, several polar and chlorinated compounds are separated using pure subcritical water on Zorbax RX-C8, PRP-1 (polystyrene-divinylbenzene), Hypersil ODS, and ZirChrom-polybutadiene columns. Isothermal separations are performed at temperatures ranging from 60 degrees C to 160 degrees C. The retention time and peak width of analytes are reduced with increasing temperature. However, the column efficiency is either improved or almost unchanged with the increasing temperature in the low-temperature range (lower than the 100 degrees C to 120 degrees C range), but it is decreased when temperature is further raised in the high-temperature range (higher than the 100 degrees C to 120 degrees C range). Therefore, a maximum in column efficiency is obtained at temperatures within the 100 degrees C to 120 degrees C range in most cases.     

Prediction of retention times and efficiency in linear gradient programmed pressure analysis on capillary columns

A method for the prediction of the retention time and the resolution of chromatographic peaks in different experimental conditions by starting from few experimental data measured in isothermal and isobaric analyses was published previously. In this paper, the same mathematical model was implemented for calculating the retention times and the column efficiency in programmed pressure runs. Some models originated from the Golay equation and reported in the literature are compared, and a new modified equation for the calculation of the peak width at half height is proposed. The procedure for the prediction of the retention time and the peak width at half height at programmed pressure of the carrier gas and different column temperature and linear gradient by using retention data of different compounds obtained in few isobaric runs is described. The prediction of the retention time and the separation efficiency of compounds with different polarity gave good results for the programmed pressure runs with linear gradient. The effect of the variation of the initial parameters of the experimental analyses and of the mathematical model on the accuracy of the prediction has been evaluated.     

A novel approach to modelling counter-current chromatography

Literature lists a number of counter-current chromatography (CCC) models that can predict the retention time and to a certain extent the peak width of a solute eluting from a CCC column. The approach described in this paper distinguishes itself from previous reports by relating all model parameters directly to column dimensions and experimental settings. Most importantly, this model can predict a chromatogram from scratch without resorting to traditional calibration using empirical values. The model validation with experimental results obtained across a range of CCC instruments demonstrated that the solute retention time, peak width, and peak resolution could be predicted within reasonable accuracy. Additionally, the effect of several process parameters, such as mobile phase flow rate, rotational speed of the column or β-value, showed that the model is robust and applicable to a wide range of CCC instruments. Overall, this model proved to be a useful tool for parameter estimation and, most significantly, separation optimisation.     

Retention prediction of polycyclic aromatic hydrocarbons in reversed phase liquid chromatography with various mobile phase compositions and column temperatures

Summary The relationship between the logarithmic capacity factor measured in reversed-phase liquid chromatography and the operating conditions including the mobile phase composition and the column temperature is investigated. The strategy described herein can offer the possibility to predict the retention of polycyclic aromatic hydrocarbons without any experiments and standard materials, by utilizing equations describing the relationships between retention, temperature, mobile phase composition and physicochemical properties of the solutes previously stored in the program of the microcomputer-assisted retention prediction system.This concept is one of the most promising techniques for the optimization of the separation conditions in reversed-phase liquid chromatography.     

不同温度模式下保留值关联的统一方法

提出了一种不同温度模式下保留值关联的统一方法,能够根据两个或多个任意温度模式下的保留数据预测其它温度条件下的保留值;作者已经把这个方法应用于自建的保留指数数据库软件中。     

Combined use of algorithms for peak picking, peak tracking and retention modelling to optimize the chromatographic conditions for liquid chromatography-mass spectrometry analysis of fluocinolone acetonide and its degradation products

A strategy for rapid optimization of liquid chromatography column temperature and gradient shape is presented. The optimization as such is based on the well established retention and peak width models implemented in software like e.g. DryLab and LC simulator. The novel part of the strategy is a highly automated processing algorithm for detection and tracking of chromatographic peaks in noisy liquid chromatography-mass spectrometry (LC-MS) data. The strategy is presented and visualized by the optimization of the separation of two degradants present in ultraviolet (UV) exposed fluocinolone acetonide. It should be stressed, however, that it can be utilized for LC-MS analysis of any sample and application where several runs are conducted on the same sample. In the application presented, 30 components that were difficult or impossible to detect in the UV data could be automatically detected and tracked in the MS data by using the proposed strategy. The number of correctly tracked components was above 95%. Using the parameters from the reconstructed data sets to the model gave good agreement between predicted and observed retention times at optimal conditions. The area of the smallest tracked component was estimated to 0.08% compared to the main component, a level relevant for the characterization of impurities in the pharmaceutical industry.     

Designing polymer matrix for microchip-based double-stranded DNA capillary electrophoresis

An optimization strategy for ternary solvent-strength gradient elution RP chromatography is described in which a two-dimensional model of gradient time (2 levels) against ternary proportions of organic modifiers (4 levels) was constructed. From the resolution surface the optimum ratio of organic modifiers could be selected. Excellent retention time and acceptable peak width and resolution simulations were obtained. The separation could be further optimized from the same input data by using a standard one-dimensional model in order to optimize for gradient slope, duration and shape. Excellent retention time and acceptable peak width and resolution simulations were obtained (< 1, 2 and 6% error, respectively).