Temperature programmed retention indices: Calculation from isothermal data. Part 1: Theory

Direct conversion of isothermal to temperature programmed indices is not possible. In this work it is shown that linear temperature programmed retention indices can only be calculated from isothermal retention data if the temperature dependence of both the distribution coefficients and the column dead time are taken into account. Procedures are described which allow calculation of retention temperatures and from these, accurate programmed retention indices. Within certain limits the initial oven temperature and programming rate can be chosen freely. The prerequisite for this calculation is the availability of reliable isothermal retention data (retention times, retention factors, relative retention times, or retention indices) at two different temperatures for one column. The use of compiled isothermal retention indices at two different temperatures for the calculation of retention temperatures and thus temperature programmed indices is demonstrated. For the column for which programmed retention indices have to be determined, the isothermal retention times of the n-alkanes and the column dead time as a function of temperature have to be known in addition to the compiled data for a given stationary phase. Once the programmed retention indices have been calculated for a given column the concept allows the calculation of temperature programmed indices for columns with different specifications. The characteristics which can be varied are: column length, column inner diameter, phase-ratio, initial oven temperature, and programming rate.     

Temperature programmed retention indices: Calculation from isothermal data. Part 2: Results with nonpolar columns

The procedure for calculating linear temperature programmed indices as described in part 1 has been evaluated using five different nonpolar columns, with OV-1 as the stationary phase. For fourty-three different solutes covering five different classes of components, including n-alkanes and alkyl-aromatic compounds, both isothermal and temperature programmed indices were determined. The isothermal information was used to calculate temperature programmed indices. For several linear programmed conditions accuracies better than 0.51^T-units were usually obtained. The results are compared with published procedures. It is demonstrated that isothermal retention information obtained on one column can be transferred to another column with the same stationary phase but different column dimensions and/or phase ratio. The temperature programmed indices calculated in this way also have an accuracy better than 0.51^T-u. The temperature accuracy and precision of the GC-instrumentation used was of the order of 0.1°C. All calculations can be run with a Basic-programmed microcomputer.     

Calculation of retention indices in temperature-programmed gas chromatography

Summary A new method is presented for the calculation of the retention indices under linear temperature programming with or without an initial isothermal period. The data calculated by the method are in good agreement with the isothermal retention indices.     

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%.     

Relationships between temperature programmed and isothermal Kovats retention indices in gas-liquid chromatography

Summary Theoretical relationships between the value of a Kovats index measured under isothermal column conditions and that measured with linear temperature programming have been re-examined. A new relationship is proposed which indicates that a retention index measured with temperature programming will correspond to an isothermally measured retention index with the column temperature at the harmonic mean of injection and elution temperatures. This has been experimentally tested for a set of non-polar compounds using OV 101 as stationary phase.Presented at the 14th International Symposium on Chromatography London, September, 1982     

Calculation of retention indices at an assigned temperature from temperature-programmed data

Summary A method is presented for the calculation of retention indices at an assigned temperature from temperature-programmed data. If the retention times at two different program rates for the solutes and the n-alkanes are known, the retention indices at an assigned temperature can be calculated directly.     

The temperature dependence of retention indices in gas chromatography

Summary A linear dependence of (T–T₁)/[1(T)–1(T₁)] on temperature (considering the retention index 1(T₁) at temperature T₁ as a standard value) is derived. Both ther retention index at an assigned temperature and the temperature dependence of the retention index can be calculated from retention data measured at two temperature-programing rates.     

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.     

Optimization and identification in any kind of multi-step temperature programmed gas chromatography

The theory which predicts the retention time, retention temperature, and peak width for any kind of multi-step TPGC and the principle of optimization has been described. Software for optimization and identification in TPGC has been developed on the basis of this theory. It has also been proven that the relationship between peak width in TPGC and the derived or “invented” retention time is similar to that between peak width and retention time in isothermal processes. The validity of the software has been proved by using it to predict retention temperature, retention time, and peak width for any kind of temperature programming and to predict the optimum temperature program for separation of a multihomolog mixture of industrial alcohols and 15 enantiomeric pairs of amino acids.     

Relation between the programmed and isothermal retention indices in chromatography

A systematic approach was utilized to deduce the relation between the programmed and isothermal retention indices in chromatography. The relation was given in the form of a chart from which the equivalent isothermal temperature T_e is plotted vs ΔT′ with I_P as the parameter. ΔT′ is a function of both the inlet and outlet temperatures during the temperature programmed run and T_e is the temperature at which the isothermal index is equal to the programmed index I_P.     

Prediction of retention times and peak widths in temperature-programmed gas chromatography using the finite element method

Optimization of separations in gas chromatography is often a time-consuming task. However, computer simulations of chromatographic experiments may greatly reduce the time required. In this study, the finite element method was used to predict the retention times and peak widths of three analytes eluting from each of four columns during chromatographic separations with two temperature programs. The data acquired were displayed in predicted chromatograms that were then compared to experimentally acquired chromatograms. The differences between the predicted and measured retention times were typically less than 0.1%, although the experimental peak widths were typically 10% larger than expected from the idealized calculations. Input data for the retention and peak dispersion calculations were obtained from isothermal experiments, and converted to thermodynamic parameters.     

Comparison of mathemical methods for the calculation of retention indices at high temperature in gas chromatography

The retention indices of three homologous series (2-alkanones, 1-alkanols, cycloalksanones) have been determined at high temperature by the application of two new adaptation methods: A multiparametric least-squares regressions iterative method based on the dertermination of the adjusted retention times and a cubic interpolation directly using the uncorrected retention times without dead time correction. The two methods were applied to two types of columns. The first group includes eight packed columns (seven OV polymethylphenylsiloxane and Apolane-87 stationary phases), while the second includes five glass capillary columns (four methyl-silicons with different film thicknesses and Apolane-87 stationary phases). The retention indices obtained with a multiparametric and a cubic interpolation methods were compared with each other and with those calculated by Grobler's, Guardino's, Kaiser's and Kovàts' methods. The influence of coating, film thickness, and temperature on them was investigated.     

Cubic splines compared with other methods for the calculation of programmed temperature retention indices

Summary Program temperature retention indices for fifteen nonalkane solutes have been determined by cubic splines, by other procedures found in the literature and by interpolation of the n-alkanes retention time logarithm for eleven temperature programs. A comparison in terms of variance of the differences between PTRI calculated by CS and each of the remaining methods is made for each of the eleven program runs, for each of the three stationary phases used and for many of the programs. The smallest variances obtained result when the Zenkevich, van den Dool & Kratz and Chen et al. methods are tested. The stationary phase polarity is of no relevance since it has no effect on the specific PTRI found by the different methods employed in this work.     

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

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

A new temperature programmed injection technique for capillary GC: Split mode with cold introduction and temperature programmed vaporization

Summary A new technique of split injection in capillary column Gas Chromatography is evaluated. The sample is introduced in the injector at low temperature and then vaporized by a fast programmed heating. The split is open all the time and the sample amount entering the column is proportional to the preset split ratio. It is demonstrated that no discrimination occurs and that it is possible to inject a very concentrated solution or undiluted sample with a high degree of accuracy and reproducibility in the same injector used for the total sample introduction or solvent — split introduction mode.Presented at the 14th International Symposium on Chromatography London, September, 1982     

Elution order inversions observed on using different carrier gas velocities in temperature programmed gas chromatography

Observations of chromatographic elution order inversions are reported which have occurred as a result of using different initial carrier gas velocities with oven temperature programming in GC and GC/MS systems.     

Prediction of the separation number of capillary columns in programmed temperature gas chromatographic analysis

The efficiency of capillary columns in programmed temperature analysis can be evaluated by calculation of the separation number (“Trennzahl”). A procedure for the prediction of this parameter at various initial temperatures, carrier gas pressures and heating rates, by using as the starting data the retention times and the peak widths obtained in some isobaric and isothermal runs is described. An equation is proposed that permits to obtain the values of the peak width at half height in any isothermal and linearly programmed temperature gas chromatographic run and therefore to calculate the separation number value. The effect on this parameter of the column polarity was investigated by using polar and non-polar compounds (n-alkanes and 1-alcohols).     

Implicit characteristic parameter of a programmed temperature retention index database

In a programmed temperature retention index (PTRI) database, there exists a characteristic parameter rt0/β that can be calculated if the experimental parameters are clearly given. This characteristic parameter can be used to flexibly reproduce the original PTRI data under chromatographic conditions different from those originally given. As this characteristic parameter is not explicitly given, it is suggested to name this parameter as the implicit characteristic parameter (TCP) of a PTRI database. The ICP in White's PTRI database was easily found and used satisfactorily to reproduce PTRI of some test compounds using either a Hewlett-Packard ultra-performance OV-1 column or a self-coated OV-1 column. The reproduction of PTRI could not be realized on columns of different materials. The fact that several PTRI databases measured on glass capillary columns could not satisfactorily be reproduced on fused silica column is explained.