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. 2023 May 23;8(22):19708–19718. doi: 10.1021/acsomega.3c01348

Retention Database for Prediction, Simulation, and Optimization of GC Separations

Tillman Brehmer †,*, Benny Duong †, Manuela Marquart †, Luise Friedemann †,‡, Peter J Faust †,§, Peter Boeker †,§, Matthias Wüst †, Jan Leppert †
PMCID: PMC10249385  PMID: 37305293

Abstract

graphic file with name ao3c01348_0010.jpg

This work presents an open source database with suitable retention parameters for prediction and simulation of GC separations and gives a short introduction to three common retention models. Useful computer simulations play an important role to save resources and time in method development in GC. Thermodynamic retention parameters for the ABC model and the K-centric model are determined by isothermal measurements. This standardized procedure of measurements and calculations, presented in this work, have a useful benefit for all chromatographers, analytical chemists, and method developers because it can be used in their own laboratories to simplify the method development. The main benefits as simulations of temperature-programed GC separations are demonstrated and compared to measurements. The observed deviations of predicted retention times are in most cases less than 1%. The database includes more than 900 entries with a large range of compounds such as VOCs, PAHs, FAMEs, PCBs, or allergenic fragrances over 20 different GC columns.

1. Introduction

Method developments in gas (liquid) chromatography can often require a lot of time and resources. More efficient, less expensive, and resource-saving perspectives are opened up by the use of appropriate computer simulations to simplify the optimization process and solve separation problems. In method development, even simple retention models and calculations can be very helpful, for example, to estimate elution orders, retention times, or resolution. Retention models and simulations need substance-specific retention parameters, for example, for the model of Clarke and Glew1 or the K-centric model of Blumberg.2−4 Because the determination of those substance-specific and stationary-phase-specific parameters is also elaborate, it is constructive to collect them in databases and share them with the scientific community.

There are other retention databases existing, such as the retention index (RI) database for example of NIST5 or the linear solvation energy relationship (LSER) database of UFZ.6 These retention data are primarily suitable for prediction of retention phenomena and the distribution in the chromatographic phases. With K-centric data, the characteristic temperature may also be suitable for identification. Via simulation, those retention data can also be used for prediction of retention indices similar to the LSER approach.7 The retention data presented in this work are temperature-independent and can therefore be used for prediction of temperature programs.8 Therefore, compared to the LSER9 approach K-centric retention data can describe the change of retention factor k with the temperature.

This work presents an available open source retention database for three common retention models and gives a short overview for the calculation of the corresponding data. All three retention models describe the temperature dependence of the retention factor with different parameter sets and can be converted into each other. To save the user of the database a conversion, the data for each of the three retention models are presented in the corresponding parameter set, which is very convenient. The benefit of the data, for example, for simulation of GC separations is demonstrated. The standardized procedure of the determination can be useful for every gas chromatographer or analytical chemist to get predictions for their own measurements.

1.1. Thermodynamic Retention Model

In gas chromatography, the partition of a solute between the mobile phase (gas) and the stationary phase (liquid) is measured by the distribution coefficient K, defined as the ratio of the concentration of the solute in the stationary phase and in the mobile phase. It can be measured by isothermal measurements of the retention factor k and the phase ratio β of the column.

1.1. 1

The distribution coefficient K depends on the temperature T and the Gibbs free energy ΔG of the evaporation of the solute from the stationary phase.10

1.1. 2

with R being the molar gas constant. The Gibbs free energy ΔG can be expressed by enthalpy ΔH and entropy ΔS changes of the solute from the stationary into the mobile phase as

1.1. 3

and therefore

1.1. 4

Both ΔH and ΔS depend on the temperature T itself. To compensate for this temperature dependency, a third parameter ΔCp (change of the isobaric molar heat capacity) can be introduced and the enthalpy ΔHref and entropy ΔSref at a reference temperature Tref are used. Equations 2 and 3 lead to the classic van’t Hoff model and further to

1.1. 5

which can be converted in a 3-parameter model of Clarke and Glew1,4 for curve fitting

1.1. 6

It was shown11 that using a 3-parameter model results in a better fit of k over a wider temperature range than using a 2-parameter model with constant ΔH and ΔS.

The parameters A, B, and C can be converted to enthalpy ΔHref and entropy ΔSref for a chosen reference temperature Tref and the change of the isobaric molar heat capacity ΔCp.

1.1. 7
1.1. 8
1.1. 9

It seems reasonable to set up a model that normalizes its reference variables to a certain temperature. In adsorption phenomena, especially in chromatography, the distribution of an analyte depends to a large extent on the temperature conditions but not on the same temperature for each analyte. Choosing one reference temperature Tref for all analytes leads to physically meaningless conditions for substances with extreme retention, such as highly volatile compounds or low volatile substances like triglycerides. For chromatography, it is more appropriate to normalize the model to the same distribution of the analyte over the stationary phase, expressed by the distribution coefficient K.4

A fully equivalent model to describe the distribution of a solute between stationary and mobile phases in a 3-parameter model is the distribution-centric 3-parameter model of Blumberg,4 the short K-centric model. In this model, the retention factor k of a solute in a GC system is defined by three parameters:

  • Tchar characteristic temperature

  • θchar characteristic thermal constant

  • ΔCp change of the isobaric molar heat capacity (eq 7)

and the equation

1.1. 10

These parameters, especially Tchar and θchar, have a direct chromatographic meaningful interpretation. The characteristic temperature Tchar is the temperature, where ln k = 0 and k = 1.4 At this temperature, the amount of the solute is evenly distributed between stationary and mobile phases. The characteristic thermal constant is the inverse declining slope of the function ln k(T) at T = Tchar. Therefore, an increase of the temperature around Tchar by θchar reduces k by a factor of e ≈ 2.72. The interpretation of ΔCp is not straightforward, but it generally defines the deviation of k from a 2-parameter model for temperature significantly lower/higher than Tchar.

The parameters Tchar, θchar, and ΔCp are specific for the phase ratio β0 used to determine these parameters. Using a column with the same stationary phase but different phase ratio β1 requires a correction factor for the retention factor calculated from eq 10.

1.1. 11

The retention factor k can be determined using the retention time from the chromatogram at the known void time tM of the GC column, which is the time the carrier gas or a substance with no retention requires to pass the column.

1.1. 12

The void time tM can be measured by detection of a non-interacting gas, for example, methane or air. For wall-coated cylindrical GC columns with length L, internal diameter d, and temperature T, tM can also be determined with

1.1. 13

where pi is the pressure at the inlet of the column, po at the column outlet, and η is the viscosity of the carrier gas.10

2. Materials and Methods

2.1. Chemicals

To create the database, 260 substances were measured, such as homologous alkanes, alcohols, ketones, phenones, BTEXs, halogen-phenols, and others. Relevant substances for the analytic in food and cosmetics were also measured, for example, 37 FAMEs, 58 allergenic fragrances, 16 EPA-PAHs, 6 PCBs, 6 triglycerides, and other volatile compounds. All used standard substances were purchased by Sigma-Aldrich with a purity of higher than 99.9%. Therefore, dilutions of the compounds were used to determine retention parameters of these substances and to measure chromatograms with different temperature programs.

2.2. Columns

Measurements for determination of the retention parameters were performed on different GC separation columns: 30 m × 0.25 mm × 0.25 μm Rxi17SilMS (75% phenyl–25% methylpolysiloxane, Restek. USA), 30 m × 0.25 mm × 0.25 μm Rxi5SilMS (75% phenyl–25% methylpolysiloxane, Restek. USA), 30 m × 0.25 mm × 0.5 μm Rxi5SilMS, and 10 m × 0.1 mm × 0.1 μm ZB-PAH-CT (proprietary stationary phase, Phenomenex, USA). Void times were measured with injections of air and detection of the oxygen signal in the TOF-MS. The L/d ratios of the columns were determined from void time measurements by using eq 13 and are shown in Table 1.

Table 1. Determined L/d Ratios for the Investigated Separation Columns.

stationary phase d [mm] df [μm] L/d L [m]
Rxi17SilMS 0.25 0.25 120,889.6 ± 170.4 30.222 ± 0.043
Rxi5SilMS 0.25 0.25 121,606.8 ± 1475.7 30.40 ± 0.37
Rxi5SilMS 0.25 0.5 119,084.0 ± 1276.0 29.77 ± 0.32
ZB-PAH-CT 0.1 0.1 102,300.0 ± 4700.0 10.23 ± 0.47
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2.3. Instrumentals

A HP 6890 series GC system from Hewlett Packard/Agilent with split/splitless injector (300 °C, 1:100 split ratio) coupled with a BenchTOF-dx time-of-flight mass spectrometer from Markes, UK, was used. The allergen fragrances on the Rxi17SilMS were measured using an internal flame ionization detector of the GC (HP), with void time measurements using methane. Carrier gas was helium with purity of 99.9%. A PAL RSI Chronect Robotic autosampler (CTC Analytics AG, Switzerland) was used for injection of 1 μL of each sample. Isothermal measurements were made in the range from 60 to 300 °C with 10 °C increments and a constant flow of 1 mL/min of the carrier gas.

To validate the parameters, temperature-programed measurements were performed on the HP 6890 GC and a flow field gradient GC (FF-TG-GC)12 (HyperChrom SA, Luxembourg). The measured chromatograms were compared to simulated data.

2.4. Literature Data

13 data sets with retention parameters were found in the literature. Table 2 gives an overview about the size of the data sets, the number of compounds and columns that are included, and the reference of the literature.

Table 2. Data sets with Retention Data Found in the Literature That are Included in the Database.

data set size of data set number of compounds number of columns references
1 88 88 1 (13)
2 47 45 1 (14)
3 5 5 1 (3)
4 7 7 1 (15)
5 51 17 3 (11)
6 22 22 1 (2)
7 76 12 3 (16)
8 6 6 1 (17)
9 25 11 3 (18)
10 11 11 1 (19)
11 25 19 1 (20)
12 34 16 2 (21)
13 135 19 8 (22)
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2.5. Software

For calculation of void times and ln k values, MS Office Professional Plus 2019 Excel was used. All other calculations were performed in a Pluto notebook23 using the programming language Julia.24 The notebook is available in the project “RetentionData” via GitHub.25 For robust fitting and outlier detection, the package RAFF.jl was used.26 For linear and multivariate fits, the package LsqFit.jl was used.27,28 Simulation of GC separations and chromatograms were performed with the open source software GasChromatographySimulator.jl.29 Detailed information to the simulation can be found elsewhere.2

3. Creation of the Database

3.1. Calculations and Processing Steps

A schematic overview of the calculation and processing steps is given in Figure 1.

Figure 1.

Figure 1

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Schematic overview of the main tasks for calculation and converting of the retention parameters and creation of the database.

K-centric parameters of each compound were determined by fitting the ln k values, calculated by eq 12, against the temperature of the investigated temperature range by using the K-centric model by Blumberg (eq 10) (see Figure 1 no. 1).

K-centric parameters were converted into the ABC parameters using eq 14 (see Figure 1 no. 3) with knowledge of nominal β.4

3.1. 14

Enthalpy ΔHref and entropy ΔSref were determined from the ABC parameters by using eq 7 and 8, respectively, with a reference temperature of 90 °C (Figure 1 no. 5). 90 °C for Tref was chosen because other the literature data are determined at these reference temperatures. With Tref = Tchar, the K-centric equivalents ΔHchar and ΔSchar, enthalpy, and entropy at the solute specific characteristic temperature were determined, which are more meaningful for chromatography.4

Data from the literature were converted into K-centric parameters by using the following steps (Figure 1 no. 2).

ABC parameters can be converted to K-centric data by using eqs 15 and 164 (Figure 1 no. 4).4

3.1. 15

with

3.1. 16

where T1 = 1 K and W(x) is the Lambert W function (also known as product log function). Per definition, the argument x has to be larger than −1/e. The Lambert W function has two branches W0 and W–1, as shown in Supporting Information, Figure S1. All data so far, show that only the branch W–1 is used; therefore, the value of x, eq 16, has to be between −1/e and 0.

With knowledge of the reference temperature Tref, thermodynamic data as ΔSref and ΔHref can be converted into ABC parameters4 (Figure 1 no. 6). As shown above, they can be converted into K-centric data (Figure 1 no. 4).

3.2. Validation and Quality Control

The calculated values have to be validated (Figure 1 no. 7). For acceptance of the compound data the following criteria are defined:

  • (a)

    The data set includes three data points as minimum for non-linear multivariate fit, ideally four data points or more. As a recommendation, the data should contain points around ln k = 0 to achieve accurate fitting results.

  • (b)

    ln k values range between −2.0 and 3.5, too high ln k values are associated with too broad peaks, increased signal-to-noise, and inaccurate retention times. Since low ln k values often result in analyte peaks merging into the solvent peak, retention does not only depend on the stationary phase.

  • (c)

    0 < θchar < 100, a negative θchar cannot be accepted because it would mean that a temperature increase leads to higher retention times than to lower. Based on available data, the parameter θchar tends to be lower than 100 °C, in most cases around 30 °C.10

  • (d)

    Tchar > −273.15 °C, a value of Tchar below the absolute zero is not possible.

  • (e)

    C > 0, negative C shows a lower bending of the fit curve, the curve becomes more linear and causes also to the wrong branch of the Lambert W function (W0).

  • (f)

    A < 0, based on available data the parameter A tends to be negative.

  • (g)

    W(x) < −1 and −1/e < x < 0, data are inacceptable if the value of the argument x of the Lambert W function gets lower than −1/e or W(x) > −1. Available data shows a value of W(x) lower than −1 and is on the W–1 branch, therefore −1/e < x < 0.

Data that failed one of the criteria will be flagged in the database. The reason of the failure will be documented.

To create the final database after validation as shown in Figure 1 no. 8, the parameters of each compound related to the stationary phase are collected in a table. For many substances, a substance category is added, for example “n-alkanes” for homologous series of alkanes, “FAMEs” for fatty acid methyl esters (FAMEs), or “Grob”, if the substance is part of the Grob mix for evaluation of GC columns. The structure of the final table is shown in Table 3.

Table 3. Structure of the Retention Database and Determined Values of the Retention Parameters of a Selection of Allergenic Fragrances, Triglycerides, PCBs, and PAHsa.

name CAS phase φ0 A errorA B errorB C errorC ΔHref
graphic file with name ao3c01348_m017.jpg
 ΔSref
graphic file with name ao3c01348_m018.jpg
 Tref
cinnamaldehyde 104-55-2 Rxi17SilMS 0.001 –82.062 0.65699 10,505 41.611 10.503 0.092476 –55,627 74.286 –80.181 0.17972 90
farnesol A 4602-84-0 Rxi17SilMS 0.001 –108.94 5.955 13,698 402.29 13.933 0.82925 –71,825 876.98 –107.01 2.0583 90
farnesol B 4602-84-0 Rxi17SilMS 0.001 –143.29 4.9454 15,819 337.2 18.806 0.68763 –74,741 757.59 –113.34 1.7679 90
geraniol 106-24-1 Rxi17SilMS 0.001 –88.825 2.3832 10,625 143.78 11.451 0.33807 –53,770 199.92 –82.087 0.49881 90
glyceryl tridecanoate 621-71-6 Rxi17SilMS 0.001 –394.74 65.672 41,657 5590.7 51.841 8.8180 –189,820 20186 –310.16 41.164 90
glyceryl trihexanoate 621-70-5 Rxi17SilMS 0.001 –188.84 20.960 22,064 1588.2 24.456 2.8654 –109,610 4636.7 –168.13 10.181 90
glyceryl trilaurate 538-24-9 Rxi17SilMS 0.001 –543.67 127.33 55,893 11394 71.568 16.969 –248,630 44256 –417.58 87.316 90
glyceryl trimyristin 555-45-3 Rxi17SilMS 0.001 –655.14 198.66 66,369 27435 86.428 25.872 –290,860 181970 –492.57 265.34 90
glyceryl trioctanoate 538-23-8 Rxi17SilMS 0.001 –211.38 27.344 25,948 2197.4 27.112 3.7033 –133,880 7159.8 –203.29 15.197 90
glyceryl tripalmitin 555-44-2 Rxi17SilMS 0.001 –493.02 661.79 53,703 529250 64.545 23.508 –251,620 4398400 –399.00 5293.9 90
iso E super A 54464-57-2 Rxi17SilMS 0.001 –94.965 2.4567 12,303 167.07 12.154 0.34177 –65,595 375.22 –92.836 0.87513 90
iso E super B 54464-57-2 Rxi17SilMS 0.001 –96.736 3.5892 12,420 243.95 12.407 0.49917 –65,801 531.2 –93.049 1.2494 90
iso E super C 54464-57-2 Rxi17SilMS 0.001 –96.021 5.5070 12,334 376.07 12.331 0.76535 –65,315 833.99 –91.485 1.9543 90
iso E super D 54464-57-2 Rxi17SilMS 0.001 –101.18 5.3862 12,802 368.57 13.014 0.74834 –67,148 823.79 –95.219 1.9272 90
limonene 138-86-3 Rxi17SilMS 0.001 –75.098 4.3818 83,93.5 240.6 9.8499 0.63146 –40,046 205.41 –59.733 0.54245 90
linalool 78-70-6 Rxi17SilMS 0.001 –83.176 2.6778 95,08.6 151.66 10.803 0.38383 –46,441 140.04 –72.290 0.36234 90
PCB 101 37680-73-2 Rxi5SilMS 0.002 –111.16 0.85969 14,804 66.924 14.179 0.11708 –80,277 209.05 –111.41 0.44911 90
PCB 138 35065-28-2 Rxi5SilMS 0.002 –107.39 2.4739 15,187 200.61 13.561 0.33499 –85,325 685.92 –115.53 1.4259 90
PCB 153 35065-27-1 Rxi5SilMS 0.002 –106.02 3.2438 14,985 260.39 13.377 0.43993 –84,199 874.59 –114.60 1.8301 90
PCB 180 35065-29-3 Rxi5SilMS 0.002 –95.041 5.9211 14,747 489.4 11.783 0.79956 –87,035 1731 –114.72 3.5510 90
PCB 28 7012-37-5 Rxi5SilMS 0.002 –101.55 2.2747 13,300 169.51 13.001 0.31176 –71,330 474.46 –98.992 1.0547 90
PCB 52 35693-99-3 Rxi5SilMS 0.002 –108.61 2.3285 14,057 175.54 13.925 0.31859 –74,832 506.49 –104.77 1.1160 90
benz[a]anthracene 56-55-3 ZB-PAH-CT 0.001 –17.543 48.568 9795.2 3816.2 0.92277 6.6114 –78,656 12497 –92.960 26.368 90
benzo[g,h,i]perylene 191-24-2 ZB-PAH-CT 0.001 –15.308 13.044 10,841 1125.3 0.57344 1.7504 –88,404 4257.1 –94.403 8.4867 90
dibenzo[a,h]anthracene 53-70-3 ZB-PAH-CT 0.001 –93.497 26.461 16,475 2300.0 11.327 3.5481 –10,2780 8853.9 –128.05 17.501 90
indeno[1,2,3-cd]pyrene 193-39-5 ZB-PAH-CT 0.001 –55.231 39.696 13,583 3436.5 6.0911 5.3263 –94,547 13175 –110.03 26.091 90
name CAS phase φ0 Tchar
graphic file with name ao3c01348_m019.jpg
 θchar
graphic file with name ao3c01348_m020.jpg
 ΔCp
graphic file with name ao3c01348_m021.jpg
 vHchar
graphic file with name ao3c01348_m022.jpg
 ΔSchar
graphic file with name ao3c01348_m023.jpg
cinnamaldehyde 104-55-2 Rxi17SilMS 0.001 174.33 0.012622 34.497 0.025762 87.329 0.76889 –48262 36.144 –61.944 0.0806
farnesol A 4602-84-0 Rxi17SilMS 0.001 210.18 0.075096 33.545 0.16568 115.85 6.8948 –57,903 286.56 –73.892 0.59201
farnesol B 4602-84-0 Rxi17SilMS 0.001 215.35 0.069363 35.982 0.15936 156.36 5.7173 –55,141 244.72 –66.971 0.50020
geraniol 106-24-1 Rxi17SilMS 0.001 150.5 0.032493 31.082 0.067725 95.209 2.8109 –48,010 104.87 –67.417 0.24708
glyceryl tridecanoate 621-71-6 Rxi17SilMS 0.001 357.50 1.20 44.375 2.8054 431.03 73.317 –74,520 4719.7 –72.255 7.4737
glyceryl trihexanoate 621-70-5 Rxi17SilMS 0.001 279.28 0.36766 35.679 0.53451 203.34 23.824 –71,117 1069.6 –82.828 1.9305
glyceryl trilaurate 538-24-9 Rxi17SilMS 0.001 393.69 3.3938 54.435 8.6086 595.05 141.09 –67,920 10764 –55.946 16.116
glyceryl trimyristin 555-45-3 Rxi17SilMS 0.001 471.37 130.28 274.27 2095.4 718.60 215.11 –16,804 128520 23.337 172.49
glyceryl trioctanoate 538-23-8 Rxi17SilMS 0.001 318.75 0.27448 35.386 0.54949 225.42 30.791 –82,318 1280.5 –93.167 2.1606
glyceryl tripalmitin 555-44-2 Rxi17SilMS 0.001 556.97 5727.5 5634.7 17350000 536.66 195.45 –10,16.8 3131000 44.683 3771.7
iso E super A 54464-57-2 Rxi17SilMS 0.001 213.41 0.043614 37.053 0.092552 101.05 2.8417 –53,123 133.03 –63.273 0.27289
iso E super B 54464-57-2 Rxi17SilMS 0.001 214.72 0.025811 37.385 0.084073 103.16 4.1503 –52,935 119.17 –62.594 0.24407
iso E super C 54464-57-2 Rxi17SilMS 0.001 217.20 0.046149 38.245 0.14648 102.52 6.3635 –52,274 200.45 –60.696 0.40842
iso E super D 54464-57-2 Rxi17SilMS 0.001 218.27 0.047197 37.694 0.14396 108.20 6.222 –53,269 203.7 –62.489 0.41412
limonene 138-86-3 Rxi17SilMS 0.001 106.20 0.05929 30.903 0.1486 81.897 5.2502 –38,719 186.58 –56.158 0.49107
linalool 78-70-6 Rxi17SilMS 0.001 120.72 0.029744 29.529 0.067299 89.817 3.1914 –43,682 99.774 –64.996 0.25290
PCB 101 37680-73-2 Rxi5SilMS 0.002 294.81 0.023455 47.780 0.053172 117.89 0.97344 –56,132 62.638 –58.687 0.11006
PCB 138 35065-28-2 Rxi5SilMS 0.002 318.7 0.12712 48.915 0.20645 112.75 2.7853 –59,539 252.59 –60.455 0.42514
PCB 153 35065-27-1 Rxi5SilMS 0.002 312.05 0.16064 47.854 0.25766 111.22 3.6578 –59,502 322.03 –61.532 0.54816
PCB 180 35065-29-3 Rxi5SilMS 0.002 330.90 0.33185 47.826 0.48932 97.972 6.6479 –63,433 652.73 –64.868 1.0760
PCB 28 7012-37-5 Rxi5SilMS 0.002 269.33 0.052128 47.105 0.085008 108.10 2.5921 –51,944 94.272 –55.609 0.17305
PCB 52 35693-99-3 Rxi5SilMS 0.002 276.10 0.050548 47.072 0.10184 115.78 2.6489 –53,285 115.7 –56.871 0.21008
benz[a]anthracene 56-55-3 ZB-PAH-CT 0.001 296.00 2.5171 34.944 2.3759 7.6724 54.97 –77,075 5284.5 –89.513 9.2267
benzo[g,h,i]perylene 191-24-2 ZB-PAH-CT 0.001 359.69 0.82067 38.222 0.71626 4.7678 14.553 –87,118 1648.1 –91.755 2.5859
dibenzo[a,h]anthracene 53-70-3 ZB-PAH-CT 0.001 362.95 2.0216 43.648 2.0490 94.176 29.501 –77,076 3651.2 –75.261 5,7012
indeno[1,2,3-cd]pyrene 193-39-5 ZB-PAH-CT 0.001 359.73 3.0879 41.172 2.7876 50.644 44.285 –80,886 5533.2 –81.899 8.6760
name CAS phase φ0 N R2 χ2
graphic file with name ao3c01348_m024.jpg
 source flag category 1 category 2
cinnamaldehyde 104-55-2 Rxi17SilMS 0.001 8 1 6.5340 × 10–7 1.3068 × 10–7 this work   aldehyde allergenic fragrances
farnesol A 4602-84-0 Rxi17SilMS 0.001 8 0.99999 3.6088 × 10–5 7.2175 × 10–6 this work   allergenic fragrances  
farnesol B 4602-84-0 Rxi17SilMS 0.001 9 0.99999 5.2339 × 10–5 8.7231 × 10–6 this work   allergenic fragrances  
geraniol 106-24-1 Rxi17SilMS 0.001 9 1 2.2404 × 10–5 3.7340 × 10–6 this work   terpene allergenic fragrances
glyceryl tridecanoate 621-71-6 Rxi17SilMS 0.001 24 0.99636 8.3195 × 10–2 3.9617 × 10–3 this work   triglyceride  
glyceryl trihexanoate 621-70-5 Rxi17SilMS 0.001 14 0.99968 9.3626 × 10–3 8.5115 × 10–4 this work   triglyceride  
glyceryl trilaurate 538-24-9 Rxi17SilMS 0.001 13 0.99883 3.9493 × 10–3 3.9493 × 10–4 this work   triglyceride  
glyceryl trimyristin 555-45-3 Rxi17SilMS 0.001 13 0.99916 9.1803 × 10–3 9.1803 × 10–4 this work θchar > 100 °C triglyceride  
glyceryl trioctanoate 538-23-8 Rxi17SilMS 0.001 20 0.99958 1.4787 × 10–2 8.6984 × 10–4 this work   triglyceride  
glyceryl tripalmitin 555-44-2 Rxi17SilMS 0.001 9 0.99897 3.4491 × 10–3 5.7485 × 10–4 this work θchar > 100 °C triglyceride  
iso E super A 54464-57-2 Rxi17SilMS 0.001 10 1 2.7114 × 10–5 3.8735 × 10–6 this work   allergenic fragrances  
iso E super B 54464-57-2 Rxi17SilMS 0.001 7 1 4.5734 × 10–6 1.1434 × 10–6 this work   allergenic fragrances  
iso E super C 54464-57-2 Rxi17SilMS 0.001 7 1 1.0752 × 10–5 2.6879 × 10–6 this work   allergenic fragrances  
iso E super D 54464-57-2 Rxi17SilMS 0.001 7 1 1.0279 × 10–5 2.5697 × 10–6 this work   allergenic fragrances  
limonene 138-86-3 Rxi17SilMS 0.001 5 1 4.0222 × 10–6 2.0111 × 10–6 this work   terpene allergenic fragrances
linalool 78-70-6 Rxi17SilMS 0.001 8 1 1.7043 × 10–5 3.4086 × 10–6 this work   allergenic fragrances terpene
PCB 101 37680-73-2 Rxi5SilMS 0.002 10 1 5.0424 × 10–6 7.2034 × 10–7 this work   PCB  
PCB 138 35065-28-2 Rxi5SilMS 0.002 11 1 4.0017 × 10–5 5.0021 × 10–6 this work   PCB  
PCB 153 35065-27-1 Rxi5SilMS 0.002 10 1 4.1581 × 10–5 5.9401 × 10–6 this work   PCB  
PCB 180 35065-29-3 Rxi5SilMS 0.002 9 0.99999 8.5642 × 10–5 1.4274 × 10–5 this work   PCB  
PCB 28 7012-37-5 Rxi5SilMS 0.002 11 0.99999 5.4783 × 10–5 6.8479 × 10–6 this work   PCB  
PCB 52 35693-99-3 Rxi5SilMS 0.002 12 0.99999 6.5045 × 10–5 7.2273 × 10–6 this work   PCB  
benz[a]anthracene 56-55-3 ZB-PAH-CT 0.001 8 0.99975 1.5696 × 10–3 3.1392 × 10–4 this work   PAH  
benzo[g,h,i]perylene 191-24-2 ZB-PAH-CT 0.001 8 0.99999 7.7010 × 10–5 1.5402 × 10–5 this work   PAH  
dibenzo[a,h]anthracene 53-70-3 ZB-PAH-CT 0.001 8 0.99994 3.1643 × 10–4 6.3287 × 10–5 this work   PAH  
indeno[1,2,3-cd]pyrene 193-39-5 ZB-PAH-CT 0.001 15 0.9996 4.1942 × 10–3 3.4952 × 10–4 this work   PAH  
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a

For each entry, N gives the number of measurement points which were used for the fit. φ0 is the dimensionless film thickness with φ0 = 1/4β.

4. Results and Discussion

4.1. Determined Parameters

The determined retention factors from isothermal measurements are plotted against the isothermal temperature. The detailed ln k values for each compound can be found in the GitHub project.25 The internet link to the data is available in the Supporting Information. The plots and fits as ln k over T for allergenic compounds, 16 EPA-PAH, FAMEs, and triglycerides on the Rxi17SilMS are shown in Figure 2. The determined retention parameters for the thermodynamic model, the ABC model and the K-centric model are shown in the Supporting Information. A selection is shown in Table 3. The value of N gives the number of measurements for the fit of each compound.

Figure 2.

Figure 2

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Determined ln k values over T with fits of the K-centric model for each substance for a selection of allergen fragrances (A), EPA-PAHs (B), FAMEs (C), and triglycerides (D) on Rxi17SilMS (β = 250) as the stationary phase.

Figure 3 shows the relationship between the characteristic temperature Tchar and the characteristic thermal constant θchar and to ΔCp. The general relationship is consistent with observations of Blumberg.10 A strong influence of different phase ratios on the correlation of θchar on Tchar, as described in ref (8) could not be observed in this data. Interactive 3D figures of the K-centric and the ABC parameters can be found in Supporting Information, Figures S3 and S4. The ABC data show a nearly straight line in the parameter space. In the parameter space of all three K-centric parameters, a general trend can be estimated, whereas some compounds from comparable substance classes show characteristic regions in the space, Figure 3. Aliphatic compounds such as n-alkanes, n-alcohols, or FAMEs lie in other regions than aromatic compounds such as PAHs, PCBs, or dioxins but even high volatiles like BETXs. The region of the triglycerides is close to FAMEs. Glyceryl trimyristin and glyceryl tripalmitin did not pass the validation because their arguments x of the Lambert W function are x < −1/e. A problem during the determination are data measured at high temperature far away from ln k = 0, if the parameters, especially Tchar, are determined as extrapolation with high standard errors. This can be observed for triglycerides but for some PAHs as well.

Figure 3.

Figure 3

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Relationships between K-centric parameters and influence of substance category. 2D projection from the 3D parameter space for Tchar against θchar (A) and ΔCp against Tchar (B).

A principal compound analysis (PCA) provides a model that can describe the relationships between the K-centric parameters, Figure 4. PCA of the ABC parameters reduces the data to one principal compound (variance explained = 99.9985%), which is close to the approximately linear trend that could be observed. These PCA models can also be used for further validation of new data and exclusion of data from the database.

Figure 4.

Figure 4

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PCA for all three K-centric parameters of different compound categories. PC1 explains 82.7% of the data and variance explained = 99.6562.

4.2. Results of the Validation Process

Table 4 shows the final data sets after the validation process. The total size of the database was reduced from 1031 to 967 listings. It is notable, that all of the compounds found by Stevenson et al., did not pass the validation.20 This data, obtained by temperature-programed rather than isothermal measurements, show nearly linear ln k over T curves, so that the Lambert W criteria could not be accepted. A similar trend is observed for some of the PAHs measured on the ZB-PAH-Column, which also show very linear curves in the investigated conditions. Figure 5 shows the primary substance categories and the number of compounds in the final database. To review the quality of the determined data, in the next step randomized GC measurements were performed and compared to simulated chromatograms.

Table 4. Data sets After the Validation Process Including the Literature Data and Own Determined Data.

data set size of data set before validation size of data after validation number of compounds number of columns references
1 88 88 88 1 (13)
2 47 47 45 1 (14)
3 5 5 5 1 (3)
4 7 7 7 1 (15)
5 51 51 17 3 (11)
6 22 22 22 1 (2)
7 76 76 12 3 (16)
8 6 6 6 1 (17)
9 25 25 11 3 (18)
10 11 11 11 1 (19)
11 25 0 0 0 (20)
12 34 29 15 2 (21)
13 135 117 19 8 (22)
14 32 22 16 2 this work
15 85 85 70 1 this work
16 355 351 128 3 this work
Total 1031 967 289 20  
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Figure 5.

Figure 5

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Distribution of different substance categories included in the database (absolute values, substances).

4.3. Benefit of the Data

The data can be used for prediction and simulation of GC separations. The determined characteristic temperatures of the substances can be directly used to estimate the general elution order of a composition. Most compounds elute in order of their characteristic temperatures. For close Tchar values, the values of θchar and heating rates also have influence on the elution order.4 Simulated chromatograms of PAHs and FAMEs compared to measurements on the same GC system are shown in Figures 6 and 7. As demonstrated the simulations well accords to measurements. The average deviation for each compound is less than 1%. The rmse (root-mean-square error) is 0.1425 min for the PAHs and 0.03532 min for the FAMEs. Figure 8 shows a simulation computed by ABC retention parameter from the literature14 on a Rxi5 compared to measurements on our own GC system on a Rxi5SilMS. These two stationary phases are similar but do not have exactly same composition; however, the deviations between the retention times for n-alkanes are almost less than 2%, which are almost equivalent to a shift by one to three peak widths. In this case, the data are transferable to different GC systems. To check the transferability of the data from one GC system to another, the authors are highly interested in data from the community to compare retention data for similar compounds and phases. As another example for a transferability, the simulation is also suitable for prediction of fast GC measurements such as FF-TG-GC.2 Measurements with PAHs30 on a FF-TG-GC system show a good match of elution order but a systematic shift in retention times, which result by a lack of knowledge of the exact gradient profile and the different used GC system. A simulation of FF-TG-GC measurements of PAHs compared to measurements is shown in Supporting Information, Figure S5.

Figure 6.

Figure 6

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Measured and simulated chromatogram of a temperature-programed GC separation of 16 polycyclic aromatic hydrocarbons (EPA-PAH) on a Rxi17SilMs. GC conditions: Tinit = 70 °C; first ramp: 20 °C/min, T1 = 150 °C, hold time = 5 min; second ramp: 12 °C/min, T2 = 250 °C, hold time = 2 min; third ramp: 15 °C/min, Tend = 360 °C, hold time = 5 min, rmse = 0.1425 min.

Figure 7.

Figure 7

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Measured and simulated chromatogram of a temperature-programed GC separation of FAMEs on a Rxi5SilMs. GC conditions: Tinit = 60 °C, first ramp: 20 °C/min, Tend = 300 °C, rmse = 0.03532 min.

Figure 8.

Figure 8

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Measured chromatogram of n-alkanes (C8–C20) on a Rxi5SilMS compared to simulation by using ABC retention parameters from Gaida et al.14 on Rxi5. GC conditions: Tinit = 40 °C, first ramp: 10 °C/min, Tend = 300 °C, rmse = 0.2646 min.

5. Conclusions

The retention parameter for a huge number of compounds, for example, allergenic fragrances, PAHs, FAMEs, and other volatile substances were determined and collected in a database. The presented calculation procedure is even suitable for method developers on their own GC systems to generate own databases for simple predictions. The presented database now includes data for more than 280 substances on up to 20 different stationary phases. The full database is available at GitHub https://github.com/JanLeppert/RetentionData.25 The data are suitable for prediction, simulation, and optimization of GC separations.

To reduce the elaborate isothermal measurements, further investigations will focus on development of easier estimation methods for the retention parameters than via isothermal measurements. The most important K-centric parameter Tchar can be well-estimated from the elution temperature. Similar to the estimations of RI or boiling points from LSER data7 from the literature, the other K-centric parameters can also be estimated. First results are promising. With suitable optimization algorithms, efficient estimates by simulation will be possible from temperature-programed measurements .

Acknowledgments

This research work was funded by the German Research Agency (DFG), grant 452897652.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c01348.

  • Plot of Lambert W function, ln k values of measurements, 3D plots of retention parameters, chromatograms, and results of PCA (PDF)

  • Databases described in this work before and after validation, and new data measured without any literature data (XLS)

The authors declare no competing financial interest.

Supplementary Material

ao3c01348_si_001.pdf (2.8MB, pdf)
ao3c01348_si_002.xls (1.2MB, xls)

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Supplementary Materials

ao3c01348_si_001.pdf (2.8MB, pdf)
ao3c01348_si_002.xls (1.2MB, xls)

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