Chrombox_O


Contents

Installing and starting Chrombox OWindows computersMac computers (OS X)Linux computersStarting Chrombox O from the Matlab desktop (on all systems)Changing settingsUpdatingTutorial 1. Optimal carrier gas velocity1.1. Theory1.2. Importing the design 1.3. Setting up the experiment:1.4. Modelling1.5. Detailed inspections and refinement of the modelsTutorial 2. The van Deemter model with an interacting effect2.1. Theory2.2. Startup and importing the design 2.3. Setting up the experiment:2.4. ModellingTutorial 3. Optimal carrier gas velocities in temperature-programmed GC3.1. Chrombox C3.2. Chrombox Optimizer3.2.1. Models for peak width in retention index units3.2.2. Model for retention time3.2.3. Combined models

The following text styling is applied in this document. Commands, paths or filenames are denoted by: command, or path\filename.ext. Buttons in the graphical user interface are shown as [Button]. Keys on the keyboard are denoted by [Key]. A parameter to be set is denoted by parameter, and a value of a parameter or an option in a menu is denoted by option.

Installing and starting Chrombox O

Windows computers

If installed on a network disk you may have to use one of the methods described below:

An example of ostart.m is shown below:

You can also create a desktop shortcut by copying the shortcut to Matlab and adding the following to the destination /automation /r ostart An example of how it can look is shown below:

C:\MATLAB6p5\bin\win32\matlab.exe /automation /r ostart

Mac computers (OS X)

As an alternative to the above procedure, Chrombox O can be started by the following method:

An example of ostart.m is shown below:

Linux computers

As an alternative to the above procedure you can also start Chrombox O by ostart.m as described for Mac computers above.

Starting Chrombox O from the Matlab desktop (on all systems)

On all operating systems you can use the following procedure to start Chrombox O.

In a minimized Matlab session (running in terminal without Matlab desktop) you can use the cd command to set the working directory and run oo_startscript to start the program.

Changing settings

Updating

The part to edit in oo_localsettings.sdv is between the two semicolons in the line shown below.

Alternatively, you may select the new code by the following procedure:

Tutorial 1. Optimal carrier gas velocity

The main purpose of this tutorial is to teach you how to find the optimal carrier gas velocity by resolving the van Deemter equation.

1.1. Theory

Chromatographic efficiency is traditionally reported as the number of plates (N). The plate height is the number of plates divided by the length of the column. The van Deemter equation (Eq.1.1) explains how plate height (H) in chromatography depends on mobile phase velocity (u), eddy diffusion (A), longitudinal diffusion (B) and the resistance to mass transfer (C).

Since H is an inverse of N. the maximal efficiency is found when H is minimized.

In temperature-programmed gas chromatography, N is not a useful measure for the chromatographic efficiency, so an alternative to N is needed. In temperature programmed GC chromatographic efficiency can be described as the number of peaks that can be separated per compound in a homologous series, and the most common measure is the separation number (SN). However, the inverse of SN may not be a suitable replacement for H in Equation 1.2. The cause is that SN is a rough approximation of the number of peaks that can be eluted between two members of a homologous series (Fig. 1.1). When SN is zero, the homologs are therefore still separated, meaning that there is still some separation efficiency. So the inverse of SN will go to infinity before all efficiency is lost.

As an alternative to SN we can use the peaks per carbon (PPC), which is the number of peaks that can be resolved with chromatographic resolution (Rs) equal to one, per compound in a homologous series. PPC therefore includes one of the homologs (Fig. 1.1). PPC is the difference in retention between the two homologs divided by the average peak width at baseline, and can be calculated by Equation 1.2.

tR is retention time of the two homologs, and wb is the peak width at baseline (defined as 4σ).

If the retention scale is converted to retention index units, the retention difference between the homologs is given by definition. Equation 1.2 can therefore be converted to Equation 1.3, where form (a) should be used when the retention index difference between homologs is 100 (e.g. Kováts’ indices) and form (b) should be used when the difference is 1 (e.g. equivalent chain lengths, ECL). The peak width can be measured at any peak.

It follows from Equation 3 that the inverse of the efficiency that can replace H in Equation 1.1 will be the peak widths measured in retention index units.

The analyzed compounds are in this case fatty acid methyl esters (FAME) and the retention indices are equivalent chain lengths (ECL), which means that Equation 3a is valid.

Fig.1.1
Figure 1.1. Illustration of PPC and SN. The two holmologs with z and z+1 carbon atoms are shown in red

1.2. Importing the design

Fig.1.2
Figure 1.2. The Design window

The design is in this case a non-standard design that must be imported from a csv file.

The CSV file is stored in the designs folder with the name design_TUTORIAL-1. All csv files that defines the designs must be named design_.....csv and semicolon must be used to separate the values if there are more than one variable. The first line should contain the variable name. In this case there is only one variable, and the content of the file is displayed below.

1.3. Setting up the experiment:

When the design is loaded you should assign the different design points to the correct box name in the design table. This is of course easier to do when the box name contains information about the applied experimental conditions. Since the box names are inherited from the imported data files, it is important to use informative names when the result files are created in the other programs.

Fig.1.3
Figure 1.3. The Experiments window

1.4. Modelling

Fig.1.4
Figure 1.4. The window for models based on the van Deemter equation

1.5. Detailed inspections and refinement of the models

The plot should now show the model for 12:0 only, and you can see that this has a significant A-term. 12:0 is the first compound in the chromatograms and it may be influenced by injector conditions that lead to extra-column effects. This compound should therefore be excluded from further calculations.

If you exclude 12:0, but select the remaining saturated compounds (14:0 to 26:0) you will see that the sum of the terms increases with the number of carbons (and retention time). You can also see that the B-term is almost identical for the different compounds, while the A and C-terms vary.

The van Deemter equation is numerically unstable in the sense that the different terms, A, B and C may be confounded if there is noise in the data, while the sum of them is still accurately predicted. From chromatographic theory one can expect that the A-term should not vary throughout the chromatogram without a clear trend. If there are extra column effects, they should have similar effects on closely eluting peaks. If you recalculate the models with the A-term set to the mean for all models the picture will be clearer.

If you repeat the process with the unsaturated FAMEs you will see a similar trend as with the saturated. The elution order of these peaks are 16:1 n-7, 18:1 n-9, 18:2 n-6 tt, 18:3 n-6, 20:3 n-6, 20:5 n-3 and 22:6 n-3. From C20 there is a clear increase in the C-term and in the sum of the terms.

Which carrier gas velocity to choose may depend on other factors than only the separation efficiency. To save time it is common to set the carrier gas velocity higher than the predicted optimum. However, it is important to consider which penalty this will give in loss of efficiency. And if there are large differences between the individual models, it may also be wise to consider in which parts of the chromatogram the efficiency may be most important.

Fig.1.5
Figure 1.5. Predicted vs. measured peak widths for models of saturated FAME, using a common A value.

Tutorial 2. The van Deemter model with an interacting effect

The main purpose of this tutorial is to study chromatographic efficiency as a function of carrier gas velocity and a second interacting variable, the temperature rate in temperature programmed gas chromatography. A modified van Deemter equation for calculating the response surface of both parameters is introduced.

2.1. Theory

In response surface methodology it is common to assume that the response can be explained by quadratic polynomials. Assume a response z that follows quadratic functions of two independent variables, u and i. The relationships are given by Equations 2.1 and 2.2.

If we want to create a response surface that explains z as a function of both u and i we combine the two equations, and it is also common to introduce a term, F, that explains any interactions between the two variables. The model for z as a function of u and i can therefore be given by Equation 2.3.

If u is mobile phase velocity in chromatography and z is the inverse of the efficiency, we know that Equation 2.1 cannot be accurate because the relationship follows the van Deemter equation (4).

So instead of combining Equations 2.1 and 2.2 into 2.3, more accurate models can be expected if equations 2.2 and 2.4 are combined by starting with the traditional van Deemter equation and adding terms for i, i/u, i·u and i2. The result is Equation 2.5:

This is the equation that is applied for calculation of response surfaces for the effect of the carrier gas velocity, u, and an interacting variable, i. The interacting variable may be the temperature rate, as in this case, but it can also be other parameters. Since the interacting variable may vary, and since there is no theoretical framework that tells us which of the terms in Equation 2.5 that will be significant, it is important to study the effects of adding and removing the different terms.

2.2. Startup and importing the design

2.3. Setting up the experiment:

2.4. Modelling

Fig.2.1
Figure 2.1. The window for models based on the van Deemter equation
Fig.2.2
Figure 2.2. Mean van Deemter models for the three temperature rates
Fig.2.3
Figure 2.3. Predicted versus measured plots for modified van Deemter models of different complexity

If you select one of the surface plots you can get information about the value of the response variable by clicking at the surface. Although it is the mean values for the different compounds that are displayed, the values for the individual models will be given in the table below the plot. If you select Marker in the surface options, the position for the displayed values will be shown. You can also choose to show the sums, the minimum or the maximum values. The maximum values can be relevant in this case, as it shows the largest predicted peak width of any of the compounds change with different conditions.

In general, the surface plots show that there is a general loss of efficiency with increasing temperature rate, and that the optimal velocities at 2, 4 and 6 °C are around 22.0, 24.2 and 27.4 cm/s. This is similar to what the individual models indicated.

You can also choose to calculate the response surface by a general quadratic equation (Equation 2.3). The response surface will shown a similar trend as the modified van Deemter models. But it is less accurate in the prediction of optimal velocities, and if you inspect the predicted versus measured plot you will see that the explained variance is lower. In addition, the models cannot be easily interpreted since there is no theoretical framework for them.

Tutorial 3. Optimal carrier gas velocities in temperature-programmed GC

The main purpose of this tutorial is to take you through the full workflow for studying the relationships between chromatographic efficiency and retention time. The column you work with is a 30 m BPX70 with 0.22 mm internal diameter and 0.25 μm film thickness. The temperature program starts at 125°C and the temperature rate and carrier gas velocity are varied according to an experimental design. For this tutorial you need some experience with Chrombox C, so it is recommended that you first do the Chrombox C Tutorial-1.

3.1. Chrombox C

Fig.3.1
Figure 3.1. Calibration compounds
Fig.3.2
Figure 3.2. Retention time (x-axis) versus ECL (y-axis) and corresponding values for sample HE_30M_1_14

The first proposal in the list is usually the correct, but watch out for orange labels that indicate that the same identity is given to several peaks. The elution order of the peaks is the same in all chromatograms.

Fig.3.3
Figure 3.3. The peaks with their correct identities.

You can now continue with the remaining chromatograms. There are 27 chromatograms (3 temperature rates, 7 velocities) in total. Always make sure that you edit the box name to include the correct temperature rate and carrier gas velocities so that you don't overwrite your previous data. Always check that the calibration curve between retention times and ECL is smooth, and always check that you find all 19 compounds in the chromatograms.

The rest of the tutorial is performed in Chrombox Optimizer.

3.2. Chrombox Optimizer

3.2.1. Models for peak width in retention index units

This will show the average response surface from all the models. You now have a plot that tells you the peak with in ECL units as a function of temperature rate and carrier gas velocity. The grey line in the response surface plot marks the predicted optimal carrier gas velocity (uopt) for a given temperature rate.

Under the response surface you can select different plot types. The ones that are relevant are Design, Surface (Fig. 3.4a), VD all levels (Fig. 3.4b), Errors (Fig. 3.4c) and Pred. vs. meas. (Fig. 3.4d). If the error plot shows that some of the analytes have much higher errors than the other, for instance 24:0 in Fig. 3.4d, it may be an idea to deselect it in the table of models (the Active column).

Fig.3.4
Figure 3.4. Typical diagnostic plots for the VD+Int models, (a) response surface, (b) Van Deemter models calculated by inserting the temperature rate, (c) errors, and (d) Predicted versus measured for each observation

3.2.2. Model for retention time

The next step is to calculate the model for retention time of the last eluting compound, 26:0/SAN‑017.

The response surface plot for the retention time model and predicted versus measured for the model are shown in Figure 3.5a and b, respectively.

Fig.3.5
Figure 3.5. Response surface (a) and predicted versus measured (b) for the model of retention time of the last compound.

3.2.3. Combined models

Now that you have models for the efficiency and a model for retention time it is time to combine the two models to evaluate the relationship between time and efficiency.

The black dots in Figure 3.6 represent the conditions where the time is minimized for each of the white wh,ECL isolines. The black curve passing through these points therefore indicates optimal conditions with respect to the trade-off between chromatographic efficiency and retention time. For any set of conditions that is not on this curve it can be claimed that higher efficiency can be achieved within the same time, or that shorter time can be used to achieve the same efficiency. Velocities along this line are therefore referred to as time-optimal velocities (utopt).

Fig.3.6
Figure 3.6. Plot for evaluating optimal velocity. The black dots show where each of the isolines from the average efficiency model has a minimum on the response surface for the retention time. The values of these points on the x-axis is the time optimal velocities, utopt, and the conditions along the black curve can be said to represent optimal conditions
Fig.3.7
Figure 3.7. Response surface plot for chromatographic efficiency divided by the retention time of the last compound (PPC/tR)