Contents

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

• Download the installation and unzip the archive oo.zip
• Move folder oo to the preferred destination, e.g. C:\CHROMBOX\. This will be the O-root folder
• If Installed on a local disk or on a memory stick Chrombox O can usually be started by using the "Chrombox O.exe" file in the O-root folder.

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

• Find the file ostart.m in the folder …\oo\various and move it to somewhere in your Mathlab path. This is the only file that needs to be in the Matlab path. Possible destinations may be found by starting Matlab and typing path.
• Open the ostart.m and edit the last line after the run command so that it points to the file oo_startscript (see example below).
• You should now be able to start Chrombox O by typing ostart in the Matlab command window.

An example of ostart.m is shown below:

xxxxxxxxxx% Startupscript for Chrombox O% Starts startscript by the run command.% Startscript must be located in the O root. % ostart must be in the matlab searchpath.% run C:\CHROMBOX\OO\oo_startscript​run C:\CHROMBOX\OO\oo_startscript

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)

• Download the installation and unzip the archive cc.zip

• Move the folder CC to the preferred destination, for example /Users/yourname/Documents/CHROMBOX/OO, This will be the O-root folder

• The shell script macstart_o.command stored in the O-root folder can be used to start the program if the file is executable and Matlab can be started with the terminal command ./matlab. Note that the extension .command may be hidden in Finder.

• To check if Matlab can executed by ./matlab open the terminal and type ./matlab. If Matlab does not start you can do the following:

• Put a symbolic link to Matlab in your path by opening the terminal and typing sudo ln -s /Applications/MATLAB_RXXXXx.app/bin/matlab /usr/local/bin where RXXXXx should be replaced by the Matlab version number, for example "R2017a". Alternatively, open Applications in Finder. Locate Matlab, right-click and select Show Package Contents. Open the folder bin and locate the application file matlab. In terminal type sudo ln -s without pressing enter. Thereafter drag the matlab application file to the terminal. Ensure there is a space between "-s" and "/Applications" and press enter.
• To make macstart_o.command executable, do the following:

• Open the terminal. Use cd to change directory to the C root where the macstart_o.command is located or open the terminal at the O root folder if that is an option. Type chmod +x macstart_o.command. Alternatively, type chmod +x without pressing enter and drag the macstart_o.command file from Finder to the terminal. Ensure there is a space between "+x" and "macstart_o.command" and press enter.

• Thereafter double-click on macstart_o.command in Finder to start the program. Depending on your security settings you may get the following message: "macstart_o.command can’t be opened because it is from an unidentified developer". To solve this, open System Preferences – Security and Privacy – General and press [Open anyway] next to the message regarding the file. An alternative way of allowing the file to be executed is to open the file in TextEdit and saving it again. Then it will no longer have status as downloaded from the Internet.

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

• Find the file ostart.m in the folder …/oo/various and move it to somewhere in your Matlab path. Possible destinations may be found by starting Matlab and typing path.
• Open the ostart.m and edit the last line after the run command so that it points to the file oo_startscript (see example below).
• You should now be able to start Chrombox O by typing ostart in the Matlab command window.

An example of ostart.m is shown below:

xxxxxxxxxx% Startupscript for Chrombox O% Starts startscript by the run command.% Startscript must be located in the O root. % ostart must be in the matlab searchpath.% run /Users/yourname/Documents/CHROMBOX/OO/oo_startscript.m​run /Users/yourname/Documents/CHROMBOX/OO/oo_startscript.m

### Linux computers

• Download the installation and unzip the archive oo.zip

• Move folder OO to the preferred destination, for example /home/yourname/CHROMBOX/OO, This will be the O-root folder

• The shell scripts linstart_o.sh stored in the O-root folder can be used to start the program, if the file is executable and Matlab can be started with the terminal command matlab.

• On Ubuntu you can use the following procedure to make linstart_o executable:

• Right-click on the file and select Properties. Select Permissions and Allow executing file as program.
• It should now be possible to start Chrombox O by double-click on linstart_o.sh and selecting the option run in terminal. If you don’t get the run in terminal option while double-clicking the file you will have to edit the preferences in the file manager. Choose Edit in the menu for Files, thereafter Preferences and select the Behaviour tab. Select Ask each time as the option for executable text files.

• There is also a file linstart_o_term.sh in the O-root folder. The difference between linstart_o and linstart_o_term is that linstart_o runs the application disconnected from the terminal while linstart_o_term runs in the terminal. Chrombox O will continue to run if you close the terminal if it was initiated by linstart_o, while it will close together with the terminal if it was initiated by linstart_o_term.

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.

• Start Matlab in the regular way, so that the Matlab desktop is opened.

• Change the current working directory of Matlab to the O-root folder, either by the line showing the working directory or by browsing in the panel in the left side of the Matlab desktop.

• You can now start Chrombox O by one of the following methods:

• Select oo_startscript.m in the panel showing the contents of the working directory, right-click and select run.
• type run oo_startscript in the Matlab command window.

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

• The program should normally start without the need to change any settings. But you may want to adjust parameters such as window size. These are specified in the oo_localsettings file in the O-root folder.
• Open oo_localsettings (.sdv or .csv) in an editor such as Notepad and edit the paths for raw data, etc, if necessary.
• An example of “oo_localsettings” is shown below. Parts to check or edit are shown in blue.
xxxxxxxxxxdefaultfolders; 1; 1 use default folder settings, 0 use paths specified belowdefaultmethod; Default; Method to load on startuppath_designs; C:\CHROMBOX\OO\designs; Folder for saved designspath_experiments; C:\CHROMBOX\OO\experiments; Folder for experimental datapath_export; C:\CHROMBOX\OO\export; Folder for import/export of various datapath_method; C:\CHROMBOX\OO\methods; Folder for methodspath_models; C:\CHROMBOX\OO\models; Folder for saved modelspath_rawdata; C:\CHROMBOX\OO\rawdata; Rawdata folderpath_reports; C:\CHROMBOX\OO\reports; Folder for reportspath_results; C:\CHROMBOX\OO\results; Folder for resultstracker; 0; For development purposes, 0 or 1user; Anonymous; User ID for info fieldsversion; O-14-09; Code version to usewindowpos; [0.05 0.05 0.9 0.9]; Window position and size [leftposition lowerposition width height] in fractions of screen size
• windowpos is position of the window in fractions of the screen size. The two first numbers in the vector is the position of the lower left corner. As specified above the lower left corner is 10% from the bottom of the screen and 10% from the left. The height and width is 75% of the screen size. Ensure that the sums of numbers 1 and 3 and numbers 2 and 4 are less than 1.
• If defaultfolders is set to 1 the program will use the standard setup for subfolders and it is not necessary to edit the paths even if they are not correct. If the parameter is set to 1 you will have to specify the location of each path for data and methods. Data can be read from other folders than the ones are specified. Folders can also be changed by using the [Settings] option within the program.
• version refers to the current version of the code. The parameter can also be updated from within the program.
• If you have created a method that you want to import on startup you specify this as defaultmethod.

### Updating

• Unzip the archive with the new code.
• The folder containing the code, e.g. O-14-09 should be placed in the folder code in the O root folder.
• Open the file oo_localsettings.sdv (may also have .csv extension) that is found in the O root folder and update the version to the folder name of the new code. The part to be edited is shown in blue in the example below.
• Note that it is not necessary to delete the folders with old code. Keeping these allows you to run previous versions if necessary.

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

xxxxxxxxxxversion; O-14-09; Code version to use

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

• Open Chrombox O
• Press the [Settings] button down in the right corner
• Select [Directories]
• Select the code version and press [Save local settings]
• Restart Chrombox O.

## 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.

### 1.2. Importing the design

• Start by opening Chrombox O as explained under "Installing and starting Chrombox O".
• The first ting you have to do is to define the design. Press the [Design] button in the main window, which will open the Design window (Figure 1.2).

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

• Select TUTORIAL-1 in the list next to the [Import CSV] button and press the button. This will import and display the applied design.

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.

xxxxxxxxxxVelocity10152022.52527.5303540
• Save the design as TUTORIAL-1 by pressing the [Save as] button and leave the window by [Close].

### 1.3. Setting up the experiment:

• The next step is to import the data and assign the data to the different conditions in the design. Press the [Experiments] button in the main window, which will take you to the window for importing and organizing your data (Figure 1.3).
• The data files are stored in TUTORIAL-1 under the rawdata folder. The files are result files from Chrombox C. Although it is possible to import files directly from the result folders of Chrombox C and Q, it is often more convenient to copy the files to subfolders under ...\OO\rawdata.
• Press the [.] button next to the data path and select the TUTORIAL-1 folder. Alternatively, you can type inn the address in the path edit, e.g. k:\CHROMBOX\OO\rawdata\TUTORIAL-1. This should display the following files:
xxxxxxxxxxTUTORIAL1_VEL_10TUTORIAL1_VEL_15TUTORIAL1_VEL_20TUTORIAL1_VEL_22p5TUTORIAL1_VEL_25TUTORIAL1_VEL_27p5TUTORIAL1_VEL_30TUTORIAL1_VEL_35TUTORIAL1_VEL_40
• Select all these files. The most convenient way to select the files is to right-click in the list, select List view and thereafter selecting the files using the left mouse button.
• After the files have been selected, press the [Read Files] button. The files should now be imported and the different lists will be filled out. There are several possible ways to read the files. Result files from Chrombox C may contain several chromatograms, and the normal mode is that all chromatograms in a data file is regarded as being acquired under the same experimental conditions and therefore organized in a single “box” in the Optimizer. In this case, each data file contains only a single chromatogram.
• You can select data boxes in the box list and view the data. In the variable type list you can select which data type to view. The important variable is in this case Peak width (RI units). Select this variable and select thereafter Export data above data table. The values for peak width in RI units that will be exported will be shown. Ensure that the data table contains no missing values (shown as NaN).
• The next step is to assign the different data boxes to the design points. Select TUTORIAL-1 in the list next to the [Load Design] button and thereafter press the button.

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.

• Use the popup menu in the list and select the designs so that all velocities match the last part of the box name.
• When all experimental points are correctly assigned you type in *TUTORIAL-1* next to the [Save Exp.] button and press the button.
• Leave the window by pressing the [Close] button.

### 1.4. Modelling

• Select [VD model] in the main window, which will take you to the window with functions for using the van Deemter equation and modifications of this.

• Select TUTORIAL-1 in the list next to the [Load Exp.] button and press the button. The window as it should look after the experiment has been loaded is shown in Figure 1.4.

• The different compounds will be referred to by their short name. Select therefore Short name on the line under the data table. Select thereafter all compounds in the list. The most convenient way to select all compounds is again to right-click in the table and selecting the compounds using the list view.

• You can now find the optimal carrier gas velocity by pressing the [Van Deemter] button. The van Deemter models for each compound are now solved by least squares regression. The models for each compound will be shown in the table, and the plot will show the sum of the terms for the average model. Further details, such as the calculated average carrier gas velocity and the predicted y-value (in this case peak width in ECL units) at the predicted optimal velocity is given in the list under the figure. You can copy the information by right-clicking in the list and selecting Copy contents.

• In the VD plot options you can select which parameters to display:

• The average of the different terms will be shown if you select ABC. Note that the A-term is close to 0, which it should be since the data were acquired using capillary gas chromatography. A significant A-term may therefore indicate extra-column effects caused by sub-optimal injector and detector conditions.
• If you select Observ. the observed values will be shown, and these should ideally fit well to the sum of the terms.
• If you select Indiv. the individual models will be shown.

### 1.5. Detailed inspections and refinement of the models

• You can now do a more detailed inspection of the individual models. Deselect the Mean and the Observ. in the VD plot options. Thereafter you deselect all compounds, except 12:0 in the models list.

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.

• Select Mean A under the [Van Deemter] button and press the button again. This will recalculate the models with a single A value for all. You can now see that from 14:0 to 17:0 the models are almost identical, but from there, the C-term increases clearly with the chain length of the compounds, meaning that the resistance to mass transfer increase with the molecular weight. If you expect the A-term to be insignificant you can also recalculate without the A-term by checking A = 0 under the [Van Deemter] button.
• If you select the Pred. vs. meas. plot in the plot options you will see how well the models fit the observed data. If you calculate with a common A-value or with A = 0 it is important to consider if the accuracy decrease. However, some reduction in the R2 value should always be expected since the models will be more constrained. The predicted versus measured plot for the models with common A is shown in Figure 1.5. The corresponding R2 values for models with free A and A = 0 was 0.9962 and 0.9933, respectively.

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.

• When finished, you can save the models by the [Save Models] button and recall them later by [Load Models].

## 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

• Start by opening Chrombox O as explained under "Installing and starting Chrombox O".
• A non-standard design is used also in this tutorial, so it must be imported from a csv file. Press the [Design] button in the main window. Select TUTORIAL-2 in the list next to the [Import CSV] button and press the button. The content of the design_TUTORIAL-2 file is displayed below.
xxxxxxxxxxGrad;Vel2;152;182;212;242;272;302;332;364;154;184;214;244;274;304;334;366;156;186;216;246;276;306;336;36
• The two varied parameters are the temperature rate in °C/min (Grad) and the carrier gas velocity in cm/s (Vel). The carrier gas is helium, so the optimum can be expected to be found within the range 15-36 cm/s. The column length is 30 m and the analytes are the same FAMEs as in Tutorial 1.
• Save the design as TUTORIAL-2 and leave the window by [Close].

### 2.3. Setting up the experiment:

• Press the [Experiments] button in the main window, which will take you to the window for importing and organizing the data
• Follow the procedure from Tutorial 1 and select TUTORIAL-2 under the rawdata folder. You should see the following file names:
xxxxxxxxxxVDOPT_IL61_2_15VDOPT_IL61_2_18VDOPT_IL61_2_21VDOPT_IL61_2_24VDOPT_IL61_2_27VDOPT_IL61_2_30VDOPT_IL61_2_33VDOPT_IL61_2_36VDOPT_IL61_4_15VDOPT_IL61_4_18VDOPT_IL61_4_21VDOPT_IL61_4_24VDOPT_IL61_4_27VDOPT_IL61_4_30VDOPT_IL61_4_33VDOPT_IL61_4_36VDOPT_IL61_6_15VDOPT_IL61_6_18VDOPT_IL61_6_21VDOPT_IL61_6_24VDOPT_IL61_6_27VDOPT_IL61_6_30VDOPT_IL61_6_33VDOPT_IL61_6_36
• Select all these files and press the [Read Files] button.
• Select the variable Peak width (RI units) and display the export data by selecting Export data on top of the data table. Note that there is one missing value, SAN-012 for Box number 17. This compound will be kept out in some of the calculations later.
• Load the design TUTORIAL-2 and assign the design points to the correct boxes in the Design table. The two last numbers in the file names are the rate and the velocity.
• Right click on the table, choose Export (txt) and carefully check that all experiments are correctly assigned.
• Save the experiment as TUTORIAL-2 and leave the window by [Close].

### 2.4. Modelling

• Select [VD model] in the main window, which will take you to the window with functions for using the van Deemter equation and modifications of this.

• Load the experiment TUTORIAL-2.

• Important functions that were not covered in Tutorial 1 are displayed in Figure 2.1.

• The first thing you may notice is that the design is now flipped 90 degrees relative to what you saw in the design window. The reason is that the velocity variable must always be variable 1 when there is more than one variable. This is handled automatically when the experiment is loaded. However, if the program does not recognize a variable name similar to “velocity” or “flow” it may be necessary to manually assign the variables. If there are more than two variables you must also assign which variable that is the interacting one. This is done by the popup menus for velocity and interaction variables.
• You will now work with more than one model type. The models to display are selected by the popup menu under the data and models table.
• The parameters to include from Equation 2.5 are selected under the [VD+Interact] button.
• Options for the response surface plot are set in the surface plot options.
• Start by setting compound labels to short names by the radio button under the data table.
• Thereafter select all compounds in the list and press the [Van Deemter] button. As in Tutorial 1, this will calculate ordinary van Deemter models. But since there are now three different temperature rates, an independent model for each level will be calculated. You can select which models to display by the popup menu under the models list.
• Set the plot to Pred. vs. meas. and inspect each of the different models. For temperature rate 6 you will see that 20:3 n-6 is poorly predicted. The cause may be that this compound has an interferent in the original chromatograms. This compound should be kept out in further calculations. The other predicted versus measured plots should look ok.
• Deselect 20:3 n-6 in the data/models list. Thereafter select VD single level as the plot to display. Inspect all models again. You will se that 12:0 is deviating from the other compounds. As in Tutorial 1, this may be caused by poor focusing after injection. Deselect 12:0 in the models table.
• After 20:3 n-6 and 12:0 has been deselected, Set the A parameter for the van Deemter calculation to A=0 and press the [Van Deemter] button again. This will calculate new models.
• Select VD all levels as the plot to display, and select ABC in the VD plot options to display the individual terms. The plot should look similar to Figure 2.1. The plot shows that the optimal velocity increase with the temperature rate, and also that the efficiency decrease with the rate since the response at the optimal velocity increases. Furthermore, the plot indicates that the cause is an increased B-term, while the C-term is basically unaffected by the rate.
• You can now calculate the model based on Equation 2.5. Deselect the A=0 option. Include all four terms that can be selected under the [VD+Interact] button. From Figure 2.2 it can be expected that the interaction between the B term and the temperature rate (BI) must be significant, but significance of the other parameters can be questioned. Select also Thresh %. When this is active it will add the interactions one by one to the models. If the explained variance does not increase more than the threshold level (default 0.1%) the parameter will be kept out.
• Press the [VD+Interact] button. The response surface will be displayed and the models will be shown in the table. There is no model for 21:0 since there was a missing value in the data, and 12:0 and 20:3 n-6 should be kept out.
• In the table you can see that the values for the two last parameters Vel·Grad (Term F in Eq. 2.5) and Grad2 (Term G in Eq. 2.5) are zero, meaning they did not contribute much to better explained variance. Deselect these parameters (CI and I2) and repeat the calculation by pressing [VD+Interact] again. You will see that there is only an insignificant change in the response surface.
• You can evaluate whether the A term and I term should be included by testing all four combinations of A=0 on/off and I on/off and thereafter inspecting the predicted versus measured plots. The plots should look similar to the plots in Figure 2.3. It can be seen that R2 is always better than 0.99. However, if you choose to exclude BI, you will see a significant drop in the value.
• It can therefore be concluded that the simple model in Equation 2.6 can explain the effects of the carrier gas velocity and temperature rate in this system. In general, the models should be kept as simple as possible. Fewer parameters increase the numerical stability, and fewer experiments are required to resolve the model.

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

• Start by opening Chrombox C. Select method VDOPT if it is not already selected, and thereafter press [Import Box]. Select the ...\VDOPT_BPX70_HE raw data folder and select the first file, HE_30M_1_14.D\FID1A.ch. Press [Imp. Selct] followed by [Accept as new].
• You should now be taken back to the main window and the chromatogram of the sample should be displayed. The next step is to integrate the peaks. Do this by pressing the [Integrate] button. Verify that the 19 largest peaks in the chromatogram is integrated. If there are missing peaks you can add peaks by right-click in the chromatogram and selecting the Add peak option. Alternatively you can press "p" on the keyboard. Move the cursor to the place where you want to add the peak and press the left mouse button or enter on the keyboard. You may have to adjust the area. This can be done by clicking on the read circles that mark the peak starts and ends. A peak can be deleted by right-clicking on the peak or on its label, and thereafter selecting Delete.
• The next step is to calibrate retention indexes, ECL values in this case. Press the [Calibrate RI] button, which will open the calibration window. There are 12 saturated FAMEs in the sample that have their ECL values given by definition. These are indicated in Figure 1. For each of these compounds, click on the labels and type in the the corresponding numbers shown in Figure 1 in the field Def. RI. After you have done this, verify that the plot of retention time versus ECL looks like Figure 2 and that the values correspond to those given in the figure. Thereafter press [Accept], which will take you back to the main window. In the main window, choose Index as retention scale and verify that the calibration peaks are positioned directly above the corresponding ECL values.
• The next step is to identify the peaks. Press the [Identify] button. The peaks should now be identified with the identities shown in Figure 3.
• For the samples you work with later, the unsaturated compounds may not always be automatically identified. To manually identify a peak, right-click on the peak or on the label and select Identify or select a peak and press [i] on the keyboard. Select the correct identity from the list.

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.

• After the peaks have been correctly identified, press on the [.] button next to the Current Box field. This allows you to change the file name. Add the temperature rate and the carrier gas velocity to the box name so that it is VDOPT_BPX70_HE_1_14 in this case. Thereafter press [Save Box] to save the results.

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.

• When you are finished with all 27 chromatograms. Press the [OR] button in the lower right corner of the main window. Select the folder results and copy all the generated files, ("res_VDOPT_BPX70_HE_1_14.mat" to "res_VDOPT_BPX70_HE_3_46.mat", to a folder named TUTORIAL-3 in the Chrombox Optimizer rawdata folder (generate the folder if it is not already there). The rawdata folder can be found by starting Chrombox Optimizer and pressing the [OR] button in this program.

The rest of the tutorial is performed in Chrombox Optimizer.

### 3.2. Chrombox Optimizer

• Start Chrombox Optimizer and press the [Design] button. Import the design named TUTORIAL-3 as csv the same way as you did for Tutorials 1 and 2 and save the design before you leave the window by the [Close] button.
• Thereafter press the [Experiments] button. In the Experiments window, press the [.] button next to the raw data path and select the folder TUTORIAL-3. Select all the files in the list (most easily done by right-clicking in the table and changing to list view). Thereafter press the [Read files] button. In the upper right of the window, select Export data and verify that the table that is shown contains no missing values (shown as NaN).
• Select the design TUTORIAL-3 and press the [Load Design] button. Thereafter you have to assign the design points to the file names so that the temperature rates and carrier gas velocities in the file names match the velocities and rates in the design points. After you have verified that all points have been correctly assigned, replace ExperimentName with TUTORIAL-3 and press the [Save Experiment] button before you close the window.

#### 3.2.1. Models for peak width in retention index units

• Press the [VD Model] button in the main window. Select TUTORIAL-3 next to the [Load Exp.] button and press the button. This will display the design and the values for peak widths in retention index units.
• Press the [VD+Interact.] button to calculate the model for peak width in ECL units based on the following equation from Mjøs and Waktola, J.Sep. Sci. 17 (2015) 3014-27, where u is carrier gas velocity and i is temperature rate:

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).

#### 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.

• Select Show all above the list box showing Peak width (RI units). Thereafter select Retention time (RT). In the list of data / models, select only 26:0 and thereafter press the [Log+Int] button that will calculate the model for retention times based on the following equation from Mjøs and Waktola, J.Sep. Sci. 17 (2015) 3014-27.

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.

#### 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.

• Press the [Eff / time] button in the lower right corner of the window. This will open a new window with a plot that shows the most important isolines from figure 3.4a superimposed on the response surface plot for the retention time model (Figure 3.5a). The plot is shown in Figure 3.6.

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).

• You can also consider the fraction between the calculated PPC (inverse of wh,ECL) and the retention time of the last compound. Change the plot from Opt Vel to Eff/time. The plot is shown in Figure 3.7, and generally shows that efficiency/time increases with increasing temperature rate within the investigated domain.