This paper aimed to develop a standalone application for optimizing flow rates in liquid chromatography (LC), gas chromatography (GC) and supercritical fluid chromatography (SFC). To do so, Van Deemter’s equation, Knox’ equation and Golay’s equation were implemented in a MATLAB script and subsequently a graphical user interface (GUI) was created. The application will show the optimal flow rate or linear velocity and the corresponding plate height for the set input parameters. Furthermore, a plot will be shown in which the plate height is plotted against the linear flow velocity. Hence, this application will give optimized flow rates for any set conditions with minimal effort.
Liquid chromatography (LC), gas chromatography (GC) and supercritical fluid chromatography (SFC) cover a wide area for quantitative analysis of organic compounds in analytical chemistry [
Since these calculations are timeconsuming and susceptible for errors, this paper aimed to develop an application in which this calculation can be performed quickly. To do so, Van Deemter’s equation, Knox’ equation and Golay’s equation were chosen for calculating the HETP for packed and capillary columns respectively. These equation were implemented in a MATLAB algorithm and thereafter a Graphical User Interface (GUI) was developed.
According to Van Deemter, the HETP (H) can be calculated as follows [
Which is often reduced to:
Equation 1 describes band broadening by eddy diffusion (A), longitudinal diffusion (B), mass transfer (C) at different flow velocities in a packed column. Eddy diffusion is dependent on the quality of the packing of the column [
Longitudinal diffusion occurs when a concentration gradient exists. Analyte molecules will migrate from a high concentration area to a low concentration area according to Ficks law. This process is dependent on the diffusion coefficient of the mobile phase (
Mass transfer is a complex process, which is described by a function
To obtain the minimum value of the HETP, Equation 2 should be differentiated with respect to
The result of Equation 3 should then be used in Equation 2. To do so, has to be Equation 2 rewritten to a function in which the linear velocity is expressed as a function of the HETP:
where,
However, more often one uses reduced parameters for calculating the optimal flow rate since these parameters can be easily transferred between system. The reduced Van Deemter equation is defined as follows [
The reduced plate height (h) is defined by respectively the Aterm, Bterm, Cterm and the reduced velocity. As can be derived from this equation, h is independent of the particle size and diffusion coefficient. The Aterm, Bterm and Cterm can be calculated according to the following equations [
Where, λ is the correction factor for the irregularity of the column packing,
Another wellused equation for calculating the contribution of flow rates to band broadening is the Knox equation [
In contrast to the Van Deemter equation, the Aterm is dependent on the reduced velocity (v) according to Knox [
The separation efficiency of a capillary column can be calculated by using Golay’s equation [
In which
To minimize the
In Table
Overview of units per variable.
Type of column  Variable  Unit 



A  Dimensionless  
B  Dimensionless  
C  Dimensionless  
D 

u  
d 
μm  
k  Dimensionless  
d 
mm  
D 

D 

u  
d 
μm  
d 
μm  
k  Dimensionless 
Diffusion coefficients of the mobile phases used in LC, GC and SFC have a magnitude of 10^{–9}
First, a blank graphical user interface (GUI) was generated (MATLAB R2016a) in which a popup menu was added for accessing all calculation sections. After, the equations described in Section 1 were implemented into corresponding section of the script. For example, Equation 1 is implemented in the section ‘Liquid Chromatography’ (packed column). To ensure only relevant data can be given as input, limitations have been set per calculation section. The limitations for Equation 1 are shown below. For calculation, first linear spaced data (
In order to check the performance of the application, guidelines for flow rate optimization in liquid chromatography were used from [
Optimal flow rates for packed columns with 5μm particles at different internal diameters according to [
Internal diameter (mm)  Optimal flow rate (mL/min) 



2  0.15–0.50 
3  0.60 
4 – 4.6  0.80–2.0 
8  2.0–4.0 
These guidelines were used to perform test calculations. For these calculations, A, B, C, the diffusion coefficient of the mobile phase and the volume fraction were set at 2, 1, 0.05, 2.369·10^{–9} m^{2}/s and 0.7 respectively. The results of the calculations can be found in Table
Results of test calculations compared to guidelines of [
Calculated values are rounded to two decimals.
Internal diameter (mm)  Optimal flow rate (mL/min)  Calculated flow rate (mL/min) 



2  0.15 – 0.50  0.28 
3  0.60  0.63 
4  0.80–2.0  1.11 
From Table
As is mentioned in the Implementation and Architecture section, limitations are set in order to enhance the quality of the calculations. Furthermore, by clicking on the push buttons, information can be obtained on common values. A brief tutorial (
The GUI was originally designed in MATLAB R2016a (Windows) and later also tested in MATLAB R2010a (Windows) without any problems. Furthermore, the
MATLAB (R2016a), but also works with older versions of MATLAB (e.g. R2010a)
Disk space: 1.98 MB
The executable file (
For running the
N/A.
English.
This application offers fast and easy calculation for the flow rate of the mobile phase in chromatographic systems under certain conditions, such as particle size, diffusion coefficients and dispersion factors. In this way, system optimization can be done easily. To make the handling of the application even more easy, a brief tutorial is available in the code repository. This tutorial shows which parameters have to be filled out. In addition, figures are shown to support the tutorial text. Additionally, this tool can be integrated to existing chemistrybased calculation tools, for example Calc98 or OpenChrom. Furthermore, the application does not need any preinstallation which means the executable file can be launched directly. However, a standalone application as only available for Windows. In the future, it will be aimed to generate also a standalone application for Linux as well as Mac OS X. Nonetheless, this application is a useful tool for optimizing chromatographic systems which can finds its use in the field of analytical chemistry.
The author declares that they have no competing interests.