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Retention Factor Formula

17 Jun 2021

When starting a new analysis project, it’s important to pick the right tools for the job. In the case of chromatography, there are several different tools at our disposal. Stationary phase, mobile phase, mobile phase additives, column temperature, and flow rate all play a part in getting that perfect chromatogram.

During the column scouting phase of initial method development, it is important to know the void volume of your column.

The void volume can help determine if your first eluting compounds are getting enough retention on the column’s stationary phase. Not having enough retention for individual components in your analysis can prove to be detrimental when applying your developed method to a matrix.

Void volume can easily be determined if your column is new. A certificate of analysis (CoA) comes with every column and contains a lot of useful information.

For reversed-phase columns, a mix containing uracil is injected on the column, and the retention times are determined. Since uracil is a polar analyte and a known material for void volume determination, it is not retained on the non-polar stationary phase and elutes with the void volume.

If you pulled a column from a stack you found in a cabinet of your lab, you likely won’t still have the CoA it was shipped with. In that case, the CoAs can be searched for online using the LC column’s serial number.

Remember, if you use the void volume value from a CoA, this will not include your system’s instrument volume from the injector to the column, so the void volume provided by the CoA will only be a rough estimate.

Void volume can also be calculated, but first, the particle type will need to be established. Fully porous (FPP) and superficially porous particles (SPP) have different areas that they occupy inside the column volume, so determining your particle type will allow you to choose the correct coefficient.

Physically, the difference between fully porous and superficially porous is that superficially porous, or “core shell”, particles contain a solid impermeable core surrounded by a porous layer of silica that analytes can partition into and out of.

To calculate the void volume, or interstitial space between the silica particles, follow these two equations:

FPP void volume= 0.68πr2

SPP void volume= 0.5πr2

Where r is the radius of the column (diameter ÷ 2) in cm, and ℓ is the length of the column, also in cm. It’s important to convert units to cm so the final answer for the calculation comes out to be cm3 (1 cm3 = 1 mL). There is some debate over the coefficients for these equations, but for the intents and purposes of this article, they will serve as a reasonable estimate. 

In the table below, some common LC column dimensions have been used to calculate void volume for FPP and SPP packed columns.

 Column Dimension
 150 x 4.6 mm100 x 2.1 mm100 x 3 mm50 x 2.1 mm30 x 2.1 mm
FPP1.695 mL0.236 mL0.481 mL0.118 mL0.071 mL
SPP1.246 mL0.173 mL0.353 mL0.087 mL0.052 mL

Table 1. Calculated void volume in mL of fully porous (FPP) and superficially porous particles (SPP) for different column dimensions.

If you would rather determine void volume experimentally, this can be done for reversed-phase columns by injecting uracil. This will produce the most accurate results for the system being used since it will take into account the instrument volume.

Choose your own adventure!

Now that we have the void volume of our column, we can use this to determine if our first eluting compound has an acceptable amount of retention based on the distance traveled through the stationary phase. This is performed by calculating the retention factor or K’.

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In the above equation, Tr is the retention time of the analyte, and T0 is the time your void volume takes to elute. This ratio provides a quantitative measure of how the compound traveled through the column.

A retention factor (also known as capacity factor) of 0 would mean that your sample spends no time in the stationary phase and is not retained on the column.

A retention factor of 1 would mean that the analyte spends equal amounts of time in the stationary phase as the mobile phase.

A retention factor of 2 means that the compound spends twice as long interacting with the stationary phase as with the mobile phase. Typically, a retention factor of less than 1 is considered not well retained, and a retention factor of 2-10 is optimal. Matrix effects are typically encountered at a retention factor of less than 2, so developing a method with >2 retention will help avoid matrix interferences in most cases.

While this article focuses on chromatographic retention, if you are doing method development you can use the free EZLC chromatogram modeler to model many LC separations in seconds.

Troubleshooting Low Retention Factor

If your retention factor calculations show that early eluting compounds have K’ values less than 2, several chromatography method adjustments can improve retention and method performance. The most common approach is to modify the mobile phase composition by decreasing the initial organic solvent percentage, which increases the retention time of poorly retained analytes on reversed-phase columns.

Alternatively, switching to a different stationary phase selectivity, such as moving from a standard C18 to a polar-embedded or phenyl column, can provide better retention for specific compound classes.

Why A Well-Retained First Peak Matters

A well-retained first peak with K’ greater than 2 helps ensure that the method is robust enough to handle minor variations in mobile phase preparation, column lot-to-lot differences, and instrument-to-instrument performance differences.

Autoren

  • Jamie York is a principal scientist in the Applications Lab at Restek Corporation. She leads the development of innovative analytical methods tailored to the food, clinical, environmental, and cannabis markets. Jamie earned her PhD in chemistry from The University of Texas at Arlington, where she gained extensive expertise in a range of analytical techniques, including gas chromatography–vacuum ultraviolet (GC–VUV); gas chromatography–mass spectrometry (GC–MS); matrix-assisted laser desorption/ionization (MALDI); and liquid chromatography– mass spectrometry (LC–MS/MS); with a research emphasis on food and environmental analysis. Today, her work focuses on complex method development and advanced sample preparation strategies to support the evolving needs of the scientific community.

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