Here is a simple formula to use when scaling up or down Internal Column Diameter to maintain retention values (under constant linear velocity). Flow rate must be adjusted to account for any changes made to the column's cross-sectional area. We usually refer to these types of changes as the "Scaling Factor". To determine the scaling factor, we need to know the internal column diameters of the two columns we are scaling from (actually, we need to know the radius, but once we have the diameter, we simply divide the diameter by 2 to obtain the radius). *In this discussion, changes in cross-sectional area are the only parameters we are concerned with as column length does not affect scaling.
- Scaling Factor = (S);
- Column #1 Radius = (R1);
- Column #2 Radius = (R2).
S = R22 / R12
Example #1: 250 x 4.60 mm column scaled down to a 250 x 2.10 mm column.
Answer = 0.208.
- If the original flow rate was 1.000 mL/min, the the scaled down flow rate would be 0.208 of the original or 0.208 mL/min for the 2.10 mm ID column. *For practical use and application, we often use either 200 ul/min or 210 ul/min to simplify the value.
Example #2: 250 x 4.60 mm column scaled up to a 250 x 10.00 mm ID semi-prep column.
Answer = 4.726.
- If the original flow rate used was 1.000 mL/min with the 4.60 mm ID column, then we would increase the flow rate to 4.726 mL/min on the 10.00 mm ID column to maintain the same relative velocity (and relative retention). *For practical use and application, we often use 5 mL/min to simplify (round off) the value.
Notes:
- Flow rate optimization should always be carried out by running a standard at different flow rates and plotting the plate height (N) vs the flow rate. Test flow rates that are slightly below the predicted linear velocity and up to 2 times higher than that rate to find and optimize the flow rate for your sample (it must be determined through experimentation for your specific method).
- HPLC Columns packed with sub 2 micron supports may have optimum flow rates 2 to 5 times more than the predicted std linear flow rate so actual testing is critical to determining the most efficient flow rate. I recommend optimizing the flow rate used with analysis methods which use any particles which are 2.5 microns or smaller in diameter.
Think of your typical porous bare silica support as a big sponge full of holes. All of those holes (pores) are where the sample will migrate through before emerging out the other side. With conventional chromatography supports, most of the interaction takes place inside the particle, not on the surface. The size and number of these openings relate to retention time. Besides particle size (particle diameter), pore size is one of the most important characteristics of silica based chromatography supports.
The pore size or pore diameter is often expressed in Angstroms (i.e. 80 A = 8 nm). The degree of porosity relates to the hydrodynamic volume of your sample and is inversely related to the surface area of the support. The larger the surface area of the support (smaller pore size), the longer the possible retention of the sample. For small drug molecule samples under 1,000 daltons (an estimate only) we often use high surface area supports with small pore sizes between 60 and 150 Angstroms (~ 200 to 500 square meters per gram). These provide high retention characteristics useful in separating apart many small compounds in one analysis run. For larger molecules (i.e. peptides and proteins), we employ supports with larger pore sizes (~300 Angstroms). Particles with small pores have larger surface areas which can provide more interaction with the sample. Note: Pore size is often determined using the BET Nitrogen adsorption/desorption equation. Due to endcapping of the support (e.g. C8 or C18), the actual value obtained is often 20-30% less than the original value.
When comparing
bare silica columns or trying to identify similar conventional columns for use in a method, pore size must be considered. Manufacturer's publish the pore size in Angstroms (*sometimes in nm) for their different supports. Choosing columns with similar pore sizes is just one of many parameters needed to provide similar retention characteristics.
For gradient analysis, most analytical scale HPLC (UHPLC) systems incorporate a solvent mixer which is designed to balance the requirements of moderate dwell volume, low noise and good mixing efficiency. Depending on the method run, the ideal mixer's volume may in fact be completely different than the one installed in your chromatography system. A high-pressure mixing Binary pump can often work well with a slightly lower volume mixer than a low-pressure mixing ternary or quaternary pumping system (because the high pressure mixing gives you a head start), but both pump types benefit from additional mixing.
- Be sure to also consider the volume of any pulse dampener used too as these often have large internal volumes and act as mixers. Some pulse dampeners also incorporate the pressure transducer and/or mixer. These types of combination modules may limit the types of modifications which can be made to optimize the mixing and reduce the dwell volume.
- Don't forget to address the dwell volume contribution of the autosampler, injector loop, interconnecting tubing (extra column volume) and detector flow cell too when optimizing the flow path of your HPLC system.
Here
are some general guidelines to help you determine the appropriate
mixer volume for your own HPLC system. Note: Since many types of mixer
designs exist (static, dynamic, shear...), these are guidelines only. There are some commercially available, high efficiency, low-volume mixers available which can reduce the need for a large volume mixer. Your specific application should be taken into account to determine which size is best.
HPLC System Mixer Volume Choices - Size Matters ("Mixer Volume")
SMALL: Fast or ultrahigh speed separations using low volume, small particle columns. These types of applications depend on a low dwell volume mixer for gradient analysis. To achieve this, your HPLC system should be plumbed with narrow bore capillary tubing (example: 0.005" ID; 0.12mm ID) and include a gradient mixer with a volume of less than 100 ul for low flow rates (example: ~35 ul is rather common size).
LARGE: High Sensitivity Analysis: Gradient analysis where sensitivity is key, benefit from larger volume mixers to minimize contributions of any UV absorbing additives (e.g. TFA) and turbulence in the flow. Traditional 300 to 750 ul mixers often work well in these applications, provided that the column volumes are also large. Smaller column volumes will require smaller mixer volumes to reduce the added dwell effect.
MEDIUM: Routine HPLC Analysis: Typical analytical separations using 3 to 5 mm ID columns (x 100 mm or longer) usually benefit from modest sized mixers within a range of 200 to 400 ul volume. For these applications, I often start with a recommendation to use a mixer which has 10% of the columns volume as a starting point. For a typical 4.6 x 250 mm, 5 micron porous support column, which has about 3 mLs of internal volume, a 300 ul volume mixer usually provides enough mixing volume for routine gradient analysis.
Additional Info:
Back in the 1980's we often related mixer volume to intended flow rate/column dimensions. For example: A mixer size of 25 ul was suggested for 50 ul/min flow rates (commonly used with 1 mm ID columns). A mixer size of 200 ul was suggested for 200 ul/min flow rates (commonly used with 2.1 mm ID columns) and 350 ul mixer volume for 1.000 ml/min flow rates (commonly used with 4.6 mm ID columns). Note: Mixers such as these, with large volumes relative to the column volume contributed to large gradient delay times, but this was, and still is, of less concern for isocratic methods.
As
mentioned before, the type of mixer, column volume, flow rate and
mobile phase characteristics will help suggest the most applicable volume
for your application. When in doubt, select a larger mixer volume for isocratic analysis (less baseline noise, better for gradients) and a smaller one if reducing gradient analysis delay volume is critical.
