HPLC Column Cross-Sectional Area and Scaling

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:

1. 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). 
    
2. 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.
   

UHPLC TIP: Reducing the Column Temperature to Offset Frictional Heating Effects (Causing Poor Resolution)

HPLC column temperature is a critical variable that we adjust and optimize during method development. We use it as a variable during the method development process to improve solubility, optimize peak shape and increase resolution. Once established, it must be carefully controlled during the method analysis to provide reliable and reproducible analysis results. Change the column temperature and you may also change the results obtained. This is a fundamental method development tool and must not be forgotten.

If you are developing a new UHPLC method OR perhaps scaling an HPLC method to utilize 2.5 micron or smaller support particles, then you may observe a loss of resolution or poor peak shape in the new method. There are many reasons why this may occur, and the most common ones relate to not optimizing all of the method parameters correctly when scaling the method (e.g. dwell volume too large, flow cell volume too large, injection volume too large, sample rate too slow, flow rate not optimized, mobile phase composition changes not in scale with the gradient...). But there is another reason...

Resolution may be reduced or lost when all of the initial scaling and instrument set-up parameters are optimized. What is the most likely reason for this? In many cases the use of substantially higher flow rates (relative to linear flow rates) and the use of smaller diameter particles results in much higher backpressures (you may recall that if you halve the particle size, the backpressure increases 4x). The resulting backpressure might be 2, 3 or even 4 times higher than observed in the original method. While these higher backpressures were well within the operating parameters of the HPLC system used, the results obtained were poor. The possible cause? The much higher backpressure increased the amount of frictional heating inside the column, raising the actual analysis method temperature and changing the separation conditions. 

Pushing mobile phase (liquid) through a chromatography column generates heat and pressure. The heat generated increases the actual temperature of the column and reduces the viscosity of the fluid. In conventional columns (i.e. 4.6 x 150 mm, 5u) at 1.00 ml/min, this heating effect is minimal, but at much greater column pressures, > 400 bars, the frictional effects may be substantial. These types of very high pressures may be seen with methods which utilize columns containing the smallest particles (1.9 to 2.5 micron). Enough to change the temperature in the column by several degrees (e.g. >5 degrees C) and result in different method conditions. So, what can you do about this? The most direct way to address the problem is to run the same method at a lower temperature (perhaps decrease by 5 C to start with). This will slightly raise the backpressure (lower temperature equals higher viscosity), but it should cool the column and restore the original temperature conditions used. Additionally, we suggest that you always start column equilibration using a flow ramp to gradually increase the flow over time and reduce the overall heating effect and resulting "shock" placed on the column. An initial delay at equilibration may help reduce these effects (gradually ramp up to the regular flow rate and hold). You may need to try several temperatures and this may be easiest to do if your HPLC has a column compartment with heating and COOLING capabilities. Optimizing the temperature and internal pressures may increase the column lifetime and result in better overall data reproducibility.