HPLC Column Support Pore VOLUME

If an HPLC column had no packing material inside it, then the volume of liquid contained in the cylinder could be calculated using the formula for the volume of a cylinder as follows: 

      Volume of Cylinder = Pi * r² * L;     

          [where Volume is in ul; Pi = 3.14; r = column radius (mm) and L= column length (mm)]

  Example: Using the above formula, a 4.6 mm x 250 mm column would have an empty volume of 4,155 ul (~ 4.16 mls).

For most chromatography applications we pack the column with a high surface area porous media. Often this is a silica based support. This support media fills the empty space inside the column reducing the total volume accessible by a liquid (or to the samples). If the media used was not porous, it would fill most of the space (depends on size and shape of media). Most commonly used chromatography supports are porous and leave about 70% (0.7) of the original volume available to the mobile phase and sample [Pore Volume = Surface Area (m²/g) x Pore Diameter  (Å) / 40,000]. Based on this information, we use a value of 0.7 as the average pore volume for a packed chromatography column (some supports will have pore volumes which are larger or smaller than this value. The manufacturer will often measure it and provide the value on their published specification sheet).


Using a typical 4.6mm x 250mm column we found the total volume to be 4,155 ul (4.16 mLs). If we now multiply this empty column volume by 0.7 (note: use 0.7 or 70% for columns with fully porous particles and 0.55 or 55% for superficially porous particles) we obtain 2,908ul total volume (2.9 mLs). This is the estimated volume of the fully packed column. This value is very important as it provides an estimate of what the column dead volume will be so we can calculate the 'T' zero time of an unretained analyte. This estimate will depend on the column dimensions, using our HPLC method (be sure and take into account the measured flow rate to determine the column "dead time"). This is one of the very first calculations you make when starting or modifying an HPLC method and is critical information to know at all stages of method development. All chromatographers should know how to estimate this value before using an HPLC system. *You should confirm this estimate by injecting an unretained sample onto the column and measure the retention volume, then compare the two values. The measured value is the most important number (the one we use for calculations), but the estimate should be close (+/- 15%). The estimate is still useful for troubelshooting and method development as when combined with K prime, it provides a quick measure if chromatography has occurred (retention).

For more information on the importance of knowing the HPLC Column Dead Time, please refer to this article link. 

Notes: The measured support pore Diameter (SIZE) is important for determining if the sample will have access to the inside of the support (e.g. A support with a pore size of 80Å will be too small for most large peptides or proteins, but a support that is 300Å will allow access to many, not all, larger molecules). A support with too small a pore diameter will not allow the sample to access the high surface area inside the support. Instead, the sample will be unretained and pass by it eluting at the column's void volume. This is the basis of SEC or GPC analysis where we use columns with different pore sizes to "filter" samples based on size. Large pores for large Mw samples and small pores for low Mw samples. A general rule is use 300Å or larger pores for samples with Mw > 10,000 and 80Å to 150Å for smaller samples.

More info on pore volume can be found at this article link: https://hplctips.blogspot.com/2014/12/hplc-column-pore-volume-or-pore.html

Common HPLC Calculations:

Capacity Factor / Retention Factor / Capacity Ratio:  k1 (K Prime)

k1 = T(R) - T(0) / T(0)
where T(R) equals the retention time of the peak in minutes and T(0) is
the retention time of an unretained peak. *For chromatography to take place, K Prime must be > 1.00 and for most modes of chromatography, should be greater than 1.5 or 2.0 for all samples !


Tailing Factor: USP: 't'

t = W(5.0)/tw/2

where tw equals the distance between peak front and T(R) at 5% of peak height units. W(5.0) equals peak width at 5% height, in minutes.


Theoretical Plates: USP and ASTM, 'N'

N = 5.54 x (T(R)/W(50))2          

Assumes width at peak half height (50)
* More info can be found at this link.


Resolution: USP, ASTM, 'R'

R = (T(R)(b)-T(R)(a)) x 2.35/(W(50)(b) + W(50)(a))/2

Assumes width at half height (50%) with peaks (a) and (b).

*Notes: Visually, "Baseline" resolution is R = 1.5. Your goal should be R = or > 2.0. ** R of 1.5 provides 99.8% separation which means you cannot accurately quantify a 0.1% impurity so develop the method to have a resolution value of at least 2.0.


Note: The appropriate formula(s) for use with your samples may depend on which of the many pharmaceutical guidelines and regulations apply in your country. Always consult the appropriate guidelines.