#### In many of my previous posts I have used the term column volume, typically abbreviated as CV, as a value used to help determine separation quality and loading capacity. However, I recently was asked a question about this topic from a chemist who understands the column volume concept but wanted to better understand its definition and how it is determined.

#### In this post I will explain what a column volume is and how it is determined empirically.

Some chemists think the internal volume of the cartridge (or column) – *without* packing material inside is the column volume. While useful in determining scale-up factors, the empty column’s volume is not the CV. The CV of any column or cartridge is the volume inside of a packed cartridge *not* occupied by the media. This volume includes both the interstitial volume (volume outside of the particles) and the media’s own internal porosity (pore volume). Combined, the two volumes constitute 70% to 80% of the packed cartridge’s volume. Of course this means that the media only occupies 20% to 30% of the space in the cartridge.

You may be wondering why the volume % is expressed as a range. Well, each chromatography packing material has its own pore volume. Because the base media, typically silica, is synthetic, there is always variability from batch to batch, within a batch, and even within a single particle.

Media manufacturers always test their product to ensure it conforms to their specifications which is always expressed as a range. One of the primary tests performed on silica is a nitrogen BET analysis that measures both surface area and porosity. Here at Biotage, we test every batch of media we purchase to ensure it meets our specifications. The test results for any media batch are an *average* surface area and an *average* pore volume. From the surface area and pore volume the *average* pore diameter is calculated.

Most flash silica used in normal-phase chromatography has an average surface area of 500 m^{2}/g and a calculated pore diameter of 60Å. This equates to a pore volume of 0.75 mL. How did I arrive at this value? I adjusted the equation below, which calculates pore diameter, to calculate pore volume.

PD = (40,000 * PV)/SA

Where:

- PD = pore diameter in Angstroms (Å)
- PV = pore volume in mL/g
- SA = surface area in m
^{2}/g - 40,000 = a unit conversion constant

To back-calculate PV…

PV = (SA * PD)/40,000

Substituting values for surface area and pore diameter noted above, the equation becomes…

PV = (500 m^{2}/g * 60Å)/40,000

Or

PV = 0.75 mL/g

So, if we multiply the pore volume (0.75 mL/g) by the amount of media in a column or cartridge we will obtain the approximate volume *inside* the particles in that cartridge. For example, if a flash cartridge contains 10 g of silica and we multiply by 0.75 mL/g we obtain an intra-particle volume of 7.5 mL; this is not the column volume as it does not include the interstitial volume.

The interstitial volume factor, at least in slurry-packed HPLC columns, is approximately 0.4__[1]__. In dry-packed, larger particle flash cartridges I estimate the interstitial factor is about 0.45 because the particles are slightly less densely packed than the typical 3 to 10 micron HPLC column media.

Using the flash cartridge interstitial volume factor (0.45), the media amount in the cartridge (10 g), and that media’s pore volume (0.75 mL/g) we can estimate the 10 g packed cartridge’s column volume using the following equation:

CV = (Media weight (g)*media pore volume (mL/g))/(1 – interstitial volume factor)

Or

CV = (10 g * 0.75 mL/g)/0.55

Or

CV = 13.6 mL

Increasing the media’s porosity of course will increase the CV for any cartridge packed with that larger porosity material.

Knowing a cartridge’s column volume helps in determining purification run length, gradient profile, and solvent consumption which becomes more critical if a purification method requires scaling up.

I hope this all makes some sense. Please let me know if you have other questions relating to flash chromatography.

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__[1]__ Neue, Uwe. HPLC Columns Theory, Technology, and Practice. Wiley-VCH 1997, p. 53

can you please provide the source link for the formula used in this article

Hi Abott,

The equation is one I learned many years ago and one for which I do not have a reference. sorry I could not be of more help.

Bob