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# DOES SHORT MEAN FAST. PART I – HPLC BLOG, K.SYCHEV© 2020

Given a fixed back-pressure, the shorter the column, the quicker is the separation – this misconception can often be encountered in some advertising brochures and even HPLC method development “guides”.

Fortunately, its speculative character is quite evident – the latter says nothing about the resolution, which drops significantly with the replacement of a longer column by a shorter one. Let us check it. 250mm/5um and 100mm/3um columns generate almost the same back-pressure (250/5^2=10; 100/3^2=11), but at a 1mL/min (for the column diameter 4.6mm) the shorter column has a 30-35% lower plate count (about 12’000) than the longer one has (about 20’000).

This simple math does not take into account extra-column effects; in real life, the loss of separation efficiency might be even greater. Therefore, the above statement describes the trivial case – the gain in throughput comes at the expense of the resolution.

But what if to reformulate the starting point as follows:

given a fixed plate count, and a fixed back-pressure, the shorter is the column, the quicker is the separation. Is this correct?

Well, this thesis is still incomplete since it misses one critical condition – it says nothing about the nature of chromatographic band dispersion. Are we talking about real-life routine analysis cases where the extra-column effects should be taken into account? Or are we talking about some other HPLC application areas where these effects can be neglected (for example, LC/MS)?

It turns out that from the viewpoint of applications where extra-column effects can be neglected – yes, the above statement is correct. But the gain in throughput is not exactly the reversed proportional to the column length (as many misleading advertisements say).

Let us check it. 250mm/5um column at a 2.0 mL/min and 125mm/3um column at a 1.5 mL/min generate almost the same back-pressure (250*2/5^2=20; 125*1.5/3^2=20.8) and almost the same plate count (about 15’000), and the shorter column is then 1.5 times faster than the longer one (250/2=125; 125/1.5=83; 125/83=1.5). Not 2 times faster as one could expect taking into account the column length ratio 250/125=2, but only 1.5 times. Therefore,

taking into account the intra-column diffusion factors only, given a fixed plate count, and a fixed back-pressure, the shorter is the column, the quicker is the separation – but not exactly proportional to the column length ratio.

Nevertheless, this nice concept cannot be applied to real-life routine analysis cases where the extra-column effects should be taken into account.

It’s not a secret that those who perform the routine analyses in pharma prefer to use longer columns and do not trust in shorter ones, no matter what advertisements say. And they have their reasons for that.

The point is that in case the extra-column effects affect the resolution, the plate count cannot be furthermore considered as a constant.

In practice, it is increasing along the chromatogram having a minimum value at the start, and the maximum nominal value somewhere at a higher k’ values (usually at a k’>10 for very short columns). More than that, how sharp the drop in plate count is, depends on the magnitude of extra-column band dispersion, which may involve a number of factors of different nature.

Fortunately, a way to reduce it is not linked to its nature; the negative impact is always reversed proportional to the retention volume 1/VR of a given analyte under given conditions.

In turn, the retention volume is proportional to the retention factor 1+k’ and a column length L, given a fixed column diameter dc: VR = V0*(1+k’) = φ*dc^2*L*(1+k’).

Thus, to reduce the negative impact of the extra-column effects upon the resolution, a column length L and the retention factors k’ of early eluted target compounds should be increased, separately or together.

Now let us consider the situation where the length L1 of the column initially used for the separation is precisely enough to negate the impact of extra-column effects for the first eluting peak having the least retention factor k’1. In order to speed up the separation, the initial longer column is replaced by a shorter column L2 (L2<L1), given a fixed back-pressure and a fixed nominal plate count.