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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.

Under the same separation conditions, a shorter column can then no longer negate the impact of extra-column effects, and thus the resolution at the start of chromatogram drops. To maintain the same resolution, the retention factors for poorly retained components should be increased by the factor L1/L2, i.e. k’2 = k’1*(L1/L2). Therefore,

for the correct scaling of a routine isocratic HPLC separation, the reduction of a column length should be complemented by the parallel reversed proportional increase in retention factors of early eluted sample components.

Coming back to the mentioned above example, 250mm/5um column at a 2.0 mL/min and the k’ range 1-5 should be replaced by a 125mm/3um column at a 1.5 mL/min and the k’ range 2-8. Both columns generate almost the same back-pressure and almost the same nominal plate count.

To maintain the resolution of early eluted sample components in case of a considerable impact of extra-column effects, the minimum retention value for the shorter column should be increased by 2.

It is not quite clear, however, what the maximum k’ value would be in this case, but we should at least provide the same peak capacity for both columns. Peak capacity is proportional to ln((1+k2’)/(1+k’1)), so, the value for a longer column is proportional to ln((5+1)/(1+1)) = ln(3). To obtain the same peak capacity for a shorter column the maximum k’ value should be equal to 8: ln((8+1)/(2+1)) = ln(3). Thus, 1-5 and 2-8 k’ intervals generate the same peak capacity, which in the given case is equal to n = 1+√15’000/4*ln(3) ≈ 35.

And now it is possible to estimate the run time for both columns. Analysis time for a longer column is proportional to L*(1+k’)/F = 250*(1+5)/2 = 750, and for a shorter column it is proportional to 125*(1+8)/1.5 = 750 (i.e. the run time for both columns is approximately equal to 750*0.01=7.5 min).

Thus, 250mm and 125mm columns appear to have the same throughput!

So, it turns out that taking into account both intra- and extra-column diffusion factors, given a fixed peak capacity, and a fixed back-pressure, shorter columns appear not to give any considerable benefit in throughput.

And it makes a difference –

now the idea of using very short HPLC columns for the routine HPLC applications seems to be at least impractical, also taking into account that a shorter column usually has a shorter lifetime, and a lower reduced plate count and peak symmetry values.

That is why those who perform routine analyses do not trust in advertisements and rely mostly on longer columns.

The next question is

what column size and particle size are optimal for routine and screening applications having an average separation difficulty, i.e. applications that require peak capacity equal to n=50-70?

For a 400 bar HPLC system and the 1:1 AcN-Water mobile phase the two main column sizes can be used for the routine applications:

1. 250x4.6 columns packed with 3um fully porous particles at a 1.0 mL/min;

k’ 0.5-5: tR = 250*6/1*0.01 ≈ 15.0 min

n = 1+√40’000/4*ln(4) ≈ 70

2. 250x4.6 columns packed with 3.5um fully porous particles at a 1.5 mL/min;

k’=0.5-5: tR = 250*6/1.5*0.01 ≈ 10.0 min

n = 1+√25’000/4*ln(4) ≈ 55

Similarly, for a 400 bar HPLC system and the 1:1 AcN-Water mobile phase the three main column sizes can be used for the screening applications:

3. 150x4.6 columns packed with 2.7um core-shell particles at a 1.25 mL/min;

k’ 0.75-6 (corrected because of a lower reduced surface area of core-shell particles):

tR = 150*7/1.25*0.01 ≈ 8.5 min

n = 1+√35’000/4*ln(4) ≈ 65

4. 150x4.6 columns packed with 3um fully porous particles at a 1.5 mL/min;

k’ 0.5-5: tR = 150*6/1.5*0.01 ≈ 6.0 min

n = 1+√20’000/4*ln(4) ≈ 50

5. 100x4.6 columns packed with 2.7um core-shell particles at a 2.0 mL/min;

k’ 0.75-6 (corrected because of a lower reduced surface area of core-shell particles):

tR = 100*7/2*0.01 ≈ 3.5 min

n = 1+√20’000/4*ln(4) ≈ 50

At last, there are two more related questions that remain uncovered in this article:

1. How to make a separation quicker without changing column size and particle size?

2. What are the optimal column and particle sizes for a higher pressure HPLC system (600 bar, 1000-1200 bar)?

Those issues, though seemingly straightforward, deserve special consideration, so they will be covered in separate articles.

Key Words: Outsourcing HPLC Method Development & Validation, Analytical Method Development Services, Pharmaceutical Outsourcing, CDMO, Pharmaceutical Analysis, ICH Method Development & Validation

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