By Robert W on Wednesday, June 30, 2004 - 05:33 am:

I am using a 10cm x 2.1 mm i.d. x 3.5um particle C18 column. Is there a practical way to determine the extracolumn volume? Is there a guideline on how small the extracolumn volume should be relative to the column volume? How much effect does the guard column have on adding to the extracolumn volume? Thanks.

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By tom jupille on Wednesday, June 30, 2004 - 12:52 pm:

That's a tough question, because all extra-column volume is not created equal (the effect varies with mixing characteristics). What really matters is the amount of extra-column dispersion (band-broadening).

A good "guesstimate" is to take the retention volume of your narrowest peak and divide by the square root of the estimated column plate number. For your column, an "early" peak (k' just over 1) would have a retention volume of about 0.5 mL. Assuming 2500 plates (makes the math easy!) gives a maximum extra-column volume of about 10 microliters.

You can determine the extra-column contribution to band broadening easily if you have a set of "well behaved" standards (i.e., no tailing or other peak shape problems). You probably should have about 5 peaks spread over a reasonable retention range to make this work. Inject the standards and measure the retention volume (product of retention time X flow rate) and the variance (sigma^2) for each peak. [in the absence of tailing problems, you can assume that the width at half-height is about 2.3 times sigma; baseline width for an ideal peak is 4 times sigma]. Plot sigma^2 versus Vr^2 for your peaks and fit the best straight line. The intercept should be the extra-column sigma^2. The slope should be the reciprocal of the column plate number (the math behind this is at the bottom of the post).

The effect of a guard column depends on its size and what it's packed with. To the extent that it's similar in diameter and packing material to your analytical column, you will be effectively lengthening your column (more plates) but adding some extra-column volume due to the fittings and tubing. As a first approximation, figure these effects cancel out.

-- Tom Jupille


The back-of-the-envelope math goes like this:

1. the observed variance [s^2(obs)] is the sum of independent variances from the column and extra column effects:

s^2(obs) = s^2(col) + s^2(ec)

2. The column plate number can be defined as the ratio of the square of retention volume to column variance:

N = Vr^2/s^2(col)

which can be rearranged to solve for column variance:

s2(col) = Vr^2/N

3. Substituting that into the first equation gives:

s^2(obs) = Vr^2/N + s^2(ec)

So a plot of s^2(obs) as a function of Vr^2 should give a straight line with a slope of 1/N and an intercept of s^2(ec).
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