SAMPLE VOLUME EFFECT ON THE CHROMATOGRAPHIC PROCESS. THEORYAlexander M.Nemirovsky (firstname.lastname@example.org)
Researchers do not like to go into detail on the sample volume effect on the
chromatographic process, because with the present state of the question, calculations
are only of theoretical interest. That is easy to understand: why waste effort
for calculations if the dispersion of the chromatographic zone in the column
cannot be satisfactorily described? Recently, however, some improvement has
been achieved as it has become possible to describe the chromatographic process
much better. In this connection, it is now important to consider the effect
of the sample volume on the width of the chromatographic peak. This can be exemplified
by a problem that could not have been resolved before. Suppose we have a histogram
with peaks which are not completely separated. We have to make a conclusion
whether the length of the chromatographic column should be increased, or the
sample injector and other factors affecting the sample volume should be re-considered.
σ is the width of the peak affected by the sample amount sin;
Application of this formula is restricted by the requirement that the concentration
profile should originally have the Gaussian shape. This is possible, e.g., in
gas-liquid chromatography, but generalizing this principle for all possible
cases would be a mistake.
However, this formula implies an approximation which should be kept in mind.
The point is that expression (2) assumes that the added peaks are equal, which
can only be possible when the number of the plates in the column is large enough.
The further conclusions cannot be applied to systems with low efficiency. The
criterion is the shape of the chromatographic peak, as for low efficiency systems
the peak will have a pronounced asymmetric shape.
where Vin is the sample volume.
The error in the range Vin
/ σo <=2 does not exceed
1%. A smaller error (<0.1%) but within a narrower range of peak widths (Vin
/ σo <0,5) is achieved
by the formula σ = σo (1 + 0,235
Vin2 / σo2
It is easy to find the constant of proportionality between Vin and σin:
Thus we have come to a very important conclusion: at small sample volumes,
the chromatographic peaks formed by different concentration profiles of the
sample are practically undistinguishable. Calculations show that a discrepancy
of, e.g., 5% between the types of dependencies appears at Vin /σo 1,2. In this
connection one does not need to bother considering the method of calculation
of the sample volume effect on the chromatographic process up to Vin
However, at greater volumes this or that method has to be chosen.
is easily linearized in the coordinates σ2 vs.VrVmr.
The figure shows an example of the calculation of a sample volume through linearization. It should be noted that the straight line sections a segment on the ordinate axis equal to squared volume of the ejected sample. (Details on chromatographic parameters calculation can be found in the work "Calculating the Efficiency of Chromatographic Systems".)
For samples with homogenous concentration distribution, linearization is hardly possible. A solution can be found in performing calculations only in the range of small values, Vin/σo <1,2. For such calculations, linearization in the manner of (6) can be harmlessly used. It is not difficult to recalculate the obtained value σin into Vin since σin0,7Vin.