.
Column efficiency refers to the performance of the stationary phase to accomplish particular separations. This entails how well the column is packed and its kinetic performance (Bidlingmeyer, 1984). The efficiency of a column can be measured by several methods which may or may not be affected by chromatographic anomalies, such as "tailing" or appearance of a "front." This is important because many chromatographic peaks do not appear in the preferred shape of normal Gaussian distribution. For this reason efficiency can be an enigmatic value since manufacturers may use different methods in determining the efficiency of their columns (Bidlingmeyer, 1984).
Calculation of column efficiency value:
All the following methods use this formula that measures N, or number
of theoretical plates:
.
Inflection Method- Calculation is based upon inflection point
which appears at 60.7% of the peak height for a normal Gaussian peak. At
this point the width of the peak is equivalent to two standard deviation
units. Any asymmetrical aspect of a peak should not affect this calculation
since the width is measured above the anomalous occurance (i.e., tailing
or fronting).
(Bidlingmeyer,
1984)
Half-peak height Method- As the name suggests, the measurement
is based upon the width at 50% of peak height. For the same reason as inflection
method, this measurement is not affected by asymmetry; however, this method
is more reproducible from person to person since width at 50% peak height
is less prone to be varied.
(Bidlingmeyer,
1984)
Tangent Method- Tangent lines are drawn on each side of the peak
and the width is the distance between the two lines at the base of the
peak. Therefore, it is more sensitive to asymmetrical peaks and variation
in efficiency values is usually seen from user to user.
(Bidlingmeyer,
1984)
Sigma Methods- These methods measure peak width at decreasing
levels of peak height. Thus, the three sigma method measures width
at 32.4% of peak height, the four sigma method measures at 13.4%,
and the five sigma method measures at 4.4%. The five sigma method
is most sensitive to asymmetry because the width is measured at the lowest
point.
(Bidlingmeyer,
1984)
Height/Area Method- This method utilizes the fact that the area
of a peak is a function of its height and standard deviation. To determine
efficiency, values for peak height and area are used in a different formula:
A computer is usually necessary to use
this method in order to calculate the area and height.
Moment Method- This method entails disregarding peak shape and expresses parameters of the peak in statistical moments. The zero moment, µ0, is the peak area. The first moment, µ1, is the mean and occurs at the center of the peak (which is the maximum peak height in normal Gaussian peaks). The second moment, µ2, is the variance of the peak. This is a detailed method where appropriate data systems are needed. For a more detailed discussion, a reference is provided (Grubner, 1958).
These methods were evaluated by computer simulation based on efficiency values obtained on a series of synthetically modified Gaussian peaks (i.e., increasing the 'tailing') and compared to the actual value based on the moment method (which was determined to be the most accurate). Briefly, the results were as follows:
CALCULATION METHOD--ACCURACY(Bidlingmeyer,
1984).
| Inflection | Low | |
| Half-peak height | Low | |
| Tangent | Low | |
| Height:Area ratio | Medium | |
| Four sigma | Medium | |
| Five sigma | High | |
| Asymmetry | High |
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