Measuring Column Efficiency

Band broadening also takes place in the injector, in the connecting tubing to the column, in the connection to the detector, in the detector, and sometimes due to slow electronics in the detector or the data system. In the connecting tubing, the band broadening is caused by the parabolic flow profile in a tube, caused by friction at the walls. 

The contribution to band broadening, of the flow in an empty tube, measured as variance is 

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The conceptual idea of a theoretical plate can be used in SEC to measure column efficiency and to compare the performance of packed coluians. For column comparisons it is usually measured with small molecules, such as toluene, acetone or benzyl alcohol, which can explore all of the pores of the packing (K jc - 1). Plate counts measured in this way produce HETP values lower than the actual values measured with monodisperse polymers and proteins. The plate count in this case can be expressed by equation (4.40)... 

Effect of Injection Volume. Table II shows the effect of injection volume on peak broadening and measured column efficiency. The bandwidths listed in Table II are due to injection volume alone, and were measured using an injector connected directly into the flowcell of a low-bandwidth detector. The plate reductions were then calculated for a 24,000 plate column, such as that represented by the bottom line of Table I, assuming 5 and 10 ml, respectively, for exclusion and total permeation volumes. Efficiencies of 23,000 plates at exclusion and 25,000 plates at permeation were actually measured for the column indicated in Table II. The effect of large injection volumes is thus to lose 25 to 50% of the potential column efficiency. 

In determining n, we assume that the detector signal changes linearly with concentration. If it does not, then n cannot measure column efficiency precisely. If Equations 2.55 or 2.57 are used to evaluate peaks that are not symmetrical, positive deviations of 10-20% may result. Since n depends on column operating conditions, these should be stated when efficiency is determined. 

The kinetics of the chromatographic process is linked to efficiency. The number of theoretical plates, N, that measures column efficiencies, is best estimated using the Foley-Dorsey equation when a departure from the Gaussian symmetrical peak shape is noted [9] ... 

Different methods of measuring column efficiency (there is a choice of measuring peak width at either half-height or baseline, see Section 6.3). 

Quantitative Calculations In a quantitative analysis, the height or area of an analyte s chromatographic peak is used to determine its concentration. Although peak height is easy to measure, its utility is limited by the inverse relationship between the height and width of a chromatographic peak. Unless chromatographic conditions are carefully controlled to maintain a constant column efficiency, variations in... 

Thus, the variance of the peak is inversely proportional to the number of theoretical plates in the column. Consequently, the greater the value of (n), the more narrow the peak, and the more efficiently has the column constrained peak dispersion. As a result, the number of theoretical plates in a column has been given the term Column Efficiency. From the above equations, a fairly simple procedure for measuring the efficiency of any column can be derived. 

Using equation (10), the efficiency of any solute peak can be calculated for any column from measurements taken directly from the chromatogram (or, if a computer system is used, from the respective retention times stored on disk). The computer will need to have special software available to identify the peak width and calculate the column efficiency and this software will be in addition to that used for quantitative measurements. Most contemporary computer data acquisition and processing systems contain such software in addition to other chromatography programs. The measurement of column efficiency is a common method for monitoring the quality of the column during use. 

The measurement of efficiency is important, as it is used to monitor the quality of the column during use and to detect any deterioration that might take place. However, to measure the column efficiency, it is necessary to identify the position of the points of inflection which will be where the width is to be measured. The inflection points are not easily located on a peak, so it is necessary to know at what fraction of the peak height they occur, and the peak width can then be measured at that height. 

Equation (18) displays the relationship between the column efficiency defined in theoretical plates and the column efficiency given in effective plates. It is clear that the number of effective plates in a column is not aii arbitrary measure of the column performance, but is directly related to the column efficiency as derived from the plate theory. Equation (18) clearly demonstrates that, as the capacity ratio (k ) becomes large, (n) and (Ne) will converge to the same value. 

The solute diffusivity will also depend on the nature of the mobile phase beitmay a gas or liquid. Very little work has been carried out on the effect of different carrier gases on column efficiency. Scott and Hazeldene [9] measured some HETP curves... 

FIGURE 2.13 From measurements of the retention volume, Vr, and the peak width at half peak height, Wr, of a gaussian peak, an estimate of column efficiency N and relative efficiency, HETP, may be calculated. The last figure is for very well packed columns close to 2 X dp. [Reproduced from Sofer and Hagel (1997), with permission.]... 

Most size exclusion chromatography (SEC) practitioners select their columns primarily to cover the molar mass area of interest and to ensure compatibility with the mobile phase(s) applied. A further parameter to judge is the column efficiency expressed, e.g., by the theoretical plate count or related values, which are measured by appropriate low molar mass probes. It follows the apparent linearity of the calibration dependence and the attainable selectivity of separation the latter parameter is in turn connected with the width of the molar mass range covered by the column and depends on both the pore size distribution and the pore volume of the packing material. Other important column parameters are the column production repeatability, availability, and price. Unfortunately, the interactive properties of SEC columns are often overlooked. 

There have been a few reports of column efficiency and reduced plate height measurements in several unified chromatography techniques. These have been based on the apparent plate height observed at the column outlet. In the notation used by Giddings (32) the apparent plate height, H, is given by the following ... 

Equation (20) allows the efficiency of any solute peak, from any column, to be calculated from measurements taken directly from the chromatogram. Many peaks, if measured manually, will be only a few millimeters wide and, as the calculation of the column efficiency requires the width to be squared, the distance (x) must be determined very accurately. The width should be measured with a comparitor reading to an accuracy of 0.1 mm. 

Before releasing a process column for chromatography, it is advisable to perform some test to measure efficiency, such as calculating height equivalent theoretical plates (HETP), both to forestall any problems in the column bed and to provide a benchmark by which to measure column reproducibility and predict degradation of the bed or material. Examples of compounds that are relatively innocuous for use in pharmaceutical applications are 1% NaCl (for gel filtration), concentrated buffer solutions (for ion exchange), and benzyl alcohol and parabens for reverse phase LC.10... 

The efficiency, or plate count of a column N is often calculated as 5.54 (tr/a)2, where tr is the retention time of a standard and a is the peak width in time units at half-height.1 2 5 This approach assumes that peaks are Gaussian a number of other methods of plate calculation are in common use. Values measured for column efficiency depend on the standard used for measurement, the method of calculation, and the sources of extra-column band broadening in the test instrument. Therefore, efficiency measurements are used principally to compare the performance of a column over time or to compare the performance of different columns mounted on the same HPLC system. 

The quantity N is approximately constant for different bands or peaks in a chromatogram for a given set of operating conditions (a particular column and mobile phase, with fixed mobile-phase velocity, and temperature). Hence N is a useful measure of column efficiency the relative ability of a given column to provide narrow bands (small values of tw) and improved separations. 

The quantity H (equal to L/N) measures the efficiency of a given column (operated under a specific set of operating conditions) per unit length of the column (see van Deemter s equation in Chapter 14). Small H values mean more efficient columns and large N values. A very important goal in HPLC is to attain small H values that lead to maximum N and highest column efficiencies. 

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