Column efficiency, measurement

B. A. Bidlingmeyer and F. V. Warren, Jr., Column Efficiency Measurement, Anal. Chem. 1984, 56, 1583A. 

Bidlingmeyer, B.A. and Waren, F.V. (1984) Column efficient measurement. Anal. Chem., 56, 1588-1595. 

Although neutral compounds such as alkylphenones have been used as RPC standards [64] and, as already noted, other neutral molecules are employed for column efficiency measurements, it is preferable to use compounds that are structurally similar to the sample of interest and that presumably interact with the reversed-phase sorbent in a similar manner in this way, a much more accurate assessment of a column can be made for a specific separation problem. For instance, as noted previously, peptides favor separation by an adsorption-desorption mechanism in contrast, small organic molecules such as alkylphenones and toluene are separated mainly by a partitioning mechanism [164,173]. Indeed, even when RPC eolumns are assessed to be suitable for basic, polar (but... 

Never forget that column efficiency measured as theoretical plates can be performed only with isocratic elution. Gradient elution requires determination of peak capacity as a measure for the separating capability of a column. 

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... 

Direct Scale-Up of Laboratory Distillation Ljficiency Measurements It has been found by Fair, Null, and Bolles [Ind. Eng. Chem. Process Des. Dev., 22, 53 (1983)] that efficiency measurements in 25- and 50-mm (1- and 2-in-) diameter laboratory Oldersbaw columns closely approach tbe point efficiencies [Eq. (14-129)] measured in large sieve-plate columns. A representative comparison of scales of operation is shown in Fig. 14-37. Note that in order to achieve agreement between efficiencies it is necessaiy to ensure that (1) tbe systems being distilled are tbe same, (2) comparison is made at tbe same relative approach to tbe flood point, (3) operation is at total reflux, and (4) a standard Oldersbaw device (a small perforated-plate column with downcomers) is used in tbe laboratoiy experimentation. Fair et al. made careful comparisons for several systems, utibzing as large-scale information tbe published efficiency studies of Fractionation Research, Inc. 

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... 

However, any given column operated at a specific flow rate will exhibit a range of efficiencies depending on the nature and capacity ratio of the solute that is chosen for efficiency measurement. Consequently, under exceptional circumstances, the predicted conditions for the separation of the critical pair may not be suitable for another pair, and the complete resolution of all solutes may still not be obtained. 

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. 

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)... 

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. 

Other parameters sometimes obtained from the chromatogram, which are mostly measures of the degree of separation and column efficiency, are resolution (R), the number of theoretical plates (N), and... 

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