Plate count column efficiency

For the optimal application of GPC to the separation of discrete small molecules, three factors should be considered. Solvent effects are minimal, but may contribute selectivity when solvent-solute interactions occur. The resolving power in SMGPC increases as the square root of the column efficiency (plate count). New, efficient GPC columns exist which make the separation of small molecules affordable and practical, as indicated by applications to polymer, pesticide, pharmaceutical, and food samples. Finally, the slope and range of the calibration curve are indicative of the distribution of pores available within a column. Transformation of the calibration curve data for individual columns yields pore size distributions from which useful predictions can be made regarding the characteristics of column sets. 

Column packing is as much art as it is science. Even the professionals in the held cannot routinely prepare columns that will give the same plate count column to column. They quality control the columns with a set of standards, and columns that deviate by more than a set amount are either dumped and repacked (not cost effective) or are sold as specialty columns. Columns that exceed QC specifications are almost as bad as poor efficiency columns ... 

Additional factors influencing column performance are the type and quality of the packing process, which mainly determines the theoretical plate count (N) of the column. In contrast to HPLC columns the efficiency of the separation itself is determined predominantly by the quality of the sorbent alone (pore... 

For SEC separations of polymers, column efficiency is better characterized by specific resolution, R,p, and efficiency, T, than by theoretical plate count. Peak resolution, R is calculated according to (7) ... 

Each SynChropak column is tested chromatographically to assure that it has been packed according to specifications. For SynChropak GPC columns, a mixture of a high molecular weight DNA and glycyltyrosine, a dipeptide, is used to evaluate internal volume and efficiency. The mobile phase used for the test is 0.1 M potassium phosphate, pH 7, and the flow rate is 0.5 ml/min for 4.6-mm i.d. columns. Minimum plate count values and operational flow rates are listed in Table 10.4 for 4.6-mm i.d. columns of all supports and the various diameters of the SynChropak GPC 100 columns. 

Figures 13.25-13.28 show the ultrahigh resolution separations in chloroform of polystyrene standards, polytetramethylene glycol, urethanes and isocyanates, and epoxy resins, respectively. Multiple column sets of anywhere from two to six columns in series have been used for well over a year with no apparent loss of efficiency. The 500- and 10 -A gels can easily tolerate 15,000 psi or more. In fact, the limiting factor in the number of columns that can be used in series is generally the pump or injector in the FIPLC system. A pump capable of 10,000 psi operation should allow the use of a column bank of 10-12 50-cm columns with a total plate count of 500,000 or more.

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. 

Column manufacturers normally provide basic information about their columns, such as plate count, particle size, exclusion limit, and calibration curve. This information is necessary and fundamental, however, it is not sufficient to allow users to make an intelligent decision about a column for a specific application. For example, separation efficiency, the dependence of separation efficiency on the mobile phase, the ability to separate the system peaks from the polymer peak, the symmetry of the polymer peak, and the possible interaction with polymers are seldom provided. 

Traditionally, column efficiency or plate counts in column chromatography were used to quantify how well a column was performing. This does not tell the entire story for GPC, however, because the ability of a column set to separate peaks is dependent on the molecular weight of the molecules one is trying to separate. We, therefore, chose both column efficiency and a parameter that we simply refer to as D a, where Di is the slope of the relationship between the log of the molecular weight of the narrow molecular weight polystyrene standards and the elution volume, and tris simply the band-broadening parameter (4), i.e., the square root of the peak variance. 

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. 

In chromatography, the separation efficiency of any single separation method is limited by the efficiency and selectivity of the separation mode, that is, the plate count of the column and the phase of the selected system. Adding more columns will not overcome the need to identify more components in a complex sample, due to the limitation of peak capacities. The peak capacity in an isocratic separation can be described, following Grushka (1970), as given in Equation (17.1) ... 

In more demanding separations that require higher plate counts, specially designed rapid analysis columns packed with very high efficiency 2 to 3 /.an porous particles are available from several manufacturers. In addition, monolithic columns with improved flow-through characteristics are also commercially available. Figure 13.4 depicts a comparison of inlet pressure and flow rate for 4.6 mm inner diameter x 50, 100, and 150 mm columns packed with 5 /an particles. 

Other matters to consider in column choice are column length, column diameter, and particle size. Column efficiency (theoretical plate count) is determined by a ratio of column length to particle size. A shorter column with the same particle size may give a shorter run time but at a loss of resolution. A shorter column with a smaller particle size with a lower flow rate may give a similar resolution in a shorter time. Retention time reproducibility improves in systems where column temperature can be controlled, especially in cases where ambient room temperature varies. 

Efficiency or plate count (N)—an assessment of column performance. N should be fairly constant for a particular column and can be calculated from the retention time and the peak widths. Selectivity (a)—the ratio of retention k ) of two adjacent peaks. Sample capacity— the maximum mass of sample that can be loaded on the column without destroying peak resolution. Capacity factor k )—a measure of solute retention obtained by dividing the net retention time by the void time. 

In chromatographic and related separation techniques the basic requirements for the resolution (Rs) of two peaks are a column with a high number of plate counts and a factor to induce some selectivity for the separation. Basically resolution is the product of separation efficiency and selectivity ... 

It is important, first, to realize that efficiency is not a function solely of the column. Bad extracolumn parameters, such as detector cell volume or tubing diameters, can make the best column in the world look terrible. Second, efficiency measurements are very poor ways of comparing or purchasing columns unless all other parameters are constant. Many columns are bought and sold because they have a higher plate count than someone else s column. The efficiency calculations could have been made with different equations, on different compounds, on different machines, at different flow rates, all of which will have a profound effect on efficiency. The only valid use of plate counts that I have found is in column comparisons where all other variables are equal, or in following column aging over a period of days or months. 

Let us look at an efficiency measurement. Efficiency, N, is usually reported in plates, a dimensionless term that is a throwback to the days of open column, flooded plate distillations. The more plates in the distillation column, the more equilibrations have occurred, and the better the separation that was produced. In an HPLC column, the larger the plate count, the sharper the peaks are, and the smaller the amount of overlap that occurs between them. 

The best way to follow column changes is by way of column standard plate counts. For discussion purposes, we will use the four-standard mixture of acetophenone, nitrobenzene, benzene, and toluene described in the discussion on efficiency factor (Chapter 4). Our column will be a Ci8 reverse-phase column run in 70% acetonitrile/water at 254 nm. In an initial run, we obtain four peaks whose interpeak a s double between each pair. After we discuss reverse phase, we will see how these killers affect normal phase columns. 

Plate Count—A measure of column efficiency derived by comparing peak width to retention time. A higher number indicates a more efficient separation. Theoretical plates are an arbitrary unit assigned to the efficiency value, in analogy to efficiency units in open column distillations. 

Because the electroosmotic flow affects the amount of time a solute resides in the capillary, both the separation efficiency and resolution are related to the direction and flow of the EOF. The EOF flow profile, as shown in Figure 4.7, is comparatively pluglike. Unlike the laminar flow that is characteristic of pressure-driven fluids,5 the EOF has minimal effect on resistance to mass transfer. As a result, the plate count in a capillary is far larger than that of a chromatography column of comparable length. 

The most commonly used criterion for judging column performance is efficiency as measured by the number of theoretical plates or column plate count (N) exhibited by the column during the separation of a test mixture. The larger the number of theoretical plates, the more likely it is that the column will produce the desired separations. However, while popular, N is not a complete performance parameter for making comparisons. For example, N does not take into account particle size as does the reduced plate height, h. Another measurement, hmin, accounts for all of these factors as well as the mobile phase linear velocity and sample diffusion. However, N is the term most commonly recognized as being related to resolution (2), as shown in Equation 1 ... 

Third, the efficiency (N) may be adapted to meet the requirements set by the values of k and a. The value of N is determined by the column characteristics and the flow rate. While increasing the plate count may require great sacrifices in terms of analysis time, the reverse is also true. If the values of k and a allow the use of a column with a low N value to achieve the separation, then the analysis time may be reduced dramatically. 

Eqn.(7.15) suggests that the sensitivity (cmax) increases with increasing plate count (N). However, this is only true if all other factors, in particular r0, are kept constant. A better way to look at the effect of the column efficiency on the sensitivity is to consider the ratio... 

Although it is not strictly valid to determine column efficiency using plate count theory under gradient elution the actual benefit... 

The most common performance indicator of a column is a dimensionless, theoretical plate count number, N. This number is also referred to as an efficiency value for the column. There is a tendency to equate the column efficiency value with the quality of a column. However, it is important to remember that the column efficiency is only part of the quality of a column. The calculation of theoretical plates is commonly based on a Gaussian model for peak shape because the chromatographic peak is assumed to result from the spreading of a population of sample molecules resulting in a Gaussian distribution of sample concentrations in the mobile and stationary phases. The general formula for calculating column efficiency is... 

The injection is a critical factor in fast LC methods and must be considered to maintain column efficiency. Injection volumes that are too large can cause volume overload of the column, which results in broad, flat-top shaped peaks with low plate counts that are more pronounced for earlier eluting components. As injection volume is increased, peak height should increase however, peak width should remain the same. If peak width increases as well, this is indicative of volume overload. As column dimensions are reduced, the maximum injection volume must be reduced by the ratio of the column volumes [see equation (17-33) in Section 17.7.4], For example, reducing... 

The efficiency at which the column or plate count is packed initially in chromatography is important because (1) it determines the shape of the individual band profiles, and (2) it can effect the void fraction and thus the operating pressure. For chromatographic processes where the plate count is important (see Section 7.8.1 on flow rate), developing methods to measure the plate count of the column after it is packed or of a prepacked column is important. There are several methods for measuring the plate count of a packed column, as given below. 

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