Plates number

Elution volume, exclusion chromatography Flow rate, column Gas/liquid volume ratio Inner column volume Interstitial (outer) volume Kovats retention indices Matrix volume Net retention volume Obstruction factor Packing uniformity factor Particle diameter Partition coefficient Partition ratio Peak asymmetry factor Peak resolution Plate height Plate number Porosity, column Pressure, column inlet Presure, column outlet Pressure drop... 

Column Efficiency. Under ideal conditions the profile of a solute band resembles that given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is expressed by the effective plate number defined from the chromatogram of a single band. 

Band Asymmetry. The peak asymmetry factor AF is often defined as the ratio of peak half-widths at 10% of peak height, that is, the ratio b/a, as shown in Fig. 11.2. When the asymmetry ratio lies outside the range 0.95-1.15 for a peak of k =2, the effective plate number should be calculated from the expression... 

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

Retention factor of mobile phase modulator A h Plate number obtained for k = IZr NpR... 

When only a few solutes are separated, they may occupy only a small portion of the total column volume at any given instant. In such cases, the productivity is improved by cyclic feed injections, timed so that the most strongly retained component from an injection elutes just before the least strongly retained component from the following injection (see Fig. 16-57). For a mixture of two components with k > 1, when the same resolution is maintained between bands of the same injections and bands of successive injections, the cycle time tc and the plate number requirement are ... 

The idea of the effective plate number was introduced and employed by Purnell [4], Desty [5] and others in the late 1950s. Its conception was evoked as a direct result of the introduction of the capillary column or open tubular column. Even in 1960, the open tubular column could be constructed to produce efficiencies of up to a million theoretical plates [6]. However, it became immediately apparent that these high efficiencies were only obtained for solutes eluted at very low (k ) values and, consequently, very close to the column dead volume. More importantly, on the basis of the performance realized from packed columns, the high efficiencies did not... 

As a secondary consideration, the chromatographer may also need to know the minimum value of the separation ratio (a) for a solute pair that can be resolved by a particular column. The minimum value of (a) has also been suggested [8] as an alternative parameter that can be used to compare the performance of different columns. There is, however, a disadvantage to this type of criteria, due to the fact that the value of (a) becomes less as the resolving power of the column becomes greater. Nevertheless, a knowledge of the minimum value of (cxa/b) can be important in practice, and it is of interest to determine how the minimum value of (aA/B) is related to the effective plate number. 

The resolution required in any analytical SEC procedure, e.g., to detect sample impurities, is primarily based on the nature of the sample components with respect to their shape, the relative size differences of species contained in the sample, and the minimal size difference to be resolved. These sample attributes, in addition to the range of sizes to be examined, determine the required selectivity. Earlier work has shown that the limit of resolvability in SEC of molecules [i.e., the ability to completely resolve solutes of different sizes as a function of (1) plate number, (2) different solute shapes, and (3) media pore volumes] ranges from close to 20% for the molecular mass difference required to resolve spherical solutes down to near a 10% difference in molecular mass required for the separation of rod-shaped molecules (Hagel, 1993). To approach these limits, a SEC medium and a system with appropriate selectivity and efficiency must be employed. 

FIGURE 2.6 Resolvability of SEC. The molecular mass ratio needed for the complete resolution of solutes of various shapes as a function of column plate number. The influence of pore volume is given by the designations (Ip), which stands for low porous for which Vp/Vo is 0.7S, and (hp), which stands for highly porous for which Vp/Vp is typically 2.0. [Reproduced from Hagel (1993), with permission.]... 

In-column solvents Column size (mm) Theoretical plate number Exclusion limit Poiystyrene PEG Particle size (/urn) Pore size (A) Flow Rate (ml/min) Maximum pressure (kgf/cm ) Maximum temperature (°C)... 

Column type Column size (mm) Theoretical plate number Range Flow rate (ml/min) Max Analytical column... 

FIGURE 14.1 Determination of the theoretical plate number N by the half-height method. 

The chromatogram of the test sample for plate number determination normally is not a Gaussian-shaped peak, which means that all three equations result in different N values. Therefore, it is important to specify which method is used for the calculation of plate number. If the method used deviates from the normal practice, it must be justified. This is especially true for a column manufacturer. 

The plate number for the same column also depends on the eluent, e.g., a permitted operation for some styrene-divinylbenzene columns is to change the eluent from tetrahydrofuran (THF) to dimethylacetamide (DMAC) and then return to THF. The plate number in DMAC is considerably lower than in THF. After the replacement of DMAC by THF the old N value is obtained again. 

The peak broadening measured for a plate number characterization is the sum of the variances a) for the column and the chromatographic equipment used ... 

The contribution of the equipment between injection unit and detector cell should be negligable in relation to the column for a sufficient column characterization short connections with narrow capillaries and zero dead volume unions are the precondition for reliable plate numbers. Every end fitting of a column causes additional band broadening. In the past a column type was offered that could be directly combined without any capillary links unfortunately, it has disappeared from the market. 

The Waters company recommends a system check of the chromatographic equipment that is used for plate number determination and analyses (2) the columns in the GPC unit used are replaced by a zero dead volume union. Then the test sample is injected under the same conditions such as a plate number determination. The 5a peak width measured on a suitable recorded peak is evaluated this 5or width of a 20-/a1 injection should be lower than 150 /a1. 

The peak measured for a plate number determination contains additional information about the packing quality of a column. The same peak may also be used to quantify information about the shape as well. The peak width on both sides of the perpendicular through the peak maximum is measured at a height of 10% of the maximum height (see Fig. 14.2). The quotient of the back by the front part of the peak is defined as the asymmetry factor (AF) ... 

The result of this equation describes the quality of the separation on the basis of an ideal size exclusion mechanism with a given pore volume distribution. The quality of the packing is deliberately excluded from this consideration. This parameter should be measured separately and judged by the plate number. The ASTM standard method for HPSEC of polystyrene (4) contains the following equation for resolution (R,) ... 

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