Resolution plate number

Jandera, P. Churacek, J. Gradient elution in liquid chromatography II. Retention characteristics (retention volume, bandwidth, resolution, plate number) in solvent-programmed chromatography—Theoretical considerations. J. Chromatogr. 1974, 91, 223-235. 

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... 

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. 

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 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.]... 

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,) ... 

Giddings pointed out (32) that separated compounds must remain resolved throughout the whole process. This situation is illustrated in Figure 1.5, where two secondary columns are coupled to a primary column, and each secondary column is fed a fraction of duration Ar from the eluent from the first column. The peak capacity of the coupled system then depends on the plate number of each individual separation and on At. The primary column eliminates sample components that would otherwise interfere with the resolution of the components of interest in the secondary columns. An efficient primary separation may be wasted, however, if At is greater than the average peak width produced by the primary column, because of the recombination of resolved peaks after transfer into a secondary column. As At increases, the system approaches that of a tandem arrangement, and the resolution gained in one column may be nullified by the elution order in a subsequent column. 

As described above, resolution can be improved by variations in plate number, selectivity or capacity factor. However, when considering the separation of a mixture which contains several components of different retention rates, the adjustment of the capacity factors has a limited influence on resolution. The retention times for the last eluted peaks can be excessive, and in some cases strongly retained sample components would not be eluted at all. 

Plate number N (as for Gaussian peaks) Resolution factor R ... 

The plate number in equation (4.56) corresponds to the value when the effective value of the capacity factor (equal to k when the band is at the column midpoint) is equal to the capacity factor in isocratic elution for the same column. The effective value of the capacity factor, k, is simply 1/1.15b. In most cases k, will be large and equation (4.57) is simplified by equating l/k, to zero. The resolution between two adjacent bands in a gradient program, again analogous to isocratic elution, is e q>ressed by equation (4.58)... 

A typical hplc column (25 cm x 4.6 mm, packed with a 5 jum bonded silica stationary phase) will have an efficiency corresponding to a plate number of 10 000-15 000. For many separations, this efficiency is far more than is needed, as often a plate number of 3000-5000 will give baseline resolution of all solutes. If this is the case, using a conventional column will waste analysis time and sol-... 

The object of a chromatographic separation is to achieve satisfactory resolution of solutes in the minimum time. Resolution is influenced by the capacity factor of the solutes and the selectivity and plate number of the column. 

The tailing is probably caused by a mixed mechanism, for instance adsorption on active silica sites that are not end-capped. To reduce this, we can try adding a salt to the water. To get better resolution we need to change the selectivity, a, which means changing the chemistry of the mobile phase, or increasing the plate number of the column, or both. 

The resolution of the three oestrogens still has to be improved, so to proceed further we can either work on the selectivity, a, by using, instead of methanol, a different water-soluble solvent such as acetonitrile, tetrahydrofuran or dioxane, or we can try to improve the separation by increasing the plate number of the column. If we change the solvent, we cannot be sure about what will happen to the selectivity, and we may have to do a lot more experimental work to get any improvement. Increasing the plate number, if it can be done, is the easier of the two options. Fig. 4.2f shows the improvement that results when two 30 cm columns are used in series, with a flow rate of 1 cm3 min-5. The oestrogens are separated from the excipients and are also separated reasonably well from one another. The separation is complete in about 20 minutes. 

Two compounds were separated by HPLC with an Rs value of 0.75, the plate number for the second compound being 4500. Calculate the number of plates required to obtain resolutions of (a) 1.0 and (b) 1.5. 

In order to evaluate the efficacy of the expanded bed technique the plate height (HETP), plate number (N), resolution (Rs), Bodenstein number (Bo), particle Peclet number (Pep) and axial dispersion coefficient (DJ have been calculated and compared with the corresponding values of a traditional HPLC column. N can be expressed by... 

The resolution can be improved by increasing the column plate number, N, and/ or the separation factor, a (a = the ratio of the retention factors of the two compounds). N is the physical parameter and a is the chemical parameter for the separation. Higher N and a values give a better separation. 

Further, an optimization of the organic modifier concentration for the separation of known compounds was proposed. When the value of the actual column plate number, the resolution, and log P of pairs of compounds a and b were known, the percentage concentration (x) required for their separation was calculated from Equations 6.4 to 6.6 19,20... 

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