Theoretical Plate Number and Resolution

these two separation parameters, theoretical plate number and resolution, are functions of both the electrophoretic mobility of the analytes and EOF mobility. N is increased with increases in electrophoretic mobility and applied potential, but it decreases with an increase in the diffusion coefficient. R in turn increases with electrophoretic mobility and applied voltage but decreases with diffusion coefficient. In general, both efficiency and resolution are higher at higher voltages and in the presence of substances having small diffusion coefficients. 

Sample volume overloading can also reduce efficiency—for example, when the sample plug length is wider than the zone length determined by diffusion. This liability of high injectable volumes is often ignored, and efficiency is intentionally sacrificed to gain sensitivity. 

Mismatched ionic conductivities between sample and running buffer can cause peak defocusing and peak distortion. These phenomena depend on local changes in the electric field and, consequently, in the migration velocity. However, a proper choice of the sample conductivity (lower than that of the buffer) allows in-capillary solute concentration with peak focusing. 

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Comparing the two methods p-LC and p-CEC, the electrochromatographic method always shows higher theoretical plate numbers and resolutions at comparable elution times [39-41] (see Fig. 9.8). The Chirasil-Dex-monolith [44] consists of a single piece of a chiral modified porous solid, thus frits are no longer required and the risk of air bubble formation decreases. Pressurization is not insisted. As shown in Fig. 9.9 the enantiomer separation of mephobarbital on a Chirasil-Dex-monolith can be performed... 

A parallel version of overpressured multilayer chromatography (OPMLC) using two or more chromatoplates is very attractive because a large number of samples (50-100 or more) can be separated during one development (23b). Serial coupled OPMLC (called long distance OPLC) can be used for the elevation of the theoretical plate number and resolution alike (23c). Personal OPLC generates an automatic separation process (23d). 

FIGURE 4,14 Example of isothermal gas chromatogram simulation. The Analysis tab (shown) displays the elution conditions plus the retention times, peak widths, effective theoretical plate numbers, and resolution for the two peaks flanking the cursor. Program GC-SOS V 5.1 (ChemSW, Inc., North Fairfield, CA). 

Resolution can be related to theoretical-plate numbers and retention characteristics. From Equation (24-7) we can write... 

The efficiency of zone electrophoretic separation may be expressed by analogy to chromatography [20] by the number of theoretical plates N, and resolution R. Separation efficiency is influenced by (a) operational conditions and (b) the dispersion process. 

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. 

According to Equation 3, the resolution of two peaks in column separation is controlled by three major variables retention defined in terms of the retention factor k column efficiency expressed as the number of theoretical plates N and selectivity characterized by the selectivity factor a [48] ... 

In the elucidation of retention mechanisms, an advantage of using enantiomers as templates is that nonspecific binding, which affects both enantiomers equally, cancels out. Therefore the separation factor (a) uniquely reflects the contribution to binding from the enantioselectively imprinted sites. As an additional comparison the retention on the imprinted phase is compared with the retention on a nonimprinted reference phase. The efficiency of the separations is routinely characterized by estimating a number of theoretical plates (N), a resolution factor (R ) and a peak asymmetry factor (A ) [19]. These quantities are affected by the quality of the packing and mass transfer limitations, as well as of the amount and distribution of the binding sites. 

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... 

Taking = 2and/ = 1.5, the required theoretical plate numbers fora = 1.05and 1.25 are 35,721 and 2,025, respectively. Therefore, a column with high selectivity can produce sufficient resolution, even with low theoretical plate numbers (short length). 

Apart from the above-discussed parameters for HPLC optimization of chiral resolution on antibiotic CSPs, some other HPLC conditions may be controlled to improve chiral resolution on these CSPs. The effect of the concentrations of antibiotics (on stationary phase) on enantioresolution varied depending on the type of racemates. The effect of the concentrations of teicoplanin has been studied on the retention (k), enantioselectivity (a), resolution (Rs), and theoretical plate number (N) for five racemates [21]. An increase in the concentration of teicoplanin resulted in an increase of a and Rs values. The most surprising fact is that the theoretical plate number (N) increases with the increase in the concentration of teicoplanin. It may be the result of the resistance of mass transfer resulting from analyte interaction with free silanol and/or the linkage chains (antibiotics linked with silica gel). This would tend to trap an analyte between the silica surface and the bulky chiral selector adhered to it. This is somewhat... 

Screen-printed carbon electrodes were also evaluated in the Topas microchip for separation and detection of pAP and AsA. The theoretical plate number (AO, half-peak width (wy2), peak current and resolution are also shown in Table 34.2. Peak current at SPEs was higher than those obtained with gold and platinum wires. 

Zhang et al. [106] resolved rhodaminel23 and fluorescein by using NCE. The migration times, theoretical plate numbers resolution, back flow rate, and peak heights of rhodaminel23 and fluorescein are given in Table 3.5. 

TABLE 3.5 Effects of Reservoir Levels on Migration Time, Theoretical Plate Numbers, Resolutions, and Peak Heights of Rhodaminel23 and Fluorescein in NLC ... 

System suitability specifications and tests, Capacity factor (k ), Preci-sion/injector repeatability (RSD), Relative retention (a), Resolution (Rs),Tailing factor (T),Theoretical plate number (N)... 

Table 1(a). Variation of Theoretical Plate Number N, and Resolution, Rs, with Variation in Methanol Concentration... 

Ruhr s group studied the separation of double- and single-stranded DNA restriction fragments in capillary electrophoresis with polymer solutions under alkaline conditions in epoxy-coated capillaries and found that at pH 11 the theoretical plate numbers exceeded several millions [96], At pH 12, single-stranded DNA molecules were still well separated in entangled hydroxyethylcellulose (HEC) solutions, but the resolution decreased significantly in dilute polymer solutions. 

When packed into chromatography columns, TRIM beads imprinted with Boc-L-Phe were shown to have column efficiencies and separation abilities superior to ground and sieved bulk material [5]. The theoretical plate number was approximately double that obtained with conventional crushed polymer under the same conditions and the resolution of a racemate was also slightly enhanced. The difference, however, was not that great considering the additional preparation time and effort involved. 

Theoretical-plate number is a useful concept with which to compare similar columns or various operating conditions for a single column. Nevertheless, the concept should not be overemphasized, and for broader comparisons resolution should be... 

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