Plate number, increase

The efficiency of a packed column increases as the size of the stationary phase particles decreases. Typical particle sizes in HPLC are 3-5 p,m. Figures 25-2a and b illustrate the increased resolution afforded by decreasing particle size from 4 to 1.7 pm. Plate number increased from 2 000 to 7 500 when the particle size decreased, so the peaks are sharper with the smaller particle size. In Figure 25-2c, a stronger solvent was used to elute the peaks from the column in trace b in less time. Decreasing particle size permits us to improve resolution or to maintain the same resolution while decreasing run time. 

In a chromatographic system, it is desirable to have a high column plate number. The column plate number increases with several factors [2] ... 

Chromatographic efficiency seems to be linked to the additive-to-surfactant concentration ratio in the micellar mobile phase. The plate numbers increase with this ratio but reach a maximum level (e.g., at pentanol/SDS = 6 and acetonitrile/CTAC= 12). - The organic solvent/surfactant ratio affects the exchange rates of the solute between micelle/stationary and aqueous phases. It also controls the extent of the surfactant coverage and the fluidity of the organic layer on the stationary phase. 

Any newly packed or acquired columns should be automatically put through at least the simple tests described in this section. Any suspicion of reduction in plate number, increased tailing or poor permeability must be verified by means of a suitable test. 

The effective plate number increases with increase of k, and approaches to N at high k values. In general, the effective plate number is a better parameter to describe the performance of a column. It is especially true when we compare the efficiency of the capillary column with the packed column. 

The plate number A/ is a compound-specific measure (it, therefore, applies to each individual peak) for the separation efficiency of a column under clearly defined mobile phase and temperature conditions. It will change over the column lifetime and can also be influenced by the HPLC instrument. The plate number increases proportional to the column length L, provided all other conditions remain constant (except for the colunm pressure). It also increases at constant column length when the stationary phase particle size, particle architecture, or bonding chemistry is optimized in way that accounts for less band dispersion. The respective columns exhibit increased separation efficiency per unit column length. Once the plate number of a column or method is increased, one can separate more analytes or separate analytes with better resolution under otherwise constant conditions. The formula to calculate the plate number from the peak parameters retention time and peak width at base Wi, or peak width at half height Wj, is as follows ... 

In practice, the design and development of sub-2 tm particles is a significant challenge. As particle size decreases, the optimum flow to reach maximum plate numbers increases and the use of smaller particles is then substantially limited by a rapid increase in pressure drop [49]. Standard HPLC instruments have a maximum operating pressure of about 400 bar (6000 psi), and these systems simply do not have the capability to take full advantage of sub-2 pm particles. 

Plate Number N. Peak resolution is proportional to the square root of the plate number. Increasing the plate number by a factor of 2 (A/=2000() to Al=40000) improves peak resolution by only 1.4 ( /2 gives /fs=1.40- 1.96). 

Therefore, the plate number increases linearly with the axial column P6clet number and the plate height decreases as N increases. Also N increases as decreases, and as... 

To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in equation 12.27 or equation 12.28. The easiest way to accomplish this is by adjusting the velocity of the mobile phase. At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. As shown in Figure 12.15 (which is interpreted in terms of equation 12.28), the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of u. 

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. 

LC-LC coupling systems are also employed to perform separations requiring very large plate numbers. However, it has been demonstrated (see equation (5.20) that for coupled columns peak capacity increases linearly with the square root of n... 

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. 

Figure 4 shows the impact of process intensification for this hypothetical case. With a temperature increase of only 41°C, the number of reactors for such comparatively big units is reduced from 20, hardly feasible in view of costs and process control, to four, feasible for the same reasons. Thus, the costs decrease by almost a factor of five (not exactly, since fixed costs have a small share). Another 21°C temperature increase halves the number of reactors again, and at 249°C, which is 149°C higher than the base temperature, an equivalent of 0.2 micro-structured reactors is needed. This means that practically one micro-structured reactor is taken and either reduced in plate number or in the overall dimensions. The costs of all microstructured reactors scales largely with their number only at very low numbers do fixed costs for microfabrication lead to a leveling off of the cost reduction. 

Data Analysis. (Arlett et al., 1989). A weighted analysis of variance is performed on the mutation frequencies, as the variation in the number of mutations per plate usually increases as the mean increases. Each dose of test compound is compared with the corresponding vehicle control by means of a one-sided Dunnett s test and, in addition, the mutation frequencies are examined to see whether there is a linear relationship with dose. 

---