Optimum column efficiency

Figure 17-16. Maximum allowable extra-column broadening for <10% loss in efficiency for varions column dimensions packed with 3.0-pm particles. Calculated with equations (17-25) and (17-27), assuming optimum column efficiency (H = 2dp) and k = 5.

Inserting Eq. 18.40 into Eq. 18.35 gives the optimum column efficiency ... 

This equation shows that there is an optimum column efficiency which permits the achievement of the maximum production rate for a given separation. This efficiency is obtained by solving the algebraic equation obtained by writing that the differential of Eq. 18.57 is equal to 0. It is easier to derive from Eq. 18.57 the production rate for several values of the column efficiency and to find the maximum value by interpolation. The optimum values of dp/L and u are obtained from Eqs. 18.55 and 18.56, respectively. 

The optimum gradient steepness is different for the less and the more retained component. It varies with the separation factor. For the less retained component, the production rate usually reaches a plateau without a maximum and, in most cases, there is no production rate gain above G = 0.4-0.6. Although the cycle time should decrease when the gradient steepness is increased, the optimum column efficiency increases with increasing gradient steepness and these two effects compensate each other, resulting in a nearly constant cycle time. 

For a given column length, optimum column efficiency is obtained when the equilibrium step or plate height is at a minimum, that is, the column band broadening processes described by the van Deemter equation (see section 2.5.1) are minimised by selecting the optimum velocity, t>f the mobile phase. Figure 5.3 shows the van Deemter plot of H against n for... 

Inlet System, (splitting type)—Split injection is necessary to maintain the actual chromatographed sample size within the limits required for optimum column efficiency and detector linearity. 

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. 

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

Thus, for significant values of (k") (unity or greater) the optimum mobile phase velocity is controlled primarily by the ratio of the solute diffusivity to the column radius and, secondly, by the thermodynamic properties of the distribution system. However, the minimum value of (H) (and, thus, the maximum column efficiency) is determined primarily by the column radius, secondly by the thermodynamic properties of the distribution system and is independent of solute diffusivity. It follows that for all types of columns, increasing the temperature increases the diffusivity of the solute in both phases and, thus, increases the optimum flow rate and reduces the analysis time. Temperature, however, will only affect (Hmin) insomuch as it affects the magnitude of (k"). 

The smallest size difference that can be resolved is related to the pore volume, the solute shape, and the efficiency of the column (see Fig. 2.6). However, this is at very low loadings. At higher loadings the sample volume will contribute to zone broadening and may, in some cases, be the dominating factor for resolution. Thus, for fractionation, an optimum exists with respect to column efficiency (represented by the flow rate as operational parameter) and sample volume for processing a particular volume of feed per unit time. As a rule of thumb this optimum can be found at a relative sample volume of 2-5% of the column volume (Hagel et al., 1989). 

For example, a 30-m column (regardless of diameter) should have a tR for argon or butane of approximately 100 sec. It appears better to set the linear velocity higher than the optimum rather than lower than the optimum to obtain good column efficiency. Determine the column temperature where the most difficult-to-separate compounds elute and set the linear velocity at that temperature. Now the column will exhibit its maximum resolving power at the point where it is needed most. 

The curve exhibits a minimum, which means that there is an optimum mobile phase velocity at which the column will give the minimum HETP and consequently a maximum efficiency. In practice this usually means that reducing the flow rate of a column will increase the efficiency and thus the resolution. In doing so, however, the analysis time will also be increased. As seen in figure 5, however, there is a limit to this procedure, as reducing the column flow rate so that the mobile phase velocity falls below the optimum will result in an increase in the HETP and thus a decrease in column efficiency. 

Now as an increase in temperature will increase the value of (Dm) its effect on (H) and consequently the column efficiency is clear. If the mobile phase velocity is above the optimum then the function (q + C2)... 

H) and thus decrease the column efficiency. LC columns are rarely operated below the optimum velocity and thus this situation is the least likely scenario. 

It is interesting to ascertain the effect of temperature at the optimum velocity where the value of (H) is a minimum and the column efficiency a maximum. 

It is seen that when operating at the optimum velocity that provides the minimum value of (H) and thus, the maximum efficiency, solute diffusivity has no effect on solute dispersion and consequently, the column efficiency is independent of temperature. 

Another example of the use of a C8 column for the separation of some benzodiazepines is shown in figure 8. The column used was 25 cm long, 4.6 mm in diameter packed with silica based, C8 reverse phase packing particle size 5 p. The mobile phase consisted of 26.5% v/v of methanol, 16.5%v/v acetonitrile and 57.05v/v of 0.1M ammonium acetate adjusted to a pH of 6.0 with glacial acetic acid and the flow-rate was 2 ml/min. The approximate column efficiency available at the optimum velocity would be about 15,000 theoretical plates. The retention time of the last peak is about 12 minutes giving a retention volume of 24 ml. 

Xt is very difficult to provide an optimum set of conditions for operation of a liquid chromatograph under overload conditions due to the coiq>lex interactions among a large number of parameters [591,592,595,608,620,625]. The following general observations seem to be applicable in most cases. The column efficiency should be as high as possible and separatimis should be carried out using concentration overload conditions. The production rate of a... 

Injection systems of a capillary gas chromatography should fulfil two essential requirements (i) the injected amount should not overload the column (ii) the width of the injected sample plug should be small compared with band broadening due to the chromatographic separation. Good injection techniques are those which achieve optimum separation efficiency of the column, allow accurate... 

Correlation was found between domain size and attainable column efficiency. Column efficiency increases with the decrease in domain size, just like the efficiency of a particle-packed column is determined by particle size. Chromolith columns having ca. 2 pm through-pores and ca. 1pm skeletons show H= 10 (N= 10,000 for 10 cm column) at around optimum linear velocity of 1 mm/s, whereas a 15-cm column packed with 5 pm particles commonly shows 10,GOO-15,000 theoretical plates (7 = 10—15) (Ikegami et al., 2004). The pressure drop of a Chromolith column is typically half of the column packed with 5 pm particles. The performance of a Chromolith column was described to be similar to 7-15 pm particles in terms of pressure drop and to 3.5 1 pm particles in terms of column efficiency (Leinweber and Tallarek, 2003 Miyabe et al., 2003). Figure 7.4 shows the pressure drop and column efficiency of monolithic silica columns. A short column produces 500 (1cm column) to 2500 plates (5 cm) at high linear velocity of 10 mm/s. Small columns, especially capillary type, are sensitive to extra-column band... 

The particle size of a solid support is critical in striking a compromise between column efficiency and speed of separation. Both the multiple path term A and the mass transfer term (CSl of equation (4.46) (p. 89)) are reduced by reducing particle size thus leading to increased efficiency. However, as particle size is reduced, the pressure drop across the column must be increased if a reasonable flow rate is to be maintained. The optimum particle sizes for 1/8 in columns are 80/100 or 100/120 mesh and for 1/4 in columns 40/60 or 60/80 mesh. 

---