Packed columns optimum velocity

A column 3 cm long, 4.6 mm in diameter packed with particles 3 Jim in diameter will give about 6,000 theoretical plates at the optimum velocity. This efficiency is typical for a commercially available column. 

Thus, the column should completely resolve about 14 equally spaced peaks. It is seen from figure 1 that a peak capacity of 14 is not realized although most of the components are separated. This means that the column may not have been packed particularly well and/or the flow rate used was significantly above the optimum velocity that would provide the maximum efficiency. The mobile phase that was used was tetrahydrofuran which was sufficiently polar to deactivate the silica gel with a layer (or perhaps bilayer) of adsorbed solvent molecules yet was sufficiently dispersive to provide adequate sample... 

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. 

An example of a separation primarily based on polar interactions using silica gel as the stationary phase is shown in figure 10. The macro-cyclic tricothecane derivatives are secondary metabolites of the soil fungi Myrothecium Verrucaia. They exhibit antibiotic, antifungal and cytostatic activity and, consequently, their analysis is of interest to the pharmaceutical industry. The column used was 25 cm long, 4.6 mm in diameter and packed with silica gel particles 5 p in diameter which should give approximately 25,000 theoretical plates if operated at the optimum velocity. The flow rate was 1.5 ml/min, and as the retention time of the last peak was about 40 minutes, the retention volume of the last peak would be about 60 ml. 

The column used was 25 cm long, 4.6 mm in diameter, and packed with silica gel particle (diameter 5 pm) giving an maximum efficiency at the optimum velocity of 25,000 theoretical plates. The mobile phase consisted of 76% v/v n-hexane and 24% v/v 2-propyl alcohol at a flow-rate of 1.0 ml/min. The steroid hormones are mostly weakly polar and thus, on silica gel, will be separated primarily on a basis of polarity. The silica, however, was heavily deactivated by a relatively high concentration of the moderator 2-propyl alcohol and thus the interacting surface would be covered with isopropanol molecules. Whether the interaction is by sorption or displacement is difficult to predict. It is likely that the early peaks interacted by sorption and the late peaks by possibly by displacement. 

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... 

Consequently the use of very flne particles, liner than thuiSe presently available with a reasonably good size distribution would pernitt significant improvement in the analysis of high molecular weight solutes which have low diffusion coefficients and for which the optimum reduced velocity, vq. is attained at a very low value of the actual flow velocity, in columns packed with particles having the usual size ... 

There is another way to look at the problem, however. Most analysts would like to have a simple column to solve separation firoblems in general. What colunm length and particle size would be optimum for such a purpose A 30-cm-long column packed well with 10-/Am particles, as now commercially available, can generate a maximum of 10,000 plates for a solute having A = 3 and = 2 x 10 cm /sec at an optimum flow velocity of 0.04 cm/sec v 2). Under these conditions the analysis time is 50 min (3.3 plates/sec) and the pressure is 6 atm with an eluent having 1) = 0.5 cP. The column is suitable to attain difficult separations which require 10 plates, but it is slow. If we raise the pressure to 30 atm, which still is relatively low, (he analysis (line and efficiency afe reduced to 10... 

The form of the HETP curve for a capillary column is the same as that for a packed column and exhibits a minimum value for (H) at an optimum velocity. 

It Is seen that, in a similar manner to the packed column, the optimum mobile phase velocity is directly proportional to the diffusiv ty of the solute in the mobile phase, However, in the capillary column the radius (r) replaces the particle diameter (dp) of the packed column and consequently, (u0pt) is inversely proportional to the column radius. 

The minimum analysis time is that achieved by employing the column of optimum length, packed with particles of optimum diameter and operated at the optimum velocity. Thus, the minimum analysis time, (t(min)), Is given by. 

In the operation of preparative columns, it is necessary to obtain the maximum mass throughput per unit time and, at the same time, achieve the required resolution. Consequently, the column will be operated at the optimum velocity as in the case of analytical columns. Furthermore, the D Arcy equation will still hold and the equation for the optimum particle diameter can be established in exactly the same way as the optimum particle diameter of the analytical column. The equation is fundamentally the same as that given for the optimum particle diameter for a packed analytical column, i.e. (18) In chapter 12, except that (a) and (k ) have different meanings. 

The approximate efficiency of a packed column operated at its optimum velocity (assuming the inlet/outlet pressure ratio is small) is given by the Van Deemter equation,... 

Figure 14.5 Plot of the optimum velocity for minimum SLT vs. the concentration step height. Curves derived from Eq. 14.40. Curve 1, conditions used for Figure 14.4. Curve 2, experimental conditions 5 cm long home packed column mobile phase 50 50 methanol-water, sample 4-tert-butylphenol (kg = 10), sample size 0.2 fig. Symbols optimum velocity under linear conditions. Reproduced with permission from J. Zhu, Z. Ma and G. Guiochon, Biotechnol. Progr., 9 (1993) 421 (Fig. 8). 1993, American Chemical Society.

Note Optimum velocity at approx, v = 3 then h = i with excellent column packing (analyte with low molar mass, good mass transfer properties). 

Some common terms used in preparative-scale liquid chromatography are summarized in Table 11.4, The production rate, specific production, or the recovery yield provide suitable objective functions to judge the relative success of individual methods. For efficient use of the separation system, the production rate and the recovery yield should be maximized. Invariably, this results in operating the column in an overloaded condition. Unfortunately, column operation under nonlinear conditions is complex, and optimum conditions are not as easy to predict as the less demanding, although less powerful, scale-up approach. To scale up an analytical separation, the same column packing, column length, and mobile phase velocity are used, and the column diameter increased... 

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