Columns optimum velocity

A number of HETP equations were developed other than that of Van Deemter. Giddings developed an alternative form that eliminated the condition predicted by the Van Deemter equation that there was a finite dispersion at zero velocity. However, the Giddings equation reduced to the Van Deemter equation at velocities approaching the optimum velocity. Due to extra-column dispersion, the magnitude of which was originally unknown, experimental data were found not to fit the Van Deemter... 

The efficiency obtained from an open tubular column can be increased by reducing the column radius, which, in turn will allow the column length to be decreased and, thus, a shorter analysis time can be realized. However, the smaller diameter column will require more pressure to achieve the optimum velocity and thus the reduction of column diameter can only be continued until the maximum available inlet pressure is needed to achieve the optimum mobile phase velocity. 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

Although the optimum column radius increases linearly with the separation ratio of the critical pair, this simple relationship is moderated by the ratio of the square of the optimum radius to the optimum velocity, both of which are functions of (a). 

As the optimum column radius is inversely proportional to (a-1), and (uopt) is inversely proportional to (ropt)> the simple linear relationship between optimum velocity and the separation ratio is to be expected. The high velocities employed for... 

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. 

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. 

The peak capacity is not pertinent as the separation was developed by a solvent program. The expected efficiency of the column when operated at the optimum velocity would be about 5,500 theoretical plates. This is not a particularly high efficiency and so the separation depended heavily on the phases selected and the gradient employed. The separation was achieved by a complex mixture of ionic and dispersive interactions between the solutes and the stationary phase and ionic, polar and dispersive forces between the solutes and the mobile phase. The initial solvent was a 1% acetic acid and 1 mM tetrabutyl ammonium phosphate buffered to a pH of 2.8. Initially the tetrabutyl ammonium salt would be adsorbed strongly on the reverse phase and thus acted as an adsorbed ion exchanger. During the program, acetonitrile was added to the solvent and initially this increased the dispersive interactions between the solute and the mobile phase. 

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. 

It is important to note that, at least for neutral compounds, temperature has only a small effect on efficiency when the column is operated at its optimum flow velocity. Above the optimum velocity, temperature has a beneficial effect on efficiency, whereas below the optimum velocity, increased solute diffusion has a relatively large negative effect on efficiency [32,82,83]. 

The Van Deemter equation (1) was the first rate equation to be developed and this took place as long ago as 1956. However, it is only relatively recently that the equation has been validated by careful experimental measurement (2). As a result, the Van Deemter equation has been shown to be the most appropriate equation for the accurate prediction of dispersion in liquid chromatography columns, The Van Deemter equation is particularly pertinent at mobile phase velocities around the optimum velocity (a concept that will shortly be explained). Furthermore, as all LC columns should be operated at, or close to, the optimum velocity for maximum efficiency, the Van Deemter equation is particularly important in column design. Other rate equations that have been developed for liquid chromatography will be discussed in the next chapter and compared with the Van Deemter equation... 

It is seen that the column length varies inversely as the product of the solute diffusivity in the mobile phase and the mobile phase viscosity in much the same way as the column efficiency does when operating at the optimum velocity. As would be expected the column length is directly proportional to the inlet pressure but, less obviously is also proportional to the cube of the particle diameter. 

Summarizing, if a column is operated at its optimum velocity and the solute concerned is eluted at a relatively high k value, and assuming the film thickness of the stationary phase is small compared with the particle diameter (a condition that is met in almost all LC separations) then,... 

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. 

Equation (13) shows that the minimum value of (H) is solely dependant on the column radius (r) and the thermodynamic properties of the solute/phase system. As opposed to the optimum velocity, the minimum value of (H) is not dependent on the solute diffusivtty. 

It is interesting to note from equation (14) that when a column is run at its optimum velocity, the maximum efficiency attainable from a capillary column is directly proportional to the inlet pressure and the square of the radius and inversely proportional to the solvent viscosity and the diffusivity of the solute in the mobile phase. This means that the maximum efficiency attainable from a capillary column increases with the column radius. Consequently, very high efficiencies will be obtained from relatively large diameter columns. 

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. 

Having determined the optimum column radius, the optimum velocity being known then the optimum flow-rate volume is given by,... 

Since carrier gas velocity enters into both the second and third terms, its effect is more complex, but there is a certain velocity at which column efficiency is best, as shown in Figure 3.3. Below the optimum velocity the change is quite drastic, but above this point a more gradual decrease in efficiency takes place. Although somewhat higher efficiencies can be obtained... 

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