The Optimum Mobile Phase Velocity

The optimum mobile phase velocity for an open tubular GC column is given in chapter 13, equation (14). Reiterating this equation, 

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 

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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. 

It is seen that by a simple curve fitting process, the individual contributions to the total variance per unit length can be easily extracted. It is also seen that there is minimum value for the HETP at a particular velocity. Thus, the maximum number of theoretical plates obtainable from a given column (the maximum efficiency) can only be obtained by operating at the optimum mobile phase velocity. 

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 optimum mobile phase velocity will also be determined in the above calculations together with the minimum radius to achieve minimum solvent consumption and maximum mass sensitivity. The column specifications and operating conditions are summarized in Table 4. 

The optimum flow rate is obviously the product of the fraction of the cross-sectional area occupied by the mobile phase and the optimum mobile phase velocity, i.e.,... 

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. 

The expression for the optimum mobile phase velocity is given by equation (28) in chapter 12 and is as follows. 

It is seen that, providing the isomers are eluted at a (kf) value greater than about 2.0, the column will separate those solute pairs having separation ratios as low as about 1.03. This, however, assumes that the column is very well packed and is operated at about the optimum mobile phase velocity. In practice, a more realistic minimum separation ratio would be between 1.035 and 1.04. However, as it will be seen, the cyclodextrin bonded phases can easily provide separation ratios significantly greater than these values. This is achieved by... 

The column, designated as TSKgel DEAE-NPR a weak anion exchanger, was 3.5 cm long and 4.6 mm in diameter packed with non-porous resin beads 2.5 ji in diameter. Thus, the maximum efficiency available at the optimum mobile phase velocity would be about 7,000 theoretical plates. The sample was a crude hexokinase product and an... 

Resolution in forced-flow development is not restricted by the same limitations that apply to capillary flow controlled systems. The maximum resolution achieved usually corresponds to the optimum mobile phase velocity and R, increases approximately linearly with the solven)t migration distance (48). Thus there is... 

The optimum mobile phase velocity can be obtained by differentiating equation 5 with respect to (u) and equating to zero,thus,... 

From d Arcy s Law for fluid flow through a packed bed, at the optimum mobile phase velocity the length of the column is given by,... 

It is seen from figure 2 that changing the particle diameter from I to 20 micron results in an efficiency change from about 3500 theoretical plates to nearly 1.5 million theoretical plates and furthermore, this very high efficiency is achieved at an inlet pressure of only 3000 p.s.i.. It is also seen that the maximum available efficiency increases as the particle diameter increases. This is because, as already discussed, if the pressure is limited, in order to increase the column length to accommodate more theoretical plates the permeability of the column must be increased to allow the optimum mobile phase velocity to be realized. It is possible to increase the inlet pressure to some extent, but ultimately the pressure will be limited and the effect of particle diameter will be the same but at higher efficiency levels. 

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. 

Furthermore, if the column is run under optimum conditions and, consequently at the optimum mobile phase velocity, (H) will be at its minimum, I.e.,... 

Equation (18) allows the optimum particle diameter to be calculated that will allow the separation to be achieved in the minimum time by utilizing the maximum available inlet pressure and operating at the optimum mobile phase velocity. It is one of the most important equations in column design. 

Differentiation of Eq. 16.29 shows that the optimum mobile phase velocity, which is a fimction of the displacer retention factor and concentration, is minimum for Kd = 1, which also corresponds to the optimum displacer conditions for iiiinimiun SLT (see previous section) [11]. This combination of results is obviously imattractive, as it does not correspond to what would have been required for a high production rate. The optimum flow velocity is almost always much lower in displacement chromatography than the optimum velocity imder linear... 

Representative properties of different column types for gas chromatography Hmin = minimum plate height at the optimum mobile phase velocity Uopt... 

Theoretical column plate count and relative operating pressure at the optimum mobile phase velocity for conventional liquid chromatography columns... 

Figure 6.3. Variation of the average plate height as a function of the solvent-front migration distance for conventional and high performance layers using capillary flow and forced flow at the optimum mobile phase velocity. (From ref. [61] Elsevier).

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