Mobile-phase velocity

Now t[i is a minimum when k = 2, that is, when = 3t . There is little increase in analysis time when k lies between 1 and 10. A twofold increase in the mobile-phase velocity roughly halves the analysis time (actually it is the ratio Wu which influences the analysis time). The ratio Wu can be obtained from the experimental plate height/velocity graph. 

Plot of the height of a theoretical plate as a function of mobile-phase velocity using the van Deemter equation. The contributions to the terms A B/u, and Cu also are shown. 

There is some disagreement on the correct equation for describing the relationship between plate height and mobile-phase velocity. In addition to the van Deemter equation (equation 12.28), another equation is that proposed by Hawkes... 

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 most common mobile phases for GC are He, Ar, and N2, which have the advantage of being chemically inert toward both the sample and the stationary phase. The choice of which carrier gas to use is often determined by the instrument s detector. With packed columns the mobile-phase velocity is usually within the range of 25-150 mF/min, whereas flow rates for capillary columns are 1-25 mF/min. Actual flow rates are determined with a flow meter placed at the column outlet. 

It is also seen that, at very low velocities, where u E, the first term tends to zero, thus meeting the logical requirement that there is no multipath dispersion at zero mobile phase velocity. Giddings also introduced a coupling term that accounted for an increase in the effective diffusion of the solute between the particles. The increased diffusion has already been discussed and it was suggested that a form of microscopic turbulence induced rapid solute transfer in the interparticulate spaces. 

It is seen that the first term differs from the Giddings equation and now contains the mobile phase velocity to the power of one-half. However, when the first... 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

In (1976) Horvath and Lin [8,9] introduced yet another equation to describe the value of(H) as a function of the linear mobile phase velocity (u). Again, it would appear... 

Figure 4. HETP Curves for the Same Column and Solute Using the Average Mobile Phase Velocity and the Exit Velocity...

Liquids have relatively low compressibility compared with gases and, thus, the mobile phase velocity is sensibly constant throughout the column. As a consequence, elution volumes measured at the column exit can be used to obtain retention volume data and, unless extreme accuracy is required for special applications, there is no need for the retention volume to be corrected for pressure effects. 

Figure 8. Graph of Variance per Unit Length against Linear Mobile Phase Velocity...

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 conditions required to minimize tube dispersion are clearly indicated by equation (10). Firstly, as the column should be operated at its optimum mobile phase velocity and the flow rate, (0) is defined by column specifications it is not a variable that can be employed to control tube dispersion. Similarly, the diffusivity of the solute (Dm)... 

The basically correct equation appears to be that of Giddings but, over the range of mobile phase velocities normally employed i.e., velocities in the neighborhood of the optimum velocity), the Van Deem ter equation is the simplest and most appropriate to use. 

Thus, from equation (13) a value for (2X,dn) can obtained by plotting (H) against (1/Dm) for data that has been obtained at a constant linear mobile phase velocity... 

Thus, a practical procedure would be as follows. Initially the HETP of a series of peptides of known molecular weight must be measured at a high mobile phase velocity to ensure a strong dependence of peak dispersion on solute diffusivity. 

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. 

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

The multipath dispersion on a thin layer plate is the process most likely to be described by a function similar to that in the van Deemter equation. However, the actual mobile phase velocity is likely to enter that range where the Giddings function (3) applies. In addition, as the solvent composition is continually changing (at least in the vast majority of practical applications) the solute diffusivity is also altered and thus, the mobile phase velocity at which the Giddings function applies will vary. 

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