Band broadening mobile phase velocity

Figure 1.3 Relationship between band broadening and mobile phase velocity (van Oeeater equation). (Reproduced with permission from ref. 48. Copyright Elsevier Scientific Publishing Co.)...

When the mobile phase is a liquid a variety of equations can be used in addition to the van Deemter equation (1.31) to describe band broadening as a function of the mobile phase velocity, equations (1.36) to (1.39) [49,53,63,85-88]. 

For an understanding of band broadening in chromatographic systems, the linear velocity of the mobile phase is more important than the column volumetric flow rate. The mobile phase velocity and flow rate in an open tubular column are simply related by... 

Since the exact profile of the mobile phase flow through a packed bed is unknown, only an approximate description of the ] and broadening process can be attained. For packed column gas chronatography at low mobile phase velocities, equation (1.35) provides a reasonable description of the band broadening process [70,82,83]. 

Dingenen [9], who studied the effect of the mobile phase velocity on the height equivalent to a theoretical plate (HETP) at different temperatures for benzotriazole derivatives, obtained the results shown in Figure 22, which represents the HETP values found for methanol and the hexane-ethanol mixture. Both curves of Figure 22 clearly demonstrate that the kinetic circumstances are less favorable at low temperatures. A slow mass transfer between the two phases clearly determines the band-broadening process at temperatures below 20°C. This... 

Relationships between mobile phase velocity and column efficiency, such as the Knox equation (equation (2.32)), are developed by taking into account all the possible contributions to band broadening. Thus the total peak variance (a oiumn) arising from band broadening in a packed column is given by... 

The contribution to band broadening by flow velocity is obvious, since the faster the mobile phase is flowing, the farther molecules will be swept downstream before they exchange phases. 

The influence of different band broadening parameters on the overall efficiency of a column is shown in Figure 2.11, where the plate height is plotted versus the mobile phase velocity. This famous relationship can be described well by the Van Deemter equation (Van Deemter, Zuiderweg, and KHnkenberg, 1956) (Equation 2.42) ... 

The multipath term (A) This term applies to columns packed with support particles. It becomes zero for open tubular columns when the mobile phase velocity is slow enough for the flow to be laminar (i.e., without mrbulent eddies). In a packed column, the paths of individual analyte molecules will differ as they take different routes through the spaces between the particles. Thus they will travel varying distances before they exit the column, and the difference between these distances contributes to band broadening. The relative magnitude of the multipath term depends on the particle and column dimensions. If Fig. 11.3 depicted a packed column, A would be a constant value for all values of u, and would appear as a horizontal line raising the curve by a constant amount. The multipath process is illustrated in Fig. 11.4. 

Equation (2.2) shows that //min is dependent on only the capillary radius and the capacity factor. Solution of the Golay equation regarding optimal mobile phase velocity, again neglecting band broadening in the stationary phase, gives ... 

Table 2.2 Order of magnitude comparison of the contribution to band broadening by non-uniform local mobile phase velocities, the flow profile (i /Dm) in capillary columns (the Cq term in Golay s equation)...

---