Plate height variations

The possibility of obtaining significant improvements in performance by using semi-packed and open tubular columns is clearly illustrated by the values for the separation impedance in Table 1.17. Variation of the reduced plate height with the reduced velocity for an open tubular column is given by equation (1.82), assuming that the resistance to mass transfer in the stationary phase can be neglected... 

Figure 7.5 Left, variation of the average plate height of fine-and coeurse-particle layers as a function of the solvent aigration distance and method of developaent. Right, relationship between the optiauB plate height and solvent migration distance for forced-flow development.

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

The plate height will vary with the flow rate (u) of the mobile phase through the column. This variation can be characterized by an H vs. u curve. Such a curve shows a minimum plate height at some optimum value of u. Again, this will not be discussed any further in this book and the reader is referred to one of many general textbooks on chromatography. 

The change of the selectivity term in the resolution is directly expressible by im. Interestingly, the effect of the EOF on the dispersion effects, expressed by the plate height H, also depends directly on im. For longitudinal diffusion. Joule self-heating, and concentration overload, the variation of the plate height in the presence of the EOF is directly dependent upon this reduced mobility according to... 

Effect of Mobile Phase Velocity on Terms in Equation 30-27 Figure 30-15 shows the variation of the three terms in Equation 30-27 as a function of mobile phase velocity. The top curve is the summation of these various effeets. Note that an optimum flow rate exists at which the plate height is at a minimum and the separation efficiency is at a maximum. 

Variation in Plate Height As shown by Equation 30-30, the resolution of a column improves as the square root of the number of plates it contains increases. Example 30-2e reveals, however, that increasing the number of plates is expensive in terms of time unless the increase is achieved by reducing the plate height and not... 

Giddings [29], Huber [49], and Horvath and Lin [50] have used alternate models to accoimt for the relationships between the rate of variation of the solute concentration in the stationary phase, its mobile phase concentration, and the various parameters characterizing the chromatographic system used. This explains the differences in the plate height equations they derived, as we see in the next section. 

This is only one of a number of similar equations that relate summed plate heights to flow rates. It is generally most valid at high flow rates but is also the most well known, and when expressed schematically, the form of the van Deemter Curve (Figure 11.6) gives an excellent feeling for how variations in flow rate can effect separation efficiency. 

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).

The variation of the reduced plate height (section 1.5.3) as a function of the reduced mobile phase velocity for a packed column and high performance layer is illustrated in Figure 6.4 [1,62]. The optimum reduced mobile phase velocity is shifted to a lower value compared with the column and the minimum in the reduced plate height ( 3.5) is higher than typical values for a good column 2.0-2.5). Also, at higher reduced mobile... 

Davis, J. M., Influence of thermal variations of diffusion coefficient on non-equilibrium plate height in capillary zone electrophoresis, J. Chromatogr., 517, 521,1990. 

Figure 4 Illustration of the measurements used to calculate the retardation factor and variation of the plate height with solvent front migration distance.

Four commercial agarose type gels have been used at enhanced flow rates for the molecular weight distribution analysis of dextran. The performances of the gels were discussed in terms of resolution, molecular weight correction factors, and variations in plate height as a function of flow rates. 

For external impedance tracks and internal plated-up tracks such as on subcores, autoth-ieving patterns will minimize large variations in plating height between tracks in dense areas and those in uncongested areas. This will increase the fabricator s ability to produce impedance values consistently within a smaller range. 

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