Plate height curve

FIGURE 9.2 Theoretical plate-height curves for 5 pm particles, illustrating the effect of temperature on plate height and linear velocity. (Reprinted from Lestremau, F. et al., J. Chromatogr., 1138, 120, 2007. Copyright 2007. With permission from Elsevier.)... 

We start by noting that the plate height curves in Figure 12.2 are of similar form (as they should be since they are described by the same equations) but are strung out widely along the velocity scale. Consequently,... 

Two basic components of plate height in packed columns are Hf and HD, given by Eqs. 11.23 and 11.28, respectively. When these two terms are equal—which occurs at the specific velocity v c = AICm—we are at the transition point between a flow-controlled and diffusion-controlled random walk. (This transition, as it turns out, occurs near the minimum of each of the plate height curves shown in Figure 12.2.) The velocity u is a fundamental parameter characterizing every packed column system. Its value can be expressed by (see Eqs. 11.23 and 11.28)... 

Curves a and b of Figure 7.2, which are plate height vs mobile phase velocity plots, are known as plate height curves. 

Plate height curves provide means of comparing the efficiency of different columns and packing materials. 

However, since H depends on the particle size, dp, a series of equally well packed columns of the same material in various size fractions will give a series of different plate height curves. 

The reduced plate height, h, is independent of the particle diameter. The reduced fluid velocity (u), a concept conceived by Giddings, is a measure of the rate of flow over a particle relative to the rate of diffusion of solute within the particle. Since both reduced parameters, h and V, are normalized for the particle diameter, when h is plotted against v, the different size fractions of the same packing materials should give similar curves. This has been confirmed in practice, so that use of h vs v curves is preferred over that of plate height curves (H versus mobile phase velocity) when comparison of the efficiency of different columns is to be carried out. 

The theoretical plate height curve has a minimum that corresponds to the optimal flow rate. The minimal theoretical plate height is influenced by the average particle size of the stationary phase. The smaller the average particle size the smaller the H and the better the resolution is [35,36]. Current technologies can provide columns... 

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

Flo. 3. Double logarithmic plots of the reduced plate height against the reduced velocity. For aH curves C is constant and equal to 0.03. A is stated for each curve on the graph. The dotted line connects the loci of the minima for the individual curves, cf. Table I. 

Plate height is reduced in an open tubular column because band spreading by multiple flow paths (Figure 23-19) cannot occur. In the van Deemter curve for the packed column in Figure 23-15. the A term accounts for half of the plate height at the most efficient flow rate (minimum H) near 30 mL/min. If A were deleted, the number of plates on the column would be doubled. To obtain high performance from an open tubular column, the radius of the column must be small and the stationary phase must be as thin as possible to ensure rapid exchange of solute between mobile and stationary phases. 

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. 

If we have reasoned correctly, we now have what amounts to a principle of corresponding states for chromatography. Given a reduced velocity v, the reduced plate height should be approximately the same for virtually all well-packed columns. In other words, a single h versus v curve should come close to representing all such chromatographic systems. 

Figure 12.3. Reduced plate height plot showing the band in which h versus v curves lie for high performance columns.

Figure 12.4. Plate height versus flow velocity plot for negligible stationary phase nonequilibrium effects (bottom curve) and for dominant stationary phase effects (top).

The optimization procedure outlined above is independent of the specific plate height equations chosen to represent chromatography. It depends only on the validity of the scaling relationships used to define reduced plate height and reduced velocity, and the emergence of universal curves from the scaling relationships. 

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