Plate height defined

Equation 10.42 is the equation given by Eble et al. [24]. We see that this equation is valid only at low values of the loading factor. The only correct equation at moderate loadings would be obtained by combining Eqs. 10.38 and 10.39 for a plate height defined from the band width at half-height (or Eqs. 10.38 and 10.41 for a plate height defined from the baseline bandwidth). Equation 10.42 is an expansion of this correct equation for low values of Lp... 

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where... 

Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoretical plate is defined as the variance per unit length of the column... 

Now, the column length (L) can be defined as the product of the minimum plate height and the number of theoretical plates required to complete the separation as specified by the Purnell equation. 

It must be emphasized that equation (4) only applies to the separation and conditions defined in Table 1. The effect of the magnitude of the separation ratio on the minimum plate height is shown in Figure 4. 

The reduced plate height, h, is defined as the number of particles to a theoretical plate and is given by... 

The more efficient the column, the smaller will be at a given value of Vr. To measure efficiency, we use quantities called the plate number (N) or the plate height (H) of the column, which are defined as follows ... 

Neither the capacity factor nor the separation factor take into account the effect of dispersion, which is measured by the plate number or the plate height of the column. These were defined in Section 2.3.2. 

As in chromatography, the most common variable to describe dispersion in FFF is the plate height (H), defined as the ratio between the spatial variance (Oj) of the band and its mean position (s) as it migrates inside the separation medium of length (L) ... 

During 1972 and 1973 Knox and his co-workers (3), (4), and (5) carried out a considerable amount of work on different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The concept of reduced plate height (h) and reduced velocity (v) was introduced by Giddings (6) and (7) in 1965 in an attempt to form a basis for the comparison of different columns packed with particles of different diameter. The reduced plate height is defined as,... 

The efficiency of chromatographic systems can be defined by the height equivalent to a theoretical plate (HETP or plate height, symbol H) or by the reduced plate height ... 

The following table provides the Martin-James compressibility factor, j,1 and the Giddings plate height correction factor, f,2 for chromatographically useful pressures. These quantities are defined as... 

For the comparison of different kinds of columns it has become increasingly common to use the reduced plate height (A), defined as... 

Eqn.(7.17) shows that an increase in the column efficiency simply by increasing the column length (L increases with h constant) has an adverse effect on the sensitivity. For open columns the reduced plate height may be defined as... 

To better understand the heightened resolving power of 2D systems, we need some measure by which 2D and ID separations can be compared. Not all criteria of separation power lend themselves to ready comparison. The resolution of a specific pair is not a suitable criterion because this resolution varies widely for different separation mechanisms irrespective of ID or 2D configurations. Plate height and plate number are not directly comparable because these are defined only for a single dimension. While H or N values can be found for each axis, it is not immediately obvious how to combine them for both axes in order to compare the overall separation effectiveness with that of a ID system. 

Clearly, departures from equilibrium—along with the resultant zone spreading—will decrease as means are found to speed up equilibrium between velocity states. One measure of equilibration time is the time defined in Section 9.4 as teq, equivalent to the transfer or exchange time between fast- and slow-velocity states. Time teq must always be minimized this conclusion is seen to follow from either random-walk theory or nonequilibrium theory. These two theories simply represent alternate conceptual approaches to the same band-broadening phenomenon. Thus the plate height from Eqs. 9.12 and 9.17 may be considered to represent simultaneously both nonequilibrium processes and random-walk effects. 

Since the geometry and flow profile (parabolic) of FFF channels is well-defined, rather exact theoretical predictions of retention and plate height can often be made. The correlation of these experimental parameters with various physicochemical properties of component species (such as molecular weight, charge, and size) is therefore possible (11, 13). 

We note that uopt is of similar magnitude to the transition velocity ve = DJdp (see Eq. 12.22). Since the reduced velocity v is defined as vlve and the reduced plate height h is Hldp (Eq. 12.25), the above optimum conditions (v near ve and H near dp) correspond roughly to unit values of h and v, a conclusion consistent with Figure 12.3. 

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. 

Horvath and Lin [10,11] showed how the different contributions to peak dispersion in a packed bed could be defined in an expression for H, which was applied [12] to CEC by Dittman et al. it was demonstrated that the major contribution of eddy diffusion to H in HPLC was considerably reduced in CEC. Minimal reduced plate heights h = (H/dp), generally found to be near 2 in HPLC, should be reduced to near 1 or less, giving rise to plate numbers over 10s for a 40-cm-long CEC column with 3-pm particles. Horvath and Lin showed [11] how their expression for H could be simplified to... 

With effects causing asymmetrical spreading assumed negligible, the plate height h (or HETP, height equivalent to a theoretical plate) for a gaussian distribution may be defined as variance per unit length of column ... 

Comparisons of columns of different lengths that are also packed with different sized particles may be made by use of the reduced plate height Qi) which is a dimensionless parameter defined by equation (2.29). 

This contribution is related to the variety of channels available for any solute molecule throughout the elution process. These channels are defined by the interstitial volume between the beads of the column package, so they correspond to a variety of shapes and flow velocities. This produces a distribution in elution time which is classically considered as Gaussian and weakly depends on flow rate. As a rule of thumb, the theoretical plate height corresponding to this effect can be considered as being equal to the bead diameter of the packing for well-packed columns. 

All separation processes are inherently accompanied by zone broadening, which is due to the dynamic spreading processes dispersing the concentration distribution achieved by the separation [1]. As long as the relative contributions of these dispersive processes decrease, the efficiency of the separation increases. A conventional empirical parameter describing, quantitatively, the efficiency of any separation system is the number of theoretical plates per separation unit, A, or the height equivalent to a theoretical plate (the theoretical plate height) H defined by... 

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