Plate height reduced

Reduced plate height h is another way of expressing column efficiency. 

In the well-packed HPLC columns, reduced plate heights of 2-3 or even less than 2 can be obtained. 

In an open tubular column, h= H/dc, where d is the column inner diameter. In capillary GC, reduced plate heights of less than 1 can be obtained. 

Reduced plate height allows us to compare the efficiency of columns with different particle sizes or different internal diameters (in open capillary columns). 

A more thorough treatment of reduced parameters can be found in Ref [4]. 

Equation 12.1 provides a good description of H in packed columns but its application is complicated by its complex form and by its dependence on unknown constants A, and or Furthermore, as with the other equations of Section 12.1, a plot of the equation as H versus v yields curves that differ 

The key step in developing a reduced coordinate system lies in identifying characteristic scaling parameters. In the case of gases, these characteristic parameters are the critical pressure, the critical volume, and the critical temperature. We seek similar scaling parameters for chromatography. 

However, since A and a are constants of order unity whose exact values are difficult to determine, we can replace v e by a simpler expression that still characterizes (i.e., provides a scale for) the transition, namely 

The state of the dynamic balance between mobile phase processes in every chromatographic column is governed by the flow velocity relative to the fundamental velocity uc, that is, by [16] 

We must now find a scale factor with length dimensions that can be used to reduce plate height to dimensionless form. In Section 11.5 we identified particle diameter dp as a fundamental unit of length to which most distances in the column are scaled. Scaling H in units of dp seems, then, a logical choice. This choice is supported by noting that when v equals the fundamental velocity vc, all mobile phase H terms are close to dp in value. Thus when v = vc, Cmv becomes Cmvc, which equals 

---

Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

High-Performance liquid Chromatography. Typical performances for various experimental conditions are given in Table 11.15. The data assume these reduced parameters h = 3, V = 4.5. The reduced plate height is... 

V = 4.5. These are optimum values from a graph of reduced plate height versus reduced... 

Hsieh and Jorgenson prepared 12-33- 4m HPFC columns packed with 5.44-pm spherical stationary phase particles. To evaluate these columns they measured reduced plate height, h,... 

In 1972-1973 Knox et al. [3, 4, 5] examined, in considerable detail, a number of different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The reduced plate height (h) and reduced velocity (v) were introduced by Giddings [6,7] in 1965 in an attempt to form a rational basis... 

It is seen that the reduced plate height is dimensionless. 

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... 

Figure 2. Graph of Log of Reduced Plate Height against Log of Reduced Velocity for Poorly and Well Packed 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... 

The uncomplicated packing procedure of traditional media to yield efficient columns is demonstrated by the reduced plate heights of 2 or slightly below as reported for Sephadex and for the qualification of Sepharose columns for the determination of MWDs. 

FIGURE 22.9 Reduced plate height versus reduced velocity. Measured data V, toluene O, PS 2200 , PS 43,900 A, PS 77S.000. Theoretical lines solid lines, Giddings, infinite diameter column dotted line, Knox, infinite diameter column dashed line Knox walled column. (Reprinted from J. Chromatogr., 634, IS4, Copyright 1993, with permission from Elsevier Science.)... 

There have been a few reports of column efficiency and reduced plate height measurements in several unified chromatography techniques. These have been based on the apparent plate height observed at the column outlet. In the notation used by Giddings (32) the apparent plate height, H, is given by the following ... 

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

Column Type Minimum Reduced Plate Height Minimum Reduced Velocity flow Resistance Parameter Separation Impedance... 

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... 

The reduced plate height is reasonably constant, independent of the capacity factor for a packed column, while equation (1.82) indicates Ithat the reduced plate height, at least for small values... 

According to chromatographic theory, the reduced plate height is related to the reduced velocity by equation (4.2)... 

Because of the time required to develop sufficient data points to make a plot similar to that shown in Figure 4.11 it is useful to have a shorter method for assessing potential problems. For a good colunn the value of the reduced plate height should not exceed 3 or 4 at a reduced velocity of about 5 and 10 to 20 at a reduced velocity of about 100. 

Upon substitution of the reduced parameters given above the separation time for a packed column and an open tubular column would be Identical if d 1.73 dp given the current limitations of open tubular column technology the column diameter cannot be reduced to the point %diere these columns can compete with packed columns for fast separations. This is illustrated by the practical txanple in Figure 6.3 (57). Ihe separation speed cannot be Increased for an open tubular column by increasing the reduced velocity since the reduced plate height is increased... 

FIGURE 6.1 A Poppe plot for the required plate number in conventional HPLC. The parameters are taken from Poppe s original paper (Poppe, 1997). The parameters are maximum pressure AP = 4x 107 Pa, viscosity / = 0.001 Pa/s, flow resistance factor

diffusion coefficient D= lx 1CT9 m2/s, and reduced plate height parameters using Knox s plate height model are A — 1, B— 1.5, C = 0.05. 

---