Plate height reduced velocity

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

Column plate count Column hold-up time (s) Column length (m) Reduced plate height Reduced velocity Separation impedance... 

Figore 3.14 Reduced plate height-reduced velocity plot for protein samples on a leversed-pbase column. The data were derived from gradient chromatography. 

These results are in agreement with the results of the calculations made above if we take into account the values of the reduced plate height and velocity. From that we can safely predict that using wider columns it is possible to achieve about 1,000,000 plates with a 20-m-long column packed with 10-/xm particles, operated under 250 atm, with an analysis time of 18 h. 

To illustrate more clearly the effect of these variables on analysis time, reduced parameters can be used for the plate height and velocity. Reduced parameters effectively normalize the plate height and velocity for the particle diameter and the diffusion coefficient to produce dimensionless parameters that allow comparison of different columns and separation conditions. The reduced plate height and reduced velocity are expressed, respectively, as... 

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... 

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... 

To compare the two equations, the reduced plate height (h) and reduced velocity (v)... 

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.)... 

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... 

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... 

CEC plate heights were smaller than observed in HPLC and essentially independent of reduced velocity. 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

A more vigorous treatment similar to the van Deemter equation but developed specifically for HPLC is the Knox equation, which uses a number of reduced parameters where h is the reduced plate height (h/dp) and vis reduced velocity (V dJD. ... 

Equation 5 Knox equation, with reduced plate height, h reduced velocity (m dpID ), V, coefficient B, describing axial diffusion (typical value 2) coefficient A, describing bed homogeneity (typical value 1-2) and coefficient C, describing mass transfer (typical value 0.05). 

Plots of reduced plate height against reduced velocity should give a single... 

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. 

I X 10 cm /sec, so that, when dp = 6 /xm, the reduced velocity for such compounds at u 0.2 m/sec is between 12 and 25. Accordingly, these columns are not operated at the maximum efficiency, i.e., the minimum reduced plate height could have a value of approximately 2. Still, with... 

---