Reduced plate height h

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). 

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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... 

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

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). 

In pHPLC, there are numerous types of columns used. The comparison and characterization of these columns are often discussed in terms of thermodynamic properties and kinetic characteristics. The retention factor, k, selectivity, a, and the peak asymmetry are believed to be representative parameters for the thermodynamic properties, while the kinetic characteristics are often expressed in dimensionless magnitudes of reduced plate height, h, separation impedance, E, and flow resistance factor, ( ). 3... 

The most commonly used criterion for judging column performance is efficiency as measured by the number of theoretical plates or column plate count (N) exhibited by the column during the separation of a test mixture. The larger the number of theoretical plates, the more likely it is that the column will produce the desired separations. However, while popular, N is not a complete performance parameter for making comparisons. For example, N does not take into account particle size as does the reduced plate height, h. Another measurement, hmin, accounts for all of these factors as well as the mobile phase linear velocity and sample diffusion. However, N is the term most commonly recognized as being related to resolution (2), as shown in Equation 1 ... 

If the reduced velocities on the two columns are equal, then the reduced plate height (h eqn.7.3) may also be expected to be equal, and, hence, the column length varies according to... 

In practice, we operate LC systems still well above the optimum flow rate. We work well below the maximum operating pressure of the pump (say 200 bar), at a higher reduced velocity (e.g. v= 10) and with a correspondingly higher reduced plate height (h = 4). Under these practical conditions we find ... 

Eqn.(7.17) shows that an increase in the column efficiency by way of a decrease in the reduced plate height (h) has a positive effect on the sensitivity. Therefore, well-packed columns should be used at (or just above) the optimum flow rate. If that is the case, then h may be considered as a constant (2 < h < 3), i.e. considered to be independent of the column diameter and the particle size. 

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. 

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... 

Fig. 1.3. (A) Three comribulion.s to the column plate height. H. according to ihe van Deemter equation (Eq. (1.10)). (B) Experimental plot of the reduced plate height, h = H /dp as a function of the mobile phase velocity, ii. for a Bio.spher Cis. -5 um. column (13.5 x 0.32 mm i.d.) for toluene in 70% aqueous methanol as the mobile phase.

Fig. 5.11. Double logarithmic plot of the reduced plate height (h) versus the linear mobile phase velocity (u) in the chromatography of D,L-PA (100 nmol) on an L-PA MIP prepared using benzene as diluent at two different column temperatures. At 20°C k l a 6, k o 2.5. At 45°C k i 2.1, Ic d LO. Mobile phase MeCN/potassium phosphate buffer 0.05 M, pH 7 70/30 (v/v). From Sellergren and Shea [59].

Material dp (jim) ratio) Optimum linear velocity u (mm s" ) Number of theoretical plates N Retention coefficient k of solute Reduced plate height h... 

Martin et al. published a paper on the theoretical limits of HPLC which is well worth reading.They used relatively simple mathematics to calculate pressure-optimized columns for which the length L, particle size and flow rate u of the mobile phase were selected such that a minimum pressure Ap is required to solve a separation problem. It has been shown that these optimized colunms are operated at their van Deemter curve minima. Some astonishing facts have emerged from the study, provided that the chromatography is performed on well packed columns (reduced plate height h = 2-3 see Section 8.5). 

First dimensionless parameter, reduced plate height, h, replaces plate height, H. His compared with the mean particle diameter, dp. ... 

By means of the reduced plate height h it is possible to calculate N. With the assumption that the column is packed very well (not excellently), i.e. that h = 2.5, we obtain ... 

Figure 24.1 Peak shapes as obtained with different column diameters and separation performances (as a function of particle diameter at a given column length). Columns 1 and 3 are packed with a coarse stationary phase, columns 2 and 4 with a fine one. The packing quality, defined as reduced plate height h, is the same in all four cases. Separation performance is independent of column inner diameter therefore peaks 1 and 3 as well as 2 and 4, respectively, are ofthe same width. The peak height in the eluate can be calculated from equation (15) it is higher when the column is thinner and the separation performance is better. Peak areas cannot be compared although the same amount is injected in any case if a concentration-sensitive detector is used optimum flow rate depends on particle size and hence also the residence time in the detector.

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