Plate height Deemter equation

Plot of the height of a theoretical plate as a function of mobile-phase velocity using the van Deemter equation. The contributions to the terms A B/u, and Cu also are shown. 

There is some disagreement on the correct equation for describing the relationship between plate height and mobile-phase velocity. In addition to the van Deemter equation (equation 12.28), another equation is that proposed by Hawkes... 

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... 

Van Deemter equation An equation relating efficiency (HEPT in mm) to linear flow velocity in a chromatographic column. The efficiency is expressed as the height equivalent to a theoretical plate HEPT = A + BIV + Cv), where A, B, and Cv are constants and V is the linear velocity of the carrier gas. This equation tells us that to obtain maximum efficiency, the carrier gas flow must be optimized. 

The efficiency of a chromatographic separation can be described by the height equivalent of a theoretical plate (H), where lower values of H correspond to more efficient separations. The Van Deemter equation describes the relationship between H and mobile phase flow velocity (u) as the sum of three major terms, A, B, and C, each of which represents a different contribution to band broadening in a chromatographic column. 

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. ... 

In liquid chromatography (LC) the plate height H is related to the various band broadening terms as described by the van Deemter equation ... 

Increasing efficiency is equivalent to decreasing plate height. H. in the van Deemter equation (23-33) ... 

Capillary electrophoresis provides unprecedented resolution. When we conduct chromatography in a packed column, peaks are broadened by three mechanisms in the van Deemter equation (23-33) multiple flow paths, longitudinal diffusion, and finite rate of mass transfer. An open tubular column eliminates multiple paths and thereby reduces plate height and improves resolution. Capillary electrophoresis reduces plate height further by knocking out the mass transfer term that comes from the finite time needed for solute to equilibrate... 

Many modifications to the original van Deemter plate height equation have appeared in the literature (19-23). Some account for mass transfer in the gas phase (19,20) and other modifications were made for velocity distribution because of retarded... 

The van Deemter equation is an empirical formula that describes the relationship between linear velocity (flow rate) and plate height (or column efficiency) (van Deemter et al., 1956). The particle size is one of the variables used in the van Deemter equation. As illustrated in Fig. 4.1, as the particle size decreases to less than 2.5 p,m, the efficiency is increased. Furthermore, when using smaller size particles, the efficiency is not affected with increasing flow rates or linear velocities. 

A, B, and C are constants. Importantly, the van Deemter equation, Eq. (8.81), states that there is a point of minimum plate height hmin, at u = (A/B)0 5, whereas h increases at both higher and lower velocity through the column. 

Excellent column efficiency delivered by a large number of theoretical plates (low plate height of about 0.005 mm) is theoretically deduced from the Van Deemter equation which predicts that use of sub 2.5 pm particles does not diminish efficiency at increased flow rates (increased speed of analysis). For more details the reader is referred to general textbooks on chromatography. Therefore, shorter columns (15— 50 and 2.1 mm I.D.) provide sufficient resolution and improved sensitivity within run times of only a few minutes or less. 

The relationship with the familiar van Deemter equation giving the HETP (height equivalent to a theoretical plate) as a function of gas velocity,... 

The van Deemter equation describes the relationship between the height equivalent to one theoretical plate (H) and the linear flow velocity ( ) ... 

Using the van Deemter equation, estimate the plate height and number of theoretical plates in a 1-m long column using particles of diameter 0.014 cm and a helium flow velocity of 10 cm/s. Ignore gas compression effects. Previous work with the column has shown that the parameters A and y are 1.0 and 0.70,... 

What is H anyway The original interpretation, taken from distillation theory, was height equivalent to a theoretical plate, or HETP. We have seen that this concept was inadequate, and the preceding discussion of the van Deemter equation has presented it as a measure of the extent of spreading of an analyte zone as it passes through a column. Thus, a more appropriate term might be column dispersivity. In fact, another, independent approach to the theory of chromatography defines H as... 

Band broadening within the chromatographic column is described as a function of mobile phase linear velocity ( ) by the well known van Deemter equation [5] that relates the height equivalent to the theoretical plate (HETP) to u the lower the HETP, the higher the plate number per unit length of a column. It follows that the highest efficiency is obtained for the shortest HETP. The van Deemter equation is ... 

The plate height depends on various experimental conditions. The most simple expression describing the relationship between H and the velocity of the mobile phase, u, is the well-known van Deemter equation (21 ... 

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.

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