Van Deemter expression

The van Deemter equation is a useful approximation however, the experimental H u plots often show some downward curvature on the right-hand branch, unpredicted by Eq. (1.10). Giddings explained this behaviour by coupling the flow and the diffusion effects which demonstrates that it is not strictly correct to consider the simple additivity of their contributions to band broadening and he suggested more sophisticated equations to account for this phenomenon [3. For practical purpose, a simple empirical equation, which accounts for the experimental behaviour and is only slightly different from the van Deemter expression was introduced by Kennedy and Knox [4. ... 

More recent studies have led to elaborations of the basic van Deemter expression, but it has been shown experimentally that Equation 26 23 is quite saiisfac-lory in explaining column efficiency. Note that the van Deemter expression contains terms linearlv and in-... 

Derive the expressions for optimum velocity and minimum plate-height using the simple Van Deemter expression. What are the dominant factors in each ... 

The purpose and role of the solid support is the accommodation of a uniform deposition of stationary phase on the surface of the support. The most commonly used support materials are primarily diatomite supports and graphitized carbon (which is also an adsorbent for GSC), to a lesser extent. Teflon, inorganic salts and glass beads. There is no perfect support material because each has limitations. Pertinent physical properties of a support for packed-column GC are particle size, porosity, surface area, and packing density. Particle size impacts column efficiency via the A term or eddy diffusion contribution in the van Deemter expression (Equation 2.44). The surface area of a support is governed by its porosity, the more porous supports requiring greater amounts of stationary phase... 

Examination of the parameters in the van Deemter expression (Equation 2.44), term by term, provides a basis for optimizing a packed column separation. The plate height, h, of a packed column may be represented as the sum of the eddy diffusion, molecular diffusion and mass transfer effects. Thus, to attain maximum column efficiency, each term in the plate height equation should be minimized ... 

The fundamental equation underlying the performance of a gas chromatographic column is the van Deemter expression (Equation 2.44 further discussed in Section 3.6.4), which may be expressed as... 

Equation 16-183 is qualitatively the same as the van Deemter equation [van Deemter and Zuiderweg, Chem. Eng. Sci., 5, 271 (1956)] and is equivalent to other empiric reduced HETP expressions such as the Knox equation [Knox,y. Chromatogi Set., 15, 352 (1977)]. 

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

Equation (5), however, would apply only to a perfectly packed column so Van Deemter introduced a constant (2X) to account for the inhomogeneity of real packing (for ideal packing (X) would take the value of 0.5). Consequently, his expression for the multi-path contribution to the total variance per unit length for the column (Hm) is... 

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 dispersion described in figure 2 shows that the longer the solute band remains in the column, the greater will be the extent of longitudinal diffusion. Since the length of time the solute remains in the column is inversely proportional to the mobile phase velocity, so will the dispersion be inversely proportional to the mobile phase velocity. Van Deemter et al derived the following expression for the... 

Van Deemter derived an expression for the contribution to variance/unit length by the resistance to mass transfer in the mobile... 

Evers R, Kool M, van Deemter L, Janssen H, Calafat J, Oomen LC et al. Drug export activity of the human canalicular multispecific organic anion transporter in polarized kidney MDCK cells expressing cMOAT (MRP2) cDNA. J Clin Invest 1998 101(7) 1310—1319. 

A van Deemter plot for a given particle size dp and diffusion coefficient Du shows the relation of the theoretical peak height H to the linear velocity u that can be expressed as column length L... 

Here, A is the random path, B the longitudinal molecular diffusion and C the RTMT contributions with the velocity of the mobile phase u shown separately. H is referred to as the Height Equivalent to a Theoretical Plate and is terminology borrowed from distillation. While the distillation HETP is not truly applicable, the terminology has persisted. It can be shown that the H in this expression is the equivalent to variance/unit length. This is the expression introduced by Van Deemter and co-workers in 1956 in a discussion of band broadening. 

Van Deemter also introduced a constant (y)into the Longitudinal Dispersion contribution to variance to account for some packing Inhomogeneity and so the expression for the Diffusion contribution to the variance per unit length of the column became,... 

The dispersion resulting from the resistance to mass transfer in the stationary phase is exactly analogous to that in the mobile phase. Those solute molecules close to the surface of the stationary phase, will leave the surface and enter the mobile phase a significant time before those that have diffused farther into the stationary phase and have a longer distance to diffuse back to the surface. Thus, as those molecules that were close to the surface will be swept along by the moving phase, they will be dispersed from those molecules still diffusing to the surface. Van Deemter deduced an expression for the contribution to variance due to this effect as,... 

Equation (3), however, was developed for a gas chromatographic column and in the case of a liquid chromatographic column, the resistance to mass transfer in the mobile phase should be taken into account. Van Deemter et al did not derive an expression for fi(k ) for the mobile phase and it was left to Purnell (3) to suggest that the function of (k ), employed by Golay (4) for the resistance to mass transfer in the mobile phase in his rate equation for capillary columns, would also be appropriate for a packed column in LC. The form of f (k ) derived by Golay was as follows,... 

In the previous relationships used to express the characteristics of a separation, the speed of the mobile phase in the column does not appear. Obviously, the speed has to affect the progression of the solutes, hence their dispersion within the column, and must have an effect on the quality of the analysis. These kinetic considerations are collected in a famous equation proposed by van Deemter. First used in gas chromatography, this equation has been expanded to liquid chromatography and relates H (HETP) to the mean linear velocity of the mobile phase in the column, it (see Fig. 1.9). The simplified form of this equation is given below ... 

Deduce from the simplified version of Van Deemter s equation for a full column the expression which calculates the optimum speed and which conveys a value for the HETP. 

The relative "goodness" of a column is expressed in terms of efficiency, n/L, as plates per foot. A 6-foot column having 2000 plates would only be half as efficient as a 3-foot column with the same number of plates. Although the total number of plates, n, influences the degree to which peaks will be resolved, column efficiency is a measure of how well the column has been prepared and operated. A performance of 1000 plates per foot can be obtained but 500 is reasonable anything less is indicative of a problem. Column efficiency is also expressed as h, which is the length of column (expressed in millimeters) equivalent to one theoretical plate. This efficiency is related to column variables by the van Deemter equation ... 

Derive expressions for uopt and Hmin from the van Deemter equation, H = A + (B/v) + Cv. 

Van Deemter plot. A graph of column efficiency, expressed as HETP versus linear velocity of the mobile phase. This plot indicates the optimum linear velocity (and, thus, flow rate) for a particular column. 

The contributions to zone spreading can be expressed with a simple relationship often referred to simply as the Van Deemter equation ... 

---