Plate height longitudinal diffusion

Golay equation 21, 611 gradient (LC) 490 height equivalent to a theoretical plate 11 longitudinal diffusion 16 mass transfer resistance 17 nonlinear chromatography SOS plate model 14 rate theory IS reduced parameters 78, 361, 611... 

To determine how the height of a theoretical plate can be decreased, it is necessary to understand the experimental factors contributing to the broadening of a solute s chromatographic band. Several theoretical treatments of band broadening have been proposed. We will consider one approach in which the height of a theoretical plate is determined by four contributions multiple paths, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase. 

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 A term represents the contribution from eddy diffusion, the B term the contribution from longitudinal diffusion, and the C terms the contributions from mass transfer in the mobile and stationary phases to the total column plate height. By differentiating equation (1.31) with respect to the mobile phase velocity and setting the result equal to zero, the optimum values of mobile phase velocity (u ) and plate height (HETP ) can be obtained. 

The B-term in the equation is the contribution to the plate height resulting from longitudinal diffusion (molecular diffusion in the axial direction) and arises from the tendency of the solute band to diffuse away from the band center as it moves down a column. It is proportional to the time that the sample spends in the column and also to its diffusion... 

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... 

Equation 9.17 can be used to obtain a plate height equation for field-flow fractionation. (The longitudinal diffusion term, Eq. 9.14, is generally negligible in FFF.) We assume that the relative flow dispersion hYIVis approximately unity. Most diffusion processes are limited to paths not much larger than thus we can write d 2(. With these assumptions we get the equation [24]... 

For those cases in which longitudinal diffusion in the stationary phase is also significant, a plate height term of the following form [1] should be added... 

Calculate the plate height contributed by longitudinal diffusion in the mobile phase of a column for which y = 0.60 and in which the mean flow velocity is 2.0 cm/s. First assume that the column is a GC column with a typical solute diffusivity of Dm = 0.10 cm2/s second, assume a LC column with Dm = 1.0 x 10"5 cm2/s. 

B longitudinal diffusion coefficient in plate height c concentration of sample component... 

The change of the selectivity term in the resolution is directly expressible by im. Interestingly, the effect of the EOF on the dispersion effects, expressed by the plate height H, also depends directly on im. For longitudinal diffusion. Joule self-heating, and concentration overload, the variation of the plate height in the presence of the EOF is directly dependent upon this reduced mobility according to... 

The contribution of longitudinal diffusion and other factors to band broadening in liquid chromatography can be quantitatively described by the following equation, which relates the column plate height H to the linear velocity of the solute, jU- ... 

The rate theory examines the kinetics of exchange that takes place in a chromatographic system and identifies the factors that control band dispersion. The first explicit height equivalent to a theoretical plate (HETP) equation was developed by Van Deemter et al. in 1956 [1] for a packed gas chromatography (GC) column. Van Deemter et al. considered that four spreading processes were responsible for peak dispersion, namely multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase, and resistance to mass transfer in the stationary phase. 

Several dispersive processes contribute to zone broadening longitudinal diffusion, nonequilibrium and relaxation processes, spreading due to the external parts of the whole separation system, such as the injector, detector, connecting capillaries, and so forth. It has theoretically been found [2] that the resulting efficiency of the FFF, characterized by the height equivalent to a theoretical plate, can very accurately be described by... 

As shown by Equation 30-27, the contribution of longitudinal diffusion to plate height is inversely proportional to the linear velocity of the eluent. Such a relationship is not surprising, inasmuch as the analyte is in the column for a briefer period when the flow rate is high. Thus, diffusion from the center of the band to the two edges has less time to occur. 

Figure 30-1 5 Contribution of various mass-transfer terms to plate height. Cgu arises from the rate of mass transfer to and from the stationary phase comes from a limitation in the rate of mass transfer in the mobile phase and B/u is associated with longitudinal diffusion.

Sample molecules spread out in the solvent without any external influence (just as a sugar lump dissolves slowly in water even without being stirred). This is longitudinal diffusion (Figure 2.4) and has a disadvantageous effect on plate height only if ... 

The van Deemter rate theory identified three major factors that cause band or zone broadening during the chromatographic process the eddy diffusion or the multi-path effect (A-term), longitudinal diffusion or molecular diffusion of the analyte molecules (B-term), and resistance to mass transfer in the stationary phase (C-term). The broadening of a zone was expressed in terms of the plate height, H, and was described as a function of the average linear velocity of the mobile phase, u. 

Skoog and West describe three causes of zone broadening eddy diffusion, longitudinal diffusion, and nonequilibrium mass transfer [1], The Van Deemter equation was developed to relate the flow rate and plate height ... 

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