Plate height mechanisms

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... 

The main argument for making MIP CEC is to combine the selectivity of the MIPs with the high separation efficiency of CEC. This argument appears to fail, however, if the adsorption isotherm of the MIP is nonlinear, which seems to be the rule. In the case of nonlinear isotherms, the peak shapes depend mainly on the isotherm, particularly so if the separation system is otherwise very efficient (has low theoretical plate height, see Fig. 1). In the case of ionized analytes the situation is more complex. If an ionized analyte is not adsorbed at all on the MIP, then it is separated only due to electrophoresis, and its peak will not be widened due to the nonlinear effect. In this case, however, the MIP is merely behaving like an inert porous material. In intermediate cases an ionized analyte may participate in both separation mechanisms and for this case we do not have exact predictions of the peak shape. 

Band broadening arises from three principal mechanisms, one of which depends on the mean velocity of the carrier and two of which are independent of . The latter two represent nonidealities in instrument and sample. The total variance of an eluting peak is the sum of variances contributed by each bandbroadening mechanism. Expressed as plate height H, which is the total variance divided by column length L (12), the zone broadening is described by... 

To better understand the heightened resolving power of 2D systems, we need some measure by which 2D and ID separations can be compared. Not all criteria of separation power lend themselves to ready comparison. The resolution of a specific pair is not a suitable criterion because this resolution varies widely for different separation mechanisms irrespective of ID or 2D configurations. Plate height and plate number are not directly comparable because these are defined only for a single dimension. While H or N values can be found for each axis, it is not immediately obvious how to combine them for both axes in order to compare the overall separation effectiveness with that of a ID system. 

The broadening of zones by molecules caught in different flow lines is the most fundamental mechanism of band dispersion in F(+) methods. In some cases ordinary diffusion up and down the separation path also contributes measurably to zone broadening. In the simplest case ordinary diffusion contributes a variance of a2 = 2Dt and thus a plate height, a2/L, of... 

In addition to the enhanced diffusivity effect, another issue needs to be taken into account when considering stationary-phase mass transfer in CEC with porous particles. The velocity difference between the pore and interstitial space may be small in CEC. Under such conditions the rate of mass transfer between the interstitial and pore space cannot be very important for the total separation efficiency, as the driving mechanism for peak broadening, i.e., the difference in mobile-phase velocity within and outside the particles, is absent. This effect on the plate height contribution II, s has been termed the equilibrium effect [35], How to account for this effect in the plate height equation is still open to debate. Using a modified mass balance equation and Laplace transformation, we first arrived at the following expression for Hc,s, which accounts for both the effective diffusivity and the equilibrium effect [18] ... 

Since the retention of the template on the imprinted polymers strongly depends on the sample load (see later Fig. 5.25), the theoretical models describing the various dispersion processes are not applicable. Nevertheless, on an imprinted CSP for L-PA, the least retained enantiomer, D-PA, elutes as a fairly Gaussian peak (Fig. 5.3), which should be governed by the same band broadening mechanisms that are considered in the models. A measure of the dispersion of a Gaussian peak is the deviation from its mean value, which is reflected in the reduced plate height as ... 

The van Deemter equation for plate height (H) as a function of flow rate (m) is the net result of the three band-broadening mechanisms just discussed ... 

Theoretical interpretations of column efficiency consider dispersion mechanisms of solutes in the mobile and stationary phases. These mechanisms influence the dependence of the height equivalent to a theoretical plate, or just plate height H, on the linear flow velocity u of the eluent. The value of H may be determined from an experimental separation from the equation... 

The Knox equation. This equation was derived following detailed consideration of the various band dispersion mechanisms which operate in chromatography under isocratic conditions. Knox decided that there were three dispersion processes operating simultaneously and that the contribution of each to the reduced plate height was additive ... 

As a general rule packing heights per su V]vort plate should not exceed 12 It lot Raschig rings or l,a-20 It Idr most other packing shapes. Othei tvpes fit within these limits. The mechanical, vibrational and thermal shock loads become important md sometimes affect the tower operation beyond these limits. 

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