Zone migration

The origin of DT is interesting. We have already noted that F( + ) systems are selective for different solutes because the enrichment processes acting in a direction perpendicular to flow work in concert with (and require) nonuniform flow. However, it is the nonuniformity in flow that tends to increase DT in Eq. 9.2, thus reducing separative efficiency. The positive and negative sides of nonuniform flow require that optimization be undertaken carefully. More details are given below. 

The net rate of displacement of a component downstream depends on how it is distributed among the regions. Species distributed mainly in high velocity regions will advance more rapidly than species favoring more stationary regions. This is the basis of all F(+) separation. The quantitative basis of this observation follows. 

The same velocity will be found at all other cross sections along the separation path if (i) the medium is homogeneous, (ii) the flowrate is constant up and down the flow path, and (iii) the microscopic concentrations c, are distributed in the same relative (not necessarily absolute) amounts. The latter condition—that the relative concentration distribution remains constant—will be met if the concentrations are fixed by equilibrium. In the most important cases they are. 

Equation 9.3 confirms that velocity V will be greatest for species which heavily populate (i.e., have high c, in) regions where the u, are large. Thus the different component distributions, leading to different displacement velocities, are responsible for separation. 

The downstream motion of component bands in F(+) methods is characterized by the retention ratio R, a dimensionless parameter defined as 

In displacement chromatography the sample is applied to the column as a discrete band and a substance (or mobile phase component) with a higher affinity for 

In elution chromatography the mobile and stationary phase are normally at equilibrium. The sample is applied to the column as a discrete band and sample components are successively eluted from the column diluted by mobile phase. The mobile phase must compete with the stationary phase for the sample components and for a separation to occur the distribution constants for the sample components resulting from the competition must be different. Elution chromatography is the most convenient method for analysis and is commonly used in preparative-scale chromatography. 

Today elution development has become synonymous with the word chromatography itself. 

For the optimization of chromatographic separations and in the formulation of theoretical models the retention factor (sometimes referred to as the capacity factor), k, is more important than retention time. The retention factor is the ratio of the time a substance spends in the stationary phase to the time it spends in the mobile phase (Eq. 1.2) 

If the distribution constant is independent of the sample amount then the retention factor is also equal to the ratio of the amounts of substance in the stationary and mobile phases. At equilibrium the instantaneous fraction of a substance contained in the mobile phase is 1 / (1 + k) and in the stationary phase k / (1 + k). The retention time and the retention factor are also related through Eq. (1.3) 

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Simulation by the improved Euler method has shown that a significant radiative heat transfer must be present before reaction zone migration can be demonstrated. 

Similar to Yamamoto et al. [60], Tennikova and co-workers [55], used the so-called quasi-steady state approach to predict SMC chromatography. The basic equation used in their modeling was the dependence of the zone migration on the composition of the mobile phase and on the gradient function, which in its differential form is given by ... 

FLOW. The rate at which zones migrate down the column is dependent upon equilibrium conditions and mobile phase velocity on the other hand, how the zone broadens depends upon flow conditions in the column, longitudinal diffusion, and the rate of mass transfer. Since there are various types of columns used in gas chromatography, namely, open tubular columns, support coated open tubular columns, packed capillary columns, and analytical packed columns, we should look at the conditions of flow in a gas chromatographic column. Our discussion of flow will be restricted to Newtonian fluids, that is, those in which the viscosity remains constant at a given temperature. 

In the electrolyte system used in capillary isotachophoresis (cITP), the sample zone migrates between a leading electrolyte at the front and a different, trailing electrolyte at the end. The leading electrolyte contains a coion with mobility greater than that of any of the analyte ions. The trailing electrolyte contains a coion with mobility that is lower than that of any of the analyte ions. In isotachophoresis, it is possible to analyze for anions or cations, but not both simultaneously. Analyses are usually performed in the constant-current mode. 

In cITP, the sample zone migrates between a leading electrolyte and a trailing electrolyte. It is possible to analyze for anions or cations, but not for both simultaneously. 

Generally irreversible subsidence. and a craion edge of sediment wedge orogeny subduction zone migration. cannibalizes iniermontane and marine basins. borders. unconformities + mild structural deformations. 

For elution, the plate height H, which by Eq. 5.40 is a2/X, becomes cr2/L because the zone migration distance X ends up as column length L upon emergence. From Eq. 5.45, cr2 = t2W which gives... 

As pointed out earlier, zone migration is slow for strongly sorbed solutes, that is, those with a low R value. This can be shown quantitatively as follows. Of the total solute in the zone, the fraction R is carried along with the mobile phase at an average velocity u. (For simplicity we henceforth use v instead of (v) for the cross-sectional average velocity.) The remaining fraction, 1 - / , is held stationary this fraction has zero velocity. The velocity of the zone as a whole is the average velocity of its solute (fraction in mobile phase, R ) x v + (fraction in stationary phase, 1 - R ) x O = R v. Thus zone velocity is directly proportional to R ... 

We examine a solute zone migrating under linear conditions. For the moment we confine our attention to the solute in the mobile phase. If complete equilibrium between phases existed at all points, the mobile-phase solute would form a Gaussian-like concentration profile as indicated by the shaded profile in Figure 10.7. However the actual profile for the mobile phase, shown by the dashed line, is shifted ahead of the shaded (equilibrium) profile due to solute migration. The basis of the profile shift is explained as follows. 

The above reasoning can be made more quantitative. The molecule spending half its time in free motion at velocity v will clearly move at an average velocity of v. The molecule spending one-tenth time in free motion will assume an overall average velocity of jqv. Since each zone migrates as a composite of many such typical molecular displacements, the observed velocities of the two zones will be v and respectively. Since retention... 

Thermodynamics of zone migration, 54 Time constant (detector), 94 Trennzahl number, 18 Trouton s rule, 78, 148 Tswett, 1... 

HPLC theory could be subdivided in two distinct aspects kinetic and thermodynamic. Kinetic aspect of chromatographic zone migration is responsible for the band broadening, and the thermodynamic aspect is responsible for the analyte retention in the column. From the analytical point of view, kinetic factors determine the width of chromatographic peak whereas the thermodynamic factors determine peak position on the chromatogram. Both aspects are equally important, and successful separation could be achieved either by optimization of band broadening (efficiency) or by variation of the peak positions on the chromatogram (selectivity). From the practical point of view, separation efficiency in HPLC is more related to instrument optimization, column... 

For symmetrical chromatographic bands, this is the ratio of the distance between peaks maxima to the peak width. The distance between peak maxima is proportional to the distance of the chromatographic zone migration, and the peak width is proportional to the square root of this distance. Figure 2-4 illustrates this relationship. 

The B term describes broadening due to axial molecular diffusion and is inversely proportional to the linear velocity. In other words, the faster an analyte zone migrates through the column, the less broadening due to diffusion it will experience. The B term coefficient is given by... 

Changing the solvent entry position for each, or some, of the development steps enables the separation in each segment to be achieved in the shortest possible time under favorable capillary flow conditions. With as few as 10 developments, it is relatively easy to achieve 15,000-25,000 apparent theoretical plates for a zone migration distance of 6-11... 

Fig. 4 (a) Representation of zone migration inside the capillary tube and (b) the corresponding chromatogram. (From Ref. 8.)... 

Fig. 3 An illustration of the zone refocusing mechanism (left) and its application to the separation of a mixture of phenylthio-hydantoin-amino acids (right). The broken line on the left-hand side represents the change in spot size due to the expansion and contraction stages in multiple development and the solid line depicts the expected zone width for a zone migrating the same distance in a single development.

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