Retention line —

Table 15.7 Retention lines of organochlorine insecticides relative to dieldrin, on some GLC columns...

Figure 3.17 Schematic illustration of the variation of the observed capacity factor (fcobs) with the pH for a weak acidic solute in RPLC according to eqn.(3.70). The retention line is calculated from eqn.(3.70) assuming kA = 1 and kHA = 9 ...

Figure 5.16a is a plot of the retention against the composition. These retention lines (surfaces) are required for the construction of the actual window diagram (figure 5.16b). In figure 5.16a the distribution coefficient (K) is shown on the vertical axis. If the total volume of the stationary phase is kept constant, then the phase ratio is constant and K is directly proportional to the capacity factor k (eqn.1.10). On the horizontal axis is the mixing ratio of the two components of the stationary phase (stationary phases 5 (left) and A (right). 

The retention lines for the individual solutes need to be known. 

Eqns.(5.15) and (5.15a) describe a hyperbolic function with a discontinuity at the point where KY= i.e. where the retention lines for the two solutes Vand Z intersect in figure... 

The window diagram method also lends itself to the optimization of different parameters. However, in order to construct the window diagram it is necessary to know the retention lines or surfaces of the individual solutes. For the optimization of the stationary phase composition in GC a linear relationship may be assumed between retention (K or k) and composition (volume fraction

window diagram method may be very useful for optimizing the stationary phase composition of... 

Linear relationships are preferred, but not mandatory. For non-linear retention lines... 

If the number of experimental data points exceeds the minimum requirements to describe the retention line by a selected function, then the coefficients may be calculated using regression analysis. The method may then be referred to as a regressive method and the initial experiments form a regression design. 

On a column with a given (average) number of plates, the critical bands can be calculated for any value of the desired resolution Rs. If the retention line (in the case of a one parameter optimization problem) for solute j is straight, then eqn.(5.16) describes another straight line. Two applications of this approach are shown in the figures 5.18 and 5.19. 

Figure 5.19 (a) Figure showing the retention surfaces for some aromatic solutes in RPLC. Only solute nr.l 1 is assumed to be of interest. Critical bands have been constructed according to eqns 5.16) and (5.17) below and above the retention line for this solute. The dashed line indicates the optimum ternary mobile phase composition, (b) Chromatogram obtained at the predicted optimum composition. Figures taken from ref. [555], Reprinted with permission. 

The solute of interest can be separated from all the other solutes at compositions at which no other retention lines fall within the critical band. This is illustrated in figure 5.19b. 

Eqn.(5.17) can also be used to allow for the occurance of a solvent peak in the chromatogram. For example, a large resolution may be demanded between an imaginary peak at k= 0 and the first peak in the chromatogram. In that case all solutes may be assigned a critical band above (eqn.1.17) rather than below (eq.1.16) their retention lines. 

The two applications shown here concern the optimization of the mobile phase composition in RPLC. However, the method may easily be adapted to other problems. It is most practical if straight retention lines can be obtained. It should be noted that this is not usually the case for retention as a function of mobile phase composition in RPLC. In fact, Colin et al. [555] adapted the value of the hold-up time (t0) such as to obtain straight lines. The fact that they succeeded in doing so for all of 11 solutes considered at the same time is remarkable, but it may not always be possible. In any case, adapting t0 in order to linearize the retention lines will be an awkward practice. 

Figure 5.32 Initial phase selection diagrams for three possible ternary mobile phase systems applied to the separation of five diphenyl amines. Top (Initial) retention lines. Bottom (initial) response line. Criterion normalized resolution product (r eqn.4.19 drawn line) Also shown is the response surface using the product resolution criterion (IIeqn.4.18 dashed line). The required chromatograms are shown in figure 5.33 (a, b and c). Figure taken from ref. [576]. Reprinted with permission.

The non-linearity of the retention lines is apparent from this figure. The response lines have been drawn for two different criteria the normalized resolution product r (drawn line eqn.4.19) and the product resolution function FIRS (dashed line eqn.4.18). It is seen that the product resolution criterion would in fact have guided us to a completely different optimum at a composition of 24.1% methanol and 25.2% THF. The chromatogram that we would have obtained at this composition is shown in figure 5.33h. Clearly, this chromatogram is less attractive than the one of figure 5.33g. Obviously, the normalized resolution product is to be preferred to the resolution product itself (see the discussion in section 4.3.2). 

In figure 5.34 the retention lines have been approximated by a series of linear line segments, rather than by a smooth curve. The alternative is to fit a mathematical equation to the data, for example a quadratic function for In k vs. the mixing ratio x. If more than... 

Figure 6.4 Schematic example of the variation of retention with temperature in gas chromatography. Retention lines are drawn for a group of 8 solutes (e.g. homologues). Vertical dashed lines (a and b) correspond to chromatograms (a and b) in figure 6.1. Horizontal dashed lines indicate the range of optimum capacity factors.

Coupled-column separations or multidimensional chromatography can be considered as a sample preparation form, as one column is used to derive fractions for the second column. It provides a two dimensional separation in which sample substances are distributed over a retention plane formed by the operation of two independent columns. This type of two dimensional based separation method is more powerful than a single dimensional based one. A retention plane has more peak capacity than a retention line and so can accommodate much more complex mixtures. Component identification is more reliable because each substance has two identifying retention measures rather than one. These type of combinations offer high selectivity and high sensitivity, and could be used with less expensive and more robust detectors (e.g., flame ionization). ... 

A shut-off valve (VI) on the hydrogen generator line while the throttle valve (V2) on the retentate line allows adjusting the pressure inside the membrane. 

The entire VPS (19 in Figure 1) except for the saturator was maintained at a temperature of at least 5°C above the temperature inside the saturator to prevent condensation of water in the system. Upon introduction of feed into the permeation cell, water vapour and methane gas permeate through the membrane and the remainder of the feed leaves through the retentate line. 

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