Window diagrams

The Window diagram method for the optimization of separation was developed by Laub and Purnell [73], and it has been used both for gas chromatography and HPLC. Recently it is applied in TLC and HPTLC [19,74—76]. 

Prus and Kowalska [75] dealt with the optimization of separation quality in adsorption TLC with binary mobile phases of alcohol and hydrocarbons. They used the window diagrams to show the relationships between separation selectivity a and the mobile phase eomposition (volume fraction Xj of 2-propanol) that were caleulated on the basis of equations derived using Soezewiriski and Kowalska approaehes for three solute pairs. At the same time, they eompared the efficiency of the three different approaehes for the optimization of separation selectivity in reversed-phase TLC systems, using RP-2 stationary phase and methanol and water as the binary mobile phase. The window diagrams were performed presenting plots of a vs. volume fraetion Xj derived from the retention models of Snyder, Schoen-makers, and Kowalska [76]. 

The Window diagram method is seldom used for ternary or quaternary mobile phases because of a large variety of intermoleeular interaetions that appear in... 

The advantage of the window diagram method is that the optimum mobile phase composition can be easily loeated visually or using a computer. 

Procedures used vary from trial-and-error methods to more sophisticated approaches including the window diagram, the simplex method, the PRISMA method, chemometric method, or computer-assisted methods. Many of these procedures were originally developed for HPLC and were apphed to TLC with appropriate changes in methodology. In the majority of the procedures, a set of solvents is selected as components of the mobile phase and one of the mentioned procedures is then used to optimize their relative proportions. Chemometric methods make possible to choose the minimum number of chromatographic systems needed to perform the best separation. 

The basis of the window diagram approach is that the relative retention of a solute on a mixed phase depends only on the volume fractions of the individual phases and the partition... 

The window diagram method can also be used to optimize the separation of mixtures when the number and identity of the components are unknown [421-423]. Two liquid phases, A and S, of different selectivity are chosen. Trial chromatograms are run on... 

Other more mathematical techniques, which rely on appropriate computer software and are examples of chemometrics (p. 33), include the generation of one-, two- or three-dimensional window diagrams, computer-directed searches and the use of expert systems (p. 529). A discussion of these is beyond the scope of this text. 

FIGURE 5.6 (A) The resolution window diagram for RP-gradient-elution separation of phenylurea herbi-... 

Including the original results reported later in this chapter, only two systematic optimization procedures have been reported simplex (38), (this chapter) and window diagrams (39), (this chapter). Due to space limitations, a somewhat greater emphasis will be placed here on original results rather than those published elsewhere. Experimental details common to the simplex and window diagram results obtained from our laboratory are summarized here for the sake of convenience and continuity of discussion. 

Experimental (simplex and window diagram). The chromatographic system consisted of a Model 501 supercritical fluid chromatograph (Lee Scientific, Salt Lake City, Utah) with the flame ionization detector (FID) set at 375°C. The instrument was controlled with a Zenith AT computer. A pneumatically driven injector with a 200 nL or a 500 nL loop was used in conjunction with a splitter. Split ratios used were between 5 1 and 50 1, depending on sample concentration and the chosen linear velocity, while the timed injection duration ranged from 50 ms to 1 s. We found that the variation of both the split ratio and injection time allowed greater control over the... 

An advantage of using S is that it can be calculated from retention data commonly supplied by electronic integrators and/or data systems, facilitating the window diagram search (vide infra). 

Table VII. Density Optimization via an Interpretive (Window Diagram) Approach...

Simultaneous Optimization of Density and Temperature. Although near-baseline resolution was achieved for all eight sample components via the optimization of a single variable (density), as illustrated in Figure 1, a better (or in rare cases, equal) result will always be obtained if all variables of interest are optimized. The window diagram method is now considered for the simultaneous optimization of density and temperature for the separation of the eight component sample of Table VI, to provide a comparison with the SFC separation obtained with the density-only optimization (Figure 6). 

Shown in Figure 10 is the chromatogram acquired at the optimum predicted by CRF-4. Baseline resolution of all 8 components was achieved in about 27 minutes, except for components 2-4 which were almost baseline resolved. Additional evidence for the accuracy of the retention model (equation 9 and Table VI) employed for this window diagram optimization is evident in Table VIII, where predicted and measured retention factors differed by less than 15%. The slight positive bias observed for all solutes at the optimum conditions in Table VIII was coincidental averaged over the entire parameter space the bias was almost completely random. 

Table Vtll. Simultaneous bensity and Temperature Optimization via an Interpretive (Window Diagram) Approach Criterion threshold separation factor (CRF-4, equation 9) Optimum conditions density, 0.19 g/mL temperature, 104 °C Chromatogram Figure 10 ...

A systematic method development scheme is clearly desirable for SFC, and as shown in the present work, both the modified simplex algorithm and the window diagram method are promising approaches to the optimization of SFC separations. By using a short column and first optimizing the selectivity and retention, rapid... 

Given the mere handful of reports in the published literature (6,38,39,52), there are many avenues open in the development of systematic approaches to optimization in SFC. In addition to the opportunities mentioned in the sections on the simplex method and window diagram approach, others include the exploration of other sequential or simultaneous optimization strategies such as optiplex, simulated annealing, method of steepest ascent, etc. that are potentially useful in SFC. 

Fig. 13.6 Schematic molding area or molding window diagram that can be determined for a given polymer and mold cavity.

In this section we will describe several optimization procedures which are simultaneous in the sense that all experiments are performed according to a pre-planned experimental design. However, unlike the methods described in section 5.2, the experimental data are now interpreted in terms of the individual retention surfaces for all solutes. The window diagram is the best known example of this kind of procedure. 

Window diagrams were developed by Laub and Purnell for the optimization of the composition of mixed stationary phases for GC (for a review see ref. [501] or ref. (544)). An example of a window diagram is given in figure 5.16. This figure will be explained below. 

---