Optimization window diagrams

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. 

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]. 

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 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... 

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. 

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). 

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. 

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. 

Figure 5.16 Example of a window diagram for optimizing the stationary phase composition in GLC. (a) (top) variation of the retention (distribution coefficient K) with composition for the individual solutes W,X, Yand Z. (b) (bottom) window diagram showing grey areas ( windows ) at compositions where all components may be separated. Figure taken from ref. [545]. Reprinted with permission.

Window diagrams, such as figure 5.16b, overcome at least the first of these three problems. Moreover, they can in principle be expanded to cover two-dimensional optimization problems (see below). In figure 5.16b lines have been constructed that... 

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... 

Figure 5.17 Application of the window diagram method for optimizing the pH in RPLC. Solutes S = scopoletin, U = umbelliferone, TF = trans-ferulic acid, TC = trans-p-coumaric acid, CF = cis-feruiic acid and CC = cis-p-coumaric acid, (a) retention surfaces, (b) window diagram. Figure taken from ref. (552J. Reprinted with permission.

However, a simple linear relationship does not usually exist. A clear example is the optimization of the pH in RPLC. The window diagram approach was applied to this problem by Deming et al. [550,551,552]. They measured the retention of each solute at a series of pH values (9 in ref. [550], 4 in refs. [551,552]) and fitted the experiments to eqn.(3.70). This is a three-parameter equation and hence a minimum of three experiments is required for it to be applied as a description of the retention surface. If more data points are available, the equation can be fitted to the data by regression analysis. 

Hsu et al. [553] applied the window diagram method to the optimization of the composition of abinary mobile phase in RPLC. However, a straight line was not obtained by plotting 1 /k vs. composition and therefore more than two experimental locations were required. 

Window diagrams and related methods may in principle be applied to optimization problems in more than one dimension. The main difference compared with one-parameter problems is that graphical procedures become much more difficult and that the role of the computer becomes more and more important. Deming et al. [558,559] have applied the window diagram method to the simultaneous optimization of two parameters in RPLC. The volume fraction of methanol and the concentration of ion-pairing reagent (1-octane sulfonic acid) were considered for the optimization of a mixture of 2,6-disubstituted anilines [558]. A five-parameter model equation was used to describe the retention surface for each solute. Data were recorded according to a three-level, two-factor experimental... 

Otto and Wegscheider [562, 563] applied the window diagram method for the simultaneous optimization of the (binary methanol-water) mobile phase composition, the ionic strength and the pH for the separation of ionic solutes in RPLC. They fitted the experimental data to a semi-empirical 13-parameter equation based on eqn.(3.45) for the composition effect, eqn.(3.71) for the effect of the ionic strength and eqn.(3.70) for the... 

A number of other methods has been used to optimize ternary solvent systems, many of them69-71 similar to the window diagram used in GC. Only one more will be described briefly here. The authors, Schoenmakers et al.,72 have prepared what they call phase selection diagrams for several reverse phase LC separations. The solvents used for their mixtures are the same ones recommended by Snyder methanol, ACN, and THF. 

---