Window diagram approach

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... 

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

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 ...

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. 

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. 

It is clear from the above, that model equations for the description of retention surfaces have to meet high demands. Preferably, equations should be used that relate to reliable chromatographic theory, such as the one used to describe the retention behaviour as a function of pH in RPLC in the window diagram approach described in section 5.5.1. The use of such a chromatographic equation was clearly better in that case than a statistical approach using (for example) polynomial equations. 

This method enables prediction of the quahty of a separation on the basis of a relatively hmited number of the experimental data, collected in previous experiments. According to this approach, the chromatographic results are interpreted in terms of the retention functions, valid for each individual solute separately. Some good examples of the interpretative strategy are the so-called window diagrams approach [20] and the search for the extremum of the multiparameter response function with the aid of the genetical algorithm [21],... 

The window diagrams approach originally developed for GC [2,3] have been extended to HPLC [4,5] and recently have been adapted to TLC. 

The window diagrams approach has a distinct disadvantage compared with this method, because in window diagrams solvent optimization methods can only be generated with binary and ternary solvents (plus the base solvent). The simplex method can be used for multicomponent solvent... 

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. 

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... 

Window Diagram" or "Simplex" methods (1—5). This approach is very useful to get optimal separation conditions however, it has one major limitation. It necessitates all materials of interest be available. 

The constants a, b, and m in eqn [3] depend on the solute and on the chromatographic system. b = (ka) " , where ka is the retention factor in a pure nonpolar solvent. Equation [2] or [3] can be used as the basis of optimization of the composition of two-component (binary) mobile phases in NPLC, using a common window diagram or overlapping resolution mapping approach, as illustrated in an example in Figure 3. 

Single-parameter optimization employs several experiments at preselected values of the optimized parameter (such as the concentration of the strong solvent in a binary mobile phase, pH, temperature) to predict the resolution as a function of the optimized parameter using empirical or simple model-based calculations. Then, plots are constructed (the window diagrams ) in which the range of the optimized parameter is searched for the value that provides the desired resolution for all adjacent bands in the chromatogram in the shortest time. An example of a window diagram (Pig. 5) illustrates the approach adopted for the optimization of a binary mobile phase in NPLC. 

---