Vector model for window-diagram optimization of tunable column ensembles for high-speed GC
A previously described vector model of multiphase separations is dramatically simplified and applied to the problem of optimization of tandem column ensembles using pressure-tunable column selectivity. In the model, retention values for a set of target compounds on the two different stationary phases used in the column ensemble are plotted on a two-dimensional retention plane. Retention values for each mixture component are expressed in units of hold-up time for the two different columns. Every mixture component occupies a single point on the retention plane. The orthogonal coordinates of a point represent retention for that component on the individual phases. A phase fraction axis is defined from the origin of the retention plane. The angle that this axis makes with the orthogonal retention axes is uniquely defined by the fractional contributions to the total hold-up time from the individual columns. Coordinates along this axis define the ensemble retention using the column combination. Points on the retention plane corresponding to the mixture components are connected pairwise by separation vectors. The geometric center of each separation vector is connected to the retention origin by a locator vector. This pair of vectors provides all necessary information regarding the separation of the corresponding pair of mixture components using the chosen pair of stationary phases in the column ensemble. The separation of a peak pair using a particular column combination (holdup time fraction) is found by projection of the separation vector onto the phase fraction axis corresponding to the holdup time fraction. The relative resolution of the peak pair is found as the ratio of the separation vector projection length to the locator vector projection length. Minimum values of relative resolution considering all non-redundant peak pairs then are plotted versus the rotation angle of the phase fraction axis. The resulting window diagram identifies the holdup time fraction giving the best relative resolution of the most difficult to separate component pair.
Link to Published Version
Smith, H., & Sacks, R. (2002). Vector model for window-diagram optimization of tunable column ensembles for high-speed GC. Journal of Separation Science, 25(1–2), 37–44. doi:10.1002/1615-9314(20020101)25:1/2<37::AID-JSSC37>3.0.CO;2-B