Vector Model of Multiphase Separations

A vector model is developed for separations using combinations of two or more stationary phase chemistries. The model is useful for the development of separation optimization strategies for methods involving series-coupled columns, parallel columns, or mixed stationary phases. In the model, each mixture component occupies a single point in a multidimensional vector space, with each orthogonal axis representing the retention on a particular stationary phase. For every pair of points, a separation vector is defined. The length and direction of the separation vector give all the necessary information on the separation of this binary mixture. The ensemble of separation vectors for the entire mixture is used to describe the multiphase separation. For the case of a separation using series-coupled columns or mixed stationary phases, the multidimensional space collapses by orthogonal projections onto a linear separation axis. The orientation of this axis defines the fractional contributions of the various phases to the overall separation selectivity. An example of the use of the vector model in establishing the optimal separation axis and thus phase fraction in a two-phase separation is presented.