Dynamic stationary separators

We seek perturbations of Hamiltonian dynamics with separable equilibria, i.e., such that p = p (//(z))p( ) is a stationary solution. 

Ion-exchange chromatography (lEC) is used mainly for the separation of ions and easily ionized substances (e.g., substances that form ions by pH manipulation or complexation) in which one of the principal contributions to retention is the electrostatic attraction between mobile phase ions, both sa le and eluent, for immobilized ion centers of opposite charge in the stationary phase. The sample ions are separated based on differences in their relative affinity for the stationary phase ion centers compared to that of the mobile phase counterions in a dynamic exchange system, in which sample ions and eluent ions interact with multiple stationary phase ion centers as they pass through the column. Ion-... 

Complexation with Chiral Metal Complexes. This idea was first suggested by Feibush et al.44 The separation is realized by the dynamic formation of diastereomeric complexes between gaseous chiral molecules and the chiral stationary phase in the coordination sphere of metal complexes. A few typical examples of metal complexes used in chiral stationary phase chromatography are presented in Figure 1-13.45... 

Ion-exchange chromatography utilizes the dynamic interactions between charged solute ions and stationary phases that possess oppositely charged groups. In separations of this type, sample ions and ions of like charge in the mobile phase, compete for sites (X) on the stationary phase ... 

Liquid chromatography (LC) and, in particular, high performance liquid chromatography (HPLC), is at present the most popular and widely used separation procedure based on a quasi-equilibrium -type of molecular distribution between two phases. Officially, LC is defined as a physical method... in which the components to be separated are distributed between two phases, one of which is stationary (stationary phase) while the other (the mobile phase) moves in a definite direction [ 1 ]. In other words, all chromatographic methods have one thing in common and that is the dynamic separation of a substance mixture in a flow system. Since the interphase molecular distribution of the respective substances is the main condition of the separation layer functionality in this method, chromatography can be considered as an excellent model of other methods based on similar distributions and carried out at dynamic conditions. 

Chromatographic approaches have been also used to separate nanoparticles from samples coupled to different detectors, such as ICP-MS, MS, DLS. The best known technique for size separation is size exclusion chromatography (SEC). A size exclusion column is packed with porous beads, as the stationary phase, which retain particles, depending on their size and shape. This method has been applied to the size characterization of quantum dots, single-walled carbon nanotubes, and polystyrene nanoparticles [168, 169]. Another approach is hydro-dynamic chromatography (HDC), which separates particles based on their hydro-dynamic radius. HDC has been connected to the most common UV-Vis detector for the size characterization of nanoparticles, colloidal suspensions, and biomolecules [170-172]. 

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