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The increasing complexity in particle science and technology requires the ability to deal with multidimensional property distributions. We present the theoretical background for multidimensional fractionations by transferring the concepts known from one dimensional to higher dimensional separations. Particles in fluids are separated by acting forces or velocities, which are commonly induces by external fields, e.g., gravitational, centrifugal or electro-magnetic fields. In addition, short-range force fields induced by particle interactions can be employed for fractionation. In this special case, nanoparticle chromatography is a recent example. The framework for handling and characterizing multidimensional separation processes acting on multidimensional particle size distributions is presented. Illustrative examples for technical realizations are given for shape-selective separation in a hydrocyclone and for density-selective separation in a disc separator.

Alternate pumping chromatography is applied to obtain atomically precise glutathione-stabilized gold nanoclusters in high purity from synthesized mixtures. On the basis of anion exchange chromatography, the feasibility of isolating a single cluster, Au10GSH10, as well as two different clusters simultaneously (Au25GSH18 and Au29GSH20) is demonstrated. In addition, Au18GSH14, which is present only in trace amounts, is successfully enriched. A simple design procedure is proposed that allows using columns with different retention behavior. Successful experiments with large injection amounts confirm the potential of the concept for preparative-scale productions of high-quality nanoparticulate products.