Solubility equilibrium gradients in the analytical ultracentrifuge: an approach towards the isolation of critical crystal nuclei in solution

Sedimentation equilibrium methods which are able to establish a solubility gradient for inorganic species in an ultracentrifugal field are presented. These methods are generally based on the concepts of density gradient and sedimentation equilibrium ultracentrifugation. However, in addition to the formation of a density or an equilibrium gradient, physicochemical parameters such as the pH or the solvent quality are varied throughout the solution column if appropriate high-density or high-molar-mass solutes are chosen or a mixture of solvents with different density is applied. This is demonstrated for two types of solubility gradients including for the case of a pH gradient; parameters for the adjustment of the overall pH are discussed. pH gradients were formed up to 3 pH units and are sensitive to addition of electrolytes, so they can only be applied to sparingly soluble salts. The gradual variation of the solubility of inorganic particles leads to the dissolution of the particles upon sedimentation when the dissolution point is reached. The ionic species formed show increased diffusion compared to the sedimenting particles, so they can diffuse back to regions of lower solubility and thus form a crystal again. This finally leads to an equilibrium situation for the critical crystal nucleus. In the case of a pH gradient with CdS, it is demonstrated that a transition from particles to dissolved ions indeed takes place and can be monitored in the analytical ultracentrifuge. For BaCrO₄, the transition to the more soluble BaCr₂O₇ with decreasing pH can readily be monitored via the associated spectral changes, clearly demonstrating the possibility to perform chemical reactions in a pH gradient.