"Solid/liquid chemical equilibrium hypotheses (sorption, solubility, solid-solution formation) are key concepts in the assessment of nuclear waste safety. For radionuclides at trace concentrations this corresponds to constant solution concentrations, or solid/liquid distribution ratios, if environmental conditions remain constant. However, these concepts do not account for irreversible incorporation of radionuclides in the solid phases. Indeed, there is often a gradual and very slow transition from simple adsorption processes to incorporation of trace elements in the surface structure of solid phases. For certain tetravalent actinides apparent solubility equilibrium applies to only the surface without bulk phase equilibrium. This can lead to very large uncertainty in solubility values and derived thermodynamic constants. Equilibrium concepts are characterized by a dynamic state of equal forward and backward reaction rates, under conditions where phase compositions remain constant. Most of the problems arise from a lack of understanding of the dynamics of slow processes close to equilibrium, specifically in the coupling of sorption with other surface equilibrium reactions such as dissolution/precipitation, recrystallisation, isotopic exchange and with the bulk phase equilibrium. The project intends to assess the effect of surface properties on apparent solubility as well as the kinetics of incorporation of radionuclides in the structure of a solid phase, and the associated reaction mechanisms for various solids in a systematic manner, using isotope exchange under close-to-equilibrium conditions.The project results will impact strongly (1) the use/misuse of solubility data for thermodynamics; (2) the understanding of affinity/rate relations close to equilibrium; (3) the inclusion of irreversibility in models on the long-term mobility of radionuclides; and (4) the coupling of radionuclide chemistry with main element chemistry in the repository environment."