First-order dissolution rate law and the role of surface layers in glass performance assessment

Abstract The first-order dissolution rate law is used for nuclear waste glass performance predictions since 1984. A first discussion of the role of saturation effects was initiated at the MRS conference that year. In paper (1) it was stated that “For glass dissolution A* (the reaction affinity) cannot become zero since saturation only involves the reacting surface while soluble elements still might be extracted from the glass” [B. Grambow, J. Mater. Res. Soc. Symp. Proc. 44 (1985) 15]. Saturation of silica at the surface and condensation of surface silanol groups was considered as being responsible for the slow down of reaction rates by as much as a factor of 1000. Precipitation of Si containing secondary phases such as quartz was invoked as a mechanism for keeping final dissolution affinities higher than zero. Another (2) paper [A.B. Barkatt, P.B. Macedo, B.C. Gibson, C.J. Montrose, J. Mater. Res. Soc. Symp. Proc. 44 (1985) 3] stated that “… under repository conditions the extent of glass dissolution will be moderate due to saturation with respect to certain major elements (in particular, Si, Al and Ca). Consequently, the concentration levels of the more soluble glass constituents in the aqueous medium are expected to fall appreciable below their solubility limit.” The formation of dense surface layers was considered responsible for explaining the saturation effect. The mathematical model assumed stop of reaction in closed systems, once solubility limits were achieved. For more than 15 years the question of the correctness of one or the other concept has seldom been posed and has not yet been resolved. The need of repository performance assessment for validated rate laws demands a solution, particularly since the consequences of the two concepts and research requirements for the long-term glass behavior are quite different. In concept (1) the stability of the `equilibrium surface region' is not relevant because, by definition, this region is stable chemically and after a potential mechanical destruction it will be reformed instantaneously. The same is true for radiation damage. The dissolution of silica from the surface in this concept is considered as rate limiting for the release of soluble elements from the glass. After surface stabilization by local solid/solution equilibrium the release of soluble radionuclides continues with lower rates, but this is considered as resulting from parallel leaching mechanism. In fact, the deconvolutions of the overall leach mechanism into individual parallel and sequential rate limiting steps (not necessarily elementary reactions) is fundamental to this concept. In concept (2) surface stability as well as surface morphology are fundamental. A fracture in the protective surface would increase glass corrosion. The protective effect is based on the low diffusivities of radionuclides and other glass constituents in this layer. However, a true relation between layer thickness and rates is seldom observed. Diffusion coefficients are considered to vary with time as well as with the surface area to solution volume S/V ratio. Sometimes, extremely low diffusivities in extremely thin layers are invoked to explain experimental data. The two concepts are not so different from each other and one is tempted to think of a problem of semantics. In fact, there are two alternative ways by which the protective layer concept can be coupled to the saturation concept: (a) the layer may be formed by solubility effects as proposed in [loc.cit] and/or (b) the layer plays the role of a silica diffusion barrier limiting glass dissolution rates according to the first-order rate law at the interface between the pristine glass and the surface layer. However, the mathematical models based on these conceptual models yield quite different long-term predictions, even though the models may equally well fit a given set of experimental data. The models are also different with respect to the number of interrelated parameters. In the case of a model based on a surface layer slowing down glass network dissolution, the numerical value of the diffusion coefficient of silica, the layer thickness and the saturation concentration of dissolved silica are interrelated. Often, none of the parameters are measured directly. As a consequence this leads to not-sufficiently constrained models with poor predictive capacity. Recent research has indicated that there might be problems with the applicability of the first-order rate law [C. Jegou, thesis, University of Montpellier II, 1998]. Fresh glass or pre-altered glass samples were put in solutions over-saturated with silica. A decrease in reaction rates by as much as a factor of 10 was observed, but the rates remained much higher than predicted from a first-order rate law. It was argued that none of the kinetic models based on the notions of `chemical affinity' and `deviation from an equilibrium' is adapted to describe the kinetics of glass corrosion. In contrast, the formation of a surface gel and condensation of silanol groups are considered responsible for the decrease in reaction rates. The present communication argues against this view. Based on recent results of Monte Carlo calculations [M. Aertsens, Mater. Res. Soc. Symp. Proc. 556 (1999) 409] it is shown that some time of surface restructuration is necessary before saturation effects become fully effective in controlling long-term release of soluble glass constituents. The formation of a gel layer is not opposed to an affinity based kinetic concept, but it is in contrast a manifestation of this concept. It is the belief of the authors that much of the confusion related to the first-order rate law results from the fact that glass network dissolution is not considered as only one of a series of reaction mechanism and that glass network hydration and alkali ion exchange were ignored as parallel leaching mechanism. Our experimental results show that glass network hydration and ion exchange are important in short-term laboratory tests and in certain cases (closed system) also in the long term.