## 4 Current Conceptual Models to Explain the Results in Reducing Conditions  
Several authors have proposed explanations for the nil or negative (or alternating between positive and negative) dissolution rates observed in reducing conditions, particularly in the presence of dissolved H\({}_{2}\) used as a reducing agent [23; 24; 25; 26; 27; 28; 29]. Arguably the most cited conceptual model for the UO\({}_{2}\) alteration is the Matrix Alteration Model (MAM), shown in Figure 3, which was initially formulated in the framework of the EU Spent Fuel Stability (SFS) project [30; 31]. The MAM conceptual model (and similar ones) is based on the idea of \"oxidative dissolution\" of spent fuel. As shown in Figure 3, water radiolysis (due to alpha, beta, or gamma radiation) produces both reductants and oxidants upon interaction with water. The MAM model always invokes oxidation of U(IV) to U(VI) as the first step of the water-spent fuel interaction. H\({}_{2}\)O\({}_{2}\) is often claimed to be the main radiolytic species involved in UO\({}_{2}\) oxidation on the basis of either its higher concentration (compared with more reactive radical species such as the hydrated electron and the \(\bullet\)OH radical) or faster kinetics compared with other molecular radiolytic species (e.g., H\({}_{2}\)). Thus, these models imply that the conditions at the spent fuel surface are oxidizing due to the presence of H\({}_{2}\)O\({}_{2}\). Furthermore, this conceptual model explains the H\({}_{2}\) effect mostly by invoking the activation of dissolved H\({}_{2}\) on the surface of UO\({}_{2}\) without acknowledging the role of the primary radiolytic products formed in the spent fuel itself and at the water-spent fuel interface. According to the MAM model, the H\({}_{2}\) dissolved in bulk water is activated on the surface of the spent nuclear fuel thereby reducing the UO\({}_{3}\) in solid form. Aqueous ligands (such as bicarbonate, HCO\({}_{3}\)\({}^{-}\)) are able to form complexes with the oxidized U(VI) leading to the dissolution of the UO\({}_{2}\) matrix. Secondary solid phases (e.g., schoepite and studtite) can also precipitate on the surface of spent nuclear fuel, if the solubility limit is reached. Of course, there is always a component of dissolution that is driven by the solubility of the solid (this process is called non-oxidative dissolution in Figure 3). The non-oxidative dissolution is part of the MAM model [31]; it involves the formation of an amorphous UO\({}_{2}\) layer leading to the release of U(IV)aq according to the solubility of UO\({}_{2}\) (solid phase). The amorphous form of UO\({}_{2}\) is more soluble than the crystalline form so the solubility limit  
Figure 3: Mechanism for UO\({}_{2}\) dissolution at macroscopic level according to the Matrix Alteration Model, initially formulated in the framework of the EU Spent Fuel Stability project [31] and further developed by [PERSON] et al. [30]. of UO\({}_{2}\)(amorphous) is typically used to compare with the concentrations of U in solution measured in leaching tests (see Section 3). The H\({}_{2}\) activation mechanism has not been fully explained. What has been clearly demonstrated is that metallic inclusions of Mo, Tc, Pd, Ru, and Rh present in spent fuel (also called epsilon particles) are able to activate H\({}_{2}\) and act as catalysts in the reduction of oxidized U(VI). H\({}_{2}\) activation on noble metal epsilon particles has been demonstrated electrochemically [24; 32] and chemically [26] using SIMFUEL specimens with different levels of simulated burn-up (i.e., different number densities of particles) or added Pd particles, or using radioactive epsilon particles extracted from spent fuel [25]. This work well established that one of the key reactions involved is the catalysis of the reversible dissociation of H\({}_{2}\) to \(\bullet\)H radicals on the noble metal epsilon particles and this process galvanically protects UO\({}_{2}\) matrix from oxidation.