Parameters from equations ( ) and ( ) used to fit the data in Fig. . Parameters k2 and c are taken from fits to the data in Fig. . The one exception is the faster adsorption (k1) that occurs during the first cycle for pH 4.5 samples, which was also observed when replacing Nd with Gd at this pH (Fig. ). Faster adsorption is accompanied by an initial surface ion density that is small (0.02 ions nm -2 ) compared with the value of 0.1 ions nm -2 observed at the beginning of subsequent cycles for pH 4.5 samples. We suggest that this effect could be the result of a non-equilibrium initial state at pH 4.5, possibly due to a large free energy barrier to unbind ions from DTPA at the higher pH. In this scenario, X-rays facilitate the release of ions over the large free energy barrier during the initial cycle and subsequent cycles are between equilibrium states. Such effects were not observed for pH 3.0.