The inverse rate constants in Table have values on the order of hundreds of seconds, which likely reveals the diffusive nature and complexity of each process in the model. For example, k1 characterizes a process which could involve X-rays producing radiolysis products that diffuse to DTPA, releasing Nd ions which then diffuse to the surface and bind to DHDP. Alternatively, k1 could represent the effect of direct release of Nd ions by X-ray exposure but would still involve diffusion of Nd ions from DTPA in the bulk water to DHDP at the surface. Similarly, the constant k2 for pH 3.0 samples involves the production of radiolysis products in the bulk water which diffuse to DHDP at the surface to release Nd ions, though the constant k2 for pH 4.5 data appears to represent an X-ray exposure process independent of radiolysis effects. Finally, the constant k3, which characterizes the X-rays-off part of the cycle represents the equilibration between a strongly binding DTPA in bulk water and a weaker binding DHDP at the surface when the initial condition contains an excess of ions at the surface. This process has a long time constant and may involve diffusion of DTPA to the surface region.