That physical exchange process in the sponge example is similar to what happens in the micro-pores of zeolite crystals, but the crystals' atomic structures are made in ways that makes them selective for just a few molecules/elements (unlike the sponge, which can absorb all kinds of liquids). Minerals like zeolites can't absorb all elements all the time, and certain microporous minerals are better at exchanging particular elements. The trick is finding the right match for the element that you want to selectively absorb, or modifying the mineral to make it work.
Gaidonnayite has small pores, so it wasn't expected to be able to exchange a large metal like cesium (having the largest diameter of all the known elements --
sans francium). It was thought that the pores were too small to allow a large atom to move into them. However, I knew that gaidonnayite would have a desirable advantage. Other researchers have found that it (and similar zirconium silicate minerals) could resist the damaging effects of high radiation doses for thousands, or perhaps millions, of years. Therefore, gaidonnayite would be a good mineral to use because of its stability, if a way could be found to actually get the radioactive elements into it.
In the end, I made it work! But I had to modify the material a little bit from the natural state. Gaidonnayite did absorb cesium when hydrogen, the smallest of all elements, occupied the crystal prior to exchanging in the cesium. But how does the smallest atom help capture the largest atom? When I investigated the details of how the exchange process took place, I found some interesting interactions between water molecules already in the structure and hydrogen atoms that I introduced artificially.