Deionized water is "made" by passing water through a R-H/R-OH resin bed where ions are removed based on the
affinity scale particular to the resin used. In most cases, the highest priority is to remove Sodium, Chlorine, and so on. The resin also acts as a filter removing some particulate. The process of capturing an ion results in the release of another ion. Either H+ or OH- in this case. The result is pH balanced water that is free of highly reactive contaminant ions.
BUT, it does not remove all contaminants.
Additionally, as resin is filled with these contaminants, it starts to run out of H+ and OH- ions to release. This is where the
affinity scale kicks in... because the resin prefers Sodium, it may release another contaminant to capture the Sodium. This is an indication the resin is "depleted."
Companies have specifications on how much of these contaminants can be "left behind" and
still be called "deionized" water. Those contaminants will eat your coins.
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Distilled water is created by boiling the water and condensing the steam. Particulate will not boil and remains behind in the brine solution. Almost all other ions separate from the water as a gas and fail to condense with the water. These are removed by air evacuation systems. The result is pure water.
This water is cointained in tanks and moved through pipes. Both introduce trace amounts of metals into the water as ions and particulate.
Immediately after the water is condensed, chemistry takes over. The container holding the water leeches some compounds into the water. There is not much you can do about this one, but it is usually benign to the coins.
Air above the water can be absorbed into the water, especially carbon dioxide, which converts to acid, eg. carbonic acid from carbon dioxide. This takes a few days to become harmful to coins, and can be limited to the air above the water by using a lid on your containers.
So, heed the advice to change out your water at least once a week, use small inert containers, fill them nearly full, and keep a lid on the container. Otherwise, even distilled water can damage your coins.