Chemical filtration is just what is sounds like. It is the use of chemically enhanced products to remove those things that ail you; copper, dissolved organics, nitrate/nitrite/ammonia, phosphates, etc. Beware of fantastical claims of effectiveness. Most of the claims are just claims.
However, there is one tried and true chemical filtration medium: activated carbon. Activated carbon helps remove dissolved organics from the water. Over time, as an aquarium matures, dissolved organics build up in a closed system. This causes the water to take on a yellow tinge. Activated carbon is great for removing this. Beware though, that is not all it removes. Activated carbon is reported to deplete some beneficial trace elements in the water. Therefore, a lot of people have taken some different approaches to using carbon other than full-time in a canister filter.
If you choose to run a sump with your system, this is a good place to drop a filter bag of carbon. The water is allowed to flow around the carbon, reducing the amount of trace element striping that is done, but still removing the yellowing compounds from the water. If you don't have a sump you can drop the same filter bag behind the rockwork in the display tank and accomplish the same thing. Some protein skimmers, particularly the CPR BackPak, have a media chamber where you can drop the filter bag in and affect the same thing.
Another issue to be careful of with activated carbon is the leaching of phosphates into the water. High phosphate levels encourage unwanted algae growth, which indirectly increases maintenance tasks. When you choose an activated carbon, make sure it specifically states that it does not leach phosphates.
Summarizing the basic filtration choices, biological filtration is mandatory, although live rock and live sand are not a requirement (just a dang good idea). Mechanical filtration is not mandatory, as some of the removal of particulate matter will occur during water changes. Protein skimming, however, should be considered a must for maintaining good water quality. Chemical filtration is completely optional, and should only be used until a specific problem is resolved, with the exception of activated carbon. Phosphate-free activated carbon can be used full-time, part-time, or not at all. Your call.
The end goal of all types of filtration is superior water quality. This is the main thing that will effect the health of all of your livestock.
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