Copper ions alone do not inhibit let alone kill fecal bacteria at all. Basically, the fecal bacteria Escherichia coli, Enterococcus faecalis and Staphylococcus aureus are commonly found in your intestines where they are exposed to copper levels similar to that used in pools. Blood serum has copper ions so these bacteria have developed mechanisms to survive and even thrive in such an environment. It takes much, much higher levels of copper to kill such bacteria. These bacteria are controlled in the body via competition with "good" bacteria such as Bifidobacterium bifidum, Lactobacillus sp. and Spirochetes and also from body immune system defenses. However, when the potentially pathogenic fecal bacteria leave your body via fecal matter and enter warm nutrient-rich pool water, they can grow uncontrollably into concentrations that when re-entering via your mouth, nose, broken skin, etc. can overwhelm your body's immune system and cause disease. Copper ions are also slow to kill other bacteria including Pseudomonas aeruginosa and Stenotrophomonas maltophilia, though do kill them faster than they can reproduce so they prevent uncontrolled growth for these bacteria. It kills Acinetobacter baumannii about as quickly as chlorine and it kills Legionella pneumophila somewhat faster than chlorine. Copper ions have little to no effect on many viruses compared to relatively fast kills from chlorine including Herpes Simplex Virus (HSV), Vacciniavirus, Poliovirus, Coliphage MS-2 and Influenza. Full technical details are in this post.
FIFRA rules explicitly state that it is illegal for a pesticide product to make bactericidal killing or disinfectant claims for swimming pools or spas without passing EPA DIS/TSS-12. All pesticide products must be registered with the EPA (see the PAN Pesticide Database) including algaecide products, though ionization systems are not separate chemicals so like saltwater chlorine generator (SWG) systems, do not require such registration. There are plenty of copper sulfate pentahydrate and related copper ion algaecides (see here, for example), but these are not disinfectants.
So this is a gray area since CL Free is not a registered EPA pesticide, but should probably not be making bactericidal disinfectant claims. Now there are copper/silver ionization systems certified through NSF Standard 50, but you will note that they ALL require a minimum of 0.4 ppm chlorine or 0.8 ppm bromine.
CL Free, nor any other metal ion system, is not allowed in any commercial/public pool or spa in the U.S. without the use of an EPA approved disinfectant. There are only three such disinfectant chemicals for pools: chlorine, bromine and Baquacil/biguanide/PHMB. These same chemicals are also approved for spas as is Nature2 (silver/zinc ions) with non-chlorine shock (MPS), but only at hot spa temperatures.
There is no real government regulation requiring disinfection of your residential pool. This is analogous to what you can do in your kitchen where you are free to leave a chicken out all day in the sun and then cut up vegetables in those uncooked chicken juices left on the cutting board. Such practices are not allowed in commercial kitchens just as CL Free by itself is not allowed in commercial pools/spas. If you want to make yourself sick in your own home, the government is not going to prevent you from doing so.
As for the oxidation, that is standard electrolysis mostly producing hydrogen and oxygen gasses. They are using titanium plates rather than boron-doped-diamond electrodes so their claim of producing hydroxyl ions (OH•) while technically true is in such low amounts as to be irrelevant. Depending on the salt level in the pool, there will be a small amount of chlorine produced and any disinfection and oxidation will likely come from the chlorine, but it is not enough in amount to maintain a chlorine residual in the bulk pool water and kill bacteria shed from bathers nor pathogens growing on pool surfaces. Obviously, with the pool being cloudy, this oxidation system isn't very effective.
As for the CL Free system and company, it has an A+ rating from the BBB, but has a complaint at ripoffreport.com and there's some interesting bantering in this thread.
Of course, we all know about the problems of copper ions in pools where one must very carefully control the copper ion concentration to prevent it from getting to high and must also control the pH to keep it low as well. Otherwise, copper can stain pool surfaces and can also make blond hair turn greenish.
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