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Why does Luxfer require cleaning for oxygen concentrations above 23.5%?

Few concepts have caused more confusion and controversy in the recreational diving industry than the so-called "40% rule." While there seems to be general agreement that special cleaning is required when a pressurized oxygen concentration reaches a particular "threshold" percentage, there is disagreement about exactly what that threshold should be and at what pressure it becomes important. Some say 40%; others say 23.5%; still others say anything more than 21% when a gas mixture is pressurized more than 100 psig. It would be helpful to explore the background of this confusion briefly before discussing Luxfer's position on this vital subject.