I was afraid someone would ask.
Okay, here goes. LOL Be warned, but this is probably going to be a LONG post.
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Elemental iodine is
very poisonous. Sodium iodide less so, but also poisonous. Drinking just a mouthful of Betadine for example could make you
very, very ill in a very short time or even kill you, so don't try that at home, kids! You don't swallow tooth soap though, so any danger from toxicity would be absolutely minimal if the soap curds happened to contain iodine or iodide. Iodide
is a halogen "relative" of fluoride and reacts in pretty much the same way, with the same things, Chloride, too. They're chemical equivalents. If someone has issues with fluoride (I don't) they might like to avoid iodine/iodide too. I wouldn't be concerned about it, but others might.
When you're removing the glycerine from the soap by using brine, what you're doing is creating a common ion situation. (Sodium hydroxide, sodium chloride and the sodium soap salts.) All those sodium ions is what causes the soap salts to precipitate out as curds, as they are the least soluble of the bunch. The solution simply cannot hold so many sodium salts. (Sodium iodide would add to the common ion situation as well, if using iodized salt.) Iodine/ iodide might possibly function as an antimicrobial in a tooth soap, (its use there being purely topical) but iodine is yellowish/purplish/black coloured and it stains. An iodine and potassium iodide solution is the stuff they use in hospitals on your skin to disinfect. That's the stuff that turns your skin yellow/brown. It's also used as a cell stain in labs and it's used in the dental profession as a mucogingival stain. It gives you funky coloured teeth. LOL .You used to be able to get a Betadine mouthwash to treat oral infections, but it has been discontinued many places and it was only recommended for very short term use. It stained the teeth brown. Not really all that attractive. LOL If anyone is familiar with "Betadine" you know how it stains. Having as little iodine/iodide in one's soap curds as possible might be desirable for that reason, too .
Also, the higher the iodine, the softer the soap. The iodine value is a measure of the saturation of a fat or oil. Saturated fats have low iodine values, and unsaturated fats have high iodine values. I have never made soap curds or toothpaste out of them, so I don't know if that would be an issue, but high iodine levels will shorten the shelf life of your soap. I suspect tooth soaps are kept around for a long time since you use so little of it each time and the thought of waking up one morning and sticking a toothbrush full of rancid soap in my mouth doesn't really sound all that appealing. LOL Hence you want to try and keep the iodine levels low for that reason too. Using iodized salt to precipate the soap curds can't be helpful towards that end.
So, to sum it up, it won't kill you to have iodine/ iodide (or fluoride) in your tooth soap or paste. Not at all. I myself don't have any fears regarding it's toxicity, but I
would mind if my soap went rancid too soon or if there was any chance that prolonged use could cause any issues with discolouration.
WOW. Sorry about the marathon rant folks. I never have been good at keeping things short, but that explains my previous suggestion to not use iodized salt and that goes especially if you also plan on recovering the glycerine from the brine solution later on. Since it's water soluble, there would be a relatively high amount of iodine in that solution. Why compromise the soap (or the glycerine) when it's not necessary.
Rant over!