Lye relaxer are harder on the scalp easier on the hair. They contain sodium hydroxide, which has the highest pH on the pH scale, but its stable, so it requires no mixing. They last longer because since no mixing is involved, if you have some left over, you can use it later. When it touches the scalp, it burns after a while, so you need to base the scalp the well. It takes a while for lye to process the hair, so it is favored among those who like a looser texture but can be used bone straight textures. It doesn't leave chemicals behind so you put it in, wash it out.
No-lye relaxers are easier on the scalp but harder on the hair. They contain calcium or guanidine hydroxide, which has a lower pH and requires mixing before it can work. It cannot be saved once mixed, just use before the chemicals break down. When it touches the scalp, it won't irritate it but will process the hair faster so the hair gets straight faster. It does leave chemical deposits behind, so you have the chelate the hair after you relax or within 3 weeks or you will experience breakage.
It's all a matter of preference. If you want a straighter texture, no lye might be a better option though you can still achieve straight hair with lye relaxers. It easier to just loosen the curl with lye though. After using both, I definitely prefer lye though.
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