From what I've read, there are three classifications: soft, hard, and brittle. Soft are those that are liquid at room temps; hard are those that are solid, but scoopable at room temps (mango butter, Shae butter, palm oil, coconut oil, etc); and those that are brittle are hard at room temp but also brittle, requiring some muscle to get the amount needed to be removed (Illipe butter, and cocoa butter). I have to take a knife and chip away at my Illipe butter, same with the cocoa butter.
Also, both the hard and brittle oils/butters will help create a harder bar when combined with soft oils. If only soft oils are used to make soap, soap will be softer vs those that have a combination. The exception is Olive oil, a soft oil but one that, even at 100%, will yield a hard bar. It takes a long time to cure though, shorter if made with much less water. It traces very slowly so it takes well to a large water reduction. I can't remember what my water to lye ratio was because it was years ago when I made my bastille soap; it was 80 Olive, 15% C.O. and 5% castor.
Fatty acids that contribute to a hard bar of soap are as follows: Lauric, Myristic; Palmitic; and Stearic. Coconut oil has a 79% combination of these:
Palm Oil has a combination of 50%:
Take a look at the combined 4 fatty acids in Babassu oil (85%):
A hard bar doesn't necessarily equal longevity; out of the 4 fatty acids that help create a hard bar of soap, two are responsible for durability--stearic and palmitic. Lauric and Myristic are responsible for the cleansing quality in soap. Coconut oil has about 48% Lauric acid and that's why it can be drying if used in high percentages. It has only a 12% combination of Stearic/Palmitic. Lard, on the other hand, is high in fatty acids that make for a long-lasting bar; 41% combined Stearic/Palmitic.....but only 1% Myristic/0 Lauric, so it's not drying like Coconut Oil.....and that's why I like using it even though (sorry vegans) it's animal fat. If no one found uses for the fats from animals that are killed for human consumption then there'd be much waste; I see using it as being environmentally responsible--waste not/want not. If an animal is going to be used for food, others might as well use all of the animal. That's just me though. Oh, and Lard has 46% Oleic acid which is good gives soap moisturizing/conditioning qualities; Argan has the same % of Oleic as Lard. It, however, has only 6% of Linoleic while Argan has 34% and this fatty acid also holds moisturizing/conditioning properties.
Getting back on track, the length of fatty chains has something to do with soap's durability. Stearate is composed of (I think) 17 carbons chains. Lauric has 12 carbon chains so, while it will add to hardness, it won't be as longlasting in soap as Stearic acid will be. Palmitic, like Stearic, is a long fatty chain, having a 16-carbon backbone. I wish I knew as much as many here in this forum (I'm learning and read A LOT) but I hope the sites below can help you in your journey of soap making. Many are so helpful to list sites that are so helpful so maybe some will add to this list for ya.
Oh, I will add that I got my %s from SoapCalc (my primary
soap calculator):
http://soapcalc.net/calc/soapcalcwp.asp. I think it is probably off a tiny bit from those who actually know first hand the fatty acid percentages of various oils.
Sites you might be interested in:
*
https://www.modernsoapmaking.com/the-most-popular-fatty-acid-profiles-in-soapmaking/
*
https://www.lovinsoap.com/oils-chart/
*
http://www.soap-making-resource.com/fatty-acids-soap-making.html
*
https://vula.uct.ac.za/access/content/group/9eafe770-4c41-4742-a414- 0df36366abe6/Chem%20Ind%20Resource%20Pack/html/learner-sheets/C/LS_C7.pdf