I used polysorbate with water and essential oils but the mixture has turned murky with a layer of oil on top. What did I do wrong?
You say ‘mixture’, but I’m not clear what you are making; water and essential oils with polysorbate could be a home-made perfume mix?
There are various Polysorbates and some are better suited for combining oily substances with watery ones. I think you probably need Polysorbate 20, although 80 would still combine them. It does rather depend on the quantities you have of each and so the percentages you are working with.
My guess is that you are using more water than essential oils and you are hoping to dilute the oils with water to use as a non-alcohol based perfume. So, again, this is a rough guide, whatever amount you have of essential oils, you need to add the same of Polysorbate 20. Mix the oils with the Polysorbate first and then, slowly add the water whilst stirring.
To make the essential oils safe to use on your skin (if that’s where they are going), you need to know which you are working with and find their recommended maximum levels, if you don’t know, dilute to 1%, but be very sure that you have none in there that are banned for perfume use - see IFRA guide or EEC/ Robert Tisserand has a very good book on the safe limits of essential oils (he doesn’t always agree with IFRA, but he will explain why when he doesn’t) The Safety of Essential Oils - Tisserand and Young.
Also be aware that whilst this should disperse the oils for a while, they will eventually separate and you will need to shake the mixture to re-distribute the EOs.
As a guide on Polysorbates:
Polysorbate 20: An emulsifier for oil-in-water emulsions. The main medium is water and you are mixing oil into it. It will evenly disperse the oil throughout the water.
Polysorbate 80: An emulsifier for water-in-oil emulsions. The main medium is oil (not essential oils, carrier oils). This keeps the water droplets dispersed in the oil (so they don’t all join together again in a puddle).