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This work presents the novel discovery of room-temperature ionic liquids that are mutually immiscible, some of which are also immiscible with solvents as diverse as water and alkanes; an archetypal biphasic system is trihexyltetradecylphosphonium chloride with 1-alkyl-3-methylimidazolium chloride (where the alkyl group is shorter than hexyl).
Arce et al. (Sun,) studied this question.