Liquid–liquid coexistence curves of re-entrant phase transitions beyond the asymptotic range: tetrahydrofuran + water and tetrahydrofuran + heavy water

Abstract

We report on the coexistence curves of mixtures of tetrahydrofuran (THF) with water and heavy water over four decades in reduced temperature, from about 35 to 0.01 K from the lower consolute points. The compositions of the coexisting phases are determined by refractive index measurements. For each system the universal asymptotic critical behaviour and the non-universal behaviour further away from the critical point are analysed using several choices of the order parameter. The volume fraction is found to form the optimum order parameter. Several definitions of the reduced temperature are tested which account for the simultaneous presence of an upper consolute point at about 65 K above the lower consolute point. The behaviour of the effective critical exponent and the signs and amplitudes of the Wegner corrections to scaling are discussed with regard to regular contributions to the order parameter and mean-field criticality further away from the critical point.