PHYSICAL REVIEW E VOLUME 47, NUMBER 3 MARCH 1993 Critical behavior of a three-component microemulsion R. Aschauer and D. Beysens Seruice de Physique de 1'Etat Condense, Centre d'Etudes de Saclay, 91191 Gif sur Yue-tte CEDEX, France (Received 28 May 1992) The critical behavior of a ternary microemulsion consisting of water, benzene, and benzyldimethyl-n- hexadecylammonium chloride is studied by light-scattering techniques, controlling temperature to ap- proach the critical point. This microemulsion is chosen since it is very stable. Great care was taken to ensure the measurements were performed at the critical concentration, and a wide range of temperature was covered. According to theory, one expects Fisher renormalized Ising critical exponents in a ternary mixture when temperature is the controlled variable. Contrary to this expectation, we find values of the exponents y = 1. 18+0.03 and v=0. 60+0. 02 indicating rather unrenormalized Ising-like behavior of ter- nary microemulsions. PACS number(s): 05.70.Jk, 64.60.Fr, 82.70.Kj I. INTRODUCTION The critical behavior of microemuslion systems is a to- pic of considerable interest. It has been shown that the phase transition is driven by increasing interactions be- tween droplets while leaving their size and polydispersity unchanged, and that the two separated phases are again microemulsions with equal droplet size distribution [1,2]. The order parameter is the volume fraction of droplets [1]. Measurements of the values of the critical exponents describing the divergences of the susceptibility and corre- lation length, y and v, have been performed in five- [3,4], four [5 — 7], and three-component [8 — 12] microemulsions. In a three-component system, the critical exponents are expected to be Fisher renormalized with respect to the respective exponents in a binary mixture if one varies temperature to approach the critical point [13,14]. The theoretical renormalized values y* and v* are y*=y/(I — a)=1.39 and v*=v/(1 — a)=0. 70 [with the three-dimensional (3D) Ising values of y=1. 24, v=0. 63, and a=0. 11, a being the exponent of the specific heat]. Also the exponent of the coexistence curve, p, should be Fisher renormalized, becoming P" =P/(1 — a) =0. 365 (with the 3D Ising value of p=0. 325). However, it was shown by Fisher and Scesney [15] that full renormaliza- tion will be visible experimentally only if the third com- ponent causes a large shift in the critical temperature T, such that the parameter x defined as x =f(T, — T, )/T, becomes of the order of unity. Here f =0. 6 to 0.9, T, is the critical temperature of the binary system, and T, is the critical temperature of the ternary mixture. Such a renormalization has been shown experimentally in a number of diff'erent ordinary ternary mixtures [16 — 19], although the values for y* and v* appear to take on rath- er values of y*=1.50 and v*=0. 75, respectively, that is, different from theoretically expected values. Ternary mi- croemulsions can be seen as good candidates in which to see Fisher renormalized exponents since the binary sys- tem of water and oil is practically immiscible, which cor- responds to a T, of infinity, and only the addition of a third component, the surfactant, creates a partially misci- ble system with a finite critical temperature T, . Hence the parameter x becomes large. The experimental situation on ternary microemulsions, however, is far from being clear. In a neutron scattering study, Kotlarchyk, Chen, and Huang [9] obtained ex- ponents of y = 1.61 and v = 0. 72. A light-scattering study by Huang and Kim [8] gave y = 1. 22 and v=0. 75, and Honorat, Roux, and Bellocq [10] measured values of y = 1.30, y = 1.25 and v=0. 76, v=0. 71. All these groups used the water-decane-AOT (sodium di-2- ethylhexylsulfosuccinate) system (which we define as WDA). Jayalakshmi and Beysens [12] determined y and v from turbidity measurements in the system water- benzene-BHDC [benzyldimethyl-n-hexadecylammonium chloride, C6Hs. CH2(CH3)2(C, 6H33)NC1] (which we define as WBB), but coupling between y and v in this type of ex- periment is such that they could not discern on purely ex- perimental grounds between Ising and renormalized Ising exponents. In all these cited experiments, temperature was used as the controlled parameter to approach the critical point. The values of the critical exponents depend on the path that one chooses to reach the critical point [20]. One can vary fields other than temperature as the controlled ex- perimental variable, which should, in general, lead to different apparent values of critical exponents. In mi- croemulsions the water-to-surfactant ratio (W-to-S ratio) X was shown to behave like a field variable [21]. Honorat, Roux, and Bellocq [10] varied X to approach the critical point at constant temperature in a water- de cane-AOT micr oemulsion and obtained values of @=1.26 and v=0. 61. In the same system, Kim, Bock, and Huang [11] performed a light-scattering experiment where they varied the pressure to approach the critical point while keeping temperature constant. This gave values of y =1.50 and v=0. 70. The experimental results obtained so far for ternary microemulsions are summa- rized in Table I. For the experiments where temperature was the con- 47 1850 1993 The American Physical Society