J. Phys. Chem. 1987, 91, 4055-4057 where means the average over the potential V,(r",A). By using this method, Stroud and Parsonageso have calculated the configuration integrals for various numbers of spherical LennardJones molecules in a zeolite cavity. The most subtle condition to be satisfied in the application of the A-integration method is that the interaction potentials in the reference system should have a hard core.l0 If the reference potentials are less hard than the real potentials and A is small, the distribution factor exp[-U,(r",X)/kT] permits close approaches of the sorbates. These configurations of the sorbates make large contributions to (Avfi,(F))x. For large values of X this will not happen. Nevertheless, on account of the uncertainties in ( Avfi,(rn))Xfor small X, the value of the integral in eq 35 will be unreliable. If the SSI potentials of the reference system have a hard core, z ',is no longer (2,)". The evaluation of such z ',was carried out by determining the fraction of randomly generated configurations which do not cause overlap of the spheres. The accuracy of the estimation, however, rapidly decreases as the sorbate concentration becomes higher (the "free volume" for each sorbate decrease^).^' On the other hand, in the present M C method, MT[Avfin(rn)] in eq 24 is nearly zero for close-encounter configurations. Even if the SSI potentials in the reference system have no hard core (like our choice), (MT[AU'in(r")])i would converge to nonzero on condition that system 1 (the first intermediate system) has a sufficiently small hard core (convergence to zero does not make sense unless z', = 0). This convergence is assured by choosing such a size of hard core that does not cause overlap of the sorbates a t high probability during the configuration space sampling governed by o,,.Of course, as the size of the hard core becomes small the convergence gets quicker, but more intermediate steps are required. Another advantage inherent to the present method As .was mentioned before, is that one can use Z, for evaluating z',, (50) Stroud. H. J. F.:Parsonage. N. G. In ref 2: D 138. ( 5 l j (a) Coldwell, R.'L. Phys.-Rev. 1973, A7, 276. (b) Coldwell, R. L. Phys. Rev. 1974, AIO, 897.
4055
2,is determined accurately with relative Equation 1 has been derived on the condition that the translational motion of the sorbate molecule in a cavity can be treated classically. Sorptions of Ar and N2 molecules in zeolite 4A satisfy this condition. However, if the molecule is sorbed at the cryogenic temperature or if the mass of the molecule is small like H,, the partition function for the translational motion must be calculated in the framework of quantum mechanics. In fact, the sorption amount of D, in zeolites is larger than that of H,; that is, the Henry's law constant KH for D2,KH(Dz),is larger than KH(H~)." This difference is ascribed to quantum effect because in classical statistical mechanics the amount of sorption is independent of the mass of the sorbate molecule (note that A = A'). Recently, many groups have been challenging quantum Monte Carlo simulat i o n ~ . ~This ~ - ~research ~ area is intriguing, but in this paper we restrict ourselves to giving a.genera1 remark upon quantum effect of sorption: if the AS1 potential is flat in the cavity, KH(D2)/ KH(H2)Y 1 (this can be understood by imagining a particle in a box which is as large as the size of the zeolite 4A cavity); if the AS1 potential has been local trap sites in the cavity, KH(D2)/ KH(H2) > 1 . The deeper the trap sites are, KH(D2)/KH(H2) becomes larger. Quantum mechanical treatment for sorption is now in progress.
Acknowledgment. We thank Mr. Y. Matsuda for his assistance in preparing the original figures. H.K. expresses his appreciation to Professors Masatoki Ito and S. Ohba for helpful discussions related to zeolite 4A structure. This work was in part supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan (61740241). ___ Barrer, R. M.; Craven, R. J. B. In ref 6; p 521. Freeman, D.L.; Doll, J. D. J . Chem. Phys. 1984, 80, 5709. Takahashi, M.; Imada, M. J . Phys. Soc. Jpn. 1984, 53,963. Suzuki, M.; Miyashita, S.; Kuroda, A. Prog. Theor. Phys. 1977, 58, ~~~
(52) (53) (54) (55) 1377.
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Kinetics of Phase Transformations In Microemulsion Systems Rich in both Water and 011. Fast Liquid Crystal Formation and Isotropic Rearrangements C. Tondre* and C. Burger-Guerrisi Laboratoire d'Etude des Solutions Organiques et Colloidales (L.E.S.O.C.),Unit; Associde au C.N.R.S.No. 406, Universitd de Nancy I , B.P. No. 239, 54506 Vandoeuvre-IPS-Nancy Cedex, France (Received: January 22, 1987; In Final Form: March 27, 1987)
The temperature-jump technique has been used to investigate the kinetics of phase transitions in microemulsion systems including a fluorinated oil, a fluorinated nonionic surfactant, and salted water. The time scale involved in two types of structural transitions has been characterized from turbidity or birefringence measurements. For the particular compositionsinvestigated, the lamellar liquid crystal formation can be completed in less than 100 ms, whereas the transition between two different isotropic phases is taking place within the heating time of the solution (T,, = 15 ws).
Introduction Ternary systems including water, an oil, and a nonionic surfactant of the alkyl polyether type are generally very sensitive to temperature changesL This is mainly due to the particular solubility behavior of the polyether moiety which is characterized by the existence of a cloud point arising at a well-defined temperature in water (1) Kunieda, H.; Friberg, S.
E. BUN. Chem. SOC.Jpn.
1981, 54, 1010.
Shinoda, K.; Saito, H. J . Colloid Interface Sci. 1968, 26, 70. Shinoda, K.; Kunieda, H. J . Colloid Interface Sci. 1973, 42, 38 1. Kunedia, H.; Shinoda, K.J . Dispersion Sci. Technol. 1982, 3,233.
0022-36541871209 1-4055$0 1.50/0
When an oil is present in the system, the "phase inversion temperat~re"~ (PIT) corresponds to the temperature at which the surfactant solubilizes preferentially in the oil phase, but the inversion is generally taking place over a certain temperature inter~al.~ Because of this peculiar behavior of nonionic surfactants, phase transitions in such systems can be induced by a simple change (2) Florin, E.; Kjellander, R.; Eriksson, J. C . J . Chem. Soc., Faraday Trans. I 1984, 80, 2889. (3) Friberg, S.; Lapczynska, I.; Gillberg, G. J . Colloid Interface Sci. 1976, 56, 19. (4) Kahlweit, M.; Lessner, E.; Strey, R. J . Phys. Chem. 1983, 87, 5032.
0 1987 American Chemical Society
4056 The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
Tondre and Burger-Guerrisi
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Birefringence Signal (a.u.1
a 40
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20lime ( m s e c )
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Figure 1. Temperature-composition phase diagram of the system W ~ ~ ~ ~ / C ~ F , , C H = C H ~ / C ~ FThe ~ ~concentration C H ~ ( E O )of~surfac. tant is fixed at 24.7% in C8F1$H=CH2, but it varies with the addition of water, so that the composition is 25.1, 56.4, and 18.5 wt 76 on line 1-2-2’and 31.9, 51.3, and 16.8 wt %on line 3-4 respectively for water, fluorocarbon, and surfactant. The arrows indicate where the temperature-jump experiments have been performed. of temperature. The Joule-heating temperature-jump technique5 is a powerful tool for studying the kinetics of these phase transformations when they are faster than a few seconds. The energy created from the discharge of a high-voltage capacitor is dissipated in the system in a few microseconds, and the reorganization of the solution can be followed by different means. Turbidity and birefringence have been used for instance to monitor the kinetics of phase transitions in binary systems of CI2EO6and water in the presence of an added s a k 6 We report here on some preliminary results obtained with a system including a fluorinated nonionic surfactant, a fluorinated oil, and water (with an added electrolyte necessary for the system to be conducting). We show that, for this particular system, fast liquid crystal formation as well as fast isotropic rearrangements can occur. In some instances we have made use of the information contained in the signal transmitted by the system when it goes back to its initial temperature equilibration, which is not a usual way of using the temperature-jump technique. These experiments were expected to give us an insight into the structural organization of these systems. Experimental Part The temperature-jump apparatus and cell used for the kinetic experiments were standard equipment purchased from Messanlagen Studienges mbH (Gottingen). The resistance of the solution was in the range 500-600 a, and the capacitance of the highvoltage discharge capacitor was 50 nF. A heating time of 12-1 5 gs can be estimated from these values. The apparatus was on-line to a Biomation 805 transient recorder interfaced to an NM 4/30 Computerautomation computer. The data can be transferred to a Tektronix 4662 digital plotter. The chemicals used were of the same origin as in a preceding paper: in which was determined a temperaturmmposition phase diagram for the system of interest here: C6FI3CH2(OCH2CH,),0H/C8F17CH=CH2/water. The phase limits were shifted down by about 3 O C by the addition of sodium chloride (0.1 M over the total solution volume). Only one-phase regions had been previously documented.’ The liquid crystalline phase was identified through crossed polarizers. Results and Discussion Figure 1 shows that the existence domain of the isotropic phase results from the interconnection of two monophasic regions. By ( 5 ) Eigen, M.; de Maeyer, L. In Techniques of Organic Chemistry; Wiley-Interscience: New York, 1963; Vol. VIII, Part 2. (6) Knight, P.; Wyn-Jones, E.; Tiddy, G . J. T. J . Phys. Chem. 1985, 89,
-7447 . ...
(7) Robert, A,; Tondre, C. J . Colloid Interface Sei. 1984, 98, 515.
0
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Figure 2. Change of birefringence with time along path 1-2-2’ for different capacitor voltages corresponding to AT = 0.75, 1.35, 1.75, 2.15, 2.6, 3.25, and 3.8 OC. The light received by the photomultiplier is increasing downward. analogy with other systems,* in which the two areas are usually not connected (but this may depend on the surfactant concentration), it can be assumed that the upper region has a water-in-oil structure whereas the lower one would be oil-in-water. In the interconnected part a continuous transition from o/w to w/o could thus be possible just by increasing the temperature, unless a bicontinuous structure prevails all through the temperature interval. On both sides of this interconnected domain, a liquid crystalline phase is separating the two isotropic regions. The exact limits of the liquid crystalline phase, which appeared to be bordered by a region of coexistence with a neighboring isotropic phase, are very hard to ascertain in such ternary systems. This is due (i) to the difficulty of detecting the presence of a very small amount of another phase and (ii) to the fact that weak thermal gradients are never completely impossible in the thickness of the examined sample. For this reason, the LC area has been bordered by dashed lines in Figure 1. Temperature-jump experiments have been performed at two different compositions as indicated by the arrows shown in Figure 1: from the lower isotropic phase to the liquid crystalline phase (path 1-2 (2’) in the figure) and from the lower isotropic region to the upper one (path 3-4). The liquid crystalline phase was used to follow the kinetics either from the change of the intensity of the transmitted light (turbidity) or from the appearance of a birefringence when working with polarized light. Fast Liquid Crystal Formation. An isotropic mixture of composition represented by “1” in Figure 1 was successively brought to the situations represented by “2-2”’ by a temperature-jump AT. The formation of the liquid crystal was followed by birefringence, crossed polarizers being placed respectively at the entrance and exit windows of the T-jump cell. The results obtained when varying the capacitor voltage (and thus the are shown in Figure 2. For the lower capacitor voltages (9-12 kV), the final temperature falls in the turbid region noted “LC + isotropic” in Figure 1, and the signal detected is slightly increasing during the first milliseconds. In this case and during a short time, the turbidity contribution is larger than the birefringence itself. For larger voltages (13-16 kV) the final temperature is within the area noted “LC” in Figure 1, and the amplitude of the relaxation signal received by the photomultiplier is increasing with the voltage up to 15 kV. In fact, a turbidity component can always be superimposed on the birefringence signal, and an additional devie would be needed to remove the turbidity contribution and get the pure birefringence signal. Nevertheless, the relaxation time characterizing the formation of the liquid crystalline phase appears to be in the range 25-30 ms or even shorter. A possible complicating factor in these experiments may come from an orientation effectgJOof the liquid crystal in the electric
An
(8) Harusawa, F.; Nakamura, S.; Mitsui, T. Colloid Polym. Sci. 1974, 252, 613. (9) Dourlent, M.; Hogrel, J. F.; Helene, C. J . Am. Chem. Sac. 1974, 96, 3398. .. . (10) Neeson, P. G.; Jennings, B. R.; Tiddy, G. J . T. Chem. Phys. Lett. 1983, 95, 533.
Phase Transformations in Microemulsion Systems
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 4057
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Figure 3. Change of turbidity with time during the thermal return along path 4 3. T h e light received by the photomultiplier is increasing downward.
field. In this case we would expect to see the disorientation effect and not the establishment of the birefringence, which should take place during the very short time where the electric field is effectively applied to the solution. In addition, the orientation would be expected to depend on the electric field strength whereas we have checked that almost identical relaxation signals are obtained for different capacitor voltages, provided that the final temperature is the same. The nucleation process leading to the formation of a liquid crystalline phase appears thus to be much faster here than for the phase transitions observed in the case of concentrated C12E06/waterbinary systems, for which the overall time scale was in the range 0.4-3 5.6 Fast Isotropic Rearrangements. A second p i n t of interest was to study how fast can be the transition represented by the path 3-4 in Figure 1: does the system have to get through the formation of the liquid crystalline phase? In this case we have used turbidity measurements instead of birefringence to answer the question. The results show that the rearrangement is completed within the heating time of the solution. This is demonstrated by two different observations: (i) the solution is clear immediately after the temperature jump (the amount of transmitted light is identical for the solutions represented by points 3 and 4 in Figure 1) and remains clear for the time allowed before the thermal return is assumed to take place; (ii) the change of transmitted light when the system goes back to its initial temperature (thermal return)
follows exactly the turbidity change expected along the path 3 4 (see Figure 3). There is thus no doubt that the state of the system after the temperature jump was corresponding to the upper isotropic phase. Another explanation of Figure 3 could have been that the system has started building up the liquid crystalline phase and then has come back to its initial state before reaching the upper isotropic region. Considering the time scale involved and the rate of formation of the liquid crystal as obtained in the preceding section, this explanation can be safely ruled out. A so fast rearrangement between the two isotropic phases is very likely indicative of a small structural change which could just be the inversion of the curvature of the surfactant layers from a concavity toward the fluorinated oil to a concavity toward water, the structure being essentially bicontinuous. (Note that the volume fractions of fluorocarbon and water are both large for the particular compositions investigated here.) A quite comparable situation has recently been studied by Olsson et al.," who reported on the diffusion coefficients of the three components of the system ~ater/C,~(E0)~/n-C~~H~~, measured in two isotropic phases like those represented in Figure 1. The fact that only small changes of the diffusion coefficients are observed when going from one isotropic phase to the other is consistent with the present kinetic observation. A quantitative comparison of the rearrangement times expected for the inversion of a micellar phase on the one hand and for changing a bicontinuous structure on the other hand is not straightforward, but the first process would very likely require a time at least of the order of the micelle dissolution time. This time is unfortunately not known for the fluorinated surfactant used, which is not soluble in pure water. Nevertheless, considering that the micelle dissos for the Triton X-100 surlution time is of the order of factant,'* a time even longer should be expected for the present fluorinated surfactant, which is less hydrophilic, whereas the rearrangement is completed within the heating time of the solution. These preliminary results have shown the interest of temperature-jump studies in certain microemulsion systems, and they have given an idea of the time scale involved in different types of structural transitions. More experiments are needed to go deeper into the understanding of the present results, which have to be correlated with observations from other techniques. A full report will be given in a forthcoming paper. (11) Olsson, U.; Shinoda, K.; Lindman, B. J . Phys. Chem. 1986, 90, 4083. (12) Herrmann, C. U.; Kahlweit, M. J . Phys. Chem. 1980, 84, 1536.
