J . Phys. Chem. 1990, 94, 3726-3728
3726
Conductlvity Fluctuation of a Microemulsion System at Transition Temperature Maki Ito, Noboru Takisawa, and Keishiro Shirahama* Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan (Received: July 17, 1989; In Final Form: November 28, 1989)
A ternary system containing water ( I O mM NaCI), toluene, and Triton X-100 (40:40:20 wt %) shows a transition from a water continuous phase to an oil continuous one with a drastic change in electric conductivity around 33-34 O C with an increase in temperature. A conductivity fluctuation from the emulsion placed in a capillary is measured. The mean square of the amplitude of the fluctuating signal becomes a maximum at a transition temperature, T, = 33.6 OC. The time-series data are analyzed by Fourier transformation to obtain a power spectrum of Lorentzian type superposed on a Ilfspectrum. The relaxation frequency decreases as the temperature approaches the transition temperature.
Introduction Microemulsions have attracted the attention of many researchers not only because of their useful application in industry but also as intriguing phenomena in science. In order to fully understand the subject, it is necessary to make both static and kinetic studies. Perplexingly complex multicomponent phase diagrams are the basis of the static research, and relevant knowledge has been accumulated.'-3 As for the kinetic study, there have appeared several papers dealing with microemulsion systems by utilizing relaxation method^,^^^ light scattering,6 and fluorescence methods.' The electric conductivity of microemulsion systems shows complicated changes reflecting very complex phase behaviors. Inversion from a water continuous phase to an oil continuous phase is especially interesting since it is accompanied by a very drastic change in electric conductivity, where a marked fluctuation is expected as a sign of dynamics occurring at the phase boundary. Actually, the electric conductivity fluctuation has been measured to obtain dynamic information from ionic c o n d u ~ t i o n , ~ionic .~ chemical reaction,1° and micellization" in a capillary, colloidal passage noise through a capillary ~ h a n n e l , ' and ~ , ~ ionic ~ conductance in a binary solvent near a critical ~ 0 n d i t i o n . I ~In the present work we also employed the same experimental technique as these to a microemulsion system containing 40% water, 40% toluene, and 20% Triton X- 100 (a typical nonionic surfactant), which shows a water-continuity to oil-continuity transition at 33.6 OC, as is shown later. This temperature is slightly above room temperature, so it was convenient to carry out the experiments.
X-100 was added 6 mL of water doped with N a C l ( l 0 mM NaCl solution) to impart electric conductivity. The whole mixture was vigorously shaken. Apparatus and Procedures. The block diagram of the whole experimental setup is shown in Figure 1. The ternary mixture was poured into a temperature-controlled cell, which was placed in a Faraday cage to shield any electromagnetic noise. The conductivity cell consists of a U-shaped glass tube separable at the center into two parts. In between them, a Teflon disk (1.13-mm thickness) with a small pore (0.5-mm diameter) was inserted, and the assembly was tightly fastened altogether. A constant electric current of 0.9 FA was fed from a driving battery (9 V) with a high resistor (10 MQ) connected in a series through a pair of platinum electrodes. The electric signals were detected by another pair of platinum electrodes immersed into both parts of the cell. The picked-up signals were sent to an amplifier (homemade, gain = 1000) with a low-pass filter (a cutoff frequency set at 5 kHz). A series of data (512 points) were sampled through an A / D converter (ADX-98, Canopus) with a sampling interval equal to 0.1 ms data point. This length of signal was Fourier-transformed to obtain a power spectrum
P v ) = (a2 + b 2 ) / 2
(1)
Materials. The toluene and Triton X-100 were obtained from Wako Pure Chemicals and used as received. The water was distilled twice. To a mixture of 6 g of toluene and 3 g of Triton
where a and b are the coefficients of real and imaginary parts of the Fourier transform, which was calculated by a computer program written in a machine language controlled by a BASIC main program. Power spectra were accumulated four times to improve the S / N ratio. The static electric conductivity was measured in a conventional dip-type conductivity cell by a conductivity meter (YokogawaHewlett-Packard, Universal Bridge Model 255a). Temperature was measured by a digital thermometer (TX560, SOAR) with a precision hO.1 "C.
(1 ) Micellization, Solubilization, and Microemulsion; Mittal, K. L., Ed.; Plenum: New York, 1977; p 713. (2) Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 2, p 627. (3) Suflactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 3, p 1501. (4) Sax, B.-M.; Schon, G.;Paasch, S.;Schwuger, M. J. frog. Colloid folym. Sci. 1988, 77, 109. ( 5 ) Tondre, C.; Burger-Guerrisi, C. frog. Colloid folym. Sci. 1988, 7 7 , 120. ( 6 ) Cazabat, A.; Langevin, D.; Meunier, J.; Pouchelon, A . Adi'. Colloid Interface Sci. 1982, 16, 175. (7) Jada. A.; Lang, J.; Zana, R. J . f h y s . Chem. 1989, 93, IO. (8) van den Berg, R. J.; de Vos, A.; de Goede, J . f h y s . Lett. 1981, M A , 433. (9) Musha, T.; Sugita, K. J . f h y s . Soc. Jpn. 1982, 51, 3820. (IO) Feher, G.;Weissman, M. froc. Natl. Acad. Sci. USA 1973, 70, 870. (1 1 ) Green, M.; Krishnamurthi, M. J . Colloid Interface Sci. 1989, 127, 295. (12) DeBlois, R. W.; Bean, C. P. J . Colloid Interface Sci. 1977, 61, 323. (13) Bezrukov, S.M.; Drabkin, G. M.; Sibilev, A . I . J . Colloid Interface Sci. 1986, 113, 194. (14) Kim, M. W.; Chou, Y. C.;Goldburg, W . I.: Kumar, A. f h y s . Reu. 1980, 22, 2138.
Results and Discussion Figure 2 shows the electric conductivity of the ternary mixture as a function of temperature. At low temperature, electric conductivity is very high, reflecting a water continuous phase, and at higher temperature, it is rather low. Between the two temperature regions, there is a drastic change of electric conductivity within a very narrow temperature range, where a slightly smoky-bluish transparent phase was observed. It is considered that a microemulsion is formed there. Above and below this temperature region, the whole system became opaque, indicating a macroemulsion formation. It is expected that the electric conductivity is fluctuating in the transition region. Figure 3 displays the time-series data of electric conductivity of the ternary system in the capillary, as measured by the apparatus shown in Figure 1, at temperatures along the transition region. The microemulsion in the conductivity cell near the transition temperature (e.g., 33.3 "C) has an electric resistivity of the order of lo5 R, which is mostly due to the tiny pore part. Thus, any fluctuation of signal must be the voltage fluctuation or, what is the same thing. the conductivity fluctuation originated from this
Experimental Section
0022-3654/90/2094-3726$02.50/0
0 1990 American Chemical Society
Conductivity Fluctuation of a Microemulsion System
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990 3727
7
1. 13nim
33
34 t e m p e r a t u r e / "C
0.5
Figure 4. Mean square of the amplitude of the time-series data: 0,
mm
ternary mixture; A, 10 mM NaCI.
p o r e
Figure 1. Schematic diagram of the experimental arrangement for the detection of the electric signals: A, amplifier, with low-pass filter; B, A/D converter: C, microcomputer (NEC PC-9801VX21); D, oscilloscope; E, high resistor (IO MQ); F, driving battery (9 V); G, switch; H, electrodes for detection; I, electrodes for driving.
I
i
2 3 4 f r e q u e n c y / ( lktlz )
Figure 5. Power spectra obtained by Fourier transformation at three typical temperatures vs frequency: A, below T,(32.6 "C); B, above T, (34.6 "C); C, at T, (33.6 "C). 31
32
33
34
35
5
07
36
teniperature/oc
Figure 2. Temperature dependence of the static electric conductivity of
the ternary mixture.
, 2
2
log [ rrequency/(kllz)
I
Figure 6. Logarithm of the power spectra versus logarithm of the frequency: A, below T, (32.6 "C); B, above T, (34.6 "C); C, at T,(33.6
"C).
time/(sec)
Figure 3. Time-series data of the electric conductivity of the ternary mixture at room temperatures around T,.
specific point, since the electric current is kept constant by virtue of the high resistor employed in the driving circuit. Figure 4 shows the mean square of the amplitude of the time-series data. It appears obvious that the nearer to the critical point (33.6 "C), the larger the fluctuation becomes. The data of 10 mM NaCl aqueous solution (triangles) were also plotted for comparison in the same scale on the same figure. They were very small and showed a monotonic increase with temperature, implying thermal noise.
It is considered that the observed fluctuation reflects the dynamics occurring in the microemulsion. In order to see the dynamic aspect of the fluctuation more explicitly, the original time-series data was Fourier-transformed to obtain a power spectrum, P v ) , in the frequency domain.I5J6 Figure 5 shows the power spectra of some typical cases. The salient feature can be noticed in the spectrum at the critical point, (15) Jenkins, G. M.;Watts, D. G. Spectral Analysis and its Applications; Holden-Day: San Francisco, 1968. ( 1 6 ) Marshall, A. G. Biophysical Chemistry, Principles, Techniques. and Applications: Wiley: New York, 1978.
3728
The Journal of Physical Chemistry, Vol. 94, No. 9, 1990
I
Ito et al.
frequPncy/( k t i z ) 1 2
Figure 7. {PV))-’ as a function offZ for the ternary system at T,. The data were smoothed by a moving average ( 5 points) method.
0
32
33
34
t e m p e r a t u r e / ‘C
while the spectra above and below T, are very small and look similar in shape and intensity. The logarithm of the power spectrum was plotted against the logarithm of the frequency in Figure 6 to show clearly the characteristics of the spectrum around the critical point. It indicates that the power spectra of the signals far from T, might be of the l/f type since the log-log plots give a straight line with a slope equal to -1. It is noted that the spectrum at T, deviates from l/f behavior. Now we assume that the fluctuation has a relaxation process. The rate process may be expressed asI6
Y = CY e x p ( - t / ~ )
(2)
where CY and 7 are the relaxation amplitude and the relaxation time, respectively, of the process. Thus, the power spectrum of a relaxation process called a Lorentzian spectrum, obtainable after Fourier transformation, is expressed as
wheref, = 1/(2nr)is the relaxation frequency, A is the amplitude, and B a constant, negligibly small in the present case. In Figure 7, {P(n)-I is plotted against f. Since a linear relation can be obtained close to T,, this spectrum may be considered to be Lorentzian, and the dynamic process must be a relaxation. It may be concluded that the relaxation process is superposed on a flickering random process (1 / f ) , I 5 * l 6 the latter being universally The amplitude and the relaxation observed in the ~
(17) Noise in Physical Systems and llf Noise; Savelli, M., Lecoy, G., Nougier, J.-P., Eds.; North-Holland: 1983.
Figure 8. Temperature dependences of the amplitude and the relaxation , amplitude ( A ) . frequency: 0,relaxation frequency cf,); .
frequency are shown in Figure 8. The amplitude reasonably has the same feature as the mean square amplitude directly obtained from the time-series data shown in Figure 3. The relaxation frequency appears to decrease as the temperature approaches T,. The frequency profile in Figure 8 may be rather truncated by such a factor as a too short sampling time (50 ms). It might be possible to observe an even lower f,around the transition temperature if the experimental setup is much improved. It is considered that the free energy difference between the electric conductive phase and the nonconductive phase becomes very small near T,. There are two aspects in such a situation. One is a passive side of the phenomena. The thermal agitation will make it easier to interchange the two states, leading to frequent occurrence of the event or percolative configuration^.^^ The amplitude increases. Another is an active side of it. The free energy difference is so small that the relaxation toward a stabler configuration may be very slow giving a large value of relaxation time, since the free energy difference could be a driving force of the process. What causes the relaxation is not known yet in the present work alone. It is necessary to carry out further studies, changing such parameters as composition and kinds of oil and surfactant and the geometry of the capillary before we arrive at a clear conclusion. Registry No. Triton X-100, 9002-93-1; toluene, 108-88-3. (18) Proceedings of Ninth International Conference on Noise in Physical Systems; Van Vliet, C. M., Ed.; World Scientific: Singapore, 1987. (19) Cazabat, A. M.; Chatenay, D.; Langevin, D. Faraday Discuss. Chem. Soc. 1982, 76, 291.
