JOURNAL OF COLLOID AND INTERFACE SCIENCE 203, 140–145 (1998)ARTICLE NO. CS985492

Coexistence Curves of a Critical Microemulsionof AOT–water–octane

Xueqin An,1 Jingyuan Chen, Youguo Huang and Weiguo Shen

Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, Peoples Republic of China

Received October 29, 1997; accepted February 19, 1997

droplet size determined by fixing the molar ratio v of waterThe coexistence curves of (T , n ) , (T , f ) and (T , C ) (n and f to AOT (2, 6) . For these mixtures, a lower consolute critical

are refractive index and volume fraction, respectively; C is defined point was observed. Above critical temperature Tc the mix-as CÅ f / [f/ fc (10f ) / (10 fc ) ] ) for a ternary microemulsion ture separates into two microemulsion phases of different[f(AOT–water) 0 (1 0 f )octane] at constant pressure and a

composition but with the same ratio v. Therefore such aconstant MOLAR ratio (40.8) of water to AOT have been deter-microemulsion system can be regarded as a pseudobinarymined within about 10 K from the critical temperature Tc bymixture (6–8). The phase behavior can be depicted in ameasurements of refractive index. This system can be regarded astwo-dimensional diagram with concentration of dropletsa pseudobinary mixture. The critical exponent b has been deducedalong the abscissa and temperature along the ordinate. Afrom (T , n ) , (T , f ) , and (T , C ) coexistence curves within 1 K

above Tc . They were 0.320, 0.325, and 0.320, respectively, and coexistence curve of temperature T against a concentrationwere consistent with the 3D Ising value. The experimental results variable, such as volume fraction f, can then be drawn inin a temperature range of (T0 Tc )õ 5 K also have been analyzed the same way as it was done for binary mixtures (1, 4) .to obtain critical amplitudes and the Wegner-correction terms, to Recently, we determined the coexistence curves for theexamine the diameters of the coexistence curves, and to discuss critical microemulsion of (water–AOT–decane) with v Åthe goodness of density variables for constricting order parame- 40.8 and fc Å 0.098, and observed an Ising value of expo-ters. q 1998 Academic Press

nent b (9) . As a continuing part of the study of criticalKey Words: microemulsion; critical phenomena; coexistencebehavior in the three component microemulsion, in this pa-curve; AOT; water ; n -octane.per we present coexistence curve measurements of a ternarymicroemulsion, consisting of water, n-octane, and AOT, atconstant pressure and a constant ratio v of 40.8 within aboutINTRODUCTION10 K range above the critical temperature. The experimentalresults are analyzed to determine the critical exponent b andCritical microemulsion and micellar systems are of con-to examine the size of asymptotical range and the anomaliessiderable interest because a controversy from experimentsof the diameters for different choices of order parameters.and theories was raised about whether these systems near

the critical points belonged to the 3D Ising universality classMATERIALS AND METHODS(1, 2) . Most of the experiments (2, 3) involved measure-

ments of critical exponents n, g, and a, which characterizeMaterialsthe divergence of the correlation length and osmotic com-

pressibility and the specific heat at constant pressure and The AOT surfactant was obtained from Fluka and purifiedcritical concentration. A few experimental studies (4, 5) according to a standard procedure (10). The n-octane (99have been carried out to determine the critical exponent b, mass per cent purity) supplied from Aldrich Chemical Co.which characterizes the shape of the coexistence curve, but was used without further treatment. The water was twicethe results were not precise enough to unambiguously sup- distilled from deionized water in our laboratory.port the Ising value or the Fisher renomalization value.

Determination of Critical Composition and CriticalThree-component mixtures of water, hydrocarbon, and theTemperaturesurfactant AOT (sodium di-2-ethylhexylsulfosuccinate) can

form water-in-oil (w/o) microemulsions of well-definedThe critical composition of the mixture was approached

by fixing the ratio v at 40.8 and adjusting the amounts of1 To whom correspondence should be addressed. n -octane to achieve equal volumes of the two phases at the

1400021-9797/98 $25.00Copyright q 1998 by Academic PressAll rights of reproduction in any form reserved.

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas

141COEXISTENCE CURVES OF A MICROEMULSION

critical temperature (11, 12) . The phase-separation temper- TABLE 1Coexistence Curves of (T,n), (T,f), and (T,C) for Microemulsionature of the mixture with the critical composition was care-

[f(AOT–Water) / (1 0 f)Octane)]afully measured and taken as the critical temperature. It wasobserved that samples of nominally the same composition

T 0 Tc n1 n2 f1 f2 C1 C2had different values of the critical temperature. Since thecritical temperature of a critical solution is known to be 0.045 1.3822 1.3818 0.067 0.115 0.416 0.564very sensitive to even a minute amount of impurities, this 0.051 1.3822 1.3817 0.069 0.122 0.424 0.582

0.074 1.3822 1.3817 0.065 0.124 0.410 0.586difference might be a result of uncontrollable impurities0.110 1.3822 1.3816 0.061 0.130 0.393 0.598introduced into the preparation of the sample or of the0.155 1.3822 1.3816 0.059 0.129 0.386 0.597hydrolysis of AOT. However, it did not affect the final0.248 1.3822 1.3814 0.053 0.144 0.359 0.627

results, because only one sample was used throughout the 0.402 1.3822 1.3813 0.045 0.150 0.319 0.639measurements of the whole coexistence curve and only the 0.669 1.3821 1.3810 0.041 0.163 0.296 0.660

0.986 1.3820 1.3806 0.037 0.172 0.277 0.674temperature difference (T 0 Tc ) was important in data re-1.311 1.3818 1.3805 0.036 0.183 0.272 0.691ductions to obtain the critical parameters. Therefore the1.635 1.3817 1.3803 0.034 0.194 0.260 0.706phase diagram of (T 0 Tc ) against a density variable is1.927 1.3815 1.3801 0.033 0.199 0.252 0.712

well reproducible. 2.236 1.3814 1.3799 0.032 0.205 0.250 0.7212.561 1.3812 1.3797 0.031 0.212 0.244 0.7282.894 1.3811 1.3796 0.030 0.215 0.237 0.732Measurements of Refractive Indexes3.189 1.3809 1.3794 0.031 0.217 0.239 0.7343.541 1.3808 1.3792 0.030 0.223 0.236 0.741The refractive indexes were measured by the method of3.928 1.3806 1.3790 0.031 0.228 0.244 0.746minimum deviation (11–13). The apparatus used in this4.279 1.3804 1.3788 0.033 0.231 0.251 0.750work was described previously (12). During measurements4.648 1.3802 1.3786 0.033 0.236 0.255 0.755

the temperature was constant to {0.001 K. The accuracy of 5.052 1.3800 1.3784 0.034 0.241 0.259 0.760measurement was about {0.01 K for temperature and 5.495 1.3798 1.3782 0.035 0.242 0.264 0.761

5.945 1.3795 1.3779 0.035 0.248 0.267 0.767{0.0001 for refractive index. A sample with the critical6.389 1.3793 1.3777 0.036 0.249 0.273 0.768composition was prepared in a rectangular fluorometer cell6.871 1.3791 1.3775 0.036 0.251 0.269 0.770provided with a Teflon plug. Continuous slow upward shifts7.375 1.3788 1.3773 0.036 0.250 0.270 0.769

of phase-separation temperature near the critical point were 7.861 1.3786 1.3771 0.036 0.251 0.270 0.770observed. The rate of shifts was determined by repeating 8.357 1.3784 1.3768 0.036 0.252 0.270 0.771

8.862 1.3781 1.3766 0.036 0.251 0.272 0.770measurements of critical temperature and was found to be9.883 1.3777 1.3761 0.025 0.255 0.206 0.764about 3 mK per day. It could be caused by a slow extraction

of impurities from the Teflon plug and the glass wall of the a Refractive indexes were measured at wavelength l Å 632.8 nm. Sub-cell or by a slow hydrolysis of AOT. A correction was made scripts 1 and 2 relate to upper and lower phases, respectively.to each observed temperature by subtraction of the shiftvalue. Several measurements with these corrections in heat-ing and cooling runs were consistent within experimental

in one-phase region at various temperatures were measured.uncertainties. This is evidence that the shift of the criticalThe results are listed in Table 2. With the assumption thattemperature does not affect the shape of the coexistenceno significant critical anomaly is present in the refractivecurve. The accuracy in measurement of temperature differ-index (14), the refractive index of the microemulsion mayence (T 0 Tc ) was about {0.002 K.be expressed as a linear function of temperature in a certaintemperature T range:

RESULTS AND DISCUSSIONS

n(f, T ) Å n(f, T 0) / (Ìn /ÌT )f(T 0 T 0) [1]The critical volume fraction of [f(AOT–water) / (1 0f)octane] was determined to be fc Å 0.091 { 0.001. The

(Ìn /ÌT )f Å f(ÌnA/ÌT ) / (1 0 f)(ÌnB/ÌT ) [2]critical temperature Tc was 321.195. The refractive indexesn of coexisting phases in the cell were measured at varioustemperatures. The results are listed in columns 2 and 3 of where T 0 is chosen as 323.5 K about the middle temperature

of the coexistence curves shown in Fig. 1, (Ìn /ÌT ) is theTable 1 and are shown in Fig. 1a for a temperature rangeof (T 0 Tc ) õ 5 K. derivative of n with respect to T , and (ÌnA/ÌT ) and (ÌnB/

ÌT ) represent the values of (Ìn /ÌT )f for f Å 1 and f Å 0,In order to obtain the (T , f) coexistence curve, a seriesof ternary mixtures of (water–AOT–octane) with known respectively. From the temperature dependence of refractive

indexes of pure n-octane listed in Table 2, the value of (ÌnB/volume fractions were prepared and their refractive indexes

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas

142 AN ET AL.

FIG. 1. Coexistence curves of (T , n) , (T , f) and (T , C) for [f(AOT–water) / (1– f)n-octane] . (a) Temperature T vs refractive index n ; (b)temperature T vs volume fraction f; (c) temperature T vs effective volume fraction C. (l) Experimental values of concentration variables (r) of thecoexisting phases. (m) Experimental values of diameter (rd) of the coexisting phases. ( —) Concentration variables (rcal ) and diameter (rd,cal ) ofcoexisting phases from calculation.

ÌT ) was calculated to be 05.0 1 1004 K01 . Rearrangement curve. One of the choices is to define an effective volumefraction C (1, 15):of Eqs. [1] and [2] yields:

C Å f / [f / R(1 0 f)] , [5]n(f, T ) Å n(f, T 0) / [f(ÌnA/ÌT )

R Å fc / (1 0 fc ) . [6]/ (1 0 f)(ÌnB/ÌT )](T 0 T 0) [3]

We converted (T , f) to (T , C) by Eqs. [5] and [6]. TheThe values of n (f, T ) listed in Table 2 were fitted to Eq.results are listed in the columns 6 and 7 in Table 1 and are[3] to obtain (ÌnA/ÌT ) , which was 02.5 1 1004 K01 , andshown in Fig. 1c for a temperature range of (T 0 Tc) õ 5 K.the values of n(f, T 0) . The small standard deviation of

The difference of concentration variables (r2 0 r1) may0.0002 in refractive index indicates that Eq. [3] is valid.be expressed by the Wegner expression:This allowed us to simplify the procedure of determination

of the dependence of n on f just by fitting a polynomialr2 0 r1 Å Btb / B1t

b/D / rrr. [7]form to n(f, T 0) for various f at T 0 . We obtained theexpression

where t Å (T 0 Tc ) /Tc , b and D are critical exponents, B1

is the amplitude of the first Wegner correction term, r is then(f, T 0) Å 1.3818 0 0.0083f 0 0.0009f 2 [4]concentration variable, and r1 and r2 are the values of r inthe upper and lower coexisting phases, respectively. In thewith a standard deviation õ 0.0002 in refractive index. Fig-region sufficiently close to the critical temperature, the sim-ure 2 shows the calibration curve of n (f, T 0) vs f. All ofple scaling is valid:our experimental data used in fitting Eq. [4] are in the range

of f Å 0–0.305, therefore extrapolating Eq. [4] to the ranger2 0 r1 Å Btb [8]of f ú 0.305 is unreliable. The values of refractive indexes

then were converted to volume fractions by calculating n(f,T 0) through Eq. [3] and iteratively solving Eq. [4] . The It is well known that the region of validity of Eq. [8] is

affected by the choices of the variables. A wrong choice ofresults are listed in columns 4 and 5 of Table 1 and shownin Fig. 1b for a temperature range of (T 0 Tc ) õ 5 K. the variable may cause a significant reduction of the region

of validity of Eq. [8]. The differences (r2 0 r1) of ‘‘density’’The choice of the concentration variable may affect thesymmetry and the size of asymptotic region of a coexistence variables of coexisting phases were fitted to Eq. [8] to

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas

143COEXISTENCE CURVES OF A MICROEMULSION

TABLE 2Refractive Indexes at Wavelength l Å 632.8 nm for [f(AOT–Water) / (1 0 f)Octane)] at Various Temperatures T

f T/K n T/K n T/K n T/K n

0.0000 315.631 1.3855 316.512 1.3851 317.262 1.3848 317.913 1.3844318.676 1.3840 319.777 1.3835 321.348 1.3827

0.0501 313.486 1.3863 314.834 1.3855 315.868 1.3850 317.216 1.3843318.517 1.3837 319.905 1.3830

0.0741 315.186 1.3853 315.755 1.3849 316.911 1.3845 317.596 1.3841318.526 1.3836 319.993 1.3829

0.0902 312.657 1.3860 313.683 1.3855 314.674 1.3851 315.473 1.3847316.127 1.3844 317.076 1.3839

0.1000 313.895 1.3857 314.504 1.3854 315.637 1.3848 316.698 1.3843317.803 1.3838 319.422 1.3831 320.678 1.3824

0.1253 313.814 1.3855 315.033 1.3849 316.253 1.3843 317.465 1.3838319.157 1.3830 320.564 1.3824

0.1507 313.487 1.3852 314.744 1.3846 316.332 1.3839 317.697 1.3833319.405 1.3825 320.596 1.3819

0.2000 316.249 1.3834 317.556 1.3829 318.976 1.3822 319.747 1.3819320.596 1.3814 321.686 1.3810 322.342 1.3807

0.2436 316.036 1.3832 316.859 1.3828 317.637 1.3825 318.441 1.3821319.413 1.3817 320.460 1.3813 321.146 1.3810 322.038 1.3805

0.2885 314.111 1.3836 315.050 1.3831 316.241 1.3826 317.287 1.3822318.519 1.3817 319.708 1.3812

0.3052 313.313 1.3834 314.271 1.3830 315.192 1.3826 315.838 1.3823316.668 1.3820 317.568 1.3816

obtain b. Table 3 lists the results of fits for three temperature critical point. The significance of the first Wegner correctionterm may be qualitatively indicated by the ratio of ÉB1 /BÉ.ranges of (T 0 Tc ) õ 10 K, (T 0 Tc ) õ 5 K and (T 0 Tc )

õ 1 K . The values of b for the three choices of variables The value of this ratio for f is significantly smaller thanthat for n and C, which implies that f is the best variablen , f, and C increase as the temperature range reduced.

Although the error in determination of b is as large as among the three. This is in contradiction with that reportedby Martin et al. (1) and is in agreement with our previous{0.01, all the values of b for the three variables in the

temperature range of 1 K approach to 3D Ising value within work (9).It is well known that when a good variable is used toexperimental uncertainties and obviously inconsistent with

the Fisher renomalized value of 0.365. The value of b for construct an order parameter, the diameter of the coexistencecurve may be expressed asf is most close to the Ising value of 0.3265 in a larger

temperature range, indicating that f is the best variableamong the three choices of the variables used to defined a

rd Å (r2 / r1) /2 Å rc / A0t / A1t10a / rrr, [9]

order parameter. These results are consistent with that weobserved for (AOT–water–decane) mixture in the previouswork (9) . otherwise the diameter shows a 2b anomaly:

The goodness of variables used to construct the orderparameters can also be tested by fitting the experimental data

rd Å (r2 / r1) /2 Å rc / A0t / Ct 2b / rrr. [10]to Eq. [7] with fixed values of b Å 0.3265 and D Å 0.5,and comparing the significance of the first Wegner correctionterm. The results are listed in Table 4. Here we only report We fitted our experimental data in the range of (T 0 Tc ) õ

5 K with Eqs. [9] and [10] in separate fitting proceduresthe results of fits in a temperature range of (T 0 Tc ) õ 5K, because the higher order Wegner correction terms could with fixed values of a Å 0.11 and b Å 0.3265. We obtained

rc , A0 , A1 , and C . The characteristics of the fits are summa-be significant when the temperature further far from the

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas

144 AN ET AL.

TABLE 4Parameters of Eq. [7] for Coexistence Curves of (T,n), (T,f),

and (T,C) for [f(AOT–Water)/ (10f)Octane] in a TemperatureRange of (T 0 Tc) õ 5 K

Orderparameter B B1 ÉB1/BÉ

n 00.0071 { 0.000100.0088 { 0.0001 0.019 { 0.002 2.16

f 0.857 { 0.0080.97 { 0.01 01.2 { 0.1 1.23

C 2.31 { 0.053.04 { 0.05 08.2 { 0.5 2.70

significant than (1 0 a) term for C. The difference in S isindeed too small to distinguish the goodness of fits betweenpowers of 2b and (1 0 a) unambiguously, but it gives someindication that f is better variable than C.

Combination of Eqs. [9] and [10] yields

FIG. 2. (n , f) calibration curve for [f(AOT–water) / (1 0 f)n-r1 Å rc / A0t / A1t

10a 0 (12)Btb 0 (1

2)B1tb/D , [11]octane] at 323.5 K. (l) Experimental values, ( —) calculated by Eq. [4]

in the text.r2 Å rc / A0t / A1t

10a / (12)Btb / (1

2)B1tb/D . [12]

When a, b, D, and Tc were fixed at 0.11, 0.3265, 0.5, andrized in Table 5. The experimental value of nc was obtained321.195 K, and the values of B , B1 , A0 , A1 , and rc wereby extrapolating refractive index again temperature in one-taken from Tables 4 and 5, and the values of r1 , r2 , and rdphase region to the critical temperature (12). The experi-were calculated from Eqs. [11], [12], and [9]. The resultsmental value of fc was determined by the technique ofare shown as lines in Fig. 1. The values from calculation‘‘equal volumes’’, and the value of Cc was obtained fromare in good agreement with experimental results.Eqs. [5] and [6]. The values nc , fc , and Cc are consistent

with the experimental results. This is evidence that the criti-cal anomaly is not significantly present in refractive indexes

TABLE 5within our experimental uncertainties and that the refractive

Parameters of Eqs. [9] and [10] and Standard Deviations S inindexes were properly converted to f and C. Although Eqs.

r for Diameters of Coexistence Curves of (T,n), (T,f), and (T,C)[9] and [10] omit the higher order Wegner correction terms of [f(AOT–Water) / (1 0 f)Octane] in a Temperature Rangeand artificially separate the effects of terms 2b and (1 0 of (T 0 Tc) õ 5 K (rc,expt. Is the Critical Value of the Ordera) , comparing the standard deviations S may give some Parameter)information about the significance of terms 2b and (1 0 a) .

(T,n) (T,f) (T,C)As Table 5 shows, the goodness of fits with 2b and (1 0a) for f are the same, but the fit with 2b is better than that

rc,expt. 1.3820 { 0.0001 0.091 { 0.001 0.500with (1 0 a) for C, which suggests the 2b term is more

rd Å rc / A0t / A1t10a

rc 1.3820 { 0.0001 0.092 { 0.001 0.499 { 0.002TABLE 3A0 00.06 { 0.01 07 { 2 36 { 5Values of Critical Exponents b for Coexistence Curves of (T,n),A1 00.072 { 0.008 6 { 1 022 { 3(T,f), and (T,c) for [f(AOT–Water) / (1 0 f)Octane]S 0.0001 0.0014 0.0041

T 0 Tc

rd Å rc / A0t / Ct2bOrder

parameter õ1 K õ5 K õ10 K rc 1.3820 { 0.0001 0.091 { 0.001 0.503 { 0.002

A0 00.145 { 0.004 0.1 { 0.5 10 { 1n 0.320 { 0.011 0.264 { 0.01 0.199 { 0.016f 0.325 { 0.012 0.292 { 0.007 0.253 { 0.009 C 00.008 { 0.001 0.7 { 0.1 02.5 { 0.3

S 0.0001 0.0014 0.0039c 0.320 { 0.012 0.244 { 0.012 0.192 { 0.014

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas

145COEXISTENCE CURVES OF A MICROEMULSION

2. See, e.g.: Aschauer, R., and Beysens, D., Phys. Rev. E. 47, 1850 (1993).CONCLUSIONS3. See, e.g.: Honorat, P., Roux, D., and Bellocq, A. M., J. Phys. Lett. 45,

961(1984).The present results confirm that the critical pseudobinary4. Aschauer, R., and Beysens, D., J. Chem. Phys. 98, 8194 (1993).

microemulsion mixture of (AOT–water–octane) belongs to 5. Bellocq, A. M., and Gazeau, D., J. Phys. Chem. 94, 8933 (1990).the 3D Ising universality class. In a region sufficient close 6. Rouch, J., Safouane, A., Tartaglia, P., and Chen, S. H., Progr. Colloid

Polym. Sci. 79, 279 (1989).to the critical temperature, the shapes of coexistence curves7. Bellocq, A. M., and Roux, D., Phys. Rev. Lett. 52, 1895 (1984).may be characterized by the simple scaling with the 3D Ising8. Kotlarchyk, M., Chen, S. H., Huang, J. S., and Kim, M. W., Phys Revvalue of critical exponent. Our results also show that f is

A 28, 508 (1983); 29, 2054 (1984).possibly the better choice of the concentration variable than 9. An, X., Feng, J., and Shen, W., J. Phys. Chem. 100, 16674 (1996).C and n used for constructing an order parameter. 10. Johnston, K. P., McFann, G. J., and Lemert, R. M., in ‘‘Supercritical

Fluid Science and Technology’’ (K. P. Johnston and J. M. L. Penninger,Eds.) , ACS Symposium Series 406. American Chemical Society, Wash-ACKNOWLEDGMENTSington, DC, 1989.

11. Shen, W., Smith, G. R., Knobler, C. M., and Scott, R. L., J. Phys.This work was supported by the State Education Committee, NationalChem. 95, 3376 (1991).Natural Science Foundation and the Natural Science Foundation of Gansu

12. An, X., Shen, W., Wang, H., and Zheng, G., J. Chem. Thermodyn. 25,Province, P. R. China.1373 (1993).

13. Levelt Sengers, J. M. H., in ‘‘Experimental Thermodynamics’’ (B. LeREFERENCES Neindre and B. Vodar, Eds.) , Vol. 2. Butterworths, London, 1975.

14. Sengers, J. V., Bedeaux, D., Mazur, P., and Greer, S. C., Physics 104A,1. Martin, A., Lopez, I., Monroy, F., Casielles, A. G., Ortega, F., and 573 (1980).

15. Sanchez, I. C., J. Appl. Phys. 58, 2871 (1985).Rubio, R. G., J. Chem. Phys. 101, 6874 (1994).

AID JCIS 5492 / 6g45$$$401 05-28-98 00:36:32 coidas