The critical behavior of {water + AOT + decane} microemulsion with various molar ratios of water to AOT

J. Chem. Thermodynamics 41 (2009) 639–644

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The critical behavior of {water + AOT + decane} microemulsion with various molar ratios of water to AOT Honglan Cai a,d, Chang Yi b, Xueqin An b,c,*, Weiguo Shen a,c a

Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China Jiangsu Key Laboratory of Biofunctional Materials, College of Chemistry and Environment Science, Nanjing Normal University, Nanjing, Jiangsu 210097, China c Department of Chemistry, East China University of Science and Technology, Shanghai 200237, China d School of Chemistry and Material Science, Ludong University, Yantai, Shandong 264025, China b

a r t i c l e

i n f o

Article history: Received 20 October 2008 Received in revised form 24 December 2008 Accepted 26 December 2008 Available online 1 January 2009 Keywords: Microemulsion Critical exponent Coexistence curve AOT

a b s t r a c t To examine the critical behavior of the microemulsion, we have determined the coexistence curves for two ternary microemulsion systems of {water + sodium di(2-ethylhexyl) sulfosuccinate (AOT) + n-decane} with the molar ratios x = (45.2 and 50.0) of water to AOT, respectively, by measuring refractive index at a constant pressure in the critical region. The critical exponent b and the critical amplitude B have been deduced from the coexistence curves. It was found that the values of b for both systems were consistent with the 3D-Ising exponent in a critical region. By increasing x, i.e. the droplet size, the critical temperature and, to a lesser extent, the critical concentration decrease. The region of coexisting two phases was drastically reduced by an increase in the droplet size. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Over the past 20 years, a great deal of progress has been made both experimentally and theoretically in understanding critical phase separation in fluids. The general concepts of scaling and universality are well established [1,2]. Recently, the study of critical phenomena in fluids has been extended to binary micellar solutions and multi-component microemulsion systems [3–20]. Critical microemulsion systems are of considerable interest because a controversy from experiments and theories was raised about whether these systems near the critical points belong to the 3D-Ising universality class [8,21]. In fact, several experiments were reported, which led to critical exponents that were different from those usually found in liquid–liquid critical points in binary mixtures of simple liquids [22]. Moreover, Fisher pointed out that due to the rescaling of the correlation length of this type of systems with the size of the microemulsion, effective critical exponent may be found under certain conditions [23]. The recent experimental works have shown that the critical behavior of the ternary microemulsion system of {AOT + water + alkane} with the molar ratio x = 40.8 of water to AOT belongs to the 3D-Ising class in a region that is sufficiently close to the critical temperature [15–17]. However, it is well known that three-com-

* Corresponding author. Address: Jiangsu Key Laboratory of Biofunctional Materials, College of Chemistry and Environment Science, Nanjing Normal University, Nanjing, Jiangsu 210097, China. Tel./fax: +86 025 85891921. E-mail address: [email protected] (X. An). 0021-9614/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2008.12.019

ponent {AOT + water + n-decane} can form water-in-oil microemulsions of well-defined droplet size determined by fixing the molar ratio x of water to AOT, and the droplet size and the polydispersity of the microemulsion system are directly proportionate to the molar ratio x. With the increase of x, both the shape and polydispersity of droplet are changed, which may affect or change the pseudobinary model of the microemulsion [24–26], thus modifying the critical behavior of the system. Therefore, the study of the critical behavior of the system with various molar ratios of water to AOT is of interest. In this paper, we present coexistence curves of two microemulsion systems with the molar ratios x = (45.2 and 50.0) of water to AOT, respectively. The experimental results were analyzed to determine the critical exponent b and the critical amplitude B, and to examine the size of asympotical range and the anomalies of the diameters for different choices of order parameters. Furthermore, we also discuss how the critical temperature Tc and the critical concentration /c change with x and the droplet size in microemulsion systems. 2. Experiment The AOT (purity >98%) surfactant was obtained from Fluka, and was purified according to a standard procedure [27]. The n-decane (purity >99%) supplied from Aldrich Chemical Co. was used without further treatment. The water was distilled twice from deionized water in our laboratory. The apparatus and experimental process for the measurements of refractive index n, and the techniques for the determination of

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the critical volume fraction /c and the critical temperature Tc have been described in detail previously [15,16]. During the measurements, the temperature was constant to ±0.002 K. The accuracy of the measurement was about ± 0.01 K for temperature and ±0.0001 for refractive index. The accuracy in the measurement of temperature difference (T  Tc) was about ±0.003 K. 3. Result and discussion The critical volume fractions /c and the critical temperatures Tc of {/(water–AOT) + (1  /)n-decane} with the molar ratios of x = 45.2 and 50.0 were determined to be /c = 0.097 ± 0.001, Tc = 305.38 K and /c = 0.096 ± 0.001, Tc = 302.82 K. With an increase in the droplet size, the critical volume fractions is almost not changed, but the critical temperature becomes significantly lower. The decrease in the critical temperature is attributed to the increase in the interaction between the droplets [27]. The refractive index n of the coexisting phases in the cell was measured at various temperatures. The results are listed in columns 3 and 4 of tables 1 and 2. The coexistence curves of (T, n)

TABLE 1 Coexistence curves of (T, n), (T, /), and (T, w) for [/(AOT–water) + (1  /)n-decane] with the molar ratio x = 45.2. T/K

(T  Tc)/K

n1

n2

/1

/2

w1

w2

305.383 305.389 305.398 305.408 305.418 305.424 305.435 305.445 305.455 305.466 305.483 305.518 305.565 305.620 305.702 305.749 305.864 305.982 306.126 306.188 306.369 306.682 307.343 308.185 308.650

0.004 0.010 0.018 0.029 0.039 0.045 0.056 0.066 0.075 0.087 0.104 0.139 0.186 0.241 0.322 0.370 0.485 0.603 0.747 0.809 0.990 1.302 1.964 2.806 3.271

1.4025 1.4025 1.4027 1.4028 1.4029 1.4029 1.4030 1.4030 1.4031 1.4031 1.4031 1.4033 1.4035 1.4034 1.4036 1.4036 1.4038 1.4038 1.4039 1.4039 1.4040 1.4039 1.4038 1.4035 1.4033

1.4014 1.4012 1.4011 1.4010 1.4008 1.4008 1.4007 1.4006 1.4005 1.4004 1.4003 1.4001 1.3998 1.3996 1.3995 1.3993 1.3993 1.3989 1.3985 1.3984 1.3981 1.3975 1.3965 1.3955 1.3950

0.081 0.078 0.073 0.069 0.066 0.065 0.063 0.061 0.059 0.058 0.057 0.051 0.046 0.045 0.040 0.038 0.031 0.027 0.024 0.021 0.018 0.014 0.010 0.006 0.005

0.114 0.121 0.126 0.130 0.134 0.135 0.139 0.141 0.144 0.147 0.150 0.157 0.165 0.172 0.176 0.181 0.181 0.192 0.201 0.205 0.213 0.229 0.257 0.278 0.291

0.450 0.440 0.423 0.409 0.397 0.394 0.385 0.375 0.368 0.365 0.361 0.333 0.308 0.305 0.277 0.266 0.232 0.207 0.187 0.168 0.145 0.117 0.087 0.056 0.048

0.546 0.562 0.572 0.582 0.590 0.592 0.601 0.605 0.611 0.617 0.622 0.634 0.648 0.659 0.665 0.673 0.673 0.688 0.701 0.706 0.716 0.734 0.763 0.782 0.793

TABLE 2 Coexistence curves of (T, n), (T, /), and (T, w) for [/(AOT–water) + (1  /)n-decane] with the molar ratio a = 50.0. T/K

(T  Tc)/K

n1

n2

/1

/2

w1

w2

302.822 302.827 302.836 302.847 302.868 302.893 302.935 302.988 303.069 303.174 303.301 303.417 303.577 303.723

0.007 0.012 0.021 0.032 0.053 0.078 0.120 0.173 0.254 0.359 0.486 0.602 0.762 0.908

1.4036 1.4038 1.4039 1.4041 1.4042 1.4044 1.4046 1.4048 1.4048 1.4051 1.4052 1.4053 1.4053 1.4053

1.4022 1.4021 1.4019 1.4018 1.4015 1.4013 1.4010 1.4009 1.4003 1.4000 1.3996 1.3992 1.3988 1.3985

0.074 0.069 0.066 0.059 0.057 0.049 0.044 0.037 0.034 0.024 0.021 0.015 0.013 0.012

0.116 0.120 0.126 0.129 0.136 0.142 0.150 0.153 0.170 0.177 0.188 0.197 0.208 0.215

0.431 0.410 0.399 0.374 0.361 0.325 0.303 0.267 0.247 0.189 0.166 0.128 0.110 0.099

0.552 0.562 0.576 0.583 0.598 0.609 0.625 0.630 0.659 0.669 0.686 0.698 0.712 0.721

are shown in figures 1a and 2a. As shown in figures 1 and 2, when the temperature range (T  Tc) of coexisting two phases for both systems exceeds by about (4 and 1) K, respectively, the system undergoes a transition from a transparent coexisting two phase into an unstable turbid macroemulsion. This macroemulsion separates on standing into a clear upper phase and a turbid lower phase, where the determination of refractive index is no longer feasible. The region of coexisting two phases of the system with a larger size of the droplet is drastically reduced, which may be attributed to the increase in the strong interaction between the droplets due to the change in the droplet size [27]. With an assumption of droplet in microemulsion being a pseudo-component and the two coexisting phases having different concentrations of the same droplets, a coexistence curve of temperature against volume fraction / can be drawn in the same way as it was done for the microemulsion with the small size of droplet [15,28]. To obtain the (T, /) coexistence curves, a series of ternary (water + AOT + n-decane) with a known volume fraction were prepared, and their refractive indexes were measured in one phase at various temperatures. The results are listed in tables 3 and 4. With the assumption that no significant critical anomaly is present in the refractive index [29], the refractive index of the microemulsion may be expressed as a linear function of temperature in a certain temperature range:

nð/; TÞ ¼ nð/; T  Þ þ ð@n=@TÞ/ ðT  T  Þ

ð1Þ

ð@n=@TÞ/ ¼ /ð@nA =@TÞ þ ð1  /Þð@nB =@TÞ

ð2Þ

where T  is chosen as (307.02 and 303.27) K for both microemulsion systems, respectively (about the middle temperature of the coexistence curves shown in figures 1 and 2), (n/T)/ is the derivative of n with respect to T, and (@nA/@T) and (@nB/@T) represent the values of (@n/@T) / for / = 1 and 0, respectively. From the temperature dependence of refractive indexes nB of pure decane listed in tables 3 and 4, the values of (nB/T) were calculated to be 4.5  104 in both microemulsion systems. Rearrangement of equations (1) and (2) yields

nð/; TÞ ¼ nð/; T  Þ þ ½/ð@nA =@TÞ þ ð1  /Þð@nB =@TÞðT  T  Þ

ð3Þ

The values of n(/, T) listed in tables 3 and 4 were fitted to equation (3) to obtain (@nA/@T), which were 1.9  104 for x = 45.2 and 1.3  104 for x = 50.0, respectively, and the values of nð/; T  Þ. The small standard deviation of 0.0001 in refractive index indicates that equation (3) is valid. This allowed us to simplify the procedure of the determination of the dependence of n on / just by fitting a polynomial form to nð/; T  Þ for various / at T  . We obtained the expression

nð/; T  Þ ¼ 1:4046  0:0309/ þ 0:00378/2

ðx ¼ 45:2Þ

ð4Þ

nð/; T  Þ ¼ 1:4059  0:0323/  0:00569/2

ðx ¼ 50:0Þ

ð5Þ

with a standard deviation <0.0002 in refractive index. The values of refractive indexes were then converted to volume fractions by equations (4) and (5). The results are listed in columns 5 and 6 of tables 1 and 2, and are shown in figures 1b and 2b. The choice of a concentration variable may affect the symmetry and the size of asymptotic region of a coexistence curve. One of the choices is to define an effective volume fraction w [3]

w ¼ /=½/ þ /c ð1  /Þ=ð1  /c Þ

ð6Þ

We converted (T, /) to (T, w) by equation (6). The results are listed in columns 7 and 8 of tables 1 and 2, and are shown in figures 1c and 2c. The difference of concentration variables (q2  q1) can be expressed by the Wegner expression

ðq2  q1 Þ ¼ Bsb þ B1 sbþD þ   

ð7Þ

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H. Cai et al. / J. Chem. Thermodynamics 41 (2009) 639–644 3.5 3.0

(T-Tc)/K

2.5 2.0 1.5 1.0 .5 0.0

(a)

(b)

(c)

1.394 1.396 1.398 1.400 1.402 1.404 1.406 0.0

.1

.2

.3 0.0

.2

.4

φ

n

.6

.8

1.0

ψ

FIGURE 1. Coexistence curves (T, n), (T, /), and (T, w) for [/(AOT–water) + (1  /)n-decane] with the molar ratio x = 45.2: (a) (T  Tc) vs. the refractive index n; (b) (T  Tc) vs. the volume fraction /; and (c) (T  Tc) vs. the effective volume fraction w. (d), (s) Experimental values of concentration variables (q) of the coexisting phases, (.) experimental values of diameter (qd) of the coexisting phases, (—) concentration variables (q) and (qd) of the coexisting phases from calculation.

1.0

(T-Tc)/K

.8 .6 .4 .2 0.0

1.398

(a)

(a)

(c)

(b) 1.400

1.402

1.404

1.406 0.00

.05

.10

.15

.20

.250.0

φ

n

.2

.4

.6

.8

ψ

FIGURE 2. Coexistence curves (T, n), (T, /), and (T, w) for [/(AOT–water) + (1  /)n-decane] with the molar ratio x = 50.0: (a) (T  Tc) vs. the refractive index n; (b) (T  Tc) vs. the volume fraction /; and (c) (T  Tc) vs. the effective volume fraction w. (d), (s) Experimental values of concentration variables (q) of the coexisting phases, (.) experimental values of diameter (qd) of the coexisting phases, (—) concentration variables (q) and (qd) of the coexisting phases from calculation.

TABLE 3 Refractive indexes n at a wavelength k = 632.8 nm of microemulsions of [/(water– AOT) + (l  /)n-decane] with the molar ratio of 45.2 at various temperatures T and volume fractions /. /

T/K

n

T/K

n

T/K

n

0.0000

311.618 310.139 309.153 308.406

1.4021 1.4028 1.4032 1.4035

307.555 306.698 305.064

1.4039 1.4043 1.4050

304.250 303.974 303.603

1.4054 1.4055 1.4057

0.0601

304.082 303.039 302.066

1.4037 1.4041 1.4046

300.989 299.956 298.947

1.4050 1.4055 1.4059

297.954 296.895

1.4063 1.4068

0.0832

304.105 303.140 302.038

1.4029 1.4033 1.4038

300.966 299.906 298.870

1.4042 1.4047 1.4051

297.835 296.758

1.4056 1.4060

0.0970

305.345 304.658 303.989

1.4019 1.4022 1.4025

303.306 302.627 301.981

1.4028 1.4031 1.4033

301.374 300.746

1.4036 1.4039

0.1197

304.087 303.087 302.089

1.4018 1.4022 1.4026

301.101 300.080 299.065

1.4030 1.4034 1.4038

297.925 296.854

1.4043 1.4047

0.1504

305.055 303.826 302.819

1.4005 1.4010 1.4015

301.818 300.809 299.832

1.4019 1.4023 1.4027

298.902 298.028

1.4031 1.4034

0.2017

304.873 303.722 302.608

1.3990 1.3994 1.3999

301.479 300.379 299.347

1.4003 1.4007 1.4012

298.392 297.407

1.4016 1.4019

0.2817

303.490 302.351 301.253

1.3971 1.3976 1.3980

300.242 299.215 298.246

1.3983 1.3987 1.3990

296.949 296.058

1.3995 1.3999

0.3413

302.610 301.360 300.321

1.3958 1.3962 1.3966

299.388 298.440 297.585

1.3970 1.3973 1.3976

296.740 295.906

1.3979 1.3982

where s = (T  Tc)/Tc, b and D are the critical exponents, B1 is the amplitude of the first Wegner correction term, q is the concentration variable, and q1 and q2 are the values of q in the upper and lower coexisting phases, respectively. In the region that is sufficiently close to the critical temperature, the simple scaling is valid

ðq2  q1 Þ ¼ Bsb

ð8Þ

The values of b were estimated for n, / and w in the different ranges of s by fitting the experimental data to equation (8). The result for / is shown in figure 3, where (T  Tc)max is the cutoff value for maximum (T  Tc). The values of b for the concentration variable / decreased within the experimental uncertainties as the temperature range was reduced. The same change was observed for the other two variables n and w. The values of b for both systems approach to 3D-Ising value 0.3265 within the experimental uncertainties, and are obviously inconsistent with the Fisher renormalized value of 0.365 and the mean theory value of 0.5. The results indicate that the critical exponent is not affected by the increase in shape and polydispersity of the droplets. The goodness of variables used to construct the order parameters can also be tested by fitting the experimental data to equation (7) with fixed values of b = 0.3265 and D = 0.5, and comparing the significance of the first Wegner correction. The results are listed in table 5. The significance of the first Wegner correction terms may be qualitatively indicated by the ratio B1/B. The smaller the value of B1/B is, the better the corresponding variable will be as an order parameter. It is evident that the value of B1/B for / is significantly smaller than that for n and w for both systems, which imply that / is the preferred order parameter. The results are in agreement with that of our previous work [15–17].

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H. Cai et al. / J. Chem. Thermodynamics 41 (2009) 639–644

TABLE 4 Refractive indexes n at a wavelength k = 632.8 nm of microemulsions of [/(water–AOT) + (1  /)n-decane] with the molar ratio of 50.0 at various temperatures T and volume fractions /. /

T/K

n

T/K

n

T/K

n

0.0000

306.698 305.064 304.250 301.708

1.4043 1.4050 1.4054 1.4066

303.974 303.603 303.334 300.747

1.4055 1.4057 1.4057 1.4070

303.127 302.916 302.605

1.4058 1.4059 1.4061

0.0593

303.966 302.900 301.885

1.4036 1.4041 1.4045

300.840 299.820 298.859

1.4050 1.4054 1.4059

297.893 296.848

1.4062 1.4067

0.0826

302.983 301.907 300.842

1.4033 1.4038 1.4042

299.787 298.772 297.849

1.4047 1.4051 1.4056

296.962 296.029

1.4059 1.4063

0.0969

302.805 301.553 300.496

1.4027 1.4032 1.4037

299.453 298.325 297.230

1.4041 1.4046 1.4050

296.259 295.266

1.4054 1.4059

0.1204

302.329 301.053 299.970

1.4023 1.4029 1.4033

299.076 297.970 297.013

1.4036 1.4041 1.4045

296.164 295.418

1.4048 1.4052

0.1512

302.943 301.800 300.868

1.4009 1.4014 1.4018

299.918 299.115 298.189

1.4022 1.4025 1.4029

297.430 296.607

1.4032 1.4035

0.1981

302.819 301.852 300.780

1.3993 1.3997 1.4001

299.693 298.622 296.698

1.4006 1.4010 1.4018

296.698 295.748

1.4018 1.4021

0.2464

302.951 301.824 300.759

1.3977 1.3981 1.3985

299.730 298.630 297.588

1.3989 1.3993 1.3997

296.613 295.730

1.4001 1.4004

Otherwise, the diameter shows a (1  a) anomaly

.340

qd ¼ ðq2 þ q1 Þ=2 ¼ qc þ A0 s þ A1 s1a þ   

.335

.330

βψ

.325

.320

.315

.310 0.0

.5

1.0

1.5

2.0

2.5

3.0

3.5

(T-Tc)/K FIGURE 3. Value of the critical exponent b in the different ranges of (T  Tc) for / obtained by fitting the experimental data to equation (8). (.) x = 45.2, (d) x = 50.0.

It is well known that when a good variable is used to construct an order parameter, the diameter of the coexistence curve may be expressed as [30]

qd ¼ ðq2 þ q1 Þ=2 ¼ qc þ A0 s þ C s2b þ   

ð9Þ

ð10Þ

We fitted our experimental data by equations (9) and (10) in separate fitting procedures with fixed values of a = 0.11 and b = 0.3265 and obtained qc, A0, A1 and C. The characteristics of the fits are summarized in tables 6 and 7, where qc,exp is the experimental critical value of the order parameter. The experimental value of nc,exp was obtained by extrapolating refractive index against temperature in the one-phase region to the critical temperature [31], and the value of wc,exp was obtained from equation (6). The experimental value of /c,exp was determined by the technique of ‘‘equal volumes of two coexistence phases”. The values of /c and nc are almost consistent with the experimental results. It is evident that no significant critical anomaly is present in refractive indexes, and that the refractive indexes were properly converted to volume fraction /. Although equations (9) and (10) omit the higher Wegner correction terms and artificially separate the effects of terms 2b and (1  a), comparing the standard deviations S and qc in fitting equations (9) and (10) may give some indication of the significance of terms of 2b and (1  a). As shown in tables 5 and 6, the goodness of fits with (1  a) and 2b for / in both systems are the same, but the fits with (1  a) are better than those with 2b for w, which suggests that w more likely leads to the (1  a) anomaly.

TABLE 5 Critical amplitude B and B1 of three order parameters for {water + AOT + n-decane} with the molar ratios x = (45.2 and 50.0).

x = 45.2

n /

w

x = 50.0

B

B1

|B1/B|

B

B1

|B1/B|

0.0384 ± 0.0002 0.0393 ± 0.0003 1.272 ± 0.006 1.283 ± 0.009 3.67 ± 0.01 3.82 ± 0.05

0.024 ± 0.004 0.0460 ± 0.0004 0.22 ± 0.13 1.370 ± 0.012 4.4 ± 0.7 4.15 ± 0.07

0.61

0.0458 ± 0.0001

0.004 ± 0.010

0.09

0.17

1.370 ± 0.004

0.01 ± 0.29

0.01

1.15

4.22 ± 0.02

1.9 ± 1.7

0.46

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H. Cai et al. / J. Chem. Thermodynamics 41 (2009) 639–644

TABLE 6 Parameters of equations (8) and (9) and standard deviations S in p for diameters of coexistence curves of (T, n), (T, /), and (T, w) of water + AOT + n-decane with the fixed molar ratio x = 45.2. Parameter

(T, n)

(T, /)

(T, w)

qc,expt

1.4019 ± 0.0001

0.097 ± 0.001

0.500 ± 0.001

0.099 ± 0.001 1.76 ± 0.17 3.8 ± 1.3 1.6  103

0.504 ± 0.001 87.01 ± 5.14 57.5 ± 3.1 3.8  l03

0.099 ± 0.001 2.69 ± 0.61 0.4 ± 0.1 1.6  l03

0.509 ± 0.002 18.02 ± 1.80 5.5 ± 0.4 4.6  l03

qd ¼ qc þ A0 s þ A1 s1a qc

1.4019 ± 0.0001 0.072 ± 0.065 0.11 ± 0.04 4.8  l05

A0 A1 S

qd ¼ qc þ A0 s þ C s2b qc

1.4019 ± 0.0001 0.201 ± 0.018 0.01 ± 0.004 4.7  l05

A C S

TABLE 7 Parameters of equations (8) and (9) and standard deviations S in p for diameters of coexistence curves of (T, n), (T, /), and (T, w) of water + AOT + n-decane with the fixed molar ratio x = 50.0. Parameter

(T, n)

qc,expt

1.4029 ± 0.0001

(T, /)

(T, w)

0.096 ± 0.001

0.500 ± 0.001

0.095 ± 0.001 12.92 ± 8.26 3.5 ± 4.4 1.3  l03

0.494 ± 0.003 185.85 ± 28.41 113.3 ± 15.0 4.4  l03

0.095 ± 0.001 8.24 ± 2.41 0.3 ± 0.3 1.3  l03

0.499 ± 0.001 33.01 ± 8.65 8.5 ± 1.2 4.6  l03

qd ¼ qc þ A0 s þ A1 s1a qc

1.4029 ± 0.0001 0.423 ± 0.320 0.04 ± 0.17 5.0  l05

A0 A1 S

qd ¼ qc þ A0 s þ C s2b qc

1.4029 ± 0.0001 0.374 ± 0.094 0.01 ± 0.01 5.0  l05

A0 C S

Combination of equations (7) and (10) yields 1a

bþD

q1 ¼ qc þ A0 s þ A1 s  ð1=2Þbs  ð1=2ÞB1 s þ    q2 ¼ qc þ A0 s þ A1 s1a þ ð1=2Þbsb þ ð1=2ÞB1 sbþD þ    b

ð11Þ

0652nm010), Keystone Foundation of Shanghai (08jc1408100), and the Nature Science Foundation of Ludong University (LY 20082901).

ð12Þ

With a, b and D fixed at 0.11, 0.3265 and 0.5, respectively, and the values of B, B1, A0, A1 and qc taken from tables 5 to 7, the values of q1, q2, and qd were calculated from equations (11) and (12), the results are shown as lines in figures 1 and 2. The values from calculation are in good agreement with the experimental results. 4. Conclusion

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We have measured the coexistence curves of ternary microemulsion of {water + AOT + decane} with various molar ratios of water to AOT (i.e. x = 45.2 and 50.0) in the critical region. Our experimental results show that the values of critical exponent b in both systems approach the 3D-Ising value of 0.3265 within the experimental uncertainties in the range of experimental temperature. The critical concentration and the critical temperature were decreased with the increase in the droplet size, but the latter was significantly reduced, and the region of coexisting two phases was drastically reduced by an increase in the droplet size. / is a better choice of the concentration variable than n and w for constructing an order parameter.

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Acknowledgements This work was supported by the National Natural Science Foundation of China (20573056, 20673059, and 20603030), the New Technique Foundation of Jiangsu Province, P.R. China (No. BG2005041), Nanometer Technology Foundation of Shanghai (No.

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JCT 08-365