Article pubs.acs.org/jced
Phase Diagrams for the Pseudoternary System of {Hexane (1) + [Hexadecyltrimethylammonium Bromide (21) + Butan-1-ol (22)] (2) + Water (3)} at a Temperature of 303.15 K Xing-Bo Chen, Na Wang, Yahui Ma, and Tong-Chun Bai* College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China ABSTRACT: The phase diagrams of the pseudoternary system {hexane (1) + [hexadecyltrimethylammonium bromide (CTAB) (21) + butan-1-ol (22)] (2) + water (3)} at a temperature of 303.15 K were constructed by visual observation and electrical conductivity methods. The effect of the mass ratio of CTAB to butan-1-ol (Km = m21/m22) and the water content on the phase diagram and on the microemulsion structure were discussed.
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INTRODUCTION The microemulsion (ME) system was first reported by Hoar and Schulman1 in 1943 and was described as transparent, optical isotropic, thermodynamically stable dispersions composed of water, oil, and surfactant molecules.2 Investigations in microemulsions generally focus on the phase transition from waterin-oil (W/O) to oil-in-water (O/W) through a bicontinuous phase.3 The size of microemulsion droplet was estimated to be 10 nm to 100 nm and does not have the tendency to coalesce. It is reported that microemulsion phase is promising for drug delivery4 and for the reaction media of nanoparticle preparation.5−7 Hexadecyltrimethylammonium bromide (CTAB) is a cationic surfactant. It is helpful to the formation of microemulsion of water in oil and is widely used in biological reactions and the synthesis of nanoparticles. For example, the synthesis of the submicrometer rod-shaped α-calcium sulfate hemihydrates by CTAB + hexan-1-ol + water reverse microemulsion,8 the preparation of α-NiMoO4 nanocrystals by CTAB + hexan-1-ol + isooctane + water reverse microemulsion,9 the synthesis of hydroxyapatite nanoparticles under hydrothermal conditions by CTAB + hexan-1-ol + toluene + water reverse microemulsion,10 and the synthesis of α-Fe2O3 and ZnO nanoparticles by CTAB + 1-butanol + n-octane + water and CTAB + 1-butanol + cyclohexane + water microemulsion11,12 were reported in recent literature. Phase diagrams provide information on microemulsion by the dependence of the dispersion state on composition. They play an important role in the process of nanoparticle preparation. The phase diagrams of CTAB + 1-butanol + cyclohexane + [LaCl3 + Ni(NO3)2], CTAB + 1-butanol + octane + water, and CTAB + 1-butanol + cyclohexane + water have been found in literature.13−15 © 2014 American Chemical Society
For the consideration of applying microemulsion to prepare nanoparticles, we selected the system in the title to construct its phase diagram and to research the dependence of dispersion state on the composition. In present work, CTAB and butan-1-ol was chosen as the surfactant and cosurfactant, respectively. Hexane was chosen as the oil phase. By visual observation and electrical conductivity methods, the phase diagram of the system of {hexane (1) + [CTAB (21) + butan-1-ol (22)] + water (3)} was constructed. The effect of the mass ratio of CTAB to butan-1-ol (Km = m21/m22) and the water content on the phase diagram and on the microemulsion structure were discussed.
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EXPERIMENTAL SECTION Materials. Hexadecyltrimethylammonium bromide, given the acronym CTAB, CAS No. 57-09-0, analytical agent grade with a purity of 0.99, was used as a surfactant. Butan-1-ol, CAS No. 71-36-3, analytical agent grade with a purity of 0.995, was used as a cosurfactant. Hexane, CAS No. 110-54-3, analytical agent grade with a purity of mass fraction 0.97, was used as the oil phase. All of the chemicals were supplied by Sinopharm Chemical Reagent Co. Ltd., China, and were used without further purification. Water was purified by a Merck Millipore Ultrapure water purifier, (Suzhou Science Instrument Co. Ltd., China), with an electric resistivity of 18.2 MΩ·m at 298 K. Phase Diagram Construction. Hexane is the oil phase and is designated as component (1). The emulsifier is designed as a virtual component (2) and is composed of CTAB (21) (surfactant) and butan-1-ol (22) (cosurfactant). Water is component (3). The masses of three components are expressed by m1, m2, and m3 in gram units, respectively, where m2 = (m21 + m22). Received: January 12, 2014 Accepted: March 31, 2014 Published: April 4, 2014 1593
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Table 1. Compositions (wi, Mass Fraction) of the Phase Transition from a Solid−Liquid Mixture (S/L) to a Microemulsion (ME) Transparent Liquid at 303.15 Ka Km = 0.50
Km = 0.33
Km = 0.25
w1
w2
w3
w1
w2
w3
w1
w2
w3
0.881 0.782 0.685 0.587 0.489 0.392 0.294 0.192 0.096
0.098 0.196 0.294 0.391 0.489 0.587 0.685 0.766 0.862
0.021 0.022 0.022 0.022 0.022 0.021 0.022 0.042 0.042
0.881 0.783 0.684 0.587 0.489 0.391 0.293 0.196 0.098
0.098 0.196 0.295 0.392 0.490 0.587 0.685 0.782 0.881
0.022 0.021 0.021 0.021 0.021 0.022 0.022 0.021 0.022
0.880 0.782 0.685 0.587 0.489 0.391 0.294 0.196 0.096
0.098 0.196 0.294 0.392 0.490 0.587 0.685 0.783 0.862
0.021 0.021 0.022 0.021 0.021 0.022 0.021 0.021 0.042
a
Three groups of samples of {hexane (1) + [CTAB (21) + butan-1-ol (22)] (2) + water (3)} were tested. Their mass ratio, Km = m21/m22, were controlled to be (0.50, 0.33, and 0.25), respectively. Km is the mass ratio of CTAB (21) to butan-1-ol (22), Km = m21/m22; wi is the mass fraction of component i. Standard uncertainties u are u(Km) = 0.02 and u(wi) = 0.005.
Table 2. Compositions (wi, Mass Fraction) for the Phase Transformation from a Microemulsion (ME) Transparent Liquid to a Two-Liquid Phase of (L1/L3) at 303.15 Ka Km = 0.50
Km = 0.33
Km = 0.25
w1
w2
w3
w1
w2
w3
w1
w2
w3
0.844 0.656 0.452 0.247 0.151 0.089 0.040 0.007 0.003
0.094 0.164 0.194 0.165 0.151 0.133 0.092 0.026 0.025
0.062 0.180 0.355 0.588 0.698 0.778 0.868 0.967 0.972
0.844 0.656 0.478 0.348 0.251 0.191 0.129 0.073 0.008
0.094 0.164 0.206 0.232 0.252 0.286 0.302 0.290 0.075
0.062 0.180 0.315 0.420 0.497 0.524 0.569 0.637 0.917
0.844 0.655 0.535 0.466 0.389 0.311 0.230 0.137 0.034
0.094 0.164 0.230 0.311 0.389 0.467 0.535 0.548 0.303
0.062 0.180 0.235 0.222 0.222 0.222 0.235 0.316 0.664
a Three groups of sample of {hexane (1) + [CTAB (21) + butan-1-ol (22)] (2) + water (3)} were tested. Their mass ratio, Km = m21/m22, were controlled to be 0.50, 0.33, and 0.25, respectively. Standard uncertainties u are u(Km) = 0.02 and u(wi) = 0.005.
Three emulsifiers with Km = m21/m22 = (0.50, 0.33, and 0.25), were prepared in the experiment to observe the effect of the emulsifier composition on phase behavior. Correspondingly, three groups of quasi-binary mixtures of {hexane (1) + [CTAB (21) + butan-1-ol (22)] (2)} with mass ratios of m1/m2 = (0.90:0.10, 0.80:0.20, 0.70:0.30, 0.60:0.40, 0.50:0.50, 0.40:0.60, 0.30:0.70, 0.20:0.80, and 0.10:0.90) were prepared for the initial composition of phase diagram construction. The mass of m1 + m2 is controlled to be 10 g. Samples were weighed using an electronic balance (model BT25S, Sartorius AG, Beijing) to 0.0001 g. [Hexane + emulsifier (CTAB + butan-1-ol)] was a solid + liquid and quasi-binary mixture. To get a uniform mixing state, they were ultrasonic dispersed for 30 min (Ultrasonic apparatus, SK3300LH, KUDOS, Shanghai) and thermostatted in a water bath at temperature 303.15 K to ± 0.01 K. To observe the phase transition of pseudoternary system, water was titrated into the quasi-binary mixtures with a micro syringe (liquid volume accuracy 0.02 mL) by 0.20 mL in each titration operation. With the water titrated in, CTAB was dissolved gradually, and the mixture changed from a turbidity state (a mixture of solid and liquid, denoted as S/L) to a transparent liquid state, and the microemulsion (denoted as ME) was formed. To observe the phase transition clearly, an aqueous solution of potassium chloride was used as a reference. The phase transition was determined by visual observation. Aqueous KCl solution and the ME phase are both clear and transparent, but the light scattering and refraction are different. This difference is helpful to observe
the ME phase transition. The composition and the electrical conductivity were recorded for this phase transition process (from S/L to ME). With water titrated further in, the system then changed from the transparent liquid to an untransparent two liquid phase, that is, in the oil and water (L1/L3) heterogeneous mixture, both liquid phases contain the emulsifier. In above phase transition process, the data of phase composition were recorded by the visual observation. The structural change of microemulsion was estimated by analyzing the curves of electrical conductivity against water mass fraction.16 Electrical Conductivity Measurements. Electrical conductivity was measured using a digital conductivity meter (CON 1500 model, EUTECH Company, with a platinum electrode). The electrode was calibrated by a 0.01 M KCl aqueous solution. The cell constant is 1.024 cm−1. The electrical conductivity was measured in a 10 mL test tube (15 mm × 150 mm, diameter × length) with a relative uncertainty of ± 0.5 %. The tube was kept in a water thermostat controlled to ± 0.01 K.
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RESULTS AND DISCUSSION Phase Transition. To test the phase transition behavior, three emulsifier mixtures of [CTAB (21) + butan-1-ol (22)] with Km = 0.50, 0.33, and 0.25 were prepared for comparison. They were mixed with hexane (1) to form three groups of samples of {hexane (1) + [CTAB (21) + butan-1-ol (22)] (2)}. In each group, there were nine samples with the mass ratio of m1/m2 (0.90:0.10, 0.80:0.20, 0.70:0.30, 0.60:0.40, 0.50:0.50, 0.40:0.60, 0.30:0.70, 0.20:0.80, and 0.10:0.90), respectively. These samples 1594
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Figure 1. Phase diagrams for systems of {hexane (1) + [CTAB + butan-1-ol] (2) + water (3)} at 303.15 K with Km = 0.50 (A); 0.33 (B); and 0.25 (C), where ● is the phase composition for phase transition from solid/liquid mixing phase (S/L) to a microemulsion phase (ME); ■ is the phase composition for the phase transition from the ME phase to a two-liquid phase L1/L3; and ⧫ expresses the composition of (S/L) for w3 = 0. Lines are the fitting results by empirical equations.
were solid−liquid two-phase mixtures (S/L). To form a microemulsion system, water was titrated in. In the titration process, CTAB was dissolved gradually, and eventually, a homogeneous microemulsion was appeared. The compositions of the dissolution equilibrium for three group samples are listed in Table 1. With more water titrated into the microemulsion (ME) phase, the phenomenon of phase separation was observed, where a twoliquid-phase mixture, water phase and hexane phase (L1/L3), is formed. The equilibrium composition of the phase transition from ME phase to (L1/L3) phase are listed in Table 2. The pseudoternary phase diagrams with Km = (0.50, 0.33, and 0.25) are shown in Figure 1A, B, and C, respectively. In each figure, there are three phase areas. The S/L phase area is a solid (CTAB) and liquid mixing phase (S/L). The microemulsion (ME) phase is a transparent homogeneous phase. The (L1/L3) phase is a two-liquid phase.17,18 The phase equilibrium data wi in Table 1 are of a linear relationship and can be fitted fairly by eq 1.
w2 = b0 + b1w1
Table 3. Fitting Parameters of eq 1 for the Phase Transition from (S/L) to (ME)a b0
b1
R
SD
0.962 0.979 0.969
−0.975 −0.999 −0.986
0.999 0.999 0.999
0.0063 0.0001 0.0061
a
R is the correlation coefficient, and the SD is the standard deviation of the fit. Standard uncertainties u are u(Km) = 0.02, u(b0) = 0.005, and u(b1) = 0.008.
Table 4. Fitting Parameters of eq 2 for the Phase Transition from (ME) to (L1/L3)a Km
b0
b1
b2
b3
R
SD
0.25 0.33 0.50
0.02 0.02 0.25
−0.42 −0.74 −2.33
−0.5 0.9 6.0
−0.9 −2.1 −6.0
0.999 0.999 0.999
0.01 0.01 0.01
a
R is the correlation coefficient, and the SD is the standard deviation of the fit. Standard uncertainties u are u(Km) = 0.02, u(b0) = 0.02, u(b1) = 0.04, u(b2) = 0.2, and u(b3) = 0.2.
(1)
The phase equilibrium data in Table 2 can be fitted by an empirical eq 2. log(w3) = b0 + b1w10.5 + b2w12 + b3w13
Km 0.50 0.33 0.25
The parameters of the fits are listed in Tables 3 and 4, respectively.
(2) 1595
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Conductivity and Structures of Microemulsion. The electrical conductivity of microemulsion solution is attributed to the microdroplets in the dispersed phase and the ions in the water phase. Equation 3 is used to express this relation.19,20 e 2(∑ Z i2Di c i + Zm2Dmcm) κ= kT
α≠1
Φ < Φc
(5)
κ(Φ) ∝ (Φ − Φc)α
α=1
Φ > Φc
(6)
Φ= (3)
ρ ·w3 ρ0
(7)
where Φc is the percolation threshold and α is a constant with different values in different Φ regions. ρ and ρo are the densities of the whole system and water phase, respectively. Because ρ/ρo approaches a constant, the water mass fraction (w3) can be used to substitute the Φ. For w3 > wc we have
In which, c i = Φcc i(c)
κ(Φ) ∝ (Φc − Φ)α
(4)
where the Zi is the effective charge of ions (i), the Zm is the effective charge of microdroplets (m), because the charge comes from the surfactant ions, so the Zm value is equal to the charge of surfactant ions; the Di is the effective diffusion coefficient of ions (i), Dm is the Stokes−Einstein diffusion coefficient of microdroplets (m); ci and cm are the concentrations of ions (i) and microdroplets (m) in the solution, respectively; k is the Boltzmann constant, Φc is the volume fraction of the continuous phase, ci(c) is the mass concentration of ions (i) in the continuous phase. The microemulsion system of Km = 0.50 and m1/m2 = 0.30/ 0.70 is selected as an illustration example. The dependence of electrical conductivity κ on the mass fraction of water w3 is shown in Figure 2. The relationship between the conductivity and the
κ(w3) ∝ (w3 − wc)α
(8)
As shown in Figure 2, in the region of w3 < wc, κ is very low, and it increases slowly with w3. In the structural scheme of Figure 3, it
Figure 3. Structural change of microemulsion system with the water mass fraction w3 (O: oil phase, W: water phase). (a) Surfactant dispersions in the oil phase; (b) the formation of W/O small particles; (c) the volume increase for W/O particles by sticky collision; (d) water tubes or channels; (e) bicontinuous model, dual channels; (f) O/W particles.
shows only few water droplets in this region (Figure 3b). The volume of the droplet is not big enough to carry more ions for charge transport. In the region of w3 > wc, α = 1, and κ increases linearly and steeply with w3 up to wb, where wc is the mass fraction of water at the onset point of the curve. It has the physical meaning of the percolation threshold of the percolative conduction model. The wb is the mass fraction of the inflection point. The percolation threshold may be attributed to the progressive clustering of water droplet. Some mechanisms have been proposed to explain the percolative conduction in W/O microemulsions; one of them is the model of “sticky droplet collisions” suggested by Fletcher and Robinson.21 According to this model, with the increase in w3, the frequent “sticky” collisions between spherical microdroplets of a W/O type microemulsion are presented after the percolation threshold (Figure 3c). The interaction collision extends the volume of water droplet. These lead to the formation of narrow water tubes or channels in the oil continuous phase (Figure 3d), and the counterions can move through these narrow channels, which results in a sudden steep increase of the conductivity. Evidently, more W/O microemulsion was formed in this region. This tendency is kept until the inflection point of wb is arrived. In the region of wb < w3 < wm, the conductivity κ increases with w3, but deviating from the linear relationship, and eventually a maximum is observed in Figure 2. It was often used to indicate the existence of a bicontinuous phases (see Figure 3e). This may be considered as a direct result of the combination of the narrow
Figure 2. Dependence of electrical conductivity (κ) on water mass fraction (w3) for the microemulsion system of {hexane (1) + [CTAB + butan-1-ol] (2) + water (3)}, with Km = 0.50 and m1/m2 = 0.30:0.70 at 303.15 K, where the wc is the mass fraction of water of the onset point of the curve, which is defined by eq 7. It has the physical meaning of the percolation threshold of the percolative conduction model and is determined from the intersection point of a linear line with the coordinate axis of w3. The wb is the mass fraction of the inflection point. It indicates the conversion of the W/O phase to the bicontinuous phase. The wm indicates the conversion of the bicontinuous phase to the O/W phase.
structural models of microemulsion, water-in-oil (W/O), bicontinuous (BC), and oil-in-water (O/W), can be analyzed from this figure. By percolative conduction model, the dependence of the conductivity κ on the water volume fraction Φ in the W/O region are expressed by following equations.18 1596
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Figure 4. (a) Experimental results of κ versus w3 for the microemulsion system of {hexane (1) + [CTAB + butan-1-ol] (2) + water (3)} at 303.15 K with Km = 0.50 and m1/m2 = 0.80:0.20 (black), 0.70:0.30 (red), 0.60:0.40 (green), 0.50:0.50 (blue), 0.40:0.60 (cyan), 0.30:0.70 (magenta), 0.20:0.80 (yellow), and 0.10:0.90 (dark yellow) (in the order from bottom to top); (b) the experimental data for w3 < wb, (m1/m2 = ■, 0.8:0.2; ●, 0.7:0.3; ▲, 0.6:0.4; ▼, 0.5:0.5). By determining the intersection point of the linear line with the coordinate axis of w3, the percolation threshold wc is obtained; (c) the variation of dκ/dw3 with w3. From the maximum point, the wb can be determined.
is shown for various m1/m2 samples. To obtained the values of wc, the experimental details for w3< wb are shown in Figure 4b. By determining the intersection point of linear line with the coordinate axis of w3, the percolation threshold wc is obtained. In Figure 4c, the variation of dκ/dw3 with w3 is shown. From the maximum point, the value of wb can be determined easily. The curve shape in Figure 4a is of three types. They can be fitted by three curve fitting equations, eqs 9 to 11. These equations were implanted in the data analysis and graphing software Origin, OriginLab Corporation.
water channels to each other. The microemulsion as a whole may be considered as a coarse network composed of water tubes in an oil continuous medium. With more water added in, the dispersion presents an intermediary equilibrium state of the bicontinuous type, in which oil and water are all locally continuous. Both W/O and O/W microemulsions are coexistence at equilibrium in this water content region (Figure 3e). In the region of w3 > wm, the conductivity κ decreases with the increasing in w3. This is the effect of water dilution. Accordingly, it indicates the formation of an O/W type microemulsion.22 After knowing the inflection point (wb) and the maximum point (wc), we can identify the structural region of microemulsion, W/O, BC, and O/W.23,24 By constructing a curve of dκ/dw3 versus w3, the maximum of dκ/dw3 at wb can be obtained easily.25 The experimental results for microemulsion system with different Km are shown in Figures 4 (Km = 0.50), 5 (Km = 0.33), and 6 (Km = 0.25), respectively. Each is composed of three subfigures. For example, in Figure 4a, the variation of κ versus w3
⎛ w − w0 ⎞ κ = κ0 + A1 exp⎜ 3 ⎟ ⎝ t1 ⎠ κ=
κi − κ f + κf [1 + exp(w3 − w0)/dw3]
κ = b0 + b1w3 + b2w32 + b3w33 1597
(9)
(10) (11)
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Figure 5. (a) Experimental results of κ versus w3 for the microemulsion system of {hexane (1) + [CTAB + butan-1-ol] (2) + water (3)} at 303.15 K with Km = 0.33 and m1/m2 = 0.80:0.20 (black), 0.70:0.30 (red), 0.60:0.40 (green), 0.50:0.50 (blue), 0.40:0.60 (cyan), 0.30:0.70 (magenta), 0.20:0.80 (yellow), and 0.10:0.90 (dark yellow) (in the order from bottom to top); (b) the experimental data for w3 < wb (m1/m2 = ■, 0.8:0.2; ●, 0.7:0.3; ▲, 0.6:0.4; ▼, 0.5:0.5). By determining the intersection point of the linear line with the axis of w3, the percolation threshold wc is obtained; (c) the variation of dκ/dw3 with w3.
Figures 5a and 6a, respectively. They are similar situations as Figure 4a as shown. Following the above fitting method, eqs 9, 10, and 11 were applied to fit the experimental data. The fitting parameters are listed in Tables 5, 6, and 7, respectively. In Figure 4a the percolation phenomena was not observed clearly, because of the initial oil mass was too low. For the curves of m1/m2 = (0.80:0.20, 0.70:0.30, 0.60:0.40, and 0.50:0.50), where the aqueous droplets begin to merge, the percolation thresholds (wc) were determined by a linear intersection method of Lagourette et al.29 This method is shown in Figure 4b. The percolation thresholds (wc) were determined from the intersection of straight line with the w3 axis. The straight line is expressed by eq 12.
Equation 9 is an equation for the curve of exponential growth with offset, where κ0 is the offset, w0 is the center, A1 is the amplitude, and t1 is the width; the center is set by a characteristic point at (w0, κ0 + A1) and its first derivative dκ/dw3 = A1/t1. In Figure 4a, for m1/m2 = 0.80:0.20, the curve is too low and short. This is attributed to the fact that the mass of emulsifier is too low and the formation of the microemulsion is few. The conductivity curve is of the feature of exponential growth with offset and can be fitted fairly by eq 9. The conductivity curves for m1/m2 = (0.70:0.30, 0.60:0.40, and 0.50:0.50) exhibited a sigmoidal nature in their raising section, after the maximum, the conductance downward. These curves can be fitted fairly by eq 10 (a Boltzmann equation, where w0 is the center, κ takes on the average of κi and κf, dw3 means the constant interval of w3, κi and κf are the initial and final conductances of the system, respectively).26,27 The curves for m1/m2 = (0.40:0.60, 0.30:0.70, 0.20:0.80, and 0.10:0.90) exhibit another nature which can be fitted fairly by eq 11 (a polynomial equation, b0, b1, b2, b3 are coefficients).28 For Km = 0.33 and 0.25, the conductivity curves are shown in
κ(w3) = A(w3 − wc)
w3 > wc
(12)
where A is a coefficient and wc is the percolation threshold. By same method, the fitting results for Km = (0.50, 0.33, and 0.25) are shown in Figures 4b, 5b, and 6b. They show that, for the cases of Km = 0.50 and 0.33, the percolation threshold (wc) shifts 1598
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Figure 6. (a) Experimental results of κ versus w3 for the microemulsion system of {hexane (1) + [CTAB + butan-1-ol] (2) + water (3)} at 303.15 K with Km = 0.25 and m1/m2 = 0.80:0.20 (black), 0.70:0.30 (red), 0.60:0.40 (green), 0.50:0.50 (blue), 0.40:0.60 (cyan), 0.30:0.70 (magenta), 0.20:0.80 (yellow), and 0.10:0.90 (dark yellow) (in the order from bottom to top); (b) the experimental data for w3 < wb, (m1/m2 = ■, 0.8:0.2; ●, 0.7:0.3; ▲, 0.6:0.4). By determining the intersection point of a linear line with the axis of w3, the percolation threshold wc is obtained; (c) the variation of dκ/dw3 with w3.
Table 6. Fitting Parameters of eq 10 for Systems with Different Km and m1/m2a
Table 5. Fitting Parameters of eq 9 for Systems with Different Km and m1/m2a m1/m2
A1
t1
0.80:0.20
25.34
0.018
0.80:0.20 0.70:0.30 0.60:0.40
23.14 67.22 40.34
0.013 0.034 0.071
0.80:0.20 0.70:0.30
14.32 3.09
0.017 0.017
w0 Km = 0.50 0.238 Km = 0.33 −0.219 −0.440 0.615 Km = 0.25 0.253 0.258
κ0
R
m1/m2
SD
−0.003
0.997
0.015
−0.001 −0.015 −0.027
0.998 0.991 0.994
0.077 0.053 0.083
−0.002 0.004
0.999 0.998
0.002 0.077
κi
κf
0.70:0.30 0.60:0.40 0.50:0.50
0.009 0.088 0.498
2.849 4.525 5.251
0.50:0.50 0.40:0.60
0.167 0.655
4.097 3.319
w0 Km = 0.50 0.301 0.410 0.470 Km = 0.33 0.438 0.436
dw3
R
SD
0.030 0.049 0.062
0.999 0.999 0.999
0.017 0.034 0.035
0.057 0.064
0.999 0.999
0.036 0.064
a
R is the correlation coefficient, and the SD is the standard deviation of the fit. w0 is the center, κ takes on the average of κi and κf, dw3 means the constant interval of w3, and κi and κf are the initial and final conductances of the system, respectively. Standard uncertainties u are u(Km) = 0.02 and u(m1/m2) = 0.02.
a
R is the correlation coefficient, and the SD is the standard deviation of the fit. The m1/m2 is the mass ratio of hexane (1) to [CTAB (21) + butan-1-ol (22)] (2). In eq 9, κ0 is the offset, w0 is the center, A1 is the amplitude, and t1 is the width; the center is set by a characteristic point at (w0, κ0 + A1) and its first derivative dκ/dw3 = A1/t1. Standard uncertainties u are u(Km) = 0.02 and u(m1/m2) = 0.02.
toward the lower direction by increasing m1/m2. However, for Km = 0.25, the percolation threshold (wc) increases with m1/m2 1599
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Figure 7. Phase diagrams for systems of {hexane (1)/ [CTAB + butan-1-ol] (2)/water (3)} at 303.15 K with three Km: (A) Km = 0.50; (B) Km = 0.33; (C) Km = 0.25, where ● is the composition for the phase transition from solid/liquid mixing phase (S/L) to the microemulsion phase (ME); ■ is the equilibrium composition for the phase transition from the ME to a two-liquid phase L1/L3; ⧫ is the composition for w3 = 0; ○ is the composition at w3 = wc; △ is the composition for the structure transition from W/O to BC; ▽ is the composition for the structure transition from BC to O/W. Lines are fitting results by empirical equations.
Table 8. Fitting Parameters of eq 12 for the Samples of Km = (0.50, 0.33, and 0.25) in the Linear Region of w3 (> wc, the Percolation Threshold)a
Table 7. Fitting Parameters of eq 11 for Systems with Different Km and m1/m2a m1/m2
b0
0.40:0.60 0.30:0.70 0.20:0.80 0.10:0.90
0.236 0.343 0.581 0.122
0.30:0.70 0.20:0.80 0.10:0.90
0.215 0.231 0.584
0.60:0.40 0.50:0.50 0.40:0.60 0.30:0.70 0.20:0.80 0.10:0.90
−0.040 −0.009 0.100 0.184 0.350 0.366
b1
b2
Km = 0.50 −0.726 34.1 2.58 34.8 6.02 33.1 15.5 19.0 Km = 0.33 3.93 9.88 7.96 7.84 10.6 10.4 Km = 0.25 2.63 −28.5 2.47 −13.7 2.56 9.85 2.92 12.3 3.56 26.3 8.87 9.88
b3
R
SD
−33.4 −37.2 −40.9 −35.3
0.999 0.999 0.999 0.999
0.02 0.04 0.10 0.07
−9.93 −15.1 −21.3
0.999 0.999 0.996
0.05 0.04 0.11
100.4 35.7 −17.2 −26.8 −55.6 −21.4
0.994 0.999 0.999 0.999 0.999 0.999
0.007 0.003 0.005 0.006 0.010 0.030
m1/m2
A
0.80:0.20 0.70:0.30 0.60:0.40 0.50:0.50
12.50 16.95 18.62 15.77
0.80:0.20 0.70:0.30 0.60:0.40 0.50:0.50
9.97 18.77 18.42 15.17
0.80:0.20 0.70:0.30 0.60:0.40
2.56 10.36 3.59
wc Km = 0.50 0.130 0.222 0.287 0.293 Km = 0.33 0.134 0.241 0.294 0.299 Km = 0.25 0.130 0.190 0.157
R
SD
0.991 0.995 0.996 0.996
0.039 0.043 0.059 0.044
0.970 0.998 0.998 0.996
0.056 0.027 0.038 0.040
0.985 0.992 0.989
0.010 0.025 0.011
a R is the correlation coefficient, and the SD is the standard deviation of the fit. Standard uncertainties u are u(Km) = 0.02 and u(m1/m2) = 0.02.
a
R is the correlation coefficient, and the SD is the standard deviation of the fit. Equation 11 is a polynomial equation, and b0, b1, b2, and b3 are coefficients. Standard uncertainties u are u(Km) = 0.02 and u(m1/m2) = 0.02.
first and then decreases. The parameters of A and wc are presented in Table 8. 1600
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Table 9. Phase Composition (wi) for the Percolation Threshold for the Structural Transition from W/O to BC and for the Structural Transition from BC to O/Wa Km = 0.50 w1
Km = 0.33
w2
w3
w1
0.696 0.544 0.428 0.353
0.174 0.234 0.285 0.354
0.130 0.222 0.287 0.293
0.486 0.352 0.266 0.262 0.205 0.146 0.082
0.209 0.235 0.266 0.393 0.479 0.582 0.738
0.305 0.413 0.468 0.345 0.316 0.272 0.180
0.181 0.130 0.094 0.067 0.038 0
0.181 0.194 0.219 0.269 0.340 0.487
0.637 0.676 0.687 0.664 0.622 0.513
Km = 0.25
w2
w3
w1
w2
w3
0.695 0.567 0.505
0.175 0.243 0.338
0.130 0.190 0.157
0.322 0.255 0.167 0.085
0.483 0.595 0.668 0.766
0.195 0.149 0.165 0.149
Phase Composition for the Transition from BC to O/W at w3 = wm 0.039 0.355 0.606 0.045 0 0.431 0.569 0
0.408 0.476
0.547 0.524
Phase Composition for the Percolation Threshold at w3 = wc 0.693 0.173 0.134 0.530 0.229 0.241 0.423 0.283 0.294 0.350 0.351 0.299 Phase Composition for the Transition from W/O to BC at w3 = wb 0.282 0.283 0.435 0.226 0.339 0.435 0.199 0.465 0.336 0.167 0.668 0.165 0.084 0.751 0.165
a
w1, w2, and w3 are the mass fraction of hexane, CTAB + butan-1-ol, and water in the {hexane (1) + [CTAB (21) + butan-1-ol (22)] (2) + water (3)} mixture, respectively. wc is the percolation threshold, wb is the maximum of d(κ)/dw3 versus w3, and wm is the maximum of κ versus w3.
w3 = wb. The transition from BC to O/W is found at w3 = wm. The compositions for these transitions are listed in Table 9. They can be fitted by polynomial eqs 1, 13, and 14.
Table 10. Fitting Parameters of eq 13 for the Composition of Percolation Threshold w3 = wc and for the Transition from W/O to BC at w3 = wba Km
b0
b1
b2
R
SD
For the Percolation Threshold at w3 = wc 0.50 0.741 −1.413 0.863 0.996 0.012 0.33 0.790 −1.644 1.089 0.998 0.008 0.25 2.620 −7.180 5.268 0.999 0.001 For the Composition of Structure Transition from W/O to BC at w3 = wb 0.50 0.931 −2.557 1.711 0.998 0.132 0.33 0.934 −1.729 −2.466 0.948 0.091 0.25 0.827 −0.675 −1.161 0.994 0.022
b2
b3
R
SD
eq 14 24.511 eq 1
−42.190
0.999
0.003
0.999 0.999
0.001 0.001
0.50
0.487
−4.744
0.33 0.25
0.431 0.476
−1.949 −1.511
(14)
CONCLUSION For the microemulsion system of {hexane + [CTAB + butan-1-ol] +water}, there are three phase areas, the homogeneous and transparent microemulsion phase area, the solid and liquid twophase area, and the two-liquid-phase area. In the microemulsion area, information about the structural transition of W/O, BC, and O/W models was obtained from the electrical conductivity curves against the water content. The percolation threshold model, the sticky collision model, and the dual channels model can be used to illustrate the conductivity behavior.
Table 11. Fitting Parameters of eqs 1 and 14 for the Composition of Structural Transition from BC to O/Wa b1
w2 = b0 + b1w1 + b2w12 + b3w13
■
R is the correlation coefficient, and the SD is the standard deviation of the fit.
b0
(13)
The relative fitting parameters are listed in Tables 10 and 11. The phase diagrams for combining phase and structural transitions are shown in Figure 7.
a
Km
w2 = b0 + b1w1 + b2w12
■
a
R is the correlation coefficient, and the SD is the standard deviation of the fit.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (Tong-Chun Bai). Tel.: 86-51265880089. Fax: 86-512-65880089.
Figure 4c show the curves of dκ/dw3 versus w3 for the case of Km = 0.50 and m1/m2 = (0.80:0.20, 0.70:0.30, 0.60:0.40, 0.50:0.50, 0.40:0.60, 0.30:0.70, 0.20:0.80, and 0.10:0.90), respectively. From the maximum point, wb can be obtained. Similarly, for the cases of Km = 0.33 and 0.25, the variation of dκ/ dw3 with w3 are shown in Figures 5c and 6c, respectively. Summarizing above analysis, the spherical microdroplet is produced at w3 = wc. The transition from W/O to BC is found at
Funding
This project was funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Notes
The authors declare no competing financial interest. 1601
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