Determination of Critical Micelle Concentration of Macroemulsions

(styrene + DMA + SDS + water + NaHCO3) solutions are determined by a ... of the sodium dodecyl sulfate (SDS) surfactant solution, whereas the cmc of t...
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Articles Determination of Critical Micelle Concentration of Macroemulsions and Miniemulsions Hong-Chi Chang, Yi-Yung Lin, Chorng-Shyan Chern, and Shi-Yow Lin* Department of Chemical Engineering, National Taiwan University of Science and Technology,† 43, Keelung Road, Sec. 4, Taipei, 106 Taiwan, Republic of China Received October 10, 1997. In Final Form: August 5, 1998 Critical micelle concentrations (cmc’s) of macroemulsion (styrene + SDS + water) and miniemulsion (styrene + DMA + SDS + water + NaHCO3) solutions are determined by a conductance technique. A four-terminal cell and an impedance spectrometer are employed in this work. An equivalent circuit of the sample cell is determined, and the solution resistance is obtained from the impedance plane plot. Cmc’s of the macro-/miniemulsions are then determined from the slope break in the conductivity-surfactant concentration (κ-C) diagram. The cmc of the macroemulsion is found to be only 10% greater than that of the sodium dodecyl sulfate (SDS) surfactant solution, whereas the cmc of the miniemulsion is about five times that of the SDS solution. The surface concentration of SDS at the styrene/water interface is evaluated from the equilibrium interfacial tension data, measured by a video-enhanced pendant drop tensiometer, and the micelle ionization degree, evaluated from the slope change in κ-C plot. A video-enhanced optical microscope is utilized to evaluate the size distribution of the emulsified monomer oil droplets. A mass balance on SDS molecules is established for the macro-/miniemulsion systems. The increase of cmc is primarily due to the adsorption of SDS onto the styrene/water interface of these tiny monomer droplets in the bulk phase of the macro-/miniemulsion solutions.

1. Introduction Emulsion polymerization is one of the major techniques for the manufacture of adhesives, coatings, thermoplastics, and elastomers. The monomer such as styrene can be emulsified in a medium, generally water, with the aid of surfactants such as sodium dodecyl sulfate (SDS). Macroemulsions do not contain cosurfactants and have monomer droplets with diameters of the order 1 to 10 µm. The monomer is thus present primarily as emulsion droplets dispersed in the continuous water phase, and there is a small amount of solubilized monomer contained in the micelles formed from surfactant molecules. The monomer-swollen micelles are believed to be the principal loci of polymerization in macroemulsions.1-4 Therefore, the number of micelles in macroemulsions, i.e., the critical micelle concentration (cmc), is an important parameter in emulsion polymerization. Miniemulsions use cosurfactants or swelling agents to provide stability to submicrometer monomer droplets (ca. 0.05-0.5 µm).5-10 The nucleation of polymer particles in * To whom correspondence should be addressed. Tel: 886-22737-6648. Fax: 886-2-2737-6644. E-mail: [email protected]. † Formerly National Taiwan Institute of Technology. (1) Smith, W. V.; Ewart, R. W. J. Chem. Phys. 1948, 16, 592. (2) Smith, W. V. J. Am. Chem. Soc. 1948, 70, 3695. (3) Blackley, D. C. Emulsion Polymerisation-Theory and Practice; Applied Science Publishers: London, 1975. (4) Wang, Q.; Fu, S.; Yu, T. Prog. Polym. Sci. 1994, 19, 703. (5) Ugelstad, J.; El-Aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Polym. Chem. Ed. 1973, 11, 503. (6) Hansen, F. K.; Ugelstad, J. J. Polym. Sci., Polym. Chem. Ed. 1973, 11, 503. (7) Chern, C. S.; Chen, T. J. Colloid Polym. Sci. 1997, 275, 546. (8) Reimers, J. L.; Skelland, A. H. P.; Schork, F. J. Polym. React. Eng. 1995, 3, 235. (9) Reimers, J. L.; Schork, F. J. Appl. Polym. Sci. 1996, 59, 1833. (10) Reimers, J. L.; Schork, F. J. Appl. Polym. Sci. 1996, 60, 251.

miniemulsion may be started out in these submicrometer monomer droplets or in the monomer-swollen micelles (ca. 3-6 nm in diameter) since the number of monomer droplets is about the same order of micelles. Therefore, cmc is one of the most important factors in determining the rate and mechanism of polymerization. For an aqueous solution consisting of only water and surfactants, surfactant molecules may stay in the bulk phase, adsorb on the wall of container, and adsorb on the air-water interface. Usually, the amount of surfactant on the air-water and water-container interface is negligible due to the very limited interfacial area. Therefore, the cmc is a property of surfactant. For the macro-/ miniemulsion solutions, however, the aqueous phase of the solutions has an extremely large oil-water interface. Cmc changes significantly since surfactant molecules prefer adsorbing onto the oil-water interface to staying in the bulk phase of water. Therefore, the cmc of the aqueous phase is dependent on the size and concentration of the oil droplets. Although cmc is an important property of macro-/ miniemulsions, to date, no cmc data of macro-/miniemulsion solutions has been reported in the literature (to our best knowledge). The aim of this paper is therefore to employ the conductance technique to determine the cmc’s of macro-/miniemulsion solutions. When styrene + SDS + water or styrene + DMA + SDS + water + NaHCO3 are emulsified, styrene is present primarily as tiny oil droplets dispersed in the water phase. A fraction of the SDS molecules adsorbs onto the oil-water interface, and this may delay the formation of micelles in the aqueous phase. An increase in cmc is thus expected. It would be also helpful in designing the recipe for the macro-/

10.1021/la971109w CCC: $15.00 © 1998 American Chemical Society Published on Web 10/24/1998

Cmc of Emulsions

miniemulsion polymerization if we know how much the increase in cmc is. Cmc is the concentration of surface active agents at which micelles first appear in the solution. At cmc, abrupt changes in several physical properties such as surface tension, turbidity, electrical conductivity, and osmotic pressure take place.11 Cmc can be determined by measuring any micelle-influenced property listed above. Surface tension measurement is the most popular technique for determining the cmc of surfactant solutions, since surface tensiometer is easy to operate and the break in the tension-concentration curve is quite clear. The surface tension method is also suitable for solutions of ionic, nonionic, zwitterionic, and mixed surfactants. The drawbacks of the surface tension technique are that the surfactant solutions must be still and it takes a very long time to reach the equilibrium tension at low surfactant concentrations. There may be a thin film of oil existing between the air-solution interface, and some tiny oil droplets may be very close to the oil-solution interface for the emulsions. Therefore, it is extremely difficult to measure the cmc of macro-/miniemulsion solutions by using the conventional surface tension technique. The electrical conductance technique can be employed to determine the bulk properties of solutions.12-18 Since some of the counterions remain associated with the micelles, the molar conductivity decreases with the surfactant concentration beyond the cmc. A slope change is observed in the specific conductivity (κ)-surfactant concentration (C) curve. In this work, the conductance method is employed for the determination of the cmc of emulsions. A four-terminal cell and an impedance spectrometer are utilized, and it is found that the solution resistance of emulsions is quite stable and reproducible. The slope change of conductance in the κ-C plot is clear, and the reproducibility is good. Therefore, the conductance method is proposed for evaluating the cmc’s of macro-/miniemulsion solutions. To confirm the accuracy of the cmc data obtained using the conductance technique, a mass balance on the surfactant molecules is also examined. An outline of this paper is as follows. Section 2 describes the emulsification process of monomer + surfactant + water solution, impedance spectroscopy experiments, determination of cmc of the emulsified solutions, and evaluation of the diameter of the tiny monomer droplets. The experimental results of cmc for macro-/miniemulsions and the analysis on the mass balance of SDS molecules are given in section 3. The paper ends with a conclusion and discussion section. 2. Experimental Measurements Materials. Anionic surfactant SDS (sodium dodecyl sulfate, CH3(CH2)10CH2OSO3 Na, technical grade) was purchased from Henkel. Cosurfactant DMA (dodecyl methacrylate, H2CdC(CH3)CO2(CH2)11CH3), which was used to prepare stable styrene (11) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York 1990; Chapter 13. (12) Goddard, E. D.; Benson, G. C. Can. J. Chem. 1957, 35, 986. (13) Mukerjee, P.; Mysels, K. J.; Dulin, C. I. J. Phys. Chem. 1958, 62, 1390. (14) Mysels, K. J.; Kapauan, P. J. Colloid Sci. 1961, 16, 481. (15) Mukhayer, G. I.; Davis, S. S.; Tomlinson, E. J. Pharm. Sci. 1975, 64, 147. (16) Garcia-Mateos, I.; Velazquez, M. M.; Rodriguez, L. J. Langmuir 1990, 6, 1078. (17) Miller, K. J., II; Goodwin, S. R.; Westermann-Clark, G. B.; Shah, D. O. Langmuir 1993, 9, 105. (18) Mendez Sierra, J. A.; Janczuk, B.; Gonzalez-Martin, M. L.; Bruque, J. M. Colloids Surf., A 1996, 117, 143.

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Figure 1. Apparatus for emulsifying the styrene + SDS + water solution: A ) motor, B ) sampling tube, C ) temperature probe, D ) rpm meter, E ) baffle, F ) 45° six-bladed agitated impeller, H ) top view of fan. miniemulsions in refs 7 and 19, was purchased from Acros with purity > 99%. Sodium bicarbonate (NaHCO3) was from Acros with purity > 99.5%. These reagents were used without modification. The monomer used in this work was styrene (from Taiwan Styrene Monomer Co.). Styrene was distilled twice under reduced pressure before use. Water was purified via a Barnstead NANOpure water purification system with a specific conductance less than 0.057 µS/cm. Interfacial Tension Measurement. To evaluate the surface coverage of SDS on the styrene-aqueous solution interface, the equilibrium interfacial tension between styrene and an aqueous solution of SDS was measured at 25.0 ( 0.1 °C. The pendant drop of styrene was generated, at the tip of a 22-gauge stainless steel inverted needle (0.016 in. i.d.; 0.028 in. o.d.), in a SDS aqueous solution, which was put inside a quartz cell of 26 × 41 × 43 mm inside diameter. A video-enhanced pendant drop tensiometry was used for the tension measurement.20-23 The system created a silhouette of a pendant drop, video imaged the silhouette, and digitized the image. A collimated beam passed through the pendant drop and formed a silhouette of a drop on a solid-state video camera. The silhouette image was digitized into 480 lines × 512 pixels with a level of gray with 8-bit resolution. The edge was defined as the x or z position, which corresponds to an intensity of 127.5.20 After the drop was formed, sequential digital images of the drop were then taken. The interfacial tension was obtained from the best fit between the theoretical curve, obtained from the Laplace equation, and the edge points of the pendant drop by minimizing an objective function. The objective function was defined as the sum of squares of the normal distance between the edge points and the theoretical curve of the Laplace equation. Minimization equations were solved by adjusting four unknown variables: the actual location of the apex, the radius of curvature at the apex, and the capillary constant. The dynamic interfacial tension profiles were obtained once all the drop images were processed. The equilibrium interfacial tension was then extracted from the long-time asymptotes. The tension measurement was performed at 25.0 ( 0.1 °C, and the accuracy and reproducibility were ≈0.1 mN/m.21,22 Macroemulsion. The styrene + SDS + water solutions were emulsified at 25.0 ( 0.5 °C in a baffled reactor with a 45° sixbladed downward impeller turbine, as shown in Figure 1. The (19) Chern, C. S.; Chen, T. J. Colloids Surf., A 1998, 138, 65. (20) Lin, S. Y.; McKeigue, K.; Maldarelli, C. AIChE J. 1990, 36, 1785. (21) Lin, S. Y.; Hwang, H. F. Langmuir 1994, 10, 4703. (22) Lin, S. Y.; Chen, L. J.; Xyu, J. W.; Wang, W. J. Langmuir 1995, 11, 4159. (23) Lin, S. Y.; Wang, W. J.; Lin, L. W.; Chen, L. J. Colloids Surf., A 1996, 114, 31.

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Figure 2. Impedance spectroscopy apparatus with fourterminal platinum electrode: A ) circulator, B ) magnetic stirrer, C ) water jacket, D ) four-terminal sample cell, E ) impedance/gain-phase analyzer, F ) computer, 1 ) working electrode, 2 and 3 ) reference electrodes, and 4 ) counter electrode. reactor with a volume of 1.5 L was immersed in a water jacket which was connected to a circulator in order to keep the emulsion at constant temperature. Anionic surfactant SDS and 765 g of water were first charged into this reactor. After SDS was dissolved completely, 135 g styrene was added into the reactor.24 The emulsion was then stirred at 400 rpm for 4 h. After that, part of the emulsified solution was transferred to a sample cell for the conductivity measurement. A video-enhanced optical microscope (Olympus, BH-2, Japan) was also utilized to monitor and record the image of emulsions. The images were processed later for measuring the average size and size distribution of the monomer oil droplets. Note that the macroemulsion at the time of conductivity measurement and image recording is kinematically stable. The above process was repeated for different levels of surfactant with fixed amounts of water and styrene. The critical micelle concentration was then determined from the slope break on the conductivity vs surfactant concentration (κ-C) curve. Miniemulsion. The styrene + DMA + SDS + water + NaHCO3 solution7,19 was homogenized by a microfluidizer (110Y, Watts Fluidair Inc.). Cosurfactant DMA was dissolved in styrene, called solution A. Anionic surfactants SDS and NaHCO3 were dissolved in water, called solution B. Solutions A and B were then mixed in the baffled reactor, the one used for preparing the macroemulsions, for 30 min at 300 rpm. This pre-emulsified solution was then put into the microfluidizer with an output pressure of 5000 psi. The output product was cooled by icewater. After the solution has been homogenized 30 times, parts of the miniemulsion were transferred to the sample cell for the conductivity measurement. The shelf stability of the miniemulsion products prepared this way was excellent. The miniemulsion was also monitored by the video-enhanced optical microscope for determining the droplet size and size distribution. The above experiment was repeated for various amounts of SDS with fixed amounts of DMA (20 mM, based on water), NaHCO3 (2.5 mM, based on water), water (200 g), and styrene (50 g). The critical micelle concentration was then determined from the slope break on the κ-C curve. Cmc Measurement. The cell for the sample solutions was made of Pyrex glass and platinum electrodes, as shown in Figure 2. It is a four-terminal cell, consisting of four parallel platinum electrodes on 10 mm intervals, two wires (reference electrodes, R1 and R2; 0.50 mm o.d.) inside and two square plates (working and counter electrodes, WE and CE; 10.0 × 10.0 mm) outside. The wires are 80 mm long, but 75 mm of the wires are sealed by Pyrex glass and only 5 mm of them contact with the aqueous solution. The outer sides of the square platinum plates are sealed also by Pyrex glass.25 The cell (50 mm i.d.; 90 mm high) is immersed in a water jacket which is connected to a circulator in order to keep the solution at constant temperature. Measurements were made at 25.0 ( 0.2 °C in the frequency (ω) range between 0.1 Hz and 2 MHz. An electrical stimulus, i(t) ) Im sin(ωt), was applied between WE and CE, and the resulting voltage v(t) ) Vm sin(ωt + θ) between R1 and R2 was measured (Schlumberger SI 1286, England; controlled by a 486 computer). (24) Chern, C. S.; Lin, S. Y.; Chang, S. C.; Lin, J. Y.; Lin, Y. F. Polymer 1998, 39, 2281. (25) Chang, H. C.; Hwang, B. J.; Lin, Y. Y.; Chen, L. J.; Lin, S. Y. Rev. Sci. Instrum. 1998, 69, 2514.

Figure 3. Equivalent circuit of the measurement system (a) and the corresponding Nyquist diagram (b). Rp (reaction resistance) and Cp (the diffuse double-layer capacitance of the polarization region near the electrode) are the responses associated with a heterogeneous electrode reaction. Rs (solution resistance) and Cs (the capacitance of polarization in bulk solution) are the responses associated with the solution. Here θ is the phase difference between the voltage and the current. The impedance Z(ω) is defined as v(t)/i(t).26 Figure 3 shows the equivalent circuit of the sample cell and the impedance plane plot (called the Nyquist diagram also), the imaginary part of impedance (Im(Z)) as a function of the real part of impedance (Re(Z)). In this complex plane plot the arrows show the direction of increasing frequency. Here Rp and Cp are the responses associated with a heterogeneous electrode reaction. Rp is a reaction resistance and Cp is the diffuse double-layer capacitance of the polarization region near the electrode. Rs and Cs are the responses associated with the solution. Rs is a solution resistance and Cs is the capacitance of polarization in bulk solution. The circuit shown in Figure 3 is appropriate for the well-separated time constants, RsCs , RpCp. In other words, when a high frequency is applied to the cell, the output signal is dominated by the Rs-Cs response. On the other hand, the Rp-Cp response is the dominant one at low frequencies. The system was calibrated by measuring the resistance Rs of the NaCl and KCl aqueous solutions. The cell constant was determined for 12 NaCl and KCl aqueous solutions of different concentrations and an average value of 0.1152 ( 0.0008 cm-1 was obtained.

3. Results The resistances of the surfactant solution and macro-/ miniemulsions of different surfactant concentrations were measured, and the conductivity κ was then calculated (κ ) cell constant/Rs). Anionic surfactant SDS aqueous solution in the absence of monomer was measured first for examination of the accuracy of measurements. The cmc values of surfactant aqueous solutions, macroemulsions, and miniemulsions were deduced from the conductivity versus surfactant concentration (κ-C) plots. The conductivity curves could be described by two straight lines. The break point in the κ-C plot indicates the usual cmc value. Anionic Surfactant SDS. Figure 4a shows the impedance plot of Im(Z) against Re(Z) at 25 °C for SDS aqueous solution at concentration (C0) of 2.85 × 10-6 mol/ cm3. There are two imperfect semicircles: a big semicircle (26) MacDonald, J. R. Impedance Spectroscopy; New York, 1987; Chapter 4.

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Figure 5. Specific conductivity (κ in mS/cm) of sodium dodecyl sulfate aqueous solution plotted as a function of bulk concentration.

Figure 6. Specific conductivity (κ in mS/cm) of styrene + SDS + water macroemulsion (400 rpm) as a function of SDS concentration.

Figure 4. Impedance plots of -Im(Z) against Re(Z) for (a) sodium dodecyl sulfate aqueous solution, C0 ) 2.85 × 10-6 mol/ cm3, (b) styrene + SDS + water macroemulsion, C0 ) 2.83 × 10-6 mol/cm3, and (c) styrene + DMA + SDS + water + NaHCO3 miniemulsion, C0 ) 2.18 × 10-6 mol/cm3. C0 ) SDS concentration based on water.

at high-frequency region followed by a tiny one at lowfrequency region. Although the semicircles are imperfect, they represent the exact impedance plane plot, corresponding to the equivalent circuit of the sample cell, as shown in Figure 3. According to the plot in Figure 3, the diameter of the semicircle at the high-frequency region is the solution resistance Rs. On the other hand, the diameter of the semicircle at the low-frequency region is the reaction resistance Rp. It is clear that the solution resistance is much larger than the reaction resistance for the four-terminal cell used in this study. Since the experimental data in the impedance plot of SDS aqueous solution is far away from a semicircle, the solution resistance of SDS aqueous solution is assigned

to be the intercept of the big circle on the x-axis (the real part of the impedance). The conductivity (κ ) cell constant/ Rs) data of SDS at different bulk concentrations are then plotted in Figure 5. These data can be described perfectly by two straight lines, and the break on the κ-C plot indicates that the cmc is 6.7 × 10-6 mol/cm3. Recently, Lin et al.25 have shown that the deviation on cmc obtained from the conductivity data originating from the diameters of the best-fit circles with the impedance data or from the intercept of the impedance data on the x-axis is usually less than 2%. Macroemulsion. Figure 4b shows the impedance plot of Im(Z) against Re(Z) at 25 °C for the styrene + SDS + water emulsion with SDS concentration (C0, based on water) of 2.83 × 10-6 mol/cm3. Similar to the SDS aqueous solution, there are two imperfect semicircles: a big semicircle at high frequencies and a tiny one at low frequencies. The semicircles are imperfect, but the impedance plane plot is exactly as shown in Figure 3. The impedance plot of the emulsion is far away from a semicircle, and therefore, the solution resistance is assigned to be the intercept of the big circle on the x-axis. Figure 6 shows one representative conductivity data. Three different runs are performed, and the data at different SDS concentrations always can be described well

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Figure 8. Size distribution of the styrene monomer droplet in the emulsion solution (400 rpm).

Figure 7. Images of styrene monomer droplets in macroemulsion (400 rpm) at magnification ×40 (a) and ×100 (b) at SDS concentration (based on water) of 7.0 × 10-6 mol/cm3.

by two straight lines. The break on the κ-C plot indicates the cmc of the macroemulsion. The cmc values are 7.38, 7.44, and 7.72 (10-6 mol/cm3) for these three runs, respectively, and an average of 7.5 ( 0.2 (10-6 mol/cm3) is obtained. This indicates that the cmc of macroemulsion is about 11.2% higher than that of the SDS aqueous solution. In other words, for the macroemulsion comprising 15% styrene, 10.7% of the SDS molecules goes to the fluid interface between water and the monomer oil droplets before any SDS micelle forms in the aqueous bulk phase. To confirm such an increase in cmc, a mass balance on SDS molecules was examined. The monomer droplets in the bulk phase of these emulsions were monitored by a video-enhanced optical microscope at magnifications ×40, ×100, and ×400, respectively. Figure 7 shows two representative images of the macroemulsion for emulsion with SDS concentration (C0, based on water) of 7.0 × 10-6 mol/cm3. The diameter of the oil droplets was measured, and the monomer droplet size distribution is shown in Figure 8 with Dn (number average diameter of droplets) ) 4.0 ( 3.0 µm and Dw (weight average diameter of droplets) ) 8.9 ( 5.0 µm, and PDI ) Dw/Dn ) 2.2. To evaluate the amount of SDS molecules at the oilwater interface, the surface coverage of SDS is needed. The surface concentration (Γ) of SDS molecules at the water-styrene interface was determined from the interfacial tension-surfactant concentration (γ-ln C) plot. The interfacial tension was determined using a video-enhanced pendant drop tensiometer, and the data are shown in

Figure 9. Equilibrium interfacial tension for styrene/SDS aqueous solution.

Figure 9. According to the Gibbs adsorption equation (dγ ) - ΓRT d ln C; R is the gas constant and T is the temperature), the surface concentration of SDS at cmc (Γcmc) is evaluated from the slope of the γ-ln C plot near, but right below, cmc (as shown in Figure 9).

Γcmc ) -

∂γ 1 (2 - R)RT ∂ ln C

(

)

(1)

where R is the micelle ionization degree. The value of R can be estimated from the ratio of the slope of the conductivity versus concentration lines above and below the cmc.27,28 From the κ-C data, as shown in Figure 6, a value of 0.62 ( 0.02 for R is obtained. The surface coverage of SDS is then calculated from eq 1, and Γcmc is equal to 3.54 × 10-10 mol/cm2. Note that the surface concentrations evaluated here are those for macro-/ miniemulsion solutions at cmc; therefore, it is believed that the surface coverage is (nearly) saturated under this condition. The calculation shows that 5.8% of the SDS molecules goes to water-styrene droplet interface in macroemulsion at cmc, N ) (∑Ai) Γcmc. The parameter N is the amount of SDS at the oil-water interface and Ai (27) Zana, R. J. Colloid Interface Sci. 1980, 78, 330. (28) Lianos, P.; Lang, J. J. Colloid Interface Sci. 1983, 96, 222.

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Figure 10. Specific conductivity (κ in mS/cm) of styrene + SDS + water emulsion (600 rpm) as a function of SDS concentration.

Figure 11. Specific conductivity (κ in mS/cm) of styrene + DMA + SDS + water + NaHCO3 miniemulsion solution as a function of SDS concentration.

is the surface area of monomer droplets. This value of 5.8% is close to, but smaller than, that obtained from the cmc measurement, 10.7%. The limitation of a video-enhanced optical microscope is about 1 µm, and there may be some oil droplets smaller than 1 µm. Therefore, the surface area of the oil droplets may be underestimated. Besides, some tiny bubbles were found on the top of the emulsion, near the air-solutionglass three phase contact circle, due to stirring, and the bubbles stayed there for a long period of time. Note that there are no bubbles observed on the SDS aqueous solution. The existence of air bubble and the microscope limitation may explain why a smaller percentage is obtained from the mass balance of surfactant and where parts of the surfactant molecules go. To investigate the bubble effect on the cmc measurement, another set of macroemulsions stirring with 600 rpm was made. Many more tiny bubbles were found on the top of the macroemulsion solutions than the 400 rpm runs. Figure 10 shows the κ-C data, and again two straight lines describe the data well. The break on the κ-C plot indicates that the cmc is 9.09 × 10-6 mol/cm3, which is 36% higher than that of the SDS aqueous solution. The number average diameter of droplets (Dn) for emulsion stirring with 600 rpm is about half of that stirring with 400 rpm (Dn,600rpm ) 0.47Dn,400rpm). In other words, the oil-water interface for 600 rpm is 4.5 times of that for 400 rpm. The mass balance calculation indicates that the adsorption of SDS molecules onto the oil-water interface contributes to 70% of the increase on cmc. It is believed that the other 30% of increase on cmc is from the adsorption of SDS at the air-bubble interfaces. Miniemulsion. The impedance plot of the styrene + DMA + SDS + water + NaHCO3 miniemulsion solution is again far away from a semicircle (as shown in Figure 4c for SDS concentration, based on water, C0 ) 2.18 × 10-6 mol/cm3), and the solution resistance is assigned to be the intercept of the big circle on the x-axis. Figure 11 shows one representative conductivity data. Two different runs are performed. In each run, two straight lines describe reasonably well the data at different SDS concentrations. The break on the κ-C plot indicates the cmc of the miniemulsion. The cmc is 3.3 and 3.57 (10-5 mol/cm3) for these two runs, respectively. An average of 3.4 ( 0.2 (10-5 mol/cm3) is obtained, which is about 4 times higher than the SDS aqueous solution (6.7 × 10-6 mol/ cm3). This is due to the extremely small droplet size

(around 50 to 500 nm) produced after homogenization, and therefore, an extremely large oil-water interface exits in the solution. The monomer droplets of miniemulsion were also monitored by the video-enhanced optical microscope at magnification ×400, but only a small part of oil droplets was large enough to be detectable. The surface concentration of SDS at the oil-water interface in miniemulsion solution is obtained from eq 1 with R ) 0.83 ( 0.06 (from the values of the conductance slope as shown in Figure 11) and the resultant Γcmc is 4.17 × 10-10 mol/ cm2. A mass balance on SDS was performed assuming that the amount of SDS adsorbed onto the oil-water interface is equal to N ) AΓcmc. The interfacial area (A ) nπD2) was estimated from the average diameter of monomer droplets (D) and the number of monomer droplets (n), which was calculated by assuming all the monomer is present as emulsion droplets. The experimental data of cmc indicates that 80% of the SDS molecules go to the water-monomer droplet interface. The value of D was then found to be 270 nm for the recipe with the SDS concentration at cmc, which is within the range of the reported diameter of monomer droplet, 50-500 nm. Therefore, the cmc data from the conductivity measurement is qualitatively in agreement with that from the mass balance calculation. 4. Conclusion and Discussions The conductivity method is found to be an effective tool for determining the cmc of macro-/miniemulsions. The success of such a technique relies on producing at least a kinematically stable macro-/miniemulsion solution and the design of four-terminal cell for the measurement of solution resistance Rs. The conductivity of solution is then calculated according to the relationship κ ) cell constant/ Rs. Care must be taken on preparing the emulsions in order to obtain relatively stable emulsion samples, accurate values of conductivity, and clear slope breaks on the κ-C plots. By use of the conductivity method, the values of cmc for the SDS aqueous solution and the styrene + SDS + water macroemulsion comprising 15 wt % styrene are found to be 6.7 and 7.5 ( 0.2 (10-6 mol/cm3), respectively. The cmc of SDS in water (same surfactant from Henkel) was found to be 3.0 × 10-6 mol/cm3 by the surface tension measure-

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ment.29 The increase of cmc is 10% according to the conductivity data, whereas it is a 250% increase when it is compared with the data from the surface tension method. In ref 29, to mimic the industrial operation, a technical grade SDS surfactant was used and a minimum in surface tension vs log C plot was obtained on the equilibrium surface tension profile. The concentration with a minimum equilibrium surface tension was assigned to be the cmc. The large deviation between the cmc measured for emulsions by the conductivity technique and that from the surface tension method is worth considering since there may be no micelles or only a very small number of micelles existing in the emulsions. The lack of micelles or only a few micelles may cause some mistakes on interpreting the kinetic data or mechanism in emulsion polymerization. To illustrate the superior performance of the four(29) Chen, L. J.; Lin, S. Y.; Chern, C. S.; Wu, S. C. Colloids Surf., A 1997, 122, 161.

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terminal cell in combination with an impedance spectrometer, a conventional conductivity meter (SC-ITA, Suntex Co.) had been tested for the conductivity measurement of the emulsions. The conductivity changes with time for the macroemulsions and, therefore, it is difficult to define the value of conductivity of macroemulsion. This is probably due to the adsorption (or contact) of the tiny oil droplets on the platinum surface. The conductivity of miniemulsion is quite stable, but the reproducibility of the cmc value is poorer than that obtained from the fourterminal cell. In addition to producing more reliable cmc data, the proposed conductance technique also allows one to gain a better understanding of the fundamental aspects of the dispersed oil droplets. Acknowledgment. The authors thank the National Science Council, R.O.C. for a grant. LA971109W