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Articles Electrokinetic Properties of Surfactant-Stabilized Oil Droplets R. Barchini and D. A. Saville* Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544 Received August 17, 1995. In Final Form: December 13, 1995X To study the electrokinetic behavior of highly charged colloidal particles, we used monodisperse oil drops suspended in water and stabilized with a surfactant, sodium dodecyl sulfate. Results from dynamic light scattering, conductivity, and electrophoretic mobility measurements show that the emulsion particles have high ζ-potentials, corresponding to a large density of surfactant ions on the surface. Attempts to reconcile results from mobility and conductivity measurements using the standard electrokinetic model were unsuccessful. The inadequacy of the standard model is ascribed to the high surface potential of the droplets and attendant changes in the counterion density and properties of the inner part of the diffuse layer.
Introduction Electrokinetic studies on latex particles provide growing evidence of anomalous behavior insofar as interpretations using the standard model are concerned. The presence of a maximum in the mobility-electrolyte concentration relation along with differences between ζ-potentials determined by different methods are two of the more common anomalies.1-6 Among the reasons postulated to explain such behavior are ion adsorption, surface “hairiness”, and anomalous conduction.7-11 Ion adsorption involves the localization of co- and counterions behind the shear plane. Accordingly, the particle charge is established by contributions from the ionization of covalently charged groups as well as ion adsorption and may vary due to polarization of the diffuse layer. With hairy particles, one evisions the surface as having a large number of polymer chains extending into the solution. The charge on the particles is due to charged groups on the surface and, in some instances, on polymer chains protruding into the solution. The presence of hairs increases the hydrodynamic drag, displaces the shear plane outward lowering the potential at the shear surface, and alters lateral transport of ions behind this surface. Anomalous conduction, per se, involves transport processes behind the shear surface. Another class of anomalies derives from approximations inherent in the standard model, e.g., the use of the Gouy* To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, February 15, 1996. (1) Midmore, B. R.; Hunter, R. J. J. Colloid Interface Sci. 1988, 122, 521. (2) Rosen, L. A.; Saville, D. A. Langmuir 1991, 7, 37. (3) Dunstan, D. E.; Saville, D. A. J. Chem. Soc., Faraday Trans. 1992, 88, 2031. (4) Voegtli, L. P.; Zukoski, C. F. J. Colloid Interface Sci. 1991, 141, 92. (5) Gittings, M. R.; Saville, D. A. Langmuir 1995, 11, 798. (6) Barchini, R.; Saville, D. A. J. Colloid Interface Sci. 1995, 173, 86. (7) Elimelech, M.; O’Melia, C. Colloids Surf. 1990, 44, 165. (8) Rosen, L. A.; Saville, D. A. J. Colloid Interface Sci. 1992, 149, 542. (9) Chow, R. S.; Takamura, K. J. Colloid Interface Sci. 1988, 125, 226. (10) Van der Put, A. G.; Bijsterbosh, B. H. J. Colloid Interface Sci. 1983, 92, 499. (11) Kijlstra, J.; van Leeuwen, H. P.; Lyklema, J. Langmuir 1993, 9, 1625.
Chapman model of the diffuse layer, the assumption that ion mobilities are uniform and derived from limiting conductances, the neglect of ion size, etc. Here deviations would arise because the high surface charge invalidates some of the assumptions employed in the standard model. To focus on the effects of a high charge and avoid problems related to the presence of polymer chains at the interface, we studied a system with molecularly smooth particles, charged oil drops dispersed in water. Surface charge arises from adsorbed ionic surfactant-sodium dodecyl sulfate (SDS). Dissociated ionic surfactant also forms the background electrolyte. Electrophoretic mobility and static conductivity measurements were analyzed with the standard electrokinetic theory. The results deviate from what would be expected if the droplets behaved in a classical fashion. Experimental Section Monodisperse emulsions, consisting of silicon oil drops dispersed in water and stabilized by sodium dodecyl sulfate (SDS), were prepared at the Exxon Corporate Laboratories by T. Mason, following a procedure proposed by Bibette.12 The silicon oil has a viscosity, η, of 110 cP. The essence of the fractionation is a creaming separation induced by attractive depletion forces originating from the presence of SDS micelles in the system. To secure a known surfactant bulk concentration, the emulsions were first redispersed in 0.01 M SDS and repeatedly centrifuged until the conductivity of the remnant was within 1% of the conductivity of 0.01 M SDS. The desired SDS concentration was achieved through dilution with the appropriate solution. All systems were prepared using filtered, deionized, doubly distilled water and SDS from Fluka. Final SDS concentrations ranged from 3 to 7 mM. This range was chosen so that the solutions remained below the critical micellar concentration (8 mM) and above the lower SDS concentration that assures emulsion stability (2.7 mM). The stability diagram for SDS emulsions13 shows two regimes of interest: (i) below 2.7 mM SDS, emulsions are unstable suggesting that the SDS coverage of the oil-water interface is low; (ii) in the surfactant-rich regime, emulsions undergo coalescence only when most of the water is squeezed from the system. This limit was never achieved in our experiments since the oil volume fractions remained below 6%. Because of the fractionating method, the amount of monodisperse emulsion (12) Bibette, J. J. Colloid Interface Sci. 1991, 147, 474. (13) Bibette, J.; Morse, D. C.; Witten, T. A.; Weitz, D. A. Phys. Rev. Lett. 1992, 69, 2439.
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Table 1. Drop Radius, a (from Light Scattering), and Double Layer Thickness, K-1, in 3, 5, and 7 mM SDS κa system
a (nm)
δa/a
3 mM
5 mM
7 mM
I II III
276 374 576
0.05 0.05 0.3
49.6 67.3 103.6
64.1 86.9 133.8
75.8 102.8 158.3
Figure 2. ζ-Potential (standard theory)-SDS concentration relation. Symbols correspond to the low potential and high potential solutions as follows: 2, a ) 276 nm; b, a ) 374 nm; (, a ) 576 nm.
Figure 1. Electrophoretic mobility of oil drops in water/SDS solutions at 25 °C: 2, a ) 276 nm; b, a ) 374 nm; (, a ) 576 nm. available for our experiments was small and this prevented us from going to higher concentrations. Drop sizes were determined by homodyne dynamic light scattering using a laser light scattering goniometer and BI 2030AT correlator (Brookhaven Instruments). Table 1 shows the droplet radii, a, and the polydispersity, δa, for the three emulsions. δa values were determined from the cumulant fit of the deviation of the correlation function from a true exponential decay. The thickness of the double layer surrounding the drops is also indicated in the table through the product κa; κ-1 corresponds to the Debye screening length. The double layer is composed primarily of Na+ counterions from the dissociation of SDS molecules. In all cases the double layer can be considered thin (κa g 50). Droplet mobilities were determined using a Doppler electrophoretic light scattering apparatus (Coulter Delsa 440) working at 25 °C. The particle velocity profile across the cell was measured and fitted to a Komogata-type equation to determine the particle mobility. In every case the curve fitting confidence limit was at least 99.8%. Measurements of emulsion conductivity were made with an Altex conductivity bridge (Beckman) and a dip-type probe. The bridge operated at 1 kHz and the samples were held in a water bath thermostated to 25 ( 0.05 °C. Conductivities were measured as a function of particle volume fraction, φ, by successive dilution of a stock emulsion. The first volume fraction was determined by drying and weighing a small sample. Intermediate values were calculated from the dilution amounts so as to preserve as much emulsion as possible. As a control, the volume fraction of the last (and most dilute) sample was measured gravimetrically.
Experimental Results Electrophoretic Mobility. Figure 1 shows the electrophoretic mobility, µ, measured at different surfactant concentrations for three emulsion systems. An increase in the absolute value of the mobility with increased surfactant concentration is observed with each emulsion. The negative values of the mobility reflect the fact that the oil drops are negatively charged due to SDS headgroups on the surface. ζ-Potentials derived using the
Figure 3. Molecular area per charged group on the drop surface for the high ζ-potential solution. 2, a ) 276 nm; b, a ) 374 nm; (, a ) 576 nm.
standard theory14 are shown in Figure 2. In the calculations we assumed the oil drops behaved as rigid bodies due to the presence of the surfactant on the interface. Shear rheology studies of dilute emulsions have shown that the drops behave like undeformed solid spheres.15 The radii were taken from the light scattering results. For each mobility there are two possible solutions for the ζ-potential. These are called, respectively, “low” and “high”. The most striking feature of the ζ-potentials shown in Figure 2 is the lack of sensitivity to either drop radius or SDS concentration. More insight into the low and high solutions can be gained by analyzing the drop charge. For values of the ζ-potential near -80 mV, the surface charge varies between -1 and -3 µC/cm2. This corresponds to a molecular area per surfactant headgroup of around 1000 Å2. The high solution (ζ ∼ -250 mV) corresponds to a larger surface charge (Figure 3). Even though surfactant adsorption is widely studied, we are not aware of adsorption studies for SDS on oil droplets. Reports on the adsorption of SDS on monodisperse synthetic lattices indicate a Langmuir isotherm with a molecular area at saturation of the same order as shown in Figure 3 (see Table 2). Two limiting situations providing further insight correspond to an SDS micelle and a flat SDS monolayer. (14) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 43, 1607. (15) Mason, T. G. Rheology of monodisperse emulsions, PhD Thesis, Princeton University, 1995.
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Table 2. Adsorption Data for SDS on Synthetic Lattices
source Sawyer et al. (24) Brodnyan et al. (25) van de Hul et al. (26) Ahmed et al. (27) Brown et al. (28)
method titration dialysis and titration surface tension serum replacement surface tension
area per particle molecule radius (Å2) (nm) 52 58 46 42 33
Table 4. Comparison of ζ-Potentials Determined from Mobility (ζµ) and Conductivity (ζσ) Measurements system I
82 230 88 95 115
II III
a
[SDS], mM
ζµ (mV)
3 5 7 3 5 7 3 5 7
-224 -227 -227 -248 -245 -246 -244 -256 -261
ζσ (mV) a -204 -191 a -212 -186 -208 -161 -164
Outside the range of the standard theory.
Figure 4. Emulsion conductivity-volume fraction relation for system II (a ) 374 nm): b, 3 mM SDS; 9, 5 mM SDS; 2, 7 mM SDS. Table 3. A Comparison of Experimental and Theoretical Values of the Slope of the Conductivity-Volume Fraction Relation for System IIa surfactant concentration
[(σ - σe)/σe]exp
[(σ - σe)/σe]theo
3 mM SDS 5 mM SDS 7 mM SDS
2.21 0.82 0.28
1.36 1.19 1.10
In the former case, the characteristic micellar radius is 20 Å with an aggregation number ∼6016 resulting in a molecular area of ∼62 Å2. At the other limit, the crosssectional area for a hydrocarbon chain in a compact monolayer film corresponds to 20.5 Å2.17 Our electrophoretic mobility data are consistent with behavior where oil/SDS drops are solid spheres with a surface charge compatible with almost complete coverage by SDS molecules. Electrical Conductivity. The charge on oil/SDS droplets has a significant influence on the emulsion conductivity, providing another means of investigating the electrokinetic charge. Figure 4 shows the normalized conductivity of system II (a ) 374 nm) at SDS bulk concentrations of 3, 5, and 7 mM. The normalization factor corresponds to the surfactant conductivity. There is a noteworthy linear increase in conductivity with increasing oil content. Increasing the bulk concentration of surfactant decreases the slope. ζ-Potentials derived from these data using the standard theory18 are shown in Table 3, along with those from mobility measurements. According to the theory, the emulsion conductivity has a linear dependence on particle volume fraction, with a slope determined by (i) counterions produced by the charging of the drops, (ii) changes in the bulk concentrations of coand counterions (nonspecific adsorption), and (iii) double layer effects. Numerical estimates of these contributions indicate that (iii) dominates here. For example, for system II contributions i and ii account for only 4% (in 3 mM (16) Gruen, D. W. R. Prog. Colloid Polym. Sci. 1985, 70, 6. (17) Becher, P. Emulsions: Theory and Practice; Robert Krieger Publishing Company: Malabar, FL, 1965. (18) Saville, D. A. J. Colloid Interface Sci. 1983, 114, 32.
Figure 5. Volume fraction dependence of the emulsion conductivity with a 3 mM SDS bulk concentration: 2, a ) 276 nm; b, a ) 374 nm; (, a ) 576 nm.
SDS), 9% (in 5 mM SDS), and 13% (in 7 mM SDS) of the total conductivity slopes. Table 4 compares the experimentally measured slopes with those calculated from the standard theory using the high ζ-potential values derived from electrophoretic mobility. Obviously the experimental values of the conductivity cannot be reproduced taking the low ζ-potential results. However, the agreement with slopes calculated using the high ζ-potentials is also poor, indicating a lack of consistency between results derived from mobility and conductivity experiments. Moreover, it is puzzling that the conductivity increment in 3 mM SDS is so high that it is not possible to estimate ζ-potentials except for the largest particle (Table 3). In the other cases (5 and 7 mM SDS) the ζ-potential determined from the conductivity is much less than that estimated from the mobility (see Table 4). Figures 5 and 6 show the influence of drop size on the conductivity increment for a fixed surfactant concentration. The increment diminishes with increasing particle radius. For system III (a ) 576 nm) the sign changes. This system has a larger polydispersity than the other two (see Table 1) which may be an indication of partial flocculation. This would tend to decrease the conductivity. Similar changes were observed with another system having a polydispersity similar to system III. A simple characterization of the effect of the particles on the bulk conductivity can be obtained from the Maxwell-Wagner mixture formula19
(
σ ) σe 1 + 3φ
)
σp - σe σp + 2σe
(1)
Here σe represents the conductivity of the background (19) Maxwell, T. G. Electricity and Magnetism; Oxford University Press (Clarendon): London, New York, 1873.
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our experiments. Ideal solution behavior of the sort envisioned in the standard model is unlikely. Another factor is a variation in counterion mobility within the thin double layer. In our calculations, bulk ionic conductances of 50.1 and 22.9 cm2/Ω s were used for sodium ions20 and dodecyl sulfate ions,21 respectively. These values are probably not appropriate here. A further appreciation of the step gradients and sharp variations in present in these systems can be obtained from the expression for the potential near a flat charged plate22
(
)
ξ 4 Ψ ) 2 ln ξ 1 - e-κy tanh 4 1 + e-κy tanh
Figure 6. Volume fraction dependence of the emulsion conductivity with a 5 mM SDS bulk concentration: 2, a ) 276 nm; b, a ) 374 nm; (, a ) 576 nm.
Figure 7. Oil drop equivalent conductivity (eq 1) normalized with surfactant bulk conductivity for system II (a ) 374 nm), b, and system III (a ) 576 nm), (.
SDS electrolyte and σp the oil drop equivalent conductivity. Figure 7 shows that σp > σe for system II but not for system III. Discussion When interpreted with the standard theory, electrokinetic measurements on the particles studied here show significant deviations from the expected behavior. The most likely reasons appear connected with the high surface charge. For example, the high field strength and counterion concentration in the vicinity of the interface would cause dielectric saturation and polarization effects not taken into account by the theory. In addition, counterion densities near the surface are extremely large. For a ζ-potential of -250 mV, the exponential factor in the Boltzmann distribution is more than 104 and this would suggest a sodium ion concentration greater than 30 M in
(2)
Here ξ and Ψ denote dimensionless potentials at the surface and at a distance y. If we interpret ξ as a potential consistent with the high packing of SDS on the surface, then one need move only 4 Å to lower the potential by 30%. The difference between the potentials determined from mobility and conductivity measurements is this order of magnitude. Noting that the sulfate headgroup has a radius of 3.6 Å23 and the hydrated sodium ion radius is 4.2 Å20 suggests that nonstandard behavior is hardly unexpected. Perhaps the finite volume occupied by the ions should be taken into account along with the factors noted above. Finally, our limited knowledge of the exact nature of the dependence of viscosity and permittivity on the field strength and electrolyte concentration makes it difficult to estimate the appropriate corrections. The focal point of this work involved determining the electrokinetic properties of highly charged colloidal particles to ascertain the extent to which the standard electrokinetic model is a good approximation. Our results pose challenging questions and show the care that must be exercised when applying the theory to highly charged colloidal particles. Acknowledgment. We thank Dr. T. Mason for the preparation of the emulsions. Our work was supported by grants from the National Science Foundation, NASA’s Microgravity Science and Applications Division, the Xerox Corporation, and the Rohm and Haas Company. LA950693A (20) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1959. (21) Parfitt, G. D.; Smith, A. L. J. Phys. Chem. 1962, 60, 942. (22) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (23) Stigter, D. J. Phys. Chem. 1974, 78, 2480. (24) Sawyer, W. M.; Rehfeld, S. J. J. Phys. Chem. 1963, 67, 1973. (25) Brodnyan, J. G.; Kelley, E. L. Polymer Prepr. 1966, 7, 827. (26) van den Hul, H. J.; Vanderhoff, J. W. In Polymer Colloids; Fitch, R. M., Ed.; Plenum Press: New York, 1971. (27) Ahmed, S. M.; El-Aasser, M. S.; Micale, F. J.; Poehlein, G. W.; Vanderhoff, J. W. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York and London, 1979; Vol. 2. (28) Brown, W.; Zhao, J. Macromolecules 1993, 26, 2711; 1995, 28, 2103, (1995).
