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Langmuir 2003, 19, 4778-4783
Charging of Latex Particles Stabilized by Sulfate Surfactant Jan Sefcik, Marcel Verduyn, Giuseppe Storti, and Massimo Morbidelli* Swiss Federal Institute of Technology Zurich, Laboratorium fu¨ r Technische Chemie, ETH Ho¨ nggerberg/HCI, CH-8093 Zurich, Switzerland Received August 21, 2002. In Final Form: December 7, 2002 Surface charging of polystyrene latex particles stabilized with sodium dodecyl sulfate (SDS) was investigated. The surfactant adsorption isotherm and electrophoretic mobilities of monodisperse latex particles were measured. Electrophoretic mobility measurements at moderate ionic strengths (around 0.1 M) indicated a substantial degree of counterion binding to adsorbed dodecyl sulfate anions, comparable to that found in SDS micelles. We offer a consistent description of surface charging of SDS-stabilized latex particles and SDS micelles taking into account binding of sodium counterions to dodecyl sulfate anions.
Introduction In this work, we study how surface charging of polymeric latex particles stabilized by an anionic surfactant (sodium dodecyl sulfate) is related to basic characteristics of the latex, such as particle size, volume fraction, and solution concentrations of surfactant and salt. The adsorption of the anionic surfactant at the polymer surface results in the formation of a charged interface, where the surface charge due to partial or full dissociation of ionic groups results in the formation of a diffuse double layer. Charging of aqueous-hydrophobic interfaces is an important physicochemical phenomenon in many industrial and biological systems, especially at moderate to high ionic strengths.1 Understanding the surface charging of colloidal particles is important for assessing their electrokinetic behavior and colloidal stability. Surfactant-free polystyrene latexes stabilized by sulfate2 and carboxylate3 groups were characterized using titration and electrophoretic mobility measurements, and accurate interpretation of surface charging in these latexes was achieved when considering the electrokinetic shear plane positioned just a few angstroms away from the particle surface. For weakly acidic (carboxylate) groups at the surface of polystyrene particles, the appropriate counterion (proton) binding constant was found to be close to that in bulk aqueous solutions.3 On the other hand, counterion binding was not demonstrated for strongly acidic (sulfate) groups at the surface of polystyrene particles.2 Many industrial and natural systems contain charged surfaces where the charges come from ionic surfactants adsorbed at water-hydrophobic interfaces. While numerous studies on surfactant adsorption to hydrophilic surfaces4 or water-soluble polymers5 indicated complex behavior due to formation of surfactant aggregates at interfaces or complexation of surfactants with polymers, the behavior of ionic surfactants at hydrophobic surfaces below the critical micelle concentration (cmc) leads to monolayer coverage.6 Although sodium dodecyl sulfate (1) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (2) Folkersma, R.; van Diemen, A. J. G.; Stein, H. N. Langmuir 1998, 14, 5973. (3) Behrens, S. H.; Christl, D. I.; Emmerzael, R.; Schurtenberger, P.; Borkovec, M. Langmuir 2000, 16, 2566. (4) Lee, E. M.; Koopal, L. L. J. Colloid Interface Sci. 1996, 177, 478. (5) Ghoreishi, S. M.; Li, Y.; Bloor, D. M.; Warr, J.; Wyn-Jones, E. Langmuir 1999, 15, 4380.
(SDS) is one of the most widely used anionic surfactants in both industrial and consumer applications, the issue of counterion binding at latex particles stabilized by SDS has not been adequately addressed. Although it is wellknown that counterion binding is significant in SDS micelles7,8 and for SDS at water-air interfaces,9,10 only limited investigations have been conducted for SDSstabilized polymer dispersions.11 Here we characterize polystyrene latexes stabilized by SDS in terms of equilibrium surface coverage (adsorption isotherm) and their electrophoretic mobility at moderate ionic strengths and provide a consistent description of their surface charging taking into account binding of sodium counterions to adsorbed dodecyl sulfate anions. Theoretical Framework Electrostatic charge on the surface of primary particles stabilized by an anionic surfactant is due to negative dissociated groups (sulfate) of surfactant molecules (sodium dodecyl sulfate) adsorbed on the particle surface. The adsorption of surfactant molecules on the surface of latex particles results in the surface concentration of dissociable groups Γ (units of mol/m2). Assuming that all sulfate groups at the surface are dissociated, we obtain the bare surface charge density
σ0 ) -F Γ
(1)
where F is the Faraday constant. The net surface charge can be calculated when we consider binding of the surfactant counterion (in this case, sodium) with the corresponding surface charge density σi (of the opposite sign than that of σ0). Consequently, the net surface charge density σ0 + σi is determined by both the adsorption of the surfactant at the particle surface (quantified by Γ) and the extent of its dissociation in the adsorbed state (quantified by the degree of counterion binding R ) -σi /σ0). (6) Windsor, R.; Neivandt, D. J.; Davies, P. B. Langmuir 2001, 17, 7306. (7) Shah, S. S.; Saeed, A.; Sharif, Q. M. Colloids Surf., A 1999, 155, 405. (8) Bales, B. L. J. Phys. Chem. B 2001, 105, 6798. (9) Kalinin, V. V.; Radke, C. J. Colloids Surf., A 1996, 114, 337. (10) Prosser, A. J.; Frances, E. I. Colloids Surf., A 2001, 178, 1. (11) Melis, S.; Kemmere, M.; Meuldijk, J.; Storti, G.; Morbidelli, M. Chem. Eng. Sci. 2000, 55, 3101.
10.1021/la026445d CCC: $25.00 © 2003 American Chemical Society Published on Web 05/01/2003
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Langmuir, Vol. 19, No. 11, 2003 4779
Interplay between energy and entropy of dissociated counterions that are free to move in the aqueous phase, together with the requirement of macroscopic electrical neutrality, implies the presence of a diffuse part of the electrical double layer around each charged latex particle. The surface charge has to balance the diffuse layer charge per unit area of the charged surface σd, so that σd + σ0 + σi ) 0, and thus the diffuse layer charge can be expressed using the surfactant coverage Γ and the degree of counterion binding R as follows:
σd ) F Γ(1 - R)
(2)
The diffuse layer charge density σd can be related to the electrostatic potential ψd using an appropriate model describing the diffuse layer. In the case where only 1-1 electrolytes are present in the aqueous phase, the GouyChapman model is physically reasonable and approximate analytical solutions to the (nonlinear) Poisson-Boltzmann equation exist for the electrostatic potential in the diffuse layer around a spherical particle, for example,12
σd ) -
[
( ) ( )]
eψd kTκ 4 eψd 2 sinh + e 2kT κa 4kT
κ)
x
(4)
I)
∑k zk2 c∞k
2
(5)
where c∞k is the bulk concentration of ions of type k, NA is the Avogadro number, e is the charge of an electron, and is the electric permittivity of the aqueous phase, equal to the product of the vacuum permittivity 0 and the relative permittivity r (dielectric constant) of water. The inner part of the electrical double layer can be described by the Stern model, introducing two hypothetical planes parallel to the charged surface: the inner Helmholtz plane (IHP), where the bound counterions are located, and the outer Helmholtz plane (OHP), located outward at some distance from the IHP, where the diffuse layer starts. Thus the electrical potential is equal to ψd at the OHP, while at the IHP it is designated by ψi. The Stern layer between the IHP and the OHP is ion free and acts as a condenser with the capacitance Cs, so that the inner layer potential can be related to the diffuse layer potential and charge as follows:
ψd - ψ i )
σd Cs
(6)
It is usually not reliable to make a priori assumptions about the Stern layer capacitance, and this is often used as a fitting parameter in trying to reconcile model (12) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. A. Particle Deposition and Aggregation; Butterworth-Heinemann: Woburn, MA, 1995. (13) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989.
[MS]s
(7)
[M+]ihp[S-]s
where KM is the counterion binding constant, and [S-]s and [MS]s denote surface concentrations of the respective sites. [M+]ihp is the counterion concentration at the IHP, related to the bulk counterion concentration c∞M through the inner layer potential ψi using the Boltzmann relation:
( )
[M+]ihp ) c∞M exp -
eψi kT
(8)
The overall degree of counterion binding R is then obtained from the surface charge balance:14
( ) ( )
eψi kT ) R) eψi [MS]s + [S ]s 1 + KMc∞M exp kT [MS]s
where the ionic strength I is
1
KM )
(3)
This equation gives the surface charge density within 5% of the accurate numerical solution of the PoissonBoltzmann equation for any value of the potential ψd and κa > 0.5.13 Here a is the radius of the particle and κ (the inverse of the Debye length) is given by
2e2NAI kT
calculations with measured quantities. Under some conditions, however, the Stern layer capacitance can be deduced from titration experiments.14 The Stern layer capacitance Cs determines the ability of the inner layer to adsorb additional counterions. As the capacitance decreases, more counterions can be bound in the inner layer electrostatically (due to the increasing absolute value of the inner layer potential ψi). This is important when considering the charging of the surface with varying solution ionic strength. Binding of the counterion M+ to the surface site S- at the IHP is described by the equilibrium relation
KMc∞M exp -
(9)
Thus, in summary, using eqs 2, 3, 6, and 9 it is possible to calculate the main characteristics of the electrical double layer, that is, ψi, ψd, σd, and R, if the adsorbed surfactant concentration Γ, the counterion binding constant KM, and the Stern layer capacitance Cs are known. To test this model quantitatively, we use experimental data on the electrophoretic mobility of latex particles. When a colloidal particle surrounded by an electrical double layer is subjected to an external electrical field, it moves toward the electrode with the charge opposite to that of its surface. The corresponding velocity vE is such that the electrical force exerted by the electrical field is balanced by viscous friction.15 An oscillating electrical field can be applied in order to force the particles to move back and forth within the measurement cell. The particle velocity is then measured through laser Doppler velocimetry, and the electrophoretic mobility is calculated as the particle velocity vE per unit of the applied electrical field E. The zeta potential ψζ is then calculated from the measured values of the electrophoretic mobility using the model of O’Brien and White, considering double layer relaxation and retardation effects.16 This model is accurate at the moderate ionic strengths considered here, where conduction behind the shear plane is not expected to be significant.14 To relate the zeta potential ψζ to the diffuse layer potential ψd, we need to consider the distance of the shear plane from the particle surface ∆shear. Then the two potentials ψζ and ψd are related through the equation
tanh
( )
( )
eψζ eψd ) tanh exp(-κ∆shear) 4kT 4kT
(10)
It is usually assumed that the shear plane distance ∆shear is fixed for a certain range of conditions. However,
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Sefcik et al.
experimental data relating the solution electrolyte concentration and the shear plane position have been reported for colloidal particles17 and surfactant micelles.18 Both of these sets of data can be described by the linear relationship
∆shear ) 0.2κ-1
(11)
Table 1. Properties of Original Latex Dispersions (a) Measured Values latex
water [g]
initiator [g]
styrene [g]
SDS [g]
solid wt fraction
mean diam [nm]
B F
937.5 937.5
1.0 1.0
200 175
7.5 1.5
0.163 0.148
75 114
(b) Calculated Values
between the shear plane distance and the Debye length. Experimental Section Preparation of Polystyrene Latex Dispersions. Polystyrene latexes were prepared by emulsion polymerization.19 The only cations present were sodium ions that came from the emulsifier (sodium dodecyl sulfate, C12H25SO4Na) and from the initiator (sodium persulfate, Na2S2O8). A typical batch polymerization recipe was as follows: 10 g of SDS was dissolved in 937.5 g of distilled water, and 200 g of styrene monomer was added. The emulsion was stripped by nitrogen to remove oxygen and further kept under a nitrogen atmosphere. The batch was thermostated at 60 °C and stirred at 400 rpm. Polymerization was initiated by adding 1 g of sodium persulfate. Monomer conversion was monitored during polymerization by gravimetry. When the monomer conversion did not change further, hydroquinone inhibitor (in solid form) was added to eliminate any residual radical activity in the latex dispersion. Finally, the residual monomer was removed by stripping with nitrogen, with negligible accompanying loss of water. Mean hydrodynamic diameter and polydispersity were determined by dynamic light scattering using the Zetasizer 5000 (Malvern Instruments). The final weight fraction of solids, that is, polymer, initiator, and surfactant, in the latex dispersion was determined by gravimetry, based on measuring the sample weight before and after complete drying, using the HG53 Halogen Moisture Analyzer (Mettler Toledo). Measurement of the Surfactant Adsorption Isotherm. The procedure followed to measure the surfactant adsorption isotherm was to add known amounts of SDS to a well-defined latex dispersion, that is, a system whose particle size and weight fraction of polymer were evaluated before (Verduyn, M. Aggregation of Polymer Particles in Emulsion. PhD Thesis, ETH Zurich, Zurich, 1999). Note that SDS is added in solid form to avoid volume changes that would affect the interphase partitioning of the surfactant at equilibrium. In this way, the surface concentration of surfactant Γ increases after each addition. To achieve surface concentrations lower than that of the initial latex, the system is diluted using distilled water. In this way, a wide range of surfactant surface concentrations can be explored and we can construct the complete SDS adsorption isotherm. An ultrafiltration unit was used to make the required phase separation between the aqueous and the particulate phase of the latex dispersion after equilibration. The ultrafiltration was done with care to avoid a shift of the surfactant adsorption equilibrium during filtration. For this reason, only a small amount of filtrate was collected, thus avoiding the deposition of a thick cake of polymer particles on top of the filter. Moreover, because of its slightly hydrophilic nature the filter offers no hindrance to the passage of SDS, which would result in a lower SDS concentration in the obtained filtrate. The absence of such a problem was verified by preparing a series of calibration standards with SDS concentrations in the range of interest. These standards were then passed through the ultrafiltration unit, and the SDS concentration was measured by ion chromatography. A maximum difference of about 5% was found for the range of SDS concentrations considered here. Ultrafiltration was performed in a batch (14) Lyklema, J. Fundamentals of Interface and Colloid Science (Vol. II); Academic Press: London, 1995. (15) Hunter, R. J. Foundations of Colloid Science, 2nd ed.; Oxford University Press: Oxford, 2001. (16) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (17) Xu, R. Langmuir 1998, 14, 2593. (18) Charlton, I. D.; Doherty, A. P. J. Phys. Chem. B 1999, 103, 5081. (19) Gilbert, R. G. Emulsion Polymerization: A Mechanistic Approach; Academic Press: London, 1995.
latex
x
B F
0.150 0.140
Na Ib Sa Γ0 % SDS cs,aqb [1014/mL] [m2/mL] [µmol/m2] adsorbed [mM] [mM] 6.80 1.81
12.0 7.37
1.93 0.634
98.4 98.0
0.537 0.116
14.0 13.6
a Particle number concentration N and surface area S refer to the latex volume. b SDS concentration cs,aq and ionic strength I refer to the aqueous phase volume.
mode to separate the aqueous phase from the latex dispersion under continuous stirring with a magnetic stirrer to prevent a significant deposition of polymer particles on the filter. An average pressure of 1.5 bar was applied to force the aqueous phase of the latex dispersion through the filter material. The average pore size of the filter (Filtron) is given as 100 kDa, corresponding to about 7 nm. Hence, it is expected that nearly complete phase separation can be achieved. The ultrafiltration device used was the Gyrosep 75 Stirred Cell (Intersep). The concentration of sodium in the separated aqueous phase was determined by atomic absorption spectroscopy (AAS), and that of SDS by ion chromatography. From the latter, it is possible to determine the adsorption isotherm of SDS on polystyrene particles. We used the Metrohm 690 Ion Chromatograph with the conductivity detector. The mobile phase was a 55/45 mixture of methanol and water with a concentration of ammonium acetate (CH3COONH4) of 17 mg/L. The column used as a stationary phase was Nucleosil 120-5 C18. Electrophoretic Mobility. A series of measurements of the electrophoretic mobility of the latex particles as a function of the electrolyte concentration were conducted at low salt concentrations where latexes are stable over many hours, much longer than the measurement time scale. To keep a good control over the surfactant coverage of the latex particles, the latex was diluted only slightly (1.2 times) by adding 10 mL of NaCl solution to 50 mL of the original latex dispersion. Since the number concentrations of these dispersions were too high to allow for in situ measurements of the particle velocity by laser Doppler velocimetry, the samples were diluted with the serum obtained by ultrafiltration of the respective dispersions. A few drops of the dispersion were added to the filtrate, and the electrophoretic mobility was measured. The measurements were carried out with the Zetasizer 5000 (Malvern Instruments).
Results and Discussion Original Latex Characterization. A standard batch emulsion polymerization process was adopted to produce latexes with the desired mean particle size by varying the amount of the surfactant (emulsifier), while keeping the particle volume fraction approximately constant and the particle size distribution narrow. Table 1a summarizes the reaction recipes (amounts of water, initiator, styrene, and SDS used) and the properties of the resulting latex dispersions (final mean particle diameter d and solid weight fraction ws). The weight fraction of solids is given by the mass ratio
ws )
P+S+I P+S+I+W
(12)
where P, S, I, and W represent the mass of polymer, surfactant, initiator, and water, respectively, assuming that only a negligible amount of unreacted monomer is present in the latex after stripping. The mass ratio of
Charging of Latex Particles Stabilized by SDS
Langmuir, Vol. 19, No. 11, 2003 4781 Table 2. Electrophoretic Mobility Measurements and Zeta Potential Calculations ionic strength latex [mM] B
F
Figure 1. SDS adsorption isotherm (experimental data and Langmuir type fit) on polystyrene latex particles at I ) 14 mM.
polymer to water in the latex is then given by
P ) W
ws -
S+I (1 - ws) W 1 - ws
(13)
Neglecting volume contributions from the surfactant and the initiator, we calculate the solid volume fraction
x)
P W Fp P + W Fw
(14)
where Fp ) 1.05 g/cm3 is the polymer density and Fw ) 1.00 g/cm3 is the water density. Using the mean particle diameter d and considering that the latexes under examination are substantially monodisperse, we obtain the particle concentration N (number of particles per unit volume of latex),
N)
x π 3 d 6
(15)
and particle surface area per unit volume of latex,
S ) Nπd2
(16)
The values of each of these quantities, calculated for all latexes, are summarized in columns 2-4 of Table 1b. At equilibrium, the SDS in a latex is partitioned between the aqueous phase and the surface of the polymer particles, as given by the following mass balance:
cs,tot ) cs,aq + SpΓ
(17)
where cs,tot is the total concentration of SDS in the latex dispersion (expressed in moles per liter of the aqueous phase), cs,aq is the SDS concentration in the aqueous phase (in moles per liter of the aqueous phase), Sp is the particle surface in m2 per liter of the aqueous phase (Sp ) S/(1 x)), and Γ is the surface coverage of SDS on the polymer particles in mol/m2. To determine the surfactant adsorption isotherm Γ ) f (cs,aq), the aqueous phase SDS concentration was measured at different values of the total SDS concentration in the system. Experimental SDS adsorption data are described well, as shown in Figure 1, by a Langmuir type adsorption isotherm,
Γ)
K1cs,aq 1 + K2cs,aq
(18)
39.9 68.4 96.9 125. 154. 39.3 67.7 96.0 124. 153.
κa
Γ low/high [µmol/m2]
24.7 1.92/1.97 32.3 38.5 43.7 48.5 37.3 0.631/0.648 48.9 58.2 66.2 73.5
mobility std dev [µm s-1/ [µm s-1/ ψζ std dev V cm-1] V cm-1] [mV] [mV] -3.94 -3.20 -2.88 -2.52 -2.44 -2.74 -2.33 -1.68 -1.46 -1.22
0.21 0.32 0.37 0.35 0.36 0.22 0.25 0.30 0.22 0.26
-59 -45 -40 -37 -33 -36 -31 -21 -19 -15
3 4 5 4 5 3 3 4 3 3
where K1 ) 6.38 × 10-3 dm3/m2 and K2 ) 1.45 × 103 dm3/ mol. Our results agree with previously published data for adsorption of SDS from water on spin-coated polystyrene layers20 but indicate a somewhat higher adsorption than an older isotherm obtained on a cleaned polystyrene latex.21 Using eqs 16 and 17, we calculated the SDS surface coverage Γ0, the aqueous phase concentration cs,aq, and the fraction of SDS adsorbed (1 - cs,aq/cs,tot) for each of the latexes considered here, knowing the amount of SDS used in the corresponding synthesis recipe. The obtained results are summarized in columns 5-7 in Table 1b. It is seen that only about 2% of the total SDS amount remains in the aqueous phase. Note that for both latex dispersions studied here the surfactant concentration in the aqueous phase was well below the cmc. At the synthesis temperature used here, only a negligible amount of the initiator is consumed during the polymerization reaction and incorporated into the polymer chains, so that essentially all the initiator is still present, in some form, in the latex aqueous phase. The bulk sodium concentration in the aqueous phase of the original latex dispersions thus corresponds to the sum of 8.96 mM from the total amount of the initiator (sodium persulfate, partially hydrolyzed to sulfate) and a small contribution (10 mM) where effects such as the “hairy layer” should not be significant.2,15 As a second approximation, we can neglect the separation between the shear plane and the particle surface and assume that the entire diffuse double layer is outside the shear plane, so that ∆shear ) 0 and σd ) σζ. Using this approximation for the surface charge density, we can calculate the corresponding degree of counterion binding as
R)
F Γ - σζ FΓ
(19)
using the average surfactant surface coverage Γ from Table 2. Thus we obtain R ) 0.83 for latex B and R ) 0.73 for latex F. Although these values have a magnitude comparable to the degree of counterion binding for SDS micelles in aqueous solutions, which was found to be close to 0.73,7,8 it is obvious that this approach is not able to explain why the degree of counterion binding is different for the two latexes. To reconcile the experimental electrophoretic mobility measurements for the two latexes, we consider the more detailed picture of the surface charging mechanism discussed above. In particular, for any given set of values for the counterion binding constant KM, the Stern layer capacitance Cs, and the shear plane distance ∆shear, we can compute the zeta potential as a function of ionic strength using eqs 2, 3, 6, 9, 17, and 18. The electrical double layer charging theory, as discussed earlier in the theoretical background, can lead to surface charge either decreasing or increasing with the ionic strength, depending on whether the bulk electrolyte is a binding or an inert ion. When the binding ion concentration is constant and the ionic strength increases due to an inert ion (as is the case for carboxylate latexes at a constant pH),3 the surface charge increases with increasing ionic strength. On the other hand, if the binding ion is the same as the bulk
Figure 2. Sodium counterion binding constant for latexes B and F as a function of the shear plane distance from the particle surface.
electrolyte (this is the case for the carboxylate latex with a strong acid added as the only electrolyte), the surface charge decreases with increasing ionic strength. In our case, with sulfate groups at the surface, we do not expect a significant degree of proton binding compared to that of sodium cations at neutral pH and relatively high ionic strength due to sodium chloride.23 We now use the Stern model to quantitatively describe sodium counterion binding to surface sulfate groups. Since the Stern layer capacitance Cs and the shear plane distance ∆shear are not accessible independently in our system, we choose reasonable ranges for their values, being guided by previous investigations. For carboxylate polystyrene latexes, it was found by careful characterization including titration, electrophoretic mobility, and aggregation rate measurements that all the data were consistently explained using infinite Cs (i.e., no potential drop in the Stern layer) and ∆shear ) 0.25 nm.3 For sulfate-stabilized latexes at high ionic strengths, the shear plane distance was found to be between 0.2 and 0.6 nm.2 The hairy layer invoked for explaining large shear plane distances of several nanometers at low ionic strengths would be collapsed at the ionic strengths (>30 mM) considered here.2 For other systems, values of the Stern layer capacitance Cs as low as 0.2 C/(V m2) were found,12 while the distance between the outer Helmholtz plane and the shear plane is typically found to be on the order of 0.1 nm.15 On the basis of these results, we consider in the following two models for ∆shear: the first one is simply to take ∆shear independent of ionic strength and equal to a constant value between 0 and 0.6 nm; the second is the one discussed above where ∆shear is proportional to the Debye length according to eq 11, that is, decreasing with ionic strength. Two extreme values for the Stern layer capacitance Cs are considered: infinite and 0.2 C/(V m2). For any combination of values for Cs and ∆shear, we determine the remaining unknown parameter, the sodium counterion binding constant KNa, by fitting the zeta potential data in Table 2 separately for latexes B and F. Let us first consider the case with infinite Stern layer capacitance and ∆shear independent of ionic strength. The estimated binding constants KNa (together with the corresponding 95% confidence intervals) are plotted in Figure 2 as a function of the assumed value of ∆shear for the two latexes B and F. It is seen that for the smaller values of the shear plane distance, that is, ∆shear < 0.5 nm, the difference between the KNa values estimated for the two latexes is statistically insignificant, considering their confidence intervals. However, the observation that such (23) Garcia-Rio, L.; Leis, J. R.; Pena, M. E.; Iglesias, E. J. Phys. Chem. 1992, 96, 7820.
Charging of Latex Particles Stabilized by SDS
a difference decreases consistently as ∆shear decreases to zero makes these results not fully satisfactory for determination of KNa. Let us now consider the shear plane distance to be proportional to the Debye length according to eq 11, while setting the Stern layer capacitance Cs to infinity. The estimated counterion binding constant is KNa ) 4.6 ((1) dm3/mol for latex B and KNa ) 6.9 ((2) dm3/mol for latex F. Considering the estimated confidence intervals indicated in parentheses, these two values can be regarded as being in a good agreement. On the other hand, when considering a small Stern layer capacitance Cs ) 0.2 C/(V m2), so that the potential drop in the Stern layer is significant, the fitted sodium binding constant KNa was always about 2 orders of magnitude larger for latex F than for latex B. This indicates that the choice of a small Stern layer capacitance is not satisfactory for this system. To validate our estimate of KNa, we apply the above model of counterion binding to SDS micelles. Taking an idealized smooth spherical micelle geometry with radius R ) 1.85 nm and aggregation number N ) 64,24 we get the surface coverage of sulfate groups Γ ) 2.47 µmol/m2 (i.e., about 25% higher than for our latex B). Using this value of Γ and assuming Cs to be infinite, we can calculate, by solving eqs 2, 3, 6, and 9, the micelle surface charge and the degree of counterion binding as a function of KNa. The calculated degree of counterion binding R for SDS micelles at ionic strength I ) 8 mM, corresponding to the critical micelle concentration (with no added salt), is plotted in Figure 3 as a function of the counterion binding constant KNa. This can be compared to the experimental value R ) 0.73 reported for SDS micelles.7,8 It is seen that our calculations are consistent with this value if we take the counterion binding constant KNa ) 6 dm3/mol, in good agreement with the values obtained above for the two latexes investigated. (24) Woolley, E. M.; Burchfield, T. E. J. Phys. Chem. 1984, 88, 2155.
Langmuir, Vol. 19, No. 11, 2003 4783
Figure 3. Degree of counterion binding for SDS micelles as a function of the sodium counterion binding constant.
Conclusions Measurements of the surfactant adsorption isotherm and the electrophoretic mobility of polystyrene latexes stabilized by SDS indicated that there is a substantial degree of counterion binding to SDS adsorbed on polystyrene particles. We used a standard Stern-GouyChapman model of the electrical double layer to describe the surface charging of SDS-stabilized latex particles. Measurements from two different latexes were consistent when the Stern layer capacitance was assumed to be very large and the shear plane was located at a distance from the particle surface given by 0.2κ-1, which at 0.1 M NaCl corresponds to 0.2 nm. The corresponding sodium counterion binding constant was estimated to be KNa ) 6 dm3/ mol. Using this value, we calculated the degree of counterion binding for SDS micelles in good agreement with experiments. Acknowledgment. We gratefully acknowledge the financial support by the Swiss National Science Foundation (Grant NF 2000-061883). LA026445D
