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Surface Electrical Properties of Polystyrene Latex
Journal of Colloid and Interface Science 209, 312–326 (1999) Article ID jcis.1998.5861, available online at http://www.idealibrary.com on
Surface Electrical Properties of Polystyrene Latex 1. Electrophoresis and Static Conductivity Mikael Rasmusson1 and Staffan Wall Department of Physical Chemistry, University of Go¨teborg, S-412 96 Go¨teborg, Sweden E-mail: [email protected] Received March 9, 1998; accepted September 10, 1998
The surface electrical properties of a polystyrene latex have been studied with several experimental methods. Previous studies by other authors have shown discrepancies between the surface potential and the surface charge density determined by different methods. This work is an attempt to produce more experimental data for the discussion concerning these discrepancies. Both electrophoretic mobility and electrical conductivity methods have been used. Also, gel permeation chromatography has been used to estimate the number of endgroups on the latex particle that carry charged surface groups. Synthesis and cleaning methods of polystyrene latex are also discussed. Calculations on a Poisson–Boltzmann level of approximation have been performed in an attempt to connect the quantities determined with dynamic (electrophoresis and static conductivity) methods and static (titration) methods. The discrepancies can be explained by introducing a pH- and electrolyte-dependent surface structure such as the hairy layer model. A Stern layer conductance model can also to some extent explain these discrepancies, but this model contains several parameters not directly attainable by experiments. This means that a unique set of parameters cannot be determined without further studies on several latex systems. © 1999 Academic Press Key Words: z-potential; Stern layer conductance; electrophoretic mobility; conductivity; polystyrene latex.
1. INTRODUCTION
Polystyrene latices have been widely used as model systems for colloids because they can be prepared as practically monodisperse spherical particles. Even if the geometrical dimensions are well defined the surface electrical properties are poorly understood. The electrical properties of latex particles have been investigated mainly by microelectrophoresis (1–7) and electrical conductivity measurements (8 –13), and in some cases dielectric response has been used also (14 –21). Comparison between the experimental results and standard theories based on the Gouy–Chapman Poisson–Boltzmann formalism shows unexpected anomalies. For instance, the magnitude of the z-potential (as determined from microelectrophoresis) often 1
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increases with increasing ionic strength up to 1–10 mM and then decreases. This is not consistent with classical double layer theory, which predicts a decreasing z-potential with increasing electrolyte concentration at constant surface charge density. The latter statement requires that the slip plane is located just outside the beginning of the diffuse double layer (z > Cd) or that ion adsorption in the Stern layer does not depend on the ionic strength. Van der Put and Bijsterbosch (22) have suggested that the polymer ends form a hairy surface, sensitive to the electrolyte content and pH, which induces a shear plan shift, so that z Þ Cd at low ionic strength. Another anomaly is that z-potentials determined from microelectrophoresis often are lower in magnitude than z-potentials determined from electrical conductivity measurements and dielectric response measurements. Zukoski and Saville (23) suggested a Stern layer conductance model that includes adsorption of ions onto underlying surface charge to reconcile the discrepancy between electrophoresis and conductivity data. Another possibility is adsorption onto available surface area, developed by Mangelsdorf and White (24). If ka is large (ka @ 1) it is possible to replace the elaborate Stern layer conductance models with a single surface conductivity parameter, l, which can be measured experimentally (11, 14 –16). Further, Seminikhin and Dukhin (25) have derived an equation that relates the electrophoretic mobility to the z-potential and Cd. In this case it is assumed that z Þ Cd, and ionic conduction occurs between the Outer Helmholtz plane and the shear plane. In this paper, we work under conditions where ka is not very large, and therefore we can not use the notion of surface conduction (i.e., large ka). Surface charge densities determined electrokinetically often correlate poorly with the surface charge densities obtained from titration data. The reason for this discrepancy has not been thoroughly investigated, but it is obvious that the comparison between z, Cd, and the surface potential C0 is complex and model dependent. According to the previously mentioned hairy layer model (22) the surface of shear should be more and more displaced from the particle surface as the electrolyte concentration decreases. Healy and White (26) also demon-
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strate (within the Gouy–Chapman model) that the potential 1–2 nm away from the particle surface is much more insensitive (compared to the surface potential) to both changes in pH and surface site (charge) density. The experimentally determined z-potential has therefore been interpreted as the potential a few nanometers from the particle surface (6, 27, 28) or the Stern plane (10, 11, 14), depending on which model the authors have used. High quality dynamic light scattering measurements on latex particles (7, 29 –31) have also shown that the hydrodynamic radius does decrease with increasing ionic strength, which tends to support the hairy layer model. The existence of a hairy layer was also introduced by Wu and van de Ven (32) to explain their colloidal particle scattering (CPS) results. The importance of cleaning the latex after synthesis must also be emphasized, but there’s still no widely accepted cleaning procedure, since different investigations have produced ambiguous results (13, 33– 40). Heating of the latex particles above the glass transition temperature does seem to produce smoother particle surfaces (19, 28, 41– 43), but the results are again ambiguous and further experimental work is needed. In this investigation, we have synthesized polystyrene latex particles according to the method outlined by Juang and Krieger (44). This method has also been used by Zukoski and Saville (8) and by Voegtli and Zukoski (9). We chose HCl as a supporting electrolyte because we wanted to compare our experimental data with the investigations mentioned above (8, 9). A characterization of the surface groups on the particles has been made using titration methods (conductometric and potentiometric), gel permeation chromatography (GPC), and X-ray photon spectroscopy (XPS). Electrophoresis and conductivity measurements have also been carried out, and the results are compared with other investigations. We also try to reconcile our data using Stern layer conductance (24) and fit our data according to a theory developed by Spitzer (45). 2. EXPERIMENTAL METHODS
2.1. Synthesis of the Latex A sulfate polystyrene latex was synthesized according to the procedure of Juang and Krieger (44). According to the authors, the incorporation of the ionic comonomer sodium styrene sulfonate (NaSS) results in predominantly strong acid groups. This is due to the stronger acidity of the sulfonate groups (pK a ' 22) compared to the sulfate groups (pK a ' 0). There is also an important structural difference between the sulfonate group and the sulfate group. The sulfur in the sulfonate group is directly attached to a carbon atom (–C–SO2 3 ), but the sulfate sulfur is attached via an oxygen bridge (–C–O–SO2 3 ) that is susceptible to hydrolysis (33).
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2.2. Cleaning Procedure A variety of cleaning methods have been used to purify latex suspensions. Harding and Healy (40) tried five different methods, namely, dialysis, ion exchange, centrifugation– decantation, ultrafiltration, and activated charcoal cloth. According to these authors, electron microscopy, surface tension measurements, and potentiometric titrations showed that only centrifugation– decantation and ultrafiltration purified the latex suspensions in a satisfactory way. After some preliminary work with centrifugation– decantation, we decided to ultrafiltrate our sample using a membrane with a pore size of around 5 nm (styrene monomers, oligomers, and other impurities should be removed). We started with a batch called UF1, which was washed with a 20-fold excess of 1 mM HCl. The filtration process was stopped when the conductivity of the filtrate was within 2% of the conductivity of 1 mM HCl. After that, a second batch called UF2 was washed with a 20-fold excess of deionized water (Milli-Q water purification system, k ' 1 mS/cm). We compared the latex suspensions before and after ultrafiltration by using scanning electron microscopy (SEM). It was seen that gel-like material was present at the particle surface in the unpurified sample (NUF), but not in the ultrafiltered samples (UF1 and UF2). This observation has also been reported by Harding and Healy (40). 2.3. Dynamic Light Scattering Dynamic light scattering (DLS) was performed with a Malvern PCS (photon correlation spectroscopy) 100 connected to a Multi-8 correlator. The NUF sample was also analyzed using a Brookhaven BI-90 particle sizer for comparison. The number-averaged diameters were 350 6 10 nm for NUF and 330 6 10 nm for UF1 and UF2. The somewhat larger particle diameter of the unpurified sample NUF (according to DLS) can be ascribed to the gel-like layer that was observed in the SEM pictures. The weight-averaged diameters were about 20 nm larger than the number-averaged diameters. 2.4. Gel Permeation Chromatography The dried fresh latex was dissolved in tetrahydrofurane (THF) and the distribution of molecular weights of the polystyrene molecules constituting the latex particles was determined by using GPC (Version 860/V2.3 from Waters Chromatography Division of Millipore Corp.). A very broad distribution of molecular weights was observed, which is usually the case in emulsion polymerization (34). For UF1, the ratio M w/M n was 54. From GPC and DLS, we calculated the surface charge assuming that two sulfate endgroups should be located at the particle surface for each polystyrene molecule formed (34). Using Mn 5 78,500 g/mol and d 5 330 nm for UF1, this should correspond to a surface charge density of 214.3 mC/cm2.
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FIG. 1. Conductometric titration of a fresh UF2 sample (}, 0.7% latex). No supporting electrolyte was added.
2.5. X-Ray Photon Spectroscopy We decided that it was necessary to perform some kind of surface analysis to determine the nature and the number of surface groups. XPS is a very sensitive method, both with respect to element analysis and the chemical environment of that particular element, and the penetration depth is seldom deeper than 5 nm. Dried latex samples (UF) were sent for XPS analysis to the Department of Solid State Physics, Risø National Laboratory, Denmark. Their XPS measurements were performed using a Sage 100 (SPECS) equipped with a Mg anode operating at 100 W. The spectrum of the fresh latex revealed that oxygen and sulfur were present at a ratio of about 4 to 1. The sulfur peak was typical for a sulfur atom surrounded by oxygen atoms. This indicates that the surface groups are mainly sulfate and/or sulfonate groups. Whether hydroxyl groups also are present cannot be ruled out by the XPS analysis.
values. Healy and White (26) define a surface acid dissociation constant Ka, K a 5 [A2]0[H1]0/[AH]0,
[1]
where [AH]0 is the surface concentration of undissociated acid groups and [A2]0 is related to the surface charge density s according to
s 5 2e[A2]0,
[2]
assuming that only dissociated acid groups contribute to the surface charge. [H1]0, the concentration of protons at the surface, is related to [H1], the bulk concentration of protons according to [H1]0 5 [H1]exp(2eC 0/kT).
[3]
2.6. Conductometric and Potentiometric Titrations Conductometric and potentiometric titrations are nonelectrokinetic experiments for determining surface charge. Conductometric titrations give information about the nature of the surface groups, and in some cases the total number of surface groups can be determined (33, 34, 36, 37, 46). Potentiometric titrations, on the other hand, provide us with more detailed information about the pH dependence of the surface charge density. This originates in the fact that ionizable surface sites are often not fully dissociated at all pH
For a negatively charged surface this means that the proton concentration is always higher at the surface than in the bulk. a, the degree of dissociation, is defined as
a 5 [A2]0/([A2]0 1 [AH]0).
[4]
If K a $ 1, the surface sites are strongly acidic, and a will be close to unity at most pH values in the bulk. However, for weakly acidic surface sites, i.e., K a 5 10 24 , half of the sites
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FIG. 2. Potentiometric titration of aged latex. Magnitude of the surface charge s0 as a function of pH at three different concentrations of NaCl: (}) 1 mM, (‚) 4 mM, and (*) 13 mM.
are undissociated at a surface pH of 4. We can now combine Eqs. [1] and [4] to get pH0 5 pK a 2 log~~1 2 a !/ a !.
[5]
Further, Eq. [5] can be combined with Eq. [3], and the result is pH 2 log~ a /~1 2 a !! 5 pK a 2 ~eC 0/kT!.
[6]
This means that pK a can be obtained as (pH 2 log(a/(1 2 a))) when C0 is zero, i.e., when a 5 0 (34). Titration of fresh latex. Most of the conductometric titrations were performed using a Radiometer ABU 91 Autoburette station metering 30 ml aliquots of NaOH to the SAM 90 sample station. the conductivity was monitored with a Radiometer CDM 83 conductivity meter. The potentiometric titrations and a few conductometric titrations were performed using the ESA8000 device, which has a resolution down to 1 ml aliquots (The ESA-8000 also measures the dynamic mobility of the particles, but these results will be discussed in a subsequent paper). Several different concentrations of NaOH were used depending on the total volume (16 –230 ml) and volume fraction (0.65– 6.05%) of the latex sample. NUF and UF1 were titrated in presence of 1 mM HCl to increase the strong acid slope (36). The unfiltered sample NUF contained 7 mC/cm2 of strong acid groups, but the titration also showed the presence of a
large amount of weak acid, probably benzoic acid (47) (pK a 5 4.19), a by-product formed during the synthesis. The weak acid was probably not attached to the particles, since it could not be detected in the ultrafiltered samples. The ultrafiltered sample UF1 only contained 1.3 mC/cm2 of strong acid groups. This indicates that the sulfate groups underwent hydrolysis during the ultrafiltration. It is also possible that some oligomers with sulfate/sulfonate groups were removed in the filtration process. UF2 was titrated a number of times using different concentrations of base and supporting electrolyte (NaCl). The equivalence point was unaffected under all conditions and the corresponding surface charge density was 21.3 6 0.1 mC/cm2. Figure 1 shows a titration of a UF2 sample without any supporting electrolyte. The marked negative slope of the left part of the titration curve suggests strongly acidic surface groups (pK a , 1) (46). Titration of aged latex. The latex was stored for about 2 years at about 5°C. When the latex was titrated conductometrically and potentiometrically again, the surface charge density had increased by an order of magnitude up to about 214 mC/cm2, as can be seen in Fig. 2. This number is in good agreement with the maximum surface charge density as calculated from DLS and GPC. This indicates that most polymer endgroups are located at the surface and that hydroxyl radicals were formed by hydrolysis of the sulfate ion radicals during the initial stage of the polymerization and during the ultrafiltration
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FIG. 3. Conductometric titration of aged latex with 4 mM NaCl as supporting electrolyte. Note the smooth transitions between the slopes, which makes the establishment of different endpoints difficult.
(33, 34). Further, the sulfate groups are not stable over a long period of time; this has also been found by Vanderhoff (48). A conductometric titration of the aged latex can be seen in Fig. 3. Between pH 4 and 9 this looks like a titration of weak acid groups attached to a particle surface (34, 36), but it is evident from Fig. 2 that about 10% of the total surface charge density develops below pH 4, which suggests that sulfonate groups still are present. We have also analyzed the potentiometric data according to Eq. [7]. In Fig. 4, pH 2 log(a/(1 2 a)) is plotted as a function of a for three different electrolyte concentrations. It can be seen that the curves tends to a value of around 4.5 6 0.2 when a 5 0. This is slightly below 4.75, which is the dissociation constant for carboxyl groups (46). Again this suggests that a small fraction of strong acid groups (probably sulfonate) still is present at the particle surface.
tween 0.1 and 100 mM HCl, which corresponds to pH 4 and 1, respectively. Table 1 shows that the magnitude of the mobility is approximately constant between 0.1 and 5 mM HCl. It then goes through a maximum at 10 mM HCl and decreases slightly at higher ionic strengths. Voegtli and Zukoski (9) and Saville and Zukoski (8) obtained a similar mobility–ionic strength behavior, both quantitatively and qualitatively, for the same type of latex particles. The measured mobilities of the fresh and aged latex were the same within experimental error (which is about 610%, on average), which indicates that the presence of the weak acid groups does not affect the electrophoretic mobility to any great extent. It seems like the small fraction of strong acid groups prevents the latex from coagulating in 100 mM HCl.
2.7. Mobility Measurements
2.8. Conductivity Measurements
Mobility measurements were performed using a Rank Brothers Mark II electrophoresis instrument. UF0 was suspended in 10 mM NaCl and this sample was analyzed using both the automated Malvern Zeta Sizer II and the manual Rank Brothers Mark II to confirm that the observed velocities were measured at the stationary levels. We decided to investigate how the mobility varies with electrolyte concentration for our latex system. Therefore, electrophoretic mobilities were measured in the range be-
Low frequency conductivity measurements are very sensitive to small changes in electrolyte composition, as investigated by Dunstan and White (13). We therefore decided to use the following procedure, which is similar to the procedure used by Midmore and O’Brien (11): The stock latex suspension was prepared by centrifugation/decantation using a Heraeus Biofuge 22R centrifuge. The latex was spun down for 30 min at 9000 rpm, and the particles were resuspended by sonication. This process was repeated until the supernatant had a conduc-
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FIG. 4. pH 2 log(a/1 2 a) as a function of the degree of dissociation a, at three different concentrations of NaCl: (}) 1 mM, (‚) 4 mM, (*) 13 mM. The intercept at a 5 0 corresponds to the pK a of the surface groups.
tivity within 1% of the added electrolyte. The supernatant obtained after the last centrifugation was then used to dilute the stock solution in the measurement series. Suspension conductivity was then measured (using a Radiometer CDM 83 conductivity meter) as a function of particle volume fraction, f, by successive dilution of the stock latex suspension with the supernatant. Figures 5a and 5b show the measured conductivity as a function of f at seven different HCl concentrations. Note the linear relationship between the conductivity and f. This is also expected at low volume fractions, because the interesting parameter from these measurements is the conductivity increment DK/K ` , defined as TABLE 1 Measured Electrophoretic Mobilities (ue) and Conductivity Increments (DK/K`) as a Function HCl Concentration c HCl (mM)
u e (mm cm/Vs)
DK/K `
0.1 0.5 1 5 10 50 100
24.0 6 0.4 24.1 6 0.4 24.0 6 0.4 24.0 6 0.4 24.9 6 0.4 24.5 6 0.5 24.4 6 0.6
1.50 0.07 20.27 20.56 20.91 21.18 21.34
Note. The accuracy of the conductivity increment determination is about 60.15.
DK/K ` 5 ~K/K ` 2 1!/ f ,
[7]
where K is the suspension conductivity (at a given f) and K ` is the bulk electrolyte conductivity. The experimentally determined DK/K ` as a function of ionic strength can be seen in Table 1. Note that DK/K ` is positive at low ionic strengths and that DK/K ` is fairly close to the limiting value of 21.5, which corresponds to an uncharged sphere, at 100 mM HCl. The accuracy of the conductivity increment determination is about 60.15, because three parameters must be measured to evaluate DK/K ` , as can be seen from Eq. [7]. Finally, it should be mentioned that all conductivity measurements were made on the aged latex. We did some conductivity measurements on the fresh latex as well, but a different sample preparation procedure was used, namely, “dilution to a known volume fraction and concentration” (13). However, the reproducibility was very poor and therefore the results are not discussed here. 3. RESULTS AND DISCUSSION
3.1. The O’Brien and White Theory The electrophoretic mobilities and suspension conductivities measured were evaluated using the program MOBILITY developed by O’Brien, White, and Mangelsdorf (49, 24). The program works on a Poisson–Boltzmann level of approxima-
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FIG. 5. Suspension conductivity as a function of f at seven different concentrations of HCl. (a) }, 0.1 mM (*10); ■, 0.5 mM (*2); Œ 1 mM. (b) }, 5 mM (*20); ■, 10 mM (*10); Œ, 50 mM (*2); 3100 mM.
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FIG. 6. The (a) electrophoretic mobility and (b) conductivity increment DK/K ` for a spherical particle (a 5 165 nm) as a function of z-potential at five different concentrations of HCl, according to the theory of O’Brien and White (49).
tion. The relaxation effect of the diffuse layer is included. For any given z-potential, particle radius, and electrolyte composition, the program calculates the corresponding mobility, conductivity increment, and electrokinetic charge density.
The O’Brien and White theory (49) predicts that the magnitude of the mobility goes through a maximum when the z-potential increases for particle sizes and ionic strengths such that 3 , ka , 100. This can be seen in Fig. 6a, where the
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FIG. 7. The z-potential of the latex as a function of HCl concentration, as determined by electrophoresis (}) and conductivity (■), respectively.
mobility is plotted as a function of z-potential. In some cases it is therefore possible to find two reasonable z-potentials for any given mobility. Such an ambiguity does not exist when the conductivity increment is evaluated, because the conductivity increment increases monotonously with increasing z-potential, as can be seen in Fig. 6b.
The z-potentials which correspond to the measured mobilities are shown in Fig. 7. The magnitude of the z-potential decreases very slowly with increasing electrolyte concentration up to about 1 mM, from where it seems to level off except for a small peak at 10 mM HCl. In Fig. 7, the z-potentials which correspond to the measured
FIG. 8. The corresponding electrokinetic charge density skin as a function of HCl concentration, as determined by electrophoresis (}) and conductivity (■), respectively.
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FIG. 9. The effect of Stern layer conductance on zel (El. mob.) and zcond (Cond.) as a function of HCl concentration. pK denotes the dissociation constant for H1. For further details, see text.
conductivity increments are also included. Note that the agreement between the z-potentials obtained from the two techniques is good at low electrolyte concentrations (#0.5 mM), which is also expected because both techniques become more accurate when the ionic strength decreases. However, the theoretical electrophoretic mobility–z-potential relationship is rather flat at low ionic strengths, but the slope increases with increasing ionic strength (see Fig. 6a). This means that the accuracy in the z-potential determination (from the electrophoretic mobility) is about the same at all ionic strengths. The z-potential determination from DK/K ` at low ionic strength is very accurate, as can be seen from Fig. 6b. It is also obvious that the precision in the z-potential determination decreases rather dramatically with increasing ionic strength. Further, the good agreement at low ionic strength suggests that we have chosen the correct (lower) z-potential when we evaluated the electrophoretic mobility. When the ionic strength is 5 mM or greater, the electrokinetic charge evaluated from the high z-potential solution is larger than 30 mC/cm2, and therefore we can also reject this alternative at higher ionic strengths. In Fig. 8, the electrokinetic charge densities are plotted as a function of ionic strength. Note that the charge increases more than one order of magnitude as the electrolyte concentration increases from 0.1 to 100 mM. This indicates that the position of the surface of shear is dependent on pH and electrolyte content (also known as the hairy layer model) and/or that ion adsorption contributes to the electrokinetic charge density (41, 50).
3.2. The Hairy Layer Model We can interpret our results in terms of the hairy layer model by calculating the distance d between Cd and z within the Gouy–Chapman model (assuming Cd 5 C0), using the z-potentials obtained from mobility and conductivity data and the titratable surface charge density s0 5 214 mC/cm2. For a flat interface (that is, when d is much smaller than the particle radius), the relation between Cd and z is tanh~ z e/4kT! 5 tanh(Cde/4kT)exp(2kd).
[8]
The calculated d increases with decreasing ionic strength, which is also predicted by the hairy layer model (22). In general, the d-values calculated from the electrophoretic mobility are slightly larger than the d-values calculated from the conductivity increment, but the difference is not larger than 1.5 nm at any ionic strength. At the lowest electrolyte concentration d (calculated from the electrophoretic mobility) is almost 13 nm, a value which is somewhat larger than 9 nm, which was calculated by Marlow and Rowell at the same ionic strength (6). Eq. [8] is strictly valid for a flat double layer (ka . 100), but we have used the corresponding analytical equations for a spherical double layer (51), although it did not alter the results significantly. d was only overestimated by 10% at c HCl 5 0.1 mM (corresponding to a ka of 5.42) using Eq. [8]. The hairy layer model has often been used to explain the electrokinetic behavior of latices, but recent investigations (41,
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FIG. 10. The (a) Stern potential C(a) and the (b) diffuse layer charge density sd as a function of concentration of a 1:1 electrolyte. 214, 3.5 Å denotes the surface charge density s0 (in mC/cm2) and the parameter p, respectively.
50) have shown that this cannot be the only mechanism present in these systems. Elimelech and O’Melia (4) proposed that counterion adsorption at low electrolyte concentration leads to neutralization of the negative charge (less negative potential). When the electrolyte concentration increases, coion adsorption
becomes the leading mechanism (more negative potential). These two processes together with the ordinary compression of the double layer compete with each other and determine how the z potential varies with the electrolyte concentration. The same qualitative adsorption behavior concerning counterions
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FIG. 11. Comparison between (a) zel (El. mob.), zcond (Cond.), and C(a) and (b) sel (El. mob.), scond (Cond.), and sd as a function of HCl concentration. 214, 3.5 Å again denotes s0 and p, respectively.
and coions is found in the Stern layer conductance model developed by Zukoski and Saville (23). We will now try to interpret our results using the Stern layer conductance model developed by Mangelsdorf and White (24), which includes adsorption of ions onto available surface area.
3.3. Stern-Layer Conductance The Stern layer conductance model, which includes adsorption of ions onto available surface area, is included as an option in the program MOBILITY developed by O’Brien, White, and
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FIG. 12. The surface potential and z-potential as a function of monovalent electrolyte concentration. HCl corresponds to our data and NaCl to the data of de las Nieves et al. (59).
Mangelsdorf (49, 24). The model introduces a Stern layer, where lateral ion motion is allowed. First, the dissociation reaction for the ith ionic species X i is represented as SX i 7 S i 1 X i,
[9]
where S i is an empty Stern layer site. The dissociation reaction is described by the dissociation constant pK i and the total number of Stern layer sites per surface area, which we fixed to 9 p 1013 cm22. This value corresponds to a charge density of 14 mC/cm2. We also have to specify an outer Stern layer thickness and dielectric constant. We have used the values 1 and 15 Å respectively, which corresponds to an outer Stern layer capacitance of about 130 mF/cm2. It was found that the model is rather insensitive to variations in the Stern layer capacitance as long as uzu , 250 mV (24). The remaining parameters are then the dissociation constants and the relative ionic drag coefficients lrel for H1 and Cl2, respectively. First we fixed pK Cl to 0, because it was found that coion adsorption is relatively unimportant (24) and the same effects can be mimicked by varying the coion drag ratio lrel,Cl. Next, we varied pK H and then adjusted the counter ion and coion drag ratio concomitantly until we obtained reasonable agreement between the z-potentials obtained from electrophoresis (zel) and conductivity (zcond), respectively. This resulted in three different fits, and the result can be seen in Fig. 9 together with the original z-potentials assuming no Stern layer conductance. zel was hardly affected by the conductance. It was only when pK H was set to 1 that zel changed by more than 2 mV at any
ionic strength. This is the reason why we only show the pK H 5 1 case for zel. zcond, on the other hand, is much more sensitive to Stern layer conductance because DK/K ` is increased by the mobile Stern layer ions for a given z-potential. Therefore, the magnitude of zcond decreases when Stern layer conductance is included. By varying pK H and lrel, Stern layer conductance becomes important in different ionic strength regimes: For the case of pK H 5 1 and lrel 5 101 , the effect is large, between 0.5 and 10 mM HCl. When pK H 5 0.5 and lrel 5 71, the effect of conductance is more smeared out over the entire ionic strength regime. Finally, when pK H 5 21 and lrel 5 1, the effect of Stern layer conductance is only important above 5 mM HCl. It is clear that Stern layer conductance can improve the agreement between zel and zcond, but whether this is the true origin of the observed discrepancies remains to be validated. 3.4. The Association Theory If we assume that the hairy layer model is not operative, why then is the electrokinetic charge density increasing with increasing ionic strength? A recent theory for spherical surfaces developed by Spitzer (45) suggests that a fraction of the double layer counterions remains associated with the charged surface according to
a 5 1/~1 1 p k !,
[10]
where p is a parameter characteristic of the double layer. Equation [10] is referred to as the LMO law after Lubetkin,
SURFACE ELECTRICAL PROPERTIES OF POLYSTYRENE LATEX, 1
Middleton, and Ottewill (52). The other fitting parameter in this theory is a, which is the position of the Stern layer. The thickness of the Stern layer is then (a 2 R), where R is the particle radius. The theory assumes that there is a coion exclusion boundary b with a corresponding potential C~b! 5 k BT/ze,
[11]
which is termed the thermal electrostatic potential of the coions (TEP). Outside b the Debye–Hu¨ckel approximation is used. If s 0 , p, R, and a are specified, b and the Stern potential C(a) can be calculated from lengthy analytical solutions not presented here. The Stern charge density s a is calculated from
s a 5 2as 0R 2/a 2.
[12]
The remaining charge in the double layer is then the diffuse layer charge, sd. We fixed R and (a 2 R) to 165 and 1 nm, respectively, and tested this theory for some different values of s0 and p. The resulting Stern potentials and diffuse layer charge densities can be seen in Figs. 10a and 10b, respectively. We have adjusted s0 and p so that the Stern potentials would fall in the range between 220 and 2120 mV. According to the association theory, highly charged particles should exhibit a maximum in the Stern potential as a function of ionic strength (45). With decreasing surface charge density, the Stern potential should decrease (in absolute values) in a monotonous fashion and the diffuse layer charge should show only a slight increase with increasing ionic strength. This agrees very well with Goff and Luner’s investigation (3), but it is not supported by some other investigations (2, 4). In Fig. 11a, we have compared zel and zcond with the predictions from the ion association theory. The best fits were obtained by using s0 5 214 mC/cm2. p was set to 3.5 Å to fit zel and 4.5 Å to fit zcond. In other terms, the difference between zel and zcond is interpreted as a slight difference in counterion association according to Eq. [10]. In Fig. 11b, the electrokinetic charge densities are compared with the diffuse layer charge densities. It can be seen that skin agrees well with the fitted diffuse layer charge. scond is somewhat higher than the association theory predicts at high ionic strength, but this is mainly because the fitted Stern potentials are lower (in magnitude) than the corresponding zcond. 3.5. Concluding Remarks We have synthesized and characterized a well-known polystyrene latex (44). The surface charge density was initially 27 mC/cm2 of strong acid groups, but had decreased to 21.3 mC/cm2 after ultrafiltration. During storage, carboxyl groups appeared (48), but the electrophoretic mobility was unaffected by the appearance of these groups. The experimentally determined zel and zcond are in reasonable agreement with earlier investigations on the same latex system (8, 9). The correspond-
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ing electrokinetic charge density increases with increasing ionic strength, which is usually the case in latex systems. It is therefore plausible that charge mechanisms other than the dissociation of surface groups also are active in polystyrene latex systems (22, 23). Recently, some investigations on polystyrene latices have been published (21, 53–55) that validate the O’Brien and White theory without invoking any ion adsorption or hairy layer; i.e., the z-potential is decreasing according to Grahame’s equation and the shear plane is very close to the particle surface at all ionic strengths. In two of these cases (21, 54), commercial latices were used, but other investigations with similar latices (4, 41) have not produced such encouraging results. Russell et al. (53) used a highly charged sulfonate/styrene latex polymerized using a two-shot process (56, 57) that produces hairy surfaces (58), although no hairy layer was needed to explain the mobility data. Likewise, Antonietti and Vorwerg (55) used surfactant in their synthesis, which also may lead to hairy surfaces. It is also interesting to note that both investigations used dialysis to clean the latices. We suggest that certain synthesis procedures (combined with a certain cleaning process) may produce ideal latices (21, 53–55). It is also clear from these investigations that the high z-potential solution of O’Brien and White’s (49) theory (cf. Fig. 6a) is experimentally attainable. In fact, it is possible to reinterpret some mobility data so that ideal electrokinetic behavior is observed; de las Nieves et al. (59) have also characterized the highly charged (s0 5 213.9 mC/cm2) sulfonate/ styrene latex used by Russell et al. (53). In their Fig. 4, they show the surface potential and z-potential of their latex FJN20. Using their mobility data from Fig. 3, we can replace the low z-potentials with the corresponding high z-potentials for ionic strengths of 10 mM NaCl and below. The result can be seen in Fig. 12. Now the z-potential is only about 30 – 40 mV lower (in absolute terms) than the corresponding surface potential. Using Eq. [9], we find that the average distance between the surface and the plane of shear is about 3 Å. In Fig. 12, we have also included the z-potentials that correspond to our mobility data. Clearly, our high z-potentials are not as plausible as in the case of de las Nieves et al. Moreover, our conductivity data do not support the high z-potential solutions. This example shows that electrophoretic mobilities may be misinterpreted, but our experience is that it is in general not possible to reinterpret literature data successfully. For example, if the latex above is prepared without the second injection of NaSS, the typical latex behavior with increasing electrokinetic charge density is found (42). The recently developed nonlinear hairy layer theory (60) can hopefully explain certain features not accounted for in the Stern layer conductance models (23, 24). Anyhow, further research on a wide variety of latex systems is definitely needed. In a subsequent paper, we will present some results on the same latex system using dielectric response and the ESA technique, which will provide us with more information about the surface electrical properties of this latex.
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ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the Swedish Research Council for Engineering Sciences and EKA Nobel AB. The authors thank Dr. Ib Johannsen for performing the XPS experiments, Dr. Derek Biddle for performing the light scattering experiments, and Peter Greenwood for use of the ultrafiltration equipment.
30. 31. 32. 33. 34. 35.
REFERENCES
36.
1. Ottewill, R. H., and Shaw, J. N., J. Electroanal. Chem. 37, 133 (1972). 2. Ma, C. M., Micale, F. J., El-Aasser, M. S., and Vanderhoff, J. W., ACS. Symp. Ser. 165, 251 (1981). 3. Goff, J. R., and Luner, P., J. Colloid Interface Sci. 99, 469 (1984). 4. Elimelich, M., and O’Melia, C. R., Colloids Surf. 44, 165 (1990). 5. Shubin, V. E., Isakova, I. V., Menshikova, M. P., Yu, A., and Eveseeva, T. G., Kolloidn. Zh. 52, 935 (1990). 6. Marlow, B. J., and Rowell, R. L., Langmuir 7, 2970 (1991). 7. Prescott, J. H., Shiau, S., and Rowell, R. L., Langmuir 9, 2071 (1993). 8. Zukoski, C. F., and Saville, D. A., J. Colloid Interface Sci. 107, 322 (1985). 9. Voegtli, L. P., and Zukoski, C. F., J. Colloid Interface Sci. 141, 92 (1991). 10. Fridrikhsberg, D. A., Sidorova, M. P., Shubin, V. E., and Ermakova, L. E., Kolloidn. Zh. 48, 967 (1986). 11. Midmore, B. R., and O’Brien, R. W., J. Colloid Interface Sci. 123, 486 (1987). 12. Shubin, V. E., Sidorova, M. P., Chechik, O. S., and Sakharova, N. A., Kolloidn. Zh. 53, 187 (1991). 13. Dunstan, D. E., and White, L. R., J. Colloid Interface Sci. 152, 297 (1992). 14. Midmore, B. R., and Hunter, R. J., J. Colloid Interface Sci. 122, 521 (1988). 15. Midmore, B. R., Hunter, R. J., and O’Brien, R. W., J. Colloid Interface Sci. 120, 210 (1987). 16. Midmore, B. R., Diggins, D., and Hunter, R. J., J. Colloid Interface Sci. 129, 153 (1989). 17. Myers, D. F., and Saville, D. A., J. Colloid Interface Sci. 131, 461 (1989). 18. Rosen, L. A., and Saville, D. A., J. Colloid Interface Sci. 140, 82 (1990). 19. Rosen, L. A., and Saville, D. A., J. Colloid Interface Sci. 149, 542 (1992). 20. Rosen, L. A., Baygents, J. C., and Saville, D. A., J. Chem. Phys. 98, 4183 (1993). 21. Barchini, R., and Saville, D. A., J. Colloid Interface Sci. 173, 86 (1995). 22. Van der Put, A. G., and Bijsterbosch, B. H., J. Colloid Interface Sci. 92, 499 (1983). 23. Zukoski, C. F., and Saville, D. A., J. Colloid Interface Sci. 114, 32 (1986). 24. Mangelsdorf, C. S., and White, L. R., J. Chem. Soc. Faraday Trans. 86(16), 2859 (1990). 25. Seminikhin, N. M., and Dukhin, S. S., Kolloidn. Zh. 37, 1123 (1975). 26. Healy, T. W., and White, L. R., Adv. Colloid Interface Sci. 9, 303 (1978). 27. Harding, I. H., and Healy, T. W., J. Colloid Interface Sci. 107, 382 (1985). 28. Chow, R. S., and Takamura, K., J. Colloid Interface Sci. 125, 226 (1988). 29. Goosens, J. W. S., and Zembrod, A., Colloid Polym. Sci. 257, 437 (1979).
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Sasaki, S., Colloid Polym. Sci. 262, 406 (1984). Zhao, J., and Brown, W., J. Colloid Interface Sci. 179, 255 (1996). Wu, X., and van de Ven, T. G. M., Langmuir 12, 3859 (1996). van den Hul, H. J., and Vanderhoff, J. W., J. Electroanal. Chem. 37, 161 (1972). Stone-Masui, J., and Watillon, A., J. Colloid Interface Sci. 52, 479 (1975). Yates, D. E., Ottewill, R. H., and Goodwin, J. W., J. Colloid Interface Sci. 62, 356 (1977). Labib, M. E., and Robertson, A. A., J. Colloid Interface Sci. 67, 543 (1978). Everett, D. H., Gu¨ltepe, M. E., and Wilkinson, M. C., J. Colloid Interface Sci. 71, 336 (1979). Ahmedt, S. M., El-Aasser, M. S., Pauli, G. H., Poehlein, G. W., and Vanderhoff, J. W., J. Colloid Interface Sci. 73, 388 (1980). Kamel, A. A., El-Aasser, M. S., and Vanderhoff, J. W., J. Colloid Interface Sci. 87, 537 (1982). Harding, I. H., and Healy, T. W., J. Colloid Interface Sci. 89, 185 (1982). Seebergh, J. E., and Berg, J. C., Colloids Surf. 100, 139 (1995). ´ lvarez, R., and de lad Nieves, F. J., J. Bastos-Gonza´lez, D., Hidalgo-A Colloid Interface Sci. 177, 372 (1996). Dunstan, D. E., J. Chem. Soc. Faraday Trans. 2 89, 521 (1993). Juang, M. S., and Krieger, I. M., J. Polymer Sci. 14, 2089 (1976). Spitzer, J. J., Colloid Polym. Sci. 270, 1147 (1992). Zwetsloot, J. P. H., and Leyte, J. C., J. Colloid Interface Sci. 163, 362 (1994). Ottewill, R. H., personal communication (1994). Vanderhoff, J. W., ACS Symp. Ser. 165, 61 (1981). O’Brien, R. W., and White, L. R., J. Chem. Soc. Faraday Trans. 2 77, 1607 (1978). Verdegan, B. M., and Anderson, M. A., J. Colloid Interface Sci. 158, 372 (1993). Oshima, H., Healy, T. W., and White, L. R., J. Colloid Interface Sci. 90, 17 (1982). Lubetkin, S. D., Middleton, S. R., and Ottewill, R. H., Philos. Trans. R. Soc. London A311, 133 (1984). Russell, A. S., Scales, P. J., Magelsdorf, C. S., and Underwood, S. M., Langmuir 11, 1112 (1995). Midmore, B. R., Pratt, G. V., and Herrington, T. M., J. Colloid Interface Sci. 184, 170 (1996). Antonietti, M., and Vorwerg, L., Colloid Polym. Sci. 275, 883 (1997). Kim, J. H., Chainey, M., El-aasser, M. S., and Vanderhoff, J. W., J. Polym. Sci. Part A 27, 3187 (1989). Kim, J. H., Chainey, M., El-aasser, M. S., and Vanderhoff, J. W., J. Polym. Sci. Part A 30, 171 (1992). Bastos, D., and de las Nieves, F. J., Prog. Colloid Polym. Sci. 93, 37 (1993). de las Nieves, F. J., Daniels, E. S., and El-aasser, M. S., Colloids Surf. 60, 107 (1991). Donath, E., Walther, D., Shilov, V. N., Knippel, E., Budde, A., Lowack, K., Helm, C. A., and Mo¨hwald, H., Langmuir 13, 5294 (1997).
Surface Electrical Properties of Polystyrene Latex 1. Electrophoresis and Static Conductivity Mikael Rasmusson1 and Staffan Wall Department of Physical Chemistry, University of Go¨teborg, S-412 96 Go¨teborg, Sweden E-mail: [email protected] Received March 9, 1998; accepted September 10, 1998
The surface electrical properties of a polystyrene latex have been studied with several experimental methods. Previous studies by other authors have shown discrepancies between the surface potential and the surface charge density determined by different methods. This work is an attempt to produce more experimental data for the discussion concerning these discrepancies. Both electrophoretic mobility and electrical conductivity methods have been used. Also, gel permeation chromatography has been used to estimate the number of endgroups on the latex particle that carry charged surface groups. Synthesis and cleaning methods of polystyrene latex are also discussed. Calculations on a Poisson–Boltzmann level of approximation have been performed in an attempt to connect the quantities determined with dynamic (electrophoresis and static conductivity) methods and static (titration) methods. The discrepancies can be explained by introducing a pH- and electrolyte-dependent surface structure such as the hairy layer model. A Stern layer conductance model can also to some extent explain these discrepancies, but this model contains several parameters not directly attainable by experiments. This means that a unique set of parameters cannot be determined without further studies on several latex systems. © 1999 Academic Press Key Words: z-potential; Stern layer conductance; electrophoretic mobility; conductivity; polystyrene latex.
1. INTRODUCTION
Polystyrene latices have been widely used as model systems for colloids because they can be prepared as practically monodisperse spherical particles. Even if the geometrical dimensions are well defined the surface electrical properties are poorly understood. The electrical properties of latex particles have been investigated mainly by microelectrophoresis (1–7) and electrical conductivity measurements (8 –13), and in some cases dielectric response has been used also (14 –21). Comparison between the experimental results and standard theories based on the Gouy–Chapman Poisson–Boltzmann formalism shows unexpected anomalies. For instance, the magnitude of the z-potential (as determined from microelectrophoresis) often 1
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increases with increasing ionic strength up to 1–10 mM and then decreases. This is not consistent with classical double layer theory, which predicts a decreasing z-potential with increasing electrolyte concentration at constant surface charge density. The latter statement requires that the slip plane is located just outside the beginning of the diffuse double layer (z > Cd) or that ion adsorption in the Stern layer does not depend on the ionic strength. Van der Put and Bijsterbosch (22) have suggested that the polymer ends form a hairy surface, sensitive to the electrolyte content and pH, which induces a shear plan shift, so that z Þ Cd at low ionic strength. Another anomaly is that z-potentials determined from microelectrophoresis often are lower in magnitude than z-potentials determined from electrical conductivity measurements and dielectric response measurements. Zukoski and Saville (23) suggested a Stern layer conductance model that includes adsorption of ions onto underlying surface charge to reconcile the discrepancy between electrophoresis and conductivity data. Another possibility is adsorption onto available surface area, developed by Mangelsdorf and White (24). If ka is large (ka @ 1) it is possible to replace the elaborate Stern layer conductance models with a single surface conductivity parameter, l, which can be measured experimentally (11, 14 –16). Further, Seminikhin and Dukhin (25) have derived an equation that relates the electrophoretic mobility to the z-potential and Cd. In this case it is assumed that z Þ Cd, and ionic conduction occurs between the Outer Helmholtz plane and the shear plane. In this paper, we work under conditions where ka is not very large, and therefore we can not use the notion of surface conduction (i.e., large ka). Surface charge densities determined electrokinetically often correlate poorly with the surface charge densities obtained from titration data. The reason for this discrepancy has not been thoroughly investigated, but it is obvious that the comparison between z, Cd, and the surface potential C0 is complex and model dependent. According to the previously mentioned hairy layer model (22) the surface of shear should be more and more displaced from the particle surface as the electrolyte concentration decreases. Healy and White (26) also demon-
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strate (within the Gouy–Chapman model) that the potential 1–2 nm away from the particle surface is much more insensitive (compared to the surface potential) to both changes in pH and surface site (charge) density. The experimentally determined z-potential has therefore been interpreted as the potential a few nanometers from the particle surface (6, 27, 28) or the Stern plane (10, 11, 14), depending on which model the authors have used. High quality dynamic light scattering measurements on latex particles (7, 29 –31) have also shown that the hydrodynamic radius does decrease with increasing ionic strength, which tends to support the hairy layer model. The existence of a hairy layer was also introduced by Wu and van de Ven (32) to explain their colloidal particle scattering (CPS) results. The importance of cleaning the latex after synthesis must also be emphasized, but there’s still no widely accepted cleaning procedure, since different investigations have produced ambiguous results (13, 33– 40). Heating of the latex particles above the glass transition temperature does seem to produce smoother particle surfaces (19, 28, 41– 43), but the results are again ambiguous and further experimental work is needed. In this investigation, we have synthesized polystyrene latex particles according to the method outlined by Juang and Krieger (44). This method has also been used by Zukoski and Saville (8) and by Voegtli and Zukoski (9). We chose HCl as a supporting electrolyte because we wanted to compare our experimental data with the investigations mentioned above (8, 9). A characterization of the surface groups on the particles has been made using titration methods (conductometric and potentiometric), gel permeation chromatography (GPC), and X-ray photon spectroscopy (XPS). Electrophoresis and conductivity measurements have also been carried out, and the results are compared with other investigations. We also try to reconcile our data using Stern layer conductance (24) and fit our data according to a theory developed by Spitzer (45). 2. EXPERIMENTAL METHODS
2.1. Synthesis of the Latex A sulfate polystyrene latex was synthesized according to the procedure of Juang and Krieger (44). According to the authors, the incorporation of the ionic comonomer sodium styrene sulfonate (NaSS) results in predominantly strong acid groups. This is due to the stronger acidity of the sulfonate groups (pK a ' 22) compared to the sulfate groups (pK a ' 0). There is also an important structural difference between the sulfonate group and the sulfate group. The sulfur in the sulfonate group is directly attached to a carbon atom (–C–SO2 3 ), but the sulfate sulfur is attached via an oxygen bridge (–C–O–SO2 3 ) that is susceptible to hydrolysis (33).
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2.2. Cleaning Procedure A variety of cleaning methods have been used to purify latex suspensions. Harding and Healy (40) tried five different methods, namely, dialysis, ion exchange, centrifugation– decantation, ultrafiltration, and activated charcoal cloth. According to these authors, electron microscopy, surface tension measurements, and potentiometric titrations showed that only centrifugation– decantation and ultrafiltration purified the latex suspensions in a satisfactory way. After some preliminary work with centrifugation– decantation, we decided to ultrafiltrate our sample using a membrane with a pore size of around 5 nm (styrene monomers, oligomers, and other impurities should be removed). We started with a batch called UF1, which was washed with a 20-fold excess of 1 mM HCl. The filtration process was stopped when the conductivity of the filtrate was within 2% of the conductivity of 1 mM HCl. After that, a second batch called UF2 was washed with a 20-fold excess of deionized water (Milli-Q water purification system, k ' 1 mS/cm). We compared the latex suspensions before and after ultrafiltration by using scanning electron microscopy (SEM). It was seen that gel-like material was present at the particle surface in the unpurified sample (NUF), but not in the ultrafiltered samples (UF1 and UF2). This observation has also been reported by Harding and Healy (40). 2.3. Dynamic Light Scattering Dynamic light scattering (DLS) was performed with a Malvern PCS (photon correlation spectroscopy) 100 connected to a Multi-8 correlator. The NUF sample was also analyzed using a Brookhaven BI-90 particle sizer for comparison. The number-averaged diameters were 350 6 10 nm for NUF and 330 6 10 nm for UF1 and UF2. The somewhat larger particle diameter of the unpurified sample NUF (according to DLS) can be ascribed to the gel-like layer that was observed in the SEM pictures. The weight-averaged diameters were about 20 nm larger than the number-averaged diameters. 2.4. Gel Permeation Chromatography The dried fresh latex was dissolved in tetrahydrofurane (THF) and the distribution of molecular weights of the polystyrene molecules constituting the latex particles was determined by using GPC (Version 860/V2.3 from Waters Chromatography Division of Millipore Corp.). A very broad distribution of molecular weights was observed, which is usually the case in emulsion polymerization (34). For UF1, the ratio M w/M n was 54. From GPC and DLS, we calculated the surface charge assuming that two sulfate endgroups should be located at the particle surface for each polystyrene molecule formed (34). Using Mn 5 78,500 g/mol and d 5 330 nm for UF1, this should correspond to a surface charge density of 214.3 mC/cm2.
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FIG. 1. Conductometric titration of a fresh UF2 sample (}, 0.7% latex). No supporting electrolyte was added.
2.5. X-Ray Photon Spectroscopy We decided that it was necessary to perform some kind of surface analysis to determine the nature and the number of surface groups. XPS is a very sensitive method, both with respect to element analysis and the chemical environment of that particular element, and the penetration depth is seldom deeper than 5 nm. Dried latex samples (UF) were sent for XPS analysis to the Department of Solid State Physics, Risø National Laboratory, Denmark. Their XPS measurements were performed using a Sage 100 (SPECS) equipped with a Mg anode operating at 100 W. The spectrum of the fresh latex revealed that oxygen and sulfur were present at a ratio of about 4 to 1. The sulfur peak was typical for a sulfur atom surrounded by oxygen atoms. This indicates that the surface groups are mainly sulfate and/or sulfonate groups. Whether hydroxyl groups also are present cannot be ruled out by the XPS analysis.
values. Healy and White (26) define a surface acid dissociation constant Ka, K a 5 [A2]0[H1]0/[AH]0,
[1]
where [AH]0 is the surface concentration of undissociated acid groups and [A2]0 is related to the surface charge density s according to
s 5 2e[A2]0,
[2]
assuming that only dissociated acid groups contribute to the surface charge. [H1]0, the concentration of protons at the surface, is related to [H1], the bulk concentration of protons according to [H1]0 5 [H1]exp(2eC 0/kT).
[3]
2.6. Conductometric and Potentiometric Titrations Conductometric and potentiometric titrations are nonelectrokinetic experiments for determining surface charge. Conductometric titrations give information about the nature of the surface groups, and in some cases the total number of surface groups can be determined (33, 34, 36, 37, 46). Potentiometric titrations, on the other hand, provide us with more detailed information about the pH dependence of the surface charge density. This originates in the fact that ionizable surface sites are often not fully dissociated at all pH
For a negatively charged surface this means that the proton concentration is always higher at the surface than in the bulk. a, the degree of dissociation, is defined as
a 5 [A2]0/([A2]0 1 [AH]0).
[4]
If K a $ 1, the surface sites are strongly acidic, and a will be close to unity at most pH values in the bulk. However, for weakly acidic surface sites, i.e., K a 5 10 24 , half of the sites
SURFACE ELECTRICAL PROPERTIES OF POLYSTYRENE LATEX, 1
315
FIG. 2. Potentiometric titration of aged latex. Magnitude of the surface charge s0 as a function of pH at three different concentrations of NaCl: (}) 1 mM, (‚) 4 mM, and (*) 13 mM.
are undissociated at a surface pH of 4. We can now combine Eqs. [1] and [4] to get pH0 5 pK a 2 log~~1 2 a !/ a !.
[5]
Further, Eq. [5] can be combined with Eq. [3], and the result is pH 2 log~ a /~1 2 a !! 5 pK a 2 ~eC 0/kT!.
[6]
This means that pK a can be obtained as (pH 2 log(a/(1 2 a))) when C0 is zero, i.e., when a 5 0 (34). Titration of fresh latex. Most of the conductometric titrations were performed using a Radiometer ABU 91 Autoburette station metering 30 ml aliquots of NaOH to the SAM 90 sample station. the conductivity was monitored with a Radiometer CDM 83 conductivity meter. The potentiometric titrations and a few conductometric titrations were performed using the ESA8000 device, which has a resolution down to 1 ml aliquots (The ESA-8000 also measures the dynamic mobility of the particles, but these results will be discussed in a subsequent paper). Several different concentrations of NaOH were used depending on the total volume (16 –230 ml) and volume fraction (0.65– 6.05%) of the latex sample. NUF and UF1 were titrated in presence of 1 mM HCl to increase the strong acid slope (36). The unfiltered sample NUF contained 7 mC/cm2 of strong acid groups, but the titration also showed the presence of a
large amount of weak acid, probably benzoic acid (47) (pK a 5 4.19), a by-product formed during the synthesis. The weak acid was probably not attached to the particles, since it could not be detected in the ultrafiltered samples. The ultrafiltered sample UF1 only contained 1.3 mC/cm2 of strong acid groups. This indicates that the sulfate groups underwent hydrolysis during the ultrafiltration. It is also possible that some oligomers with sulfate/sulfonate groups were removed in the filtration process. UF2 was titrated a number of times using different concentrations of base and supporting electrolyte (NaCl). The equivalence point was unaffected under all conditions and the corresponding surface charge density was 21.3 6 0.1 mC/cm2. Figure 1 shows a titration of a UF2 sample without any supporting electrolyte. The marked negative slope of the left part of the titration curve suggests strongly acidic surface groups (pK a , 1) (46). Titration of aged latex. The latex was stored for about 2 years at about 5°C. When the latex was titrated conductometrically and potentiometrically again, the surface charge density had increased by an order of magnitude up to about 214 mC/cm2, as can be seen in Fig. 2. This number is in good agreement with the maximum surface charge density as calculated from DLS and GPC. This indicates that most polymer endgroups are located at the surface and that hydroxyl radicals were formed by hydrolysis of the sulfate ion radicals during the initial stage of the polymerization and during the ultrafiltration
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FIG. 3. Conductometric titration of aged latex with 4 mM NaCl as supporting electrolyte. Note the smooth transitions between the slopes, which makes the establishment of different endpoints difficult.
(33, 34). Further, the sulfate groups are not stable over a long period of time; this has also been found by Vanderhoff (48). A conductometric titration of the aged latex can be seen in Fig. 3. Between pH 4 and 9 this looks like a titration of weak acid groups attached to a particle surface (34, 36), but it is evident from Fig. 2 that about 10% of the total surface charge density develops below pH 4, which suggests that sulfonate groups still are present. We have also analyzed the potentiometric data according to Eq. [7]. In Fig. 4, pH 2 log(a/(1 2 a)) is plotted as a function of a for three different electrolyte concentrations. It can be seen that the curves tends to a value of around 4.5 6 0.2 when a 5 0. This is slightly below 4.75, which is the dissociation constant for carboxyl groups (46). Again this suggests that a small fraction of strong acid groups (probably sulfonate) still is present at the particle surface.
tween 0.1 and 100 mM HCl, which corresponds to pH 4 and 1, respectively. Table 1 shows that the magnitude of the mobility is approximately constant between 0.1 and 5 mM HCl. It then goes through a maximum at 10 mM HCl and decreases slightly at higher ionic strengths. Voegtli and Zukoski (9) and Saville and Zukoski (8) obtained a similar mobility–ionic strength behavior, both quantitatively and qualitatively, for the same type of latex particles. The measured mobilities of the fresh and aged latex were the same within experimental error (which is about 610%, on average), which indicates that the presence of the weak acid groups does not affect the electrophoretic mobility to any great extent. It seems like the small fraction of strong acid groups prevents the latex from coagulating in 100 mM HCl.
2.7. Mobility Measurements
2.8. Conductivity Measurements
Mobility measurements were performed using a Rank Brothers Mark II electrophoresis instrument. UF0 was suspended in 10 mM NaCl and this sample was analyzed using both the automated Malvern Zeta Sizer II and the manual Rank Brothers Mark II to confirm that the observed velocities were measured at the stationary levels. We decided to investigate how the mobility varies with electrolyte concentration for our latex system. Therefore, electrophoretic mobilities were measured in the range be-
Low frequency conductivity measurements are very sensitive to small changes in electrolyte composition, as investigated by Dunstan and White (13). We therefore decided to use the following procedure, which is similar to the procedure used by Midmore and O’Brien (11): The stock latex suspension was prepared by centrifugation/decantation using a Heraeus Biofuge 22R centrifuge. The latex was spun down for 30 min at 9000 rpm, and the particles were resuspended by sonication. This process was repeated until the supernatant had a conduc-
SURFACE ELECTRICAL PROPERTIES OF POLYSTYRENE LATEX, 1
317
FIG. 4. pH 2 log(a/1 2 a) as a function of the degree of dissociation a, at three different concentrations of NaCl: (}) 1 mM, (‚) 4 mM, (*) 13 mM. The intercept at a 5 0 corresponds to the pK a of the surface groups.
tivity within 1% of the added electrolyte. The supernatant obtained after the last centrifugation was then used to dilute the stock solution in the measurement series. Suspension conductivity was then measured (using a Radiometer CDM 83 conductivity meter) as a function of particle volume fraction, f, by successive dilution of the stock latex suspension with the supernatant. Figures 5a and 5b show the measured conductivity as a function of f at seven different HCl concentrations. Note the linear relationship between the conductivity and f. This is also expected at low volume fractions, because the interesting parameter from these measurements is the conductivity increment DK/K ` , defined as TABLE 1 Measured Electrophoretic Mobilities (ue) and Conductivity Increments (DK/K`) as a Function HCl Concentration c HCl (mM)
u e (mm cm/Vs)
DK/K `
0.1 0.5 1 5 10 50 100
24.0 6 0.4 24.1 6 0.4 24.0 6 0.4 24.0 6 0.4 24.9 6 0.4 24.5 6 0.5 24.4 6 0.6
1.50 0.07 20.27 20.56 20.91 21.18 21.34
Note. The accuracy of the conductivity increment determination is about 60.15.
DK/K ` 5 ~K/K ` 2 1!/ f ,
[7]
where K is the suspension conductivity (at a given f) and K ` is the bulk electrolyte conductivity. The experimentally determined DK/K ` as a function of ionic strength can be seen in Table 1. Note that DK/K ` is positive at low ionic strengths and that DK/K ` is fairly close to the limiting value of 21.5, which corresponds to an uncharged sphere, at 100 mM HCl. The accuracy of the conductivity increment determination is about 60.15, because three parameters must be measured to evaluate DK/K ` , as can be seen from Eq. [7]. Finally, it should be mentioned that all conductivity measurements were made on the aged latex. We did some conductivity measurements on the fresh latex as well, but a different sample preparation procedure was used, namely, “dilution to a known volume fraction and concentration” (13). However, the reproducibility was very poor and therefore the results are not discussed here. 3. RESULTS AND DISCUSSION
3.1. The O’Brien and White Theory The electrophoretic mobilities and suspension conductivities measured were evaluated using the program MOBILITY developed by O’Brien, White, and Mangelsdorf (49, 24). The program works on a Poisson–Boltzmann level of approxima-
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FIG. 5. Suspension conductivity as a function of f at seven different concentrations of HCl. (a) }, 0.1 mM (*10); ■, 0.5 mM (*2); Œ 1 mM. (b) }, 5 mM (*20); ■, 10 mM (*10); Œ, 50 mM (*2); 3100 mM.
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FIG. 6. The (a) electrophoretic mobility and (b) conductivity increment DK/K ` for a spherical particle (a 5 165 nm) as a function of z-potential at five different concentrations of HCl, according to the theory of O’Brien and White (49).
tion. The relaxation effect of the diffuse layer is included. For any given z-potential, particle radius, and electrolyte composition, the program calculates the corresponding mobility, conductivity increment, and electrokinetic charge density.
The O’Brien and White theory (49) predicts that the magnitude of the mobility goes through a maximum when the z-potential increases for particle sizes and ionic strengths such that 3 , ka , 100. This can be seen in Fig. 6a, where the
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FIG. 7. The z-potential of the latex as a function of HCl concentration, as determined by electrophoresis (}) and conductivity (■), respectively.
mobility is plotted as a function of z-potential. In some cases it is therefore possible to find two reasonable z-potentials for any given mobility. Such an ambiguity does not exist when the conductivity increment is evaluated, because the conductivity increment increases monotonously with increasing z-potential, as can be seen in Fig. 6b.
The z-potentials which correspond to the measured mobilities are shown in Fig. 7. The magnitude of the z-potential decreases very slowly with increasing electrolyte concentration up to about 1 mM, from where it seems to level off except for a small peak at 10 mM HCl. In Fig. 7, the z-potentials which correspond to the measured
FIG. 8. The corresponding electrokinetic charge density skin as a function of HCl concentration, as determined by electrophoresis (}) and conductivity (■), respectively.
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FIG. 9. The effect of Stern layer conductance on zel (El. mob.) and zcond (Cond.) as a function of HCl concentration. pK denotes the dissociation constant for H1. For further details, see text.
conductivity increments are also included. Note that the agreement between the z-potentials obtained from the two techniques is good at low electrolyte concentrations (#0.5 mM), which is also expected because both techniques become more accurate when the ionic strength decreases. However, the theoretical electrophoretic mobility–z-potential relationship is rather flat at low ionic strengths, but the slope increases with increasing ionic strength (see Fig. 6a). This means that the accuracy in the z-potential determination (from the electrophoretic mobility) is about the same at all ionic strengths. The z-potential determination from DK/K ` at low ionic strength is very accurate, as can be seen from Fig. 6b. It is also obvious that the precision in the z-potential determination decreases rather dramatically with increasing ionic strength. Further, the good agreement at low ionic strength suggests that we have chosen the correct (lower) z-potential when we evaluated the electrophoretic mobility. When the ionic strength is 5 mM or greater, the electrokinetic charge evaluated from the high z-potential solution is larger than 30 mC/cm2, and therefore we can also reject this alternative at higher ionic strengths. In Fig. 8, the electrokinetic charge densities are plotted as a function of ionic strength. Note that the charge increases more than one order of magnitude as the electrolyte concentration increases from 0.1 to 100 mM. This indicates that the position of the surface of shear is dependent on pH and electrolyte content (also known as the hairy layer model) and/or that ion adsorption contributes to the electrokinetic charge density (41, 50).
3.2. The Hairy Layer Model We can interpret our results in terms of the hairy layer model by calculating the distance d between Cd and z within the Gouy–Chapman model (assuming Cd 5 C0), using the z-potentials obtained from mobility and conductivity data and the titratable surface charge density s0 5 214 mC/cm2. For a flat interface (that is, when d is much smaller than the particle radius), the relation between Cd and z is tanh~ z e/4kT! 5 tanh(Cde/4kT)exp(2kd).
[8]
The calculated d increases with decreasing ionic strength, which is also predicted by the hairy layer model (22). In general, the d-values calculated from the electrophoretic mobility are slightly larger than the d-values calculated from the conductivity increment, but the difference is not larger than 1.5 nm at any ionic strength. At the lowest electrolyte concentration d (calculated from the electrophoretic mobility) is almost 13 nm, a value which is somewhat larger than 9 nm, which was calculated by Marlow and Rowell at the same ionic strength (6). Eq. [8] is strictly valid for a flat double layer (ka . 100), but we have used the corresponding analytical equations for a spherical double layer (51), although it did not alter the results significantly. d was only overestimated by 10% at c HCl 5 0.1 mM (corresponding to a ka of 5.42) using Eq. [8]. The hairy layer model has often been used to explain the electrokinetic behavior of latices, but recent investigations (41,
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FIG. 10. The (a) Stern potential C(a) and the (b) diffuse layer charge density sd as a function of concentration of a 1:1 electrolyte. 214, 3.5 Å denotes the surface charge density s0 (in mC/cm2) and the parameter p, respectively.
50) have shown that this cannot be the only mechanism present in these systems. Elimelech and O’Melia (4) proposed that counterion adsorption at low electrolyte concentration leads to neutralization of the negative charge (less negative potential). When the electrolyte concentration increases, coion adsorption
becomes the leading mechanism (more negative potential). These two processes together with the ordinary compression of the double layer compete with each other and determine how the z potential varies with the electrolyte concentration. The same qualitative adsorption behavior concerning counterions
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FIG. 11. Comparison between (a) zel (El. mob.), zcond (Cond.), and C(a) and (b) sel (El. mob.), scond (Cond.), and sd as a function of HCl concentration. 214, 3.5 Å again denotes s0 and p, respectively.
and coions is found in the Stern layer conductance model developed by Zukoski and Saville (23). We will now try to interpret our results using the Stern layer conductance model developed by Mangelsdorf and White (24), which includes adsorption of ions onto available surface area.
3.3. Stern-Layer Conductance The Stern layer conductance model, which includes adsorption of ions onto available surface area, is included as an option in the program MOBILITY developed by O’Brien, White, and
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FIG. 12. The surface potential and z-potential as a function of monovalent electrolyte concentration. HCl corresponds to our data and NaCl to the data of de las Nieves et al. (59).
Mangelsdorf (49, 24). The model introduces a Stern layer, where lateral ion motion is allowed. First, the dissociation reaction for the ith ionic species X i is represented as SX i 7 S i 1 X i,
[9]
where S i is an empty Stern layer site. The dissociation reaction is described by the dissociation constant pK i and the total number of Stern layer sites per surface area, which we fixed to 9 p 1013 cm22. This value corresponds to a charge density of 14 mC/cm2. We also have to specify an outer Stern layer thickness and dielectric constant. We have used the values 1 and 15 Å respectively, which corresponds to an outer Stern layer capacitance of about 130 mF/cm2. It was found that the model is rather insensitive to variations in the Stern layer capacitance as long as uzu , 250 mV (24). The remaining parameters are then the dissociation constants and the relative ionic drag coefficients lrel for H1 and Cl2, respectively. First we fixed pK Cl to 0, because it was found that coion adsorption is relatively unimportant (24) and the same effects can be mimicked by varying the coion drag ratio lrel,Cl. Next, we varied pK H and then adjusted the counter ion and coion drag ratio concomitantly until we obtained reasonable agreement between the z-potentials obtained from electrophoresis (zel) and conductivity (zcond), respectively. This resulted in three different fits, and the result can be seen in Fig. 9 together with the original z-potentials assuming no Stern layer conductance. zel was hardly affected by the conductance. It was only when pK H was set to 1 that zel changed by more than 2 mV at any
ionic strength. This is the reason why we only show the pK H 5 1 case for zel. zcond, on the other hand, is much more sensitive to Stern layer conductance because DK/K ` is increased by the mobile Stern layer ions for a given z-potential. Therefore, the magnitude of zcond decreases when Stern layer conductance is included. By varying pK H and lrel, Stern layer conductance becomes important in different ionic strength regimes: For the case of pK H 5 1 and lrel 5 101 , the effect is large, between 0.5 and 10 mM HCl. When pK H 5 0.5 and lrel 5 71, the effect of conductance is more smeared out over the entire ionic strength regime. Finally, when pK H 5 21 and lrel 5 1, the effect of Stern layer conductance is only important above 5 mM HCl. It is clear that Stern layer conductance can improve the agreement between zel and zcond, but whether this is the true origin of the observed discrepancies remains to be validated. 3.4. The Association Theory If we assume that the hairy layer model is not operative, why then is the electrokinetic charge density increasing with increasing ionic strength? A recent theory for spherical surfaces developed by Spitzer (45) suggests that a fraction of the double layer counterions remains associated with the charged surface according to
a 5 1/~1 1 p k !,
[10]
where p is a parameter characteristic of the double layer. Equation [10] is referred to as the LMO law after Lubetkin,
SURFACE ELECTRICAL PROPERTIES OF POLYSTYRENE LATEX, 1
Middleton, and Ottewill (52). The other fitting parameter in this theory is a, which is the position of the Stern layer. The thickness of the Stern layer is then (a 2 R), where R is the particle radius. The theory assumes that there is a coion exclusion boundary b with a corresponding potential C~b! 5 k BT/ze,
[11]
which is termed the thermal electrostatic potential of the coions (TEP). Outside b the Debye–Hu¨ckel approximation is used. If s 0 , p, R, and a are specified, b and the Stern potential C(a) can be calculated from lengthy analytical solutions not presented here. The Stern charge density s a is calculated from
s a 5 2as 0R 2/a 2.
[12]
The remaining charge in the double layer is then the diffuse layer charge, sd. We fixed R and (a 2 R) to 165 and 1 nm, respectively, and tested this theory for some different values of s0 and p. The resulting Stern potentials and diffuse layer charge densities can be seen in Figs. 10a and 10b, respectively. We have adjusted s0 and p so that the Stern potentials would fall in the range between 220 and 2120 mV. According to the association theory, highly charged particles should exhibit a maximum in the Stern potential as a function of ionic strength (45). With decreasing surface charge density, the Stern potential should decrease (in absolute values) in a monotonous fashion and the diffuse layer charge should show only a slight increase with increasing ionic strength. This agrees very well with Goff and Luner’s investigation (3), but it is not supported by some other investigations (2, 4). In Fig. 11a, we have compared zel and zcond with the predictions from the ion association theory. The best fits were obtained by using s0 5 214 mC/cm2. p was set to 3.5 Å to fit zel and 4.5 Å to fit zcond. In other terms, the difference between zel and zcond is interpreted as a slight difference in counterion association according to Eq. [10]. In Fig. 11b, the electrokinetic charge densities are compared with the diffuse layer charge densities. It can be seen that skin agrees well with the fitted diffuse layer charge. scond is somewhat higher than the association theory predicts at high ionic strength, but this is mainly because the fitted Stern potentials are lower (in magnitude) than the corresponding zcond. 3.5. Concluding Remarks We have synthesized and characterized a well-known polystyrene latex (44). The surface charge density was initially 27 mC/cm2 of strong acid groups, but had decreased to 21.3 mC/cm2 after ultrafiltration. During storage, carboxyl groups appeared (48), but the electrophoretic mobility was unaffected by the appearance of these groups. The experimentally determined zel and zcond are in reasonable agreement with earlier investigations on the same latex system (8, 9). The correspond-
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ing electrokinetic charge density increases with increasing ionic strength, which is usually the case in latex systems. It is therefore plausible that charge mechanisms other than the dissociation of surface groups also are active in polystyrene latex systems (22, 23). Recently, some investigations on polystyrene latices have been published (21, 53–55) that validate the O’Brien and White theory without invoking any ion adsorption or hairy layer; i.e., the z-potential is decreasing according to Grahame’s equation and the shear plane is very close to the particle surface at all ionic strengths. In two of these cases (21, 54), commercial latices were used, but other investigations with similar latices (4, 41) have not produced such encouraging results. Russell et al. (53) used a highly charged sulfonate/styrene latex polymerized using a two-shot process (56, 57) that produces hairy surfaces (58), although no hairy layer was needed to explain the mobility data. Likewise, Antonietti and Vorwerg (55) used surfactant in their synthesis, which also may lead to hairy surfaces. It is also interesting to note that both investigations used dialysis to clean the latices. We suggest that certain synthesis procedures (combined with a certain cleaning process) may produce ideal latices (21, 53–55). It is also clear from these investigations that the high z-potential solution of O’Brien and White’s (49) theory (cf. Fig. 6a) is experimentally attainable. In fact, it is possible to reinterpret some mobility data so that ideal electrokinetic behavior is observed; de las Nieves et al. (59) have also characterized the highly charged (s0 5 213.9 mC/cm2) sulfonate/ styrene latex used by Russell et al. (53). In their Fig. 4, they show the surface potential and z-potential of their latex FJN20. Using their mobility data from Fig. 3, we can replace the low z-potentials with the corresponding high z-potentials for ionic strengths of 10 mM NaCl and below. The result can be seen in Fig. 12. Now the z-potential is only about 30 – 40 mV lower (in absolute terms) than the corresponding surface potential. Using Eq. [9], we find that the average distance between the surface and the plane of shear is about 3 Å. In Fig. 12, we have also included the z-potentials that correspond to our mobility data. Clearly, our high z-potentials are not as plausible as in the case of de las Nieves et al. Moreover, our conductivity data do not support the high z-potential solutions. This example shows that electrophoretic mobilities may be misinterpreted, but our experience is that it is in general not possible to reinterpret literature data successfully. For example, if the latex above is prepared without the second injection of NaSS, the typical latex behavior with increasing electrokinetic charge density is found (42). The recently developed nonlinear hairy layer theory (60) can hopefully explain certain features not accounted for in the Stern layer conductance models (23, 24). Anyhow, further research on a wide variety of latex systems is definitely needed. In a subsequent paper, we will present some results on the same latex system using dielectric response and the ESA technique, which will provide us with more information about the surface electrical properties of this latex.
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ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the Swedish Research Council for Engineering Sciences and EKA Nobel AB. The authors thank Dr. Ib Johannsen for performing the XPS experiments, Dr. Derek Biddle for performing the light scattering experiments, and Peter Greenwood for use of the ultrafiltration equipment.
30. 31. 32. 33. 34. 35.
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