Langmuir 1995,11, 1553-1558
1553
High-FrequencyDielectric Response of Highly Charged Sulfonate Latices Adrian S. Russell, Peter J. Scales,” Christine S. Mangelsdorf, and Lee R. White Advanced Mineral Products Research Centre, School of Chemistry and Department of Mathematics, The University of Melbourne, Parkville 3052, Australia Received November 4, 1994. I n Final Form: February 7, 1995@ High-frequencydielectric response measurements on highly charged sulfonate/styrenelatices have been performed and analyzed using extant theories. The zeta potentials derived from this study were compared to those obtained from electrophoretic measurements. Very good correlation between the two techniques was observed. It is concluded that Stern layer conduction is not significant in these latices.
Introduction Electrokinetic techniques are widely used to determine the electrical charge on the surface of a colloid. Recently there has been intense discussion concerningelectrokinetic techniques and the theories used for interpretation of data. Several concerns have been raised relating to the inability of the different techniques to yield the same electrokinetic p~tentials.l-~ Two widely used techniques for the measurement of the electrokinetic potential are microelectrophoresis and conductivity measurements. The latter can be separated into static conductivity and low or high frequency dependent dielectric response measurements. In previous studies, latex particles have often been used in fundamental work.3,4,6~s,9-13 The benefits of latex include the ease of obtaining spherical monodisperse particles with a characterizable surface charge. The volume of electrokinetic data obtained and its subsequent interpretation have led previous workers to show concern about problems such as ion binding,8J4-16nonlinearities between potential and electrolyte c o n ~ e n t r a t i o n , l ~ surface J ~ - ~ ~ hairiness or structure,1~4J9~z0 and ion conduction behind the Stern
* Author to whom correspondence should be addressed.
Abstract published in Advance ACS Abstracts, April 1, 1995. (1)Dunstan, D. E. J . Chem. Soc., Faraday Trans. 1993,89,521. (2)Dunstan, D. E.J . Colloid Interface Sci. 1994,163,255. (3)Zukoski, C. F., N, Saville, D. A. J . Colloid Interface Sci. 1985, 107, 322. (4)Rosen, L. A,; Saville,D. A. J . Colloid Interface Sci. 1990,140,82. ( 5 ) Rosen, L. A,; Saville, D. A.Langmuir 1991,7, 36. (6)Rosen, L. A,; Saville, D. A. J . Colloid Interface Sci. 1992,149, 542. (7)Kijlstra, J.;van Leeuwen, H. P.; Lyklema, J. Langmuir 1993,9, 1625. (8) Midmore, B. R.; Hunter, R. J. J . Colloid Interface Sci. 1988,122, 521. (9)Shubin, V. E.;Hunter, R. J.;OBrien, R. W. J . Colloid Interface Sci. 1993,159,174. (10)Dunstan, D. E.; White, L. R. J . Colloid Interface Sci. 1992,152, 297. (11)Dunstan, D. E.; White, L. R. J . ColloidInterface Sci. 1992,152, 308. (12)Zukoski, C. F., IV; Saville, D. A. J . Colloid Interface Sci. 1986, 114,45. (13)Chow, R. S.; Takamura, K. J . Colloid Interface Sci. 1988,125, 226. (14)Voegtli, L. P.;Zukoski, C. F., IV J . Colloid Interface Sci. 1991, 141,92. (15)Meijer, A.E. J.;van Megen, W. J.;Lyklema, J. J . Colloid Interface Sci. 1978,66,99. (16)Elimelech, M.; O’Melia, C. R. Colloids Surf. 1990,44, 165. (17)Dunstan, D. E.J . Chem. SOC.,Faraday Trans. 1994,90,1261. (18)Goff, J. R.; Luner, P. J . Colloid Interface Sci. 1984,99,468. (19)Batos, D.; de las Nieves, F. J. Prog. Colloid Polym. Sci. 1993, 93,37. (20)Van Der Put, A. G.;Bijsterbosch, B. H. J . Colloid Interface Sci. 1982,92,499. @
0743-746319512411-1553$09.00/0
Table 1. Molar Ratios of Styrene Monomer to NaSS Monomer Used in the Synthesis of the Latices
styrenemass ratio latex A latex B
shot 1
shot 2
424 594
3.96 4.82
plane.1zzz1-23This has led many workers to conclude that the electrokinetic potential, namely the zeta potential cannot be fully characterized using a single electrokinetic technique. In a previous paper,z4we investigated the validity of the O’Brien and Whitez5theory of static electrophoretic mobility and found that the theory correctly predicted the mobility minimums (for a negatively charged particle) observed a t high potentials in the Ka 10 to 50 regime, where “K” is the Debye parameter and “a” is the particle radius. This work showed that the theory of O’Brien and Whitez5 correctly predicts the electrokinetic potential without the need to invoke surface conduction (ionic mobility behind the shear or Stern plane). It should be noted that surface conduction (also referred to as Stern layer conduction) is frequently used to rationalize noncompliance of electrokinetic potentials from various techniques.1z~z1-z3The electrophoresis study was conducted using a polystyrendsodium styrenesulfonak. (NaSS) latex as a model colloid. In this paper, results of a highfrequency dielectric response study on the same particles are presented and the zeta potentials interpreted from the dielectric response comapred to those from electrophoresis.
(c),
Experimental Section All experiments were performed at 25 =k 0.1 “C. Water was obtained from a Millipore “Milli-Qsystem. KCl was used as the background electrolyte. All reagents were AR grade or purer and all reactants for latex synthesis were purified prior to use. Polystyrene latices were synthesizedaccording to the method of Kim et al.26,27 The styreneMaSSmolar ratios utilized are listed in Table 1. (21)Rosen, L. A,;Baygents, J. C.; Saville, D. A. J . Chem. Phys. 1993, 98,4183. (22)Kijlstra, J.;van Leeuwen, H. P.; Lyklema, J. J. Chem. Soc., Faraday Trans. 1992,88,3441. (23)Fernandez-Barbero, A,; Martin-Rodriguez, A.; Callejas-Fernandez, J.; Hidalgo-Alvarez, R. J . Colloid Interface Sci. 1994,162,257. (24)Russell, A.S.; Scales, P. J.; Mangelsdorf, C. S.; Underwood, S. Langmuir, in press. (25)O’Brien, R. W.; White, L. R. J . Chem. SOC.,Faraday Trans. 2 1978. 74.1607.
Polym. Sci., Part A 1992,30,17
0 1995 American Chemical Society
Russell et al.
1554 Langmuir, Vol. 11, No. 5, 1995 The latices were cleaned by a combination of centrifugation, decantation, and redispersion steps until both the suspension conductivity and surface tension of the dispersing medium were similar to that of pure water. The final electrolyteconcentration of the latex dispersion (and hence the KU condition of the suspension) was achieved by equilibration through dialysis of the cleaned latex to a known electrolyteconcentration. For each KU the pH was chosen to correspond to the mobility of maximum magnitude. The pH of the series of experimentsvaried between 4.0 and 9.0. The final diallate was then used as the background electrolyte for the dielectric response measurements. Two sizes of latices were prepared. Latex A had a radius of 97.5 nm with a uniformity ratio U = 1.03. Latex B had a radius of 125 nm with U = 1.01. The uniformity ratio was calculated as
U = DJD, = weight averaged diameter/
number averaged diameter where
D, = CniDi4/CniD; and D, = CniDi/& Particle sizing was performed on a Philips CM-10 transmission microscope against calibration graticules. Electrophoresis measurements and data are described in a previous paper.24 Dielectric response measurements were performed using a two-electrodecell and Hewlett-Packard4194A impedance/gain-phaseanalyzer. The complex conductivity of a particulate suspensionwas measured over a frequency range of 0.1-40 MHz at two different volume fractions (4) for each KU condition. The volume fractionswere typically in the range 0.020.03 and 0.10-0.18. Multiple measurements were conducted at each volume fraction to eradicateirregularities. A M 1 description of the experimental equipment and the procedure may be found el~ewhere.~,~
Theory The aim of the high-frequency conductivity and dielectric response experiment is to find the complex conductivity ofa suspension as well as that ofthe background electrolyte in the frequency regime wI2n = 0.1-40 MHz. Experimentally, the complex conductivity of a suspension is obtained by measuring the admittance (impedance-l) of a capacitor filled with the suspension in question. The admittance Y ( w ) is converted into the complex conductance K*(w) using the resultz8
Y = CJ* where C, is the geometric cell constant of the measurement vessel. The complex conductivity of the suspension can be expressed in terms of the conductivity A K ( w ) and the dielectric response AE’(w) iAc”(w) of the suspension due to the presence of the colloidal particles, viz.28
+
+
+
K* = P,,#J[M - i ~ / 4 n . ( A ~~’ A E ” ) ] ( 2 ) where Pel is the complex conductivity of the bulk electrolyte. Alternatively, the complex conductivity of the suspension can be expressed in terms of the complex dipole strength Co(o), vi^.^^
K* = KYF,,(l+
34x3
(3)
Deciding on which expression to use to analyze the experimental data depends on the frequency range of (28) Delacey, E. H. B.; White, L. R. J.Chem. SOC.,Faraday Trans. 2 1981, 77, 2007.
interest. The choice is related to the structure of CO,A d , and AE“when plotted against frequency. At low frequency, the real and imaginary parts of Co are approximately constant whereas a t high frequency these curves possess greater structure, exhibiting well-defined maxima and minima for frequencies beyond 0.1 MHzeZ9In the case of A d and Ad’, all of the structure in the curves is observed a t low frequency with relaxation of A d occurring around 1MHz and A€‘‘ decreases sharply to zero after reaching a maximum around 0.1 M H Z . ~ ~ Since we are interested in the high-frequency regime 0.1 to 40 MHz, we chose to analyze IP in terms of the real and imaginary parts of the dipole strength using eq 3. Most previous workers in the field were concerned with low-frequency dielectric response and so analyzed their experimental data in terms of A d and Ad‘. Since the theoretical dipole strength is a function of the zeta potential, a comparison of experimental and theoretical data will yield a zeta potential. The zeta potential was determined as follows. For each system, the real and imaginary parts of the experimental dipole strength were plotted as a function of frequency. The experimental curves were compared to theoretical curves computed a t various zeta potentials using the numerical electrokinetic theory of Mangelsdorf and White.29 The theory of Mangelsdorf and Whitez9is a n extension of that of DeLacey and Whitez8to higher frequency by the inclusion of terms to account for particle inertia. The theoretical curve of best fit was obtained by minimizing the mean square deviation for the real and imaginary parts of Co simultaneously, i.e., we minimize
M.S.D. = C[(CF- COer)2 + ( C t - C,“’l21
(4)
where the sum is over all experimental data points. Here, superscript “e”refers to the experimental data point and superscript “t”is the corresponding theoretical value. Also, superscripts “r” and “i”refer to the real and imaginary parts of CO,respectively. Then, the zeta potential for the system is simply the zeta potential corresponding to the theoretical curve that best fits the experimental data for the dipole strength.
Results Figure 1shows the plots of COfor latex A and latex B at various KU values and volume fractions. The fits are good and are atypical of many of the plots of A& and Ad‘ a t low frequency presented by other ~ o r k e r s . ~ , While ~-~s~~ care must be taken in comparing the two methods of plotting the data, it is clear that most workers have seen extremely large magnitude differences beween theory and experiment. This is clearly not the case in our data. The fits shown in Figure 1 are the first comparison between the extant theory of Mangelsdorf and Whitez9 and experimental data. On the whole the fits are much superior a t low KU’S values. The fits in parts b, c, d, and i of Figure 1are near to perfect, while other low KU plots such as in parts e and j of Figure 1are also very good. The trend is for the fits to be poorer at higher KU. Despite this trend, the data of Figure l q show good agreement while Figure l a has a poor fit, which may indicate that the observations are quite random. The deviation in the fits is characterized by deviations in both the real and imaginary parts of COa t high frequency. Some workers in this field have attributed deviations between theory and experiment to the movement of ions (29)Mangelsdorf, C. S.; White, L. R. The Response of a Dilute Suspension of Spherical Particles to an Oscillating Electric Field. To be submitted for publication.
Dielectric Response of Sulfonate Latices Table 2. KU
5 Values Calculated for Both Latex A and B by the Theory of Mangelelsdorf and WhitezBa
PH
@1
51(mV)
$2
13 17 23 30 50
4.25 4.65 4.83 5.29 7.40
0.029 0.026 0.017 0.024 0.026
a. Latex A -123 0.112 -110 0.135 b 0.080 b 0.114 -119 0.070
17 20 23 30 50
4.58 4.72 4.91 5.55 7.07
0.037 0.041 0.05 0.037 0.03
b. Latex B -155 0.145 b 0.177 -156 0.18 -15Q 0.20 -156 0.134
a
Langmuir, Vol. 11, No. 5, 1995 1555
52
(mV)
Caverage
- 124 -114 -107 - 107 -101
- 124 -112 -107 -107 -110
- 159 -156 -151 - 143 -130
-157 -156 -154 -151 -143
Shown is the 5 calculated for both volume fractions for each K U .
Part relates to latex A and part b to latex B. Indicates that a reasonable fit could not be obtained and thus no 5 could be obtained.
within the Stern layer,9Jz,z1-23,30,31 a contribution which is not included in the classical theory of Mangelsdorf and White.z9 This phenomenon was thus investigated. Stern layer effects are predicted to be more prominent when there are more ions in the Stern layer and a t higher K a . The trend will be to lower the magnitude of electrophoretic mobilities and increase the magnitude of the potential from dielectric response. This is consistent with the observation that more deviation from the theory is observed a t higher K a . The recently developed Stern layer conduction model of Mangelsdorf and White3z was used to compare the theory with experimental observations. This model builds upon ref 29 and uses the same approach as that used for their model for electrophoretic mobility.33 The model has a large range of adjustable parameters. Despite the array of adjustable parameters the fits to experiment could not be improved. Furthermore, the corrections to the theoretical curves using the mobile Stern layer model were in the opposite direction to that required. In a n attempt to explain the observed deviations, the scales of Figure 1 should be inspected closely. Of significance is the magnitude of the difference between the background and sol impedances, which is smaller a t higher Ka. The associated analysis errors are thus smaller a t lower K a according a more accurate experimental curve. Indeed, the deviations may not be related to theory or anomalous effects such as Stern layer conduction but merely experimental limitations. Having established that the theory of Mangelsdorf and Whitez9 is able to fit the form and magnitude of the experimental data, zeta potentials were calculated. These are displayed in Table 2. From Table 2, it is apparent that no theoretical fit was obtained for three samples. In all cases these were for low volume fraction. In the case of latex A the inconsistency occurred a t the lowest 4 values. It is evident from the quality of fits obtained for this latex that these poor fits are due to random errors in such quantities as the background electrolyte and volume fraction. Such errors will have a greater effect a t lower volume fraction. It is further evident from Table 2 that where zeta potentials were measured for two volume fractions, the 5 value from both 4’s is very similar, especially a t low K a . (30) O’Brien,R. W.; Rowlands, W. N. J . Colloid Interface Sci. 1993, 189, 471.
(31) Hidalgo-Alvarez,R.; Moleon, J. A.; DeLas Nieves, F. J.; Bijsterbosch, B. H. J . Colloid Interface Sci. 1992,149, 23. (32)Mangelsdorf, C. S.; White, L. R. Effects of Stern Layer Conductanceon Variable Frequency ElectrokineticTransport Properties of Colloid Particles. To be submitted for publication. (33) Mangelsdorf, C. S.; White, L. R. J . Chem. SOC.,Faraday Trans. 1990,86,2859.
At higher K a , the values are increasingly dissimilar, with the lower volume fraction consistently having the lower (higher in magnitude) zeta potential. The reason for this is not clear, but the differences are small enough that a comparison with the zeta potential from the mobility measurements is warranted. The zeta potentials from Table 2 were then compared to those interpreted from electrophoretic mobility measurement~ using ~ ~ the theory of O’Brien and WhiteeZ5 The comparisons are shown in Figures 2 and 3. For latex A, the comparison in the middle K a range is excellent with the K a 13 value having a slight discrepancy. The K a 50 value is somewhat erroneous and clearly not due to errors in measurement or comparison. For latex B, the maximum difference in the values from the two techniques is less than 11%. The deviations in the two data sets are put down to the accuracy in conversion of the mobility to a zeta potential in the high potential regime. Observation of the appropriate mobility zeta potential relationz5 shows the curves to be very flat at the mobility maxima (minima in this case). As the mobility measurements were purposely measured a t or close to the mimima,z4small errors in the mobility give large variations in the calculated zeta potential. An example of this is for latex B a t K a 30. A 2% confidence range gives a mobility range of f0.12 pmcml (V*s). This translates to a zeta potential range of f 1 8 mV, substantially greater than the differences in Figure 3. The similarity of the results from the two techniques is best expressed in a conversion of f values from the dielectric response to mobilities using the theory of O’Brien and White.25 This comparison is shown in Figures 4 and 5. From these figures, it is clear that the two techniques do yield the same electrokinetic parameters, the one exception being that of latex A a t K a 50. Stern layer conduction did not resolve this difference. The use of this concept would have caused a large divergence on the remainder of the data. Therefore the authors have no explanation of the divergence of this point short of possible difference in charging behavior between the two systems. The sensitivity of most systems to the accuracy of the electrophoretic mobility measurements will be much less than in the above example. Indeed most latices and inorganic oxides have potentials much lower in magnitude than 100 mV. Perusal of the literature shows that agreement between the two electrokinetic techniques is a rare occurrence. For example, Shubin et al.9 observed a zeta potential of - 100 mV from mobility measurements and - 177 mV from dielectric response. Similarly Rosen and Saville4observed a zeta potential of 81 mV with mobility measurements but could not obtain a satisfactory fit to their dielectric response measurements on the same system, even for a potential as high as 250 mV. However by heating their latices above the glass transition temperature, the potential predicted by both techniques was similar, and in one case, a satisfactory fit to experiment was obtained. To the authors’ knowledge, the only other instance of a fit between the zeta potential calculated from mobility and dielectric response measurements appears incidentaLs In studies of latex heat treatment, Rosen and S a ~ i l l e ~ . ~ obtained the zeta potential from mobility measurements and then used this value to generate the theoretical curve for dielectric response comparison. In their first study Rosen and Saville4 observed unacceptable fits for the unheated latices but, upon heating above the latex glass transition temperature, observed reasonable fits for one case. They also measured mobilities up to one unit higher than the theoretical predicted maximum of OBrien and White.25 In the context of our recently presented mobility
1556 Langmuir, Vol. 11, No. 5, 1995
Russell et al.
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Figure 1. Measured (solid line) and theoretical (dashed line) values of the real and imaginary parts of the dipole strength (CO): (a) latex A at KU 13 with 4 = 0.029; (b) latex A at KU 13 with 4 = 0.112; (c) latex A at KU 17 with 4 = 0.026; (d) latex A at KU 17 with 4 = 0.135; (e! latex A at Ka 23 with 4 = 0.080; (f) latex A at Ka 30 with 4 = 0.114; (g) latex A at Ka 50 with 4 = 0.026; (h) latex A at Ka 50 wlth 4 = 0.070; (i) latex B at Ka 17 with 4 = 0.037; (i)latex B at Ka 17 with 4 = 0.145; (k) latex B at Ka 20 with 4 = 0.177; (1) latex B at KU 23 with 4 = 0.050; (m) latex B at Ka 23 with 4 = 0.180; (n) latex B at Ka 30 with = 0.037; (0)latex B at Ka 30 with 4 = 0.200; (p) latex B at KU 50 with 4 = 0.030; (9) latex B at Ka 50 with 4 = 0.134.
+
in which the O’Brien and White theory25correctly predicts the zeta potential mobility relationship, there is a possibility discrepencies in electrolyte concentration were present. In the second of Rosen and Saville’s6studies, there were no such anomalies. They further investigated the notion of surface hairinesslstructure by comparing heat treatment of a ‘13are”latexpossessing only the surface structure introduced by the polymerization process and one which had neutral polymeric hairs artificially grafted onto the surface. Before being heated, both showed large irregularities between mobility and dielectric response measurements, but after heating, the (‘bare’’latex gave good agreement. Upon being heated, the hairy latex showed significant improvement but the fits were still unsatisfactory. From Rosen and Saville’s study6 it is obvious that significant surface structure plays a role in the observed anomalies. The fact that agreement could be achieved by heating and “smoothing” a colloid surface shows that for some colloids only one electrokinetic technique would be needed in order to characterize the electrokinetic charge. The results of our study are in direct contrast to most previous work in the field of frequency-dependent conductivity measurements. It is clear for this latex system that only one technique is needed to characterize the electrokinetic properties of the surface. The applicability to other systems is not clear. However, it is encouraging that this system behaves according to classical expectations. It is highly unlikely that this latex is unique, a notion the study of Rosen and Saville6would support. The two-shot polymerization process employed to manufacture these latices will lead to a highly charged “hairy”surface,lg with high concentrations of specifically absorbed counterions. Extant hypothesis would make it a prime candidate for Stern layer c o n d ~ c t i o n . Despite ~~ this postulate, there was no evidence of surface conduction, and only one dielectric response measurement out of ten systems studied showed any anomalies. Poor correlation between dielectric response and mobility measurements has also been observed for other surfaces such as Stober and haematite.7,2This, despite the fact the surfaces of these colloids are more “ideal” than those ofthis study or ofRosen and Saville.6 Therefore care must be taken in postulating the reason for such
-70 I
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mobility (filledboxes) and dielectric response (emptyboxes) for latex B. poor correlation. An example is Stern layer conduction.21,22 Use of this notion can give results which on the surface appear to fix the problem but still contain inconsistencies. Some examples follow. Bastos and de las N i e ~ e susing ,~ the same latices as this study, claimed that the problem of a maxima in the magnitude of 5 with increasing electrolyte concentration
1558 Langmuir, Vol. 11, No. 5, 1995
v1
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Russell et al.
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1MHz) have usually produced good fits to t h e ~ r y ,in ~ ,contrast ~ to measurements a t lower frequencies. The method of sample preparation may also be of importance. Dunstan and White’OJl have already discussed this matter in detail and dialysis was found to be the preferred sample preparation technique. To our knowledge, no other study has used this technique. The last area of possible investigation is the volume fraction used for the dielectric response measurements. In many studies, the volume fractions were lower than used in this study. At low volume fractions, the magnitude of the difference between the admittance of the background and the admittance of the colloid sol may be small enough to be significantly effected by systematic error. A low-frequency dielectric response study is planned.
Acknowledgment. We thank Ms K. Grant and Dr. S. Underwood for synthesis of the latices and Drs. R. W. O’Brien and W. N. Rowlands of the University of Sydney, Australia, for the use of their conductivity bridge and for assistance with the measurements. Support for this work was obtained through the Advanced Mineral Products Research Centre, a Special Research Centre of the Australian Research Council. LA94087OS ~
(35)Dunstan, D. E.; White, L. R.J.Colloid Interface Sci. 1990,134, 147.
