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Langmuir 1995,11, 1112-1115
An Electrophoretic Investigation of the Relaxation Term in
Electrokinetic Theory Adrian S. Russell, Peter J. Scales,* Christine S. Mangelsdorf, and Sylvia M. Underwood? Advanced Mineral Products Research Centre, School of Chemistry and Department of Mathematics, The University of Melbourne, Parkville 3052, Australia Received June 20, 1994. In Final Form: December 16, 1994@ Electrophoretic mobility measurements on highly charged sulfonate/styrenelatices have been performed to test the validity of the relaxation term associated with the theory of O’Brien and White (J.Chem.SOC. Faraday Trans. 2 1978, 74, 1607). This theory links the electrophoretic mobility of a particle to the potential of the plane of shear. Good correlationwith the theoreticallypredicted maximum mobilities and experimental observations has been observed.
Introduction The measurement of particle electrophoretic mobility for the prediction of the colloidal instability or stability of a collection of particles is a widely used technique in colloid science. The measurement relies heavily on the conversion of the electrophoretic mobility to a zeta potential (5)or shear plane potential. The shear plane is envisaged as a hydrodynamic plane of shear, close to the particle surface. The movement of ions behind the shear plane is classically considered to be negligible. The repulsive interaction between surfaces is then calculated from this potential to assess the ability of the particle to resist coagulative processes. A number of analytic and numerical theories exist for the conversion of electrophoretic mobility to zeta potential, the most widely used being due to O’Brien and White.’ Their theory was a response to earlier theories that were either limited in applicability in terms of particle size or potential and/or cumbersome in the solution to the mobility-potential relationship. The characterizing parameter used in all models that address the magnitude of the potential is the product of the ionic strength (characterized by the Debye parameter, K ) and the radius of the particle (a), i.e. K U . In simple terms, the theory of O’Brien and White predicts the measured electrophoretic mobility of a colloidal particle in an applied electric field to be the sum of three forces, viz: (1) an electric force propelling the particle, due to the charged nature of the particle, (2) a drag force due to hydrodynamic drag, and (3)a relaxation force due to an electric field induced in the opposite direction to the applied field as a result of the induced polarization within the diffuse layer of ions surrounding the particle. The electrical force propelling the particle is predicted to be proportional to 5, whereas the retarding forces are predicted to be proportional to C2. A maximum in the conversion of mobility to zeta potential is thus predicted for particles size and ionic strength conditions such that 5 < Ka s 100. A number of studies have been undertaken to demonstrate the validity of the O’Brien and White theory’ and, in particular, the relaxation term. In direct tests of the
* Author to whom correspondence should be addressed. Present address: IC1 Valchem, Newsom Street, Ascot Vale, 3032, Australia. Abstract published in Advance A C S Abstracts, March 1,1995. (1)O’Brien, R. W.; White, L. R. J . Chem. Soc.Faraday Trans.2 1978, 74, 1607. @
theory using the methodology outlined by O’Brien and White,’ Chow and Takamura2s3found mobilities of higher magnitude than predicted by theory. They measured electrophoretic mobilities for a heat-treated carboxylate latex at constant K a as a function of pH and observed a definite maximum in electrophoretic mobility. Their conclusion was that the relaxation term provided a n underestimate of the true mobility-zeta potential interrelationship. Other electrokinetic studies4y5have also yielded mobilities with greater magnitudes than predicted by the theory. In contrast, a number of works have indicated that theoretical mobilities are too high in magnitudee6-11 Despite that lack of a consistent correlation with theory, there is only limited electrophoretic mobility data at high mobilities and in a suitable K a regime to rigorously test the theory. The difficulty is in obtaining suitable colloids of spherical shape, correct size, and high charge to observe an experimental mobility maximum for a fixed K a . In this paper we present the results of an electrophoresis study using the recently developed sulfonatdstyrene latices of Kim et al.12J3 These latices have a very high surface charge (reported to be in the range 30-8OpC cm-2), and perhaps more importantly, this charge is assumed to be fully developed in the neutral pH regime where the maintenance of constant K a (i.e. background salt conditions) is not problematic. The aims of this study were to monitor the form of the electrophoresis versus pH curve for a series ofKa conditions to elucidate the presence or absence of a maximum in the (2) Chow, R. S.; Takamura, K. J . Colloid Interface Sci. 1988, 125, 212. (3) Chow, R. S.; Takamura, K. J . Colloid Interface Sci. 1988, 125, 2%
(4) Dunstan, D. E.; Rosen, L. A,; Saville, D. A. J. Colloid Interface Sci. 1992, 153, 581. ( 5 ) Rosen, L. A.; Saville, D. A. J . Colloid Interface Sci. 1990,140,82. (6) Rosen, L. A.: Saville, D. A. J . Colloid Interface Sci. 1992. 149. 542. (7) Kylstra, J.;van Leeuwen, H. P.;LyMema,J.J . Chem.Soc.Faraday Trans. 1992,88, 3441. (8)Kijlstra, J . ; van Leeuwen, H. P.; Lyklema, J. Langmuir 1993,9, 1625. (9)Shubin, V. E.; Hunter, R. J.;O’Brien, R. W. J . Colloid Interface Sci. 1993, 159, 174. (10) Zukoski, C. F., W,Saville, D. A. J . Colloid Znterface Sci. 1985, 107, 322. (11)Hidalgo-Alvarez, R.; Moleon, J. A.; De Las Nieves, F. J.; Bijsterbosch, B. H. J . Colloid Interface Sci. 1992, 149, 23. (12) Kim, J. H.; Chainey, M.; El-aasser, M. S.; Vanderhoff, J. W. J . Polymer Sci. Part A 1989, 27, 3187. (13) Kim, J. H.; Chainey, M.; El-aasser, M. S.; Vanderhoff, J. W. J . Polymer Sci. Part A 1992, 30, 171.
0743-7463/95/2411-1112$09.00/0 0 1995 American Chemical Society
Electrophoretic Investigation of the Relaxation Term 01
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Langmuir, Vol. 11, No. 4, 1995 1113
Sizing was performed on a Philips CM-10 transmission electron microscope against calibration graticules. Electrophoresismeasurements were performed on a Coulter DELSA440laser Doppler apparatus. Avery low volume fraction latex dispersion was temperature-equilibratedin a glass cell with nitrogen gas flushing. A minimum 45 min equilibration time was allowed prior to measurementand after each pH adjustment. Measurements were made at both stationary layers of the electrophoresis cell, and reported values are an average of the two. All reported values show an agreement between the stationary levels to within 2%. Theoretical mobilities were computed using the mobility program provided by the authors of the O'Brien and White theory.
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Zeta Potential (mV) Figure 1. OBrien and White theoretical curves showing the
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magnitude of the measured mobilities and, depending on the observations, compare the measured maximum value of the mobility to theoretical predictions. O'Brien and White,' in their proposed test of the relaxation term, stated, albeit for a AgI colloid, "The experiment would consist simply of measuring mobilities as a function of pAg and looking for maxima for various K a values. The agreement of the theoretical muximum would be a sensitive test of the model which does not require aprecise knowledge of 5 (i.e. the zeta potential)." The proposed test does not need to assume anything of the charging behavior of the colloid, only that the charge is sufficient to cause dominance of the second-order relaxation term. In addition, it does not require that a distinct maximum is observed, although this is desirable, since it is the only point of nonambiguity in the conversion of mobility to zeta potential for highly charged colloids. In the absence of a distinct maximum, it is still possible that the maximum observed value of the mobility is representative of the true value. The colloids used in this study had a negative surface charge such that any maxima in the magnitude of the mobility would be manifested as a minimum in the measured mobility. Theoretical curves depiciting the presence of the mobility minima for a number of K a conditions of interest are shown in Figure 1. Colloids of two particle sizes were examined such that sensitivities relating to background salt concentration could be established.
Experimental Section All experiments were performed at 25 "C using water from a Millipore Milli-Q system and KC1 as the background electrolyte. All reagents were AR grade or purer and all chemicals for latex synthesis were distilled or recrystallised prior to use. Sulfonatedpolystyrene latices were synthesized according to the method of Kim e t al.12J3and then cleaned by a combination
of centrifugation, decantation,and redispersion steps until both the suspension conductivity and surface tension ofthe dispersing medium were similar to that of purified water. The final electrolyte concentration of the latex dispersion and hence the KU condition of the suspension were achieved by equilibration through dialysis of the cleaned latex to a known electrolyte
concentration. Two sizes oflatices 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
Results and Discussion The mobility of the latices was measured as a function of pH for various values of K a . In Figures 2 and 3 we report the mobilities observed for latex A and B, respectively, for the case where either a maximum in the magnitude of the mobility was observed or where the magnitude of the mobility was constant or was constant and then decreased with increasing pH. The assumption in all cases is that points associated with or extremely close to a maximum in the magnitude of the mobility can be clearly identified. The data of Figures 2 and 3 show the magnitude of the mobility to be increasing with increasing salt concentration. This observation is counterintuitive in a classical colloidal sense but is the expected result for mobility data in the vicinity of the mobility minimum. It should be noted at this point that mobilities were measured at both higher and lower K a values than reported, but the criteria to test the theory of O'Brien and White,' namely observation of either a distinct minimum, a constant mobility with increasing pH, or a constant mobility followed by a decrease in the magnitude of the mobility with pH, was not achieved for latex B a t low K a and latex A a t high K a . The measured data indicates that a distinct minima would have been observed a t low K a for latex A and B but at lower pH values than constant K a measurement would allow. An example of this is shown in Figure 4, where mobility is plotted against pH for latex B at K a = 20. The magnitude of the mobility decrease with increasing pH. This observation is consistent with the data being associated with the high zeta potential side of the mobility minimum where the relaxation term is dominant. I t should be noted further that the magnitude of the mobility is less than the predicted maximum value but approaches the maximum value at lower pH's. At high K a for latex A, the magnitude of the mobility increased continuously with increasing pH, even at p H s approaching 10. This is consistent with the observation of Chow and T a k a m ~ r afor ~ , ~heat-treated carboxylate latices where they observed a distinct mobility maxima at low salt concentrations, but the same trend was not observed a t higher salt concentrations. For the experimental data presented here, the magnitude of the mobility did not reach the predicted maximum value at high salt concentrations. A possible explanation for this trend is that screening of the surface charge is such that the potential required to reach the minimum in mobility is not attained. This is in line with the observation in Figures 2 and 3 that the point at which the magnitude of the mobility decreases with increasing pH is moving to higher
Russell et al.
1114 Langmuir, Vol. 11,No. 4, 1995
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(Relative Cell Depth)* Figure 5. Komagata plot of the electrophoretic cell profile for measurement ofthe mobility for latexA at KU = 23. The mobility calculatedfromthisplotis -5.51pmcmV-'s-l, whichcompares calculated from the well with the value of -5.57pm cm V-l average of the readings at the stationary layers of the cell.
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PH Figure 3. Electrophoretic mobility versus pH at KU = 23,30, and 50 for latex B. The point corresponding t o the minimum measured mobility is highlighted. -4,
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therefore to meet the test criteria with increasing electrolyte concentration. This and associated observations suggest that the latex used in these experiments is charging across the pH 4-10 regime. A charge titration in this regime showed this assumption to be correct in that the surface increased in charge by e l 0 pC cm-2, but the titration showed hysteresis. This is more consistent with the opening up of the latex surface, thus exposing more charge, rather than a protonatiorddeprotonation of the sulfonate groups on the surface. This observation, although not understood, does not change the data interpretation. It does however highlight the 'nonideal' nature of these latices and the difficultyhmpossibility associated with interpreting, in isolation, electrokinetic data as a function of salt a t constant pH. The interpretation of results from this work are highly dependent on the accuracy of the electrophoretic mobility measurement and the monodispersity of the colloids. An error of 2%in the mobility indicates the precision to which the mobilities were measured. Error bars were not shown in Figures 2 and 3 to aid clarity. To demonstrate the precision of the results, the accuracy of finding the stationary layers in the measurement cell was also checked by measuring a profile of the cell and using a Komogata plot.14 An example of one such plot is shown in Figure 5. The correlation between the mobilities measured at the stationary levels and values calculated from plots such as the one shown in Figure 5 is excellent. The lowest mobility measured at each tca was then compared to the minimum predicted by the theory of O'Brien and White.' A plot of this comparison is shown in Figure 6. The points chosen for comparison are highlighted in Figures 2 and 3, and the possibility exists that the points do not represent the mobility of highest magnitude for the particular Ka. Despite this argument, the agreement between experiment and the predicted mobility minima is very good. In the data comparison of Figure 6, it is necessary to highlight the errors in K U , the sizing o f the particles, and the measurement of the mobilities which are predicted to give a composite error on the order of f4%. The f4% error value is shown in Figure 6. For latex A, the comparison of theory and experiment shows excellent agreement at low tca's. At tca = 30 the agreement between (14)Komagata, S. Res. EZectrotech. Lab. 1933,348,l.
Electrophoretic Investigation of the Relaxation Term
potential. This work was similarly associated with a dielectricresponse study.15J6In contrast, good agreement between potentials predicted from the dielectric response work and this work was observed. This correlationfurther highlights that the form and magnitude of the relaxation term is correct. By definition,it also negates the presence of surface conduction (ion mobility by the electrokinetic shear plane) for these latices. This is an interesting observation in itself since highly charges latices are generally viewed to be nonideal in this sense.
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Langmuir, Vol. 11, No. 4, 1995 1115
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electrophoretic mobility measured by experiment with the minimum as predicted by the theory ofO’Brien and White. The data is for both latex A and B in the K a regime of highest sensitivity of the measured mobility t o the relaxation term. experiment and theory is poorer, but the deviation is still less than f 5 % . Latex B shows excellent agreement with the theory of O’Brien and Whitel at the higher Ka’s but shows some deviation from theory at the lowest KU. This deviation from the expected theoretical result is still less than f8%. The slight difference between theory and experiment at this K a may be due to the fact that the minimum is actually at a lower pH than was measured. As discussed, interpretation of measurements below pH 4 is less straightforward and, although not impossible, impractical to display against a single K a theory curve. There are numerous experimental examples in the literature showing serious discrepanciesbetween the zeta potential calculated from electrophoretic mobilities and techniques such as dielectric r e s p o n ~ e . The ~ ~ ,conclusion ~ from all studies is that the electrophoretic mobility of a particle is an inadequate determinant of the electrokinetic
Conclusions Two highly charged latex samples of different particle size have been examined in the K a = 10-50 regime, where the sensitivity of the measured magnitude of the electrophoretic mobility to relaxation processes is expected to be maximal. The correlation between experimentally measured mobilities, where there was either a distinct mobility minimum or the mobility was constant, and the theory of O’Brien and White was shown to be excellent, indicating that, for this system, the theory correctly predicts the mobility minimum. It is concluded that the O’Brien and White theory1correctly predicts the relaxation term in electrophoretic mobility measurements and a further implicationis that deviations from theory observed in previous studies cannot be attributed to an incorrect relaxation term. The highly charged sulfonate/styrene latices represent a model colloidal system for further study. Acknowledgment. We thank Ms. K. Grant for synthesis of the latices. Support for this work was obtained through the Advanced Mineral Products Research Centre, a Special Research Centre of the Australian Research Council. Discussions with Professors L. R. White and T. W. Healy are gratefully acknowledged. LA940486V (15)Russell, A. S.; Scales, P. J.; White, L. R.; Mangelsdorf, C. S. Langmuir, submitted. (16) Mangelsdorf, C . S.; White, L. R. The response of a dilute suspension of spherical colloidal particles to an oscillatory electric field. Manuscript in preparation.
