© Copyright 1998 American Chemical Society
OCTOBER 13, 1998 VOLUME 14, NUMBER 21
Letters Electrophoretic Properties of Polystyrene Spheres Rudy Folkersma,* Alois J. G. van Diemen, and Hans N. Stein Laboratory of Colloid Chemistry, Department of Chemical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Received February 25, 1998. In Final Form: August 3, 1998 The zeta-potential of monodisperse polystyrene latices as a function of ionic strength is reported. Latices exhibit anomalous electrokinetic behavior: instead of the expected decrease in mobility with increasing electrolyte concentration, a maximum occurs. In this paper it is shown that both in electrophoresis of dilute dispersions and in electroomosis of concentrated plugs, the zeta-potential as a function of ionic strength passes through approximately the same maximum at about the same electrolyte concentration. After the correction for the influence of conductance by ions in the diffuse electrical double layer, using O’Briens model, still a slight maximum exists. The results provided an estimate of the Stern layer thickness. An analysis using the hairy layer model, when surface conductance was neglected, provided an estimate of the hairy layer thickness.
1. Introduction Electrophoresis, as a method of determining zeta-potentials, does have its limitations since it cannot be employed in concentrated dispersions because, in many practical situations, the system under consideration is not a dilute stable sol, which is necessary for electrophoresis measurements. In addition the theory on electrophoresis has some restrictions. For theories1-4 employed in most cases, dispersed particles are assumed to be spherical and have to be nonconducting (no conductance between the particle surface and the slipping plane). Theories5 that try to incorporate the conductance by ions * Corresponding author: fax, +31 402463966; phone, +31 40473066; e-mail,
[email protected]. (1) Van der Put, A. G.; Bijsterbosch, B. H. Acta Polym. 1981, 6, 1981. (2) Van der Put, A. G.; Bijsterbosch, B. H. J. Colloid Interface Sci. 1982, 92, 499. (3) Hidalgo Alvarez, R.; De Las Nieves, F. J.; Van der Linde, A. J.; Bijsterbosch, B. H. Colloids Surf. 1986, 21, 259. (4) Van der Linde, A. J.; Bijsterbosch, B. H. Croat. Chem. Acta 1990, 63, 455. (5) Van den Hoven, Electrokinetic Properties and Conductance of Polystyrene and Silver Iodide Plugs. Ph.D. Thesis, 1984, Wageningen.
in the region between the phase boundary and the slipping plane lead to rather conflicting results. In this paper, data obtained by electrophoresis applied to dilute sols are compared with data obtained with concentrated systems by performing electroosmosis experiments. We selected polystyrene as the disperse material because monodisperse, spherical polystyrene latices are frequently considered to be useful model systems. However they exhibit a typical electrokinetic behavior: one expects a continuous decrease in electrophoretic mobility or zeta-potential, ζ, with increasing electrolyte concentration, but for many latices this is only observed at high electrolyte concentrations (>0.01 M). At lower concentrations, the zeta-potential typically increases with increasing concentration.1-4 In the present Letter we considered this behavior and tried to explain this maximum by (i) applying the model of O’Brien6-8 for surface conductance and (ii) the hairy layer model,9 which postulates that the latex surface is (6) O’Brien, R. W. J. Colloid Interface Sci. 1982, 92, 204. (7) O’Brien, R. W.; Perrins, W. T. J. Colloid Interface Sci. 1983, 99, 20. (8) O’Brien, R. W. J. Colloid Interface Sci. 1986, 110, 477.
S0743-7463(98)00225-X CCC: $15.00 © 1998 American Chemical Society Published on Web 09/16/1998
5974 Langmuir, Vol. 14, No. 21, 1998
covered by a layer of flexible polymer chains having terminal ionic groups.
Letters Table 1. Determined Values of the Surface Charge Density (σ0)
2. Experimental Section
titration
amt of latex (mL)
volume fraction (%)
[OH-] in mM
e.p. (mL)
σ0 (µC/cm2)
2.1. Polystyrene Latex. The method for the preparation of the polystyrene latex is described elsewhere.10 The polystyrene latex particles used for these experiments had a number averaged diameter of 1.879 µm. Their volume averaged diameter was 2.030 µm. These particle sizes were determined with a Coulter LS-130. In this apparatus and accompanying software, the particle size is calculated on static light scattering using a Fraunhofer diffraction for large particles and Mie scattering for intermediate sizes (1 < d < 10 µm, in combination with polarization intensity differential scattering for small particles11). The surface roughness of the particles was in the order of 0.070.6% of the particle radius. 2.2. Determination of Surface Charge by Conductometric Titration with OH-.12 Conditioning of the Ion-Exchange Resins. The sulfate groups of the latex particles were ionexchanged before the titrations. The ion-exchange resins used were DOWEX 50W-X4 (cation exchange, H+-form) and DOWEX 1-X4 (anion exchange, OH--form). These resins were cleaned by the procedure described by Van den Hul and Vanderhoff.12 After the resins were cleaned, the wash water of the ionexchange resins exhibited no surface active impurities (surface tension 72 mN/m at 20 °C), and the conductivity of the wash water had the same value as the inlet water used (0.85 µS cm-1). Equal quantities of the two ion-exchange resins were then mixed. The wash water from the mixed resin had a considerably lower conductivity (0.3 µS cm-1) than, the inlet water used. Preparation of the Latex in the H+-Form.13 The freshly cleaned latex (by the serum replacement technique13) was diluted with ion-exchanged water to a solids percentage of 3% and was transferred into a Pyrex glass bottle with a large amount (2 L) of mixed ion-exchange resin. The bottle was rolled for 24 h on a roller-bank. The latex and the ion-exchange resin were separated by decantation and filtration through a glass-filter (type 25G3). Conductometric Titration Procedure. Titrations were performed at 20 °C under a nitrogen atmosphere and starting at pH 5.5. The conductivity was followed using a conductivity meter (Radiometer Kopenhagen) equipped with a Schott conductivity cell. A 4.6 mM NaOH solution (nitrogen flushed) was added with an automatic titration buret. Since at any point the total amount of added OH- and the total latex surface (on the assumption of a smooth surface) are known, the surface charge density (σ0) is calculated assuming complete dissociation of charged groups at the end of the condutometric titration and complete charge compensation of the charged groups by H+ at the start of the titration 2.3. ζ-Potential Measurements (Electroosmosis, Electrophoresis). Electroosmosis. Measurements were performed with a polystyrene dispersion at different NaCl concentrations (varying from 0.001 to 0.5 M). The experimental setup consists of a U-tube with two electrodes, coupled with two capillaries.14 The Zn/ZnSO4 electrode consists of the following parts: a reversible Zn/ZnSO4 electrode (the ZnSO4 solution is saturated); a compartment with a 0.5 M KNO3 solution that prevents contact between the saturated ZnSO4 solution and the electrolyte. Glass spheres prevent mixing between these parts during filling and handling. The liquid films, between the glass spheres and the walls of the electrodes, suffice for conducting the current. The displacement of the electrolyte in the capillaries, the current, and the conductivity were measured, and the ζ-potential was calculated for different electrolyte concentrations, using the Von
1 2 3 4 5
146 140 144 144 158
1.56 1.56 1.29 1.29 1.29
4.6 4.6 4.6 4.6 4.6
1.00 0.95 0.78 0.80 0.90
6.46 6.40 6.14 6.34 6.50
(9) Verdegan, B. M.; Anderson, M. A. J. Colloid Interface Sci. 1993, 158, 372. (10) Tuin, G.; Peters, A. C. I. A.; van Diemen, A. J. G.; Stein, H. N. J. Colloid Interface Sci. 1993, 158 (2), 508. (11) Van de Hulst, H. C. Light Scattering by Small Particles; Dover Publications: New York, 1981; Chapter 9. (12) Van den Hul, H. J.; Vanderhoff, J. W. Electroanal. Chem. 1972, 37, 161. (13) Tuin, G.; Stein, H. N. Langmuir 1994, 10 (4), 1054. (14) Verwey, E. J. W. Revl. Trav. Chim. Pays-Bas 1941, 60, 625.
Figure 1. Zeta-potential (ζ), calculated according to Von Smoluchowski versus NaCl concentration for L-93 at pH 5.5: b, electroosmosis; 2, electrophoresis; O, after correction for surface conductance according to O’Brien8 (electroosmosis). Diffuse double layer potential, ψ0, calculated from σ0 by means of the Gouy-Chapman theory,17 on the assumption of absence of a Stern layer. Smoluchowski15 equation based on the following assumptions: (i) all conduction occurs through the bulk liquid and no conduction occurs by ions behind the electrokinetic shear plane; (ii) the curvature of the interface is small, a . 1/κ, where a is the particle radius. Electrophoresis. ζ-potential measurements by electrophoresis were performed using a Coulter Delsa 440 SX. This apparatus uses laser-Doppler velocimetry to measure the electrophoretic mobility. The latex used was polystyrene latex. The ζ-potential was calculated using von Smoluchowski’s equation.15 Since it is not a priori clear whether all assumptions implicit in using von Smoluchowski’s equation are fulfilled in the case at hand, we will indicate it by ζSmol. The ζSmol-potential was measured as a function of electrolyte concentration (NaCl).
3. Results and Discussion 3.1. Conductometric Titrations. We found that both the descending and ascending legs of the plot of conductivity versus quantity of NaOH solution added are linear, with the exception of a region near the intersection point, which means that only one type of charged surface group is observed.13 The charged surface groups are sulfate groups (-SO4-).16 Five titrations were performed, and the determined values of σ0 are given in Table 1. No correction has been made for the surface roughness. 3.2. ζSmol-Potentials (Electroosmosis/Electrophoresis). In Figure 1 the dependence of the ζSmol-potential of the polystyrene latex investigated on the concentration of NaCl at pH 5.5 is shown for both electroosmosis and electrophoresis. Figure 1 also illustrates that over the whole concentration range the magnitude of ζSmol is far below the value of ψ0 calculated from σ0 by means of the Gouy-Chapman theory.16 This effect becomes even more obvious when (15) Von Smoluchowski, Bull. Akad. Sci. Bracovie classe Sci. Math. Natur 1 1903, 182. (16) Van den Hul, H. J.; Vanderhoff, J. W. Br. Polym. J. 1970, 2, 121.
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Langmuir, Vol. 14, No. 21, 1998 5975
Figure 2. Relation between Kplug and Kel for the electroosmosis experiments. The slope is equal to 0.28.
expressed in terms of charge densities as demonstrated in Figure 3. It is clear that only a limited part of the countercharge of the particles is transported in the electrokinetic process. As can be seen from Figure 1, ζsmol exhibits a maximum at a concentration of about 5 × 10-3 M NaCl for electroosmosis and 3.5 × 10-3 M NaCl for electrophoresis. Although this phenomenon has been studied extensively by Van der Put and Bijsterbosch,1,2 Hidalgo-Alvarez,3 and Van der Linde,4 a definitive formula is not yet agreed upon. At present there are two explanations for this result: I. A first explanation is surface conductance by ions in the diffuse double layer.18,19 In the present letter this influence will be analyzed using the theory of O’Brien.6-8 According to O’Brien7 the relation between the conductivity of a plug (Kplug) and the conductivity of the electrolyte (Kel) is given by
[
e2zi2ωini∞ Kplug ) 1 + 3φ f(0) + (f(β) - f(0)) Kel Kel
]
(1)
where φ is the particle volume fraction, e is the absolute value of electron charge, ω is the mobility of the ions, and n∞i is the equilibrium density of ions beyond the double layer. β indicates the importance of the tangential flux of counterions in the diffuse double layer. The values of f(β) and β are tabulated in ref 7, Table 1. Figure 2 shows the relation between Kplug and Kel for our electroosmosis experiments. The slope in this plot is equal to 0.28, which corresponds to a solid volume fraction of 0.60 for the plug and a value of -0.4 for f(0) according to O’Brien.7 At high electrolyte concentrations surface conductance is negligible and β is equal to zero. At low electrolyte concentrations (0.001 and 0.002 M in our experiments), surface conductance is not negligible. For these concentrations f(β) has been calculated, and the corresponding value for β has been determined using ref 7, Table 1. According to O’Brien8 the electroosmotic velocity is given by
〈v〉 )
eζ -kT eζ [1 + 3φf(0)] - γ g(β) 〈E〉 (2) ηe kT kT
(
[
] )
For a symmetric, two-species electrolyte γ ) 2/z ln 2, g(β) (17) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989; Chapter 5. (18) Minor, M.; Van der Linde, A. J.; Van Leeuwen, H. P.; Lyklema, J. J. Colloids Interface Sci. 1997, 189, 370. (19) Van den Hoven, Th. J. J.; Bijsterbosch, B. H. Colloids Surf. 1987, 22, 187.
Figure 3. σ0 and σζ for latex L-93 at pH ) 5.5; dashed line represents σ0. No correction for surface conductance has been made.
is tabulated in Table 1 in ref 8. When β is known (e.g., from f(β) which was experimentally determined in combination with Table 1 in ref 7, g(β) can be found and it is possible to calculate the zeta-potential for a given electroosmotic velocity. In our experiments plotted in Figure 1, the absolute value of the zeta-potential at 0.001 M, when surface conductance is taken into account, will rise to approximately 95 mV, and at 0.002 M to approximately 90 mV. II. A second explanation is the hairy layer model. Hairy layer models postulate that the latex is covered by a layer of flexible polymer chains having terminal ionic groups.9 As a result of repulsion between the surface and ionic groups, the chains extend into solution over a distance that varies as a function of ionic strength and pH. In this analysis the double layer characteristics are important. Information on the charge distribution in the electrical double layer can be given by conversion of the zeta-potential into the charge density behind the electrokinetic shear plane and comparison of this value with the surface charge density. For high κa-values the GouyChapman theory (Hunter20) for flat double layers gives the following conversion
σζ ) -x8000c0rNAkT sinh
( ) ze0ζ 2kT
(3)
where c is the bulk concentration of ions (moles/liter), NA is Avogadro’s number, 0 is the permittivity of vacuum, r is the solvent dielectric constant, z is the valency, e0 is the elementary charge, ζ is the zeta-potential, k is Boltzmann’s constant, and T is the temperature. The layer between the surface of a latex particle and the electrokinetic shear plane is often called the δ-layer. The charge density in the δ-layer can be determined by calculating the difference in charge densities between the surface and behind the electrokinetic shear plane. This is illustrated in the following equation.
σ 0 + σδ - σζ ) 0
(4)
where σζ is the charge density behind the electrokinetic shear plane, σδ is the charge density in the delta layer, and σ0 is the surface charge density. In Figure 3 the surface charge density of the polystyrene latex and the charge density at the electrokinetic shear plane at different concentrations of the electrolyte NaCl at a pH of 5.5 are shown. (20) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1991; Vol. 1, p 335.
5976 Langmuir, Vol. 14, No. 21, 1998
Letters
latex comparable to the one reported here, in a 0.01 M KCl solution, using the colloidal particle scattering technique. Summary
Figure 4. δ-layer thickness as a function of electrical double layer thickness: b denotes the case when surface conductance is neglected and 2 denotes the case when surface conductance is not neglected (according to O’Brien6-8).
The position of the shear plane, which corresponds to the thickness of the δ-layer, can then be determined from data on zeta-potential and surface charge density, by applying the Gouy-Chapman model. Figure 4 shows a plot of the δ-layer thickness, as calculated from the ζ-potential and surface charge density data, as a function of κ-1 (double layer thickness) when surface conductance is neglected and when surface conductance is not neglected (O’Brien6-8). As can be seen from the results shown in the figure, the thickness of the δ-layer varies between 2 and 6 Å (approximately 1 to 2 times the radius of a hydrated Na+ ion) when surface conductance is not neglected. When surface conductance is neglected and the hairy layer model is applied, the δ-layer corresponds to the thickness of the hairy layer. It can be seen that when the NaCl salt concentration is lowest, the hairy layer extends to a thickness of approximately 6.5 nm. On interpretation of the results, it was assumed that (i) ions within the hairy layer follow Gouy-Chapman behavior, (ii) the titrable surface charge is the true surface charge, and (iii) there is no specific adsorption. The first two assumptions are valid at small κ-1 when the postulated hairy layer has collapsed; when the hairy layer extends, titration will give σ0 + σhairy layer. Recently Wu and van de Ven21 reported a value of the hairy layer thickness of 3 nm for a type of polystyrene
The maximum in the NaCl salt concentration vs ζ-potential curves, reported by previous investigators, was confirmed both with dilute dispersions by electrophoresis and for concentrated ones by electroosmosis experiments, at approximately the same electrolyte concentration. The results can be explained partially by the surface conductance of ions in the diffuse double layer at low electrolyte concentrations. After O’Brien’s model was applied, still a slight maximum exists in the zeta-potential versus electrolyte concentration plot. Van der Linde4 indicates under most circumstances not only that the diffuse double layer contributes to the surface conductance but that a process of additional conductance between slipping plane and particle surface is operative (a contribution that is properly accounted for in O’Brien’s theory). The discrepancy between the electrokinetic charge and the titratable charge arises because there is a Stern layer. From the charge densities and the ζ-potentials at high electrolyte concentrations, it can be concluded that the thickness of the δ-layer is in the range of 2 to 6 Å when surface conductance is taken into account, according to O’Brien’s model. So the work presented here provides an estimate of the Stern layer thickness. Applying the hairy layer model, when surface conductance is neglected, a hairy layer thickness of 6.5 nm was calculated. One can conclude that a combination of surface conductance and hairy layers can explain the electrophoretic properties of polystyrene spheres. Our conclusions are in line with Van den Hoven and Bijsterbosch19 who conclude that the presence of a layer of variable thickness on the surface of polystyrene particles is well established and that under a number of conditions anomalous conductance occurs that is of considerable importance for the theoretical description of electrokinetic phenomena. LA980225B (21) Wu, X.; van de Ven, T. G. M. Langmuir 1996, 12, 3859.
