Colloid Journal, Vol. 63, No. 3, 2001, pp. 301–305. Translated from Kolloidnyi Zhurnal, Vol. 63, No. 3, 2001, pp. 332–337. Original Russian Text Copyright © 2001 by Zhukov, Duda, Fedorova.
Effect of the Surface Conductance on Electrokinetic Potential Measured in Nonaqueous Media A. N. Zhukov, L. V. Duda, and I. L. Fedorova Department of Chemistry, St. Petersburg State University (Petrodvorets branch), Universitetskii pr. 2, Petrodvorets, St. Petersburg, 198904 Russia Received March 29, 2000
Abstract—The effect of the surface conductance on the ζ-potential of dispersed particles determined from their electrophoretic mobility in nonaqueous electrolyte solutions was considered. The conductivity of dilute quartz suspensions and the electrophoretic mobility of quartz particles in NaBr solutions in butanol-1 and dimethyl sulfoxide as well as in LiBr solutions in acetone at the salt concentration C = 10–5–10–2 M were determined by conductometry and microelectrophoresis. The dependences of surface conductivity and ζ-potential on the electrolyte content were calculated by formulas of the Wagner and Henry theories. It was shown that, in the region of dilute solutions, ζ( log C ) curves thus obtained significantly differ from corresponding functions calculated by the Smoluchowski equation. At the same time, these dependences agreed closely with the ζ( log C ) dependences determined for the same systems by the streaming potential method with allowances for experimental values of the surface conductivity. Using aluminum oxide suspensions in NaBr and HBr ethanol solutions as examples, it was shown that, to obtain correct values of the ζ-potential from electrophoretic mobility of porous particles impregnated with a solution, it is necessary to allow for the bulk conductance of the particles.
INTRODUCTION Complex study of electrosurface properties of solid particles in electrolyte solutions includes electrokinetic and conductometric measurements by different methods. Results obtained are interpreted in terms of the ζ-potential, whose values are determined using the classical and current theories of electrokinetic phenomena with allowances for complications due to the surface conductance and the polarization of the electrical double layer at the solid–liquid interface. The effect of the surface conductance on electrokinetic phenomena was discussed in detail in monographs [1–5] and reviews [6–8], which most comprehensively and systematically outline basic results of theoretical and experimental studies of the above-cited phenomena occurring in capillary and disperse systems. In the early studies of electrokinetic phenomena, it was shown [9] that, to obtain correct values of the ζpotential for capillary systems in aqueous dilute electrolyte solutions from data of electroosmotic and streaming potential measurements using equations of the Smoluchowski theory, in place of the solution conductivity (Kν) involved in these equations, it is necessary to use the average conductivity of the solution confined in capillaries and pores (Kd). The difference Kd – Kν = ∆Ks is due to an excess of ions in the electrical double layer and determines the surface conductance; in the case of cylindrical capillaries of radius a, Ks = ∆Ksa/2. In works of the scientific school headed by I.I. Zhukov [9], the surface conductance was accounted for by introducing the correction factor α = Kd /Kν = 1 + ∆Ks/Kν referred to as the efficiency factor into the
Smoluchowski equation. Experimental values of this factor are usually determined by conductometric measurements. In particular, it was shown that, for porous collodion membranes and packed diaphragms from oxide powders, dependences of the ζ-potential on the indifferent electrolyte concentration calculated by equations of the classical Smoluchowski theory have, as a rule, an extremal character, which is leveled off when the surface conductance is accounted for. In regard to electrophoresis, Henry was the first to extend the Smoluchowski theory to the case of solid spherical particles at an arbitrary κr parameter (κ is the Debye parameter and r is the particle radius) and arbitrary ratios of the bulk and surface conductivities of particles to the solution conductivity (Kp /Kν and ∆Ks /Kν, respectively). The theory of electrophoresis was further developed with the allowance for the polarization of the electrical double layer under the action of an external electric field. In works by Overbeek, Booth, Wiersema, Hunter, O’Brien, and White [3–5], allowance was made for the effect of an external field on the equilibrium ion distribution over the diffuse layer, the ions being present in the solution up to the slipping plane. Dukhin [1, 2, 7] has developed a theory of concentration polarization in the approximation of a thin electrical double layer (κr Ⰷ 1). Based on this theory, analytical expressions for the electrophoretic mobility of both nonconducting and conducting, ideally polarized spherical particles were derived; in this case, allowances were made for the contribution to the surface conductance from all ions in the diffuse part of the electrical double layer, including those residing between the slipping
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plane having a potential of ζ and the Helmholtz outer plane having a potential of ψd. These expressions involve the dimensionless parameter Rel = Ks/Kνr determining the intensity of the concentration polarization (relaxation) in electrophoresis and analogous to the efficiency factor of a capillary system α = 1 + 2Rel. Analysis of different theories of polarization of the electrical double layer shows that the polarization is essential in all cases when the surface or bulk conductance of a particle is significant. However, all analytical solutions to the problem of electrophoresis taking into consideration the polarization were obtained for limiting cases, such as a nonconducting or conducting, ideally polarized particle with a thin electrical double layer, at various limiting conditions (the unipolar conductance of a particle, a binary symmetrical electrolyte, a strong or weak charge of a particle, identical mobilities of electrolyte ions, etc.). According to the classical Bikerman theory of surface conductance [10], Ks is determined by the surface excesses of all ions in the hydrodynamically mobile part of the electrical double layer and, consequently, is a function of the ζ-potential. Results of numerous works summarized in the reviews [1, 2, 5, 7, 8] show that experimental Ks values are at least one order of magnitude higher than those obtained theoretically by the Bikerman equation and, as a rule, differ from zero at the isoelectric points. This is attributable to the fact that the surface conductance is due to the mobility of all ions in the electrical double layer, those residing in the liquid both in front of and beyond the slipping plane, including ions specifically adsorbed in the Stern layer and ions in the porous and gellike layers when present on the solid surface [5]. Consequently, Ks is represented as a sum of two components corresponding to contributions of the diffuse and inner parts of the electrical doud i ble layer to the surface conductance: Ks = K s + K s . A theory of electrophoresis including such representation of the conductance was advanced in [11, 12], where an analytical expression for the electrophoretic mobility of a strongly charged nonconducting particle in a binary electrolyte solution was derived. However, practical use of this expression is complicated, because d i it requires the knowledge of K s and K s values or corresponding values of the ion mobility and the ion surface density. Therefore, as was shown in [12–15], correct interpretation of results of electrokinetic measurements for such disperse systems as latexes, bacterial cells, and liposomes in dilute solutions is impossible without additional conductometric measurements, which allow Ks values to be found experimentally. Significant surface conductance was also found in the study of electrosurface properties of silicon, titanium, and aluminum oxides in nonaqueous electrolyte solutions in 1-butanol [16, 17], ethanol [18], and dimethyl sulfoxide (DMSO) [19]. In particular, it was shown that the high Ks values monotonically increasing with
the electrolyte concentration even when passing through the isoelectric points are due to the mobility of counterions and coions specifically adsorbed in the Stern layer. The aim of this work is to determine the ζ-potential of SiO2 particles in various nonaqueous electrolyte solutions by the microelectrophoresis and streaming potential methods with allowance for the surface conductance and to calculate the ζ-potential of porous γ-Al2O3 particles impregnated with electrolyte ethanol solutions from data of electrophoretic and conductometric measurements. MATERIALS AND METHODS Natural quartz powder with a grain size of 10–15 µm in the form of packed diaphragms was used in the system study by the streaming potential method; fractions with grain sizes of 5–10 and 1–5 µm were used in conductometric and microelectrophoretic measurements, respectively. Quartz was first treated with a 30% nitric acid solution, washed with distilled water to constant pH and conductivity values of washing water, subjected to fractionation by sedimentation, and then dried at 105–110°C. For the used γ-Al2O3 powder with a grain size of 2–10 µm, the specific surface area determined by the BET method was equal to 88 m2 g–1, which is indicative of an internal porosity of particles. Aluminum oxide was first calcined in a muffle at 600°C, washed with distilled water, and then dried at 105°C. All powders were kept in desiccators over freshly calcined CaCl2 and dried again immediately prior to use. Ethanol, 1-butanol, DMSO, and acetone were used as solvents. Alcohols were purified by the fractional distillation at the atmospheric pressure; DMSO, by the distillation at a pressure of 25 mm Hg. Chemically pure acetone was allowed to stand over molecular sieves with a pore size of 0.4 nm and was not subjected to an additional purification. Prior to use, NaBr and LiBr salts, both chemically pure, were purified by recrystallization from ethanol solutions and dried at 110°C to a constant weight. Solutions of these salts in the abovecited solvents at concentrations C = 10–5–10–2 M were prepared by the dilution of corresponding saturated solutions. The streaming potential Us was measured using a Takeda Riken TR-84M electrometer with an input resistance larger than 1014 Ω and also using an U-shaped glass cell of the Samartsev–Ostroumov type [20] equipped with two platinum grid electrodes coated with AgBr, between which packed quartz diaphragms were formed. The average pore radius in the diaphragms, a = 4.1 ± 0.2 µm, was determined from their permeability and coefficient of structural resistance [20]. The electrophoretic mobility of particles ue was determined from their velocity measured using a microscope at stationary levels in a plane-parallel quartz-glass capillary in a closed cell. COLLOID JOURNAL
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EFFECT OF THE SURFACE CONDUCTANCE ON ELECTROKINETIC POTENTIAL
The conductivities of solutions (Kν) and dilute oxide suspensions (K) were measured in a conductometric cell with plane-parallel platinum electrodes using an ac bridge at 1 kHz. The conductivity of the pore-confined solutions in a diaphragm (Kd) was determined from the electrical resistance of the diaphragm and its structure constant calculated from the resistance of the diaphragm impregnated with above-cited concentrated solutions with known conductivities [20]. The surface conductivity was determined from the dependences of the relative conductivity of suspensions K/Kν on the particle volume fraction p. At a high dilution when p Ⰶ 1, these dependences were linear. According to the Wagner theory of interfacial polarization [21, 22], the slope of such dependences is determined by the formula 3 ( K 'p – K ν ) K -p ------ = 1 + -------------------------Kν 2K ν + K 'p
2
2F K ν κ = ------------------- εε 0 RT λ 0
1/2
,
where ε and λ0 are, respectively, the relative permittivity and the equivalent conductivity of infinitely dilute solutions, whose values, as well as viscosity (η) values, are reported in [23]. It was established that, for all systems under investigation, κr > 20; in this case, the lowest value, κr = 20, was noted for a C = 10–5 M NaBr solution in butanol. The ζ-potential was determined from the streaming potential using the formula [5] εε 0 P U s = – -----------ζ, ηK d where P is the pressure drop across the diaphragm. The ζ-potential was also calculated from the electrophoretic mobility of particles using the Henry formula [5] 2εε u e = -----------0 ζ [ 1 + 2λ ( f – 1 ) ], 3η where λ = (1 – K 'p /Kν)/(2 + K 'p /Kν), and f(κa) is the Henry function whose value is equal to 1.5 at κr Ⰷ 1. RESULTS AND DISCUSSION Dependences of the surface conductivity of quartz on the electrolyte concentration calculated using the Wagner formula from measured relative conductivities K/Kν of dilute suspensions in 1-butanol, DMSO, and acetone are presented in Fig. 1. Similar Ks values and its COLLOID JOURNAL
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Ks × 1010, S 25
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20 2 15 10 5 3
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from which we can determine K 'p = Kp + 2Ks/r, where Kp is the conductivity of a particle; in the case of nonconducting particle, Ks = K 'p r/2. The parameter κ required for estimating κr value was calculated by the formula
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–4
–3
–2 logC
Fig. 1. Dependences of the surface conductivity of SiO2 particles on the molar concentration of electrolyte solutions: (1) LiBr in acetone, (2) NaBr in DMSO, and (3) NaBr in 1-butanol.
dependences on the electrolyte concentration were previously obtained from data of the measurements of the conductivity of packed quartz diaphragms in NaBr solutions in butanol [16] and DMSO [19]. It was shown that experimental Ks values are two orders of magnitude higher than those calculated by the Bikerman equation and that the surface conductance of oxides in these solvents is due largely to specifically adsorbed ions [18]. Dependences of the ζ-potential of quartz in the above-cited nonaqueous solutions calculated, with allowances for the surface conductivity, from the results of measurements of the electrophoretic mobility of particles in dilute suspensions and the streaming potential in packed diaphragms are presented in Fig. 2. For comparison, the ζ( log C ) dependences calculated by the classical Smoluchowski equation for electrophoresis are also presented in this figure. At C = 10–2 M, the ζ values determined by different methods agree within the limits of experimental error. At the same time, for dilute solutions, the ζ-potential values calculated from data obtained by the streaming potential and electrophoresis methods with the consideration of the surface conductivity are in close agreement but dramatically differ from the corresponding ζ values calculated by the Smoluchowski formula. Note that the previously mentioned ζ values show only a slight dependence on the electrolyte concentration, which does not consist with theoretical notions: with an increase in the electrolyte concentration from 10–5 to 10–3 M, the thickness of the diffuse part of the electrical double layer decreases by a factor of 10 for all investigated systems, whereas the ζ-potential of particles was virtually unchanged, for
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Kp × 104, S m –1 15
(a) 1
1
–40
2 10
–60
–80
2
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5
–20
(b)
–5
–4
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Fig. 3. Dependences of the effective conductivity of γ-Al2O3 particles on the NaBr molar concentration in ethanol (94 vol %) solutions (1) containing 10–4 M HBr and (2) containing no HBr.
–30 1
acetone and DMSO solutions, and passed through a minimum in the case of butanol solutions.
–40 2
–50
3
0
(c)
–10 1 –20
–30 2 3
–40 –5
–4
logC
–3
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Fig. 2. Dependences of the ζ-potential of SiO2 particles on the molar concentration of (a) LiBr in acetone and NaBr in (b) DMSO and (c) 1-butanol solutions determined by the electrophoretic mobility of particles using the (1) Smoluchowski and (2) Henry formulas, as well as (3) by the streaming potential method with allowances for the surface conductivity.
Of great interest is also the study of the effect of the conductance of porous γ-Al2O3 particles impregnated with a nonaqueous electrolyte solution on the magnitude of the ζ-potential determined by electrophoresis. In this case, the results of conductometric measurements allowed us to determine the average effective conductivity of particles K 'p = Kp + 2Ks/r and also its dependence on the NaBr content in ethanol solutions containing 6 vol % of water in the absence of HBr and at its concentration equal to 10–4 M (Fig. 3). The monotonic increase in K 'p with the NaBr concentration varying from 10–5 to 10–3 M coincide with an increase in the conductivity of equilibrium solutions; in this case, the relative conductivity K 'p /Kν varies only slightly, within the range 0.05–0.03. The ζ( log C ) dependences calculated from the electrophoretic mobility of porous particles by the Henry and Smoluchowski equations (Fig. 4) differ from one another to a greater extent than those obtained for quartz. The ζ-potential calculated by the Smoluchowski formula is virtually not affected by the change in the electrolyte concentration by two orders of magnitude. In the presence of 10–4 M HBr (i.e., at an increased concentration of the potential-determining ion), only a small increase of positive ζ-values occurs. Allowance for the conductivity of particles results in a significant correction of the ζ-potential for dilute solutions and allows us to obtain the ζ( log C ) dependences consistent with commonly accepted notions of the COLLOID JOURNAL
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EFFECT OF THE SURFACE CONDUCTANCE ON ELECTROKINETIC POTENTIAL ζ, mV 60 1a 40 2a
20
1b 2b
0
–5
–4
–3 logC
Fig. 4. Dependences of the ζ potential of γ-Al2O3 on the NaBr concentration in ethanol (94 vol %) solutions (1) containing 10–4 M HBr and (2) containing no HBr calculated by the electrophoretic mobility of particles using the (a) Henry and (b) Smoluchowski formulas.
behavior of this quantity in response to changes in the ionic strength [4, 5]. Thus, results of our studies show the electrokinetic potential of dispersed particles can be correctly determined from their electrophoretic mobility in nonaqueous electrolyte solutions with the use of the Henry equation and data available on the surface conductivity, which can be calculated from the experimental dependences of the relative conductivity of dilute suspensions on the volume fraction of particles by the Wagner formula. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basis Research, projects nos. 96-03-3413 and 00-15-97375. The authors are grateful to O.G. Us’yarov for his participation in the discussion of this work and useful remarks. REFERENCES 1. Dukhin, S.S., Elektropoverkhnostnye i elektrokineticheskie svoistva dispersnykh sistem (Electrosurface and Electrokinetic Properties of Disperse Systems), Kiev: Naukova Dumka, 1975.
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2. Dukhin, S.S. and Derjaguin, B.V., Elektroforez (Electrophoresis), Moscow: Nauka, 1976. 3. Hunter, R.J., Zeta Potential in Colloid Science. Principles and Applications, London: Academic, 1981. 4. Hunter, R.J., Foundations of Colloid Science, Oxford: Clarendon, 1989, vol. 2. 5. Lyklema, J., Fundamentals of Interface and Colloid Science, vol. 2: Solid-Liquid Interfaces, London: Academic, 1995. 6. Hidalgo-Alvarez, R., Adv. Colloid Interface Sci., 1991, vol. 34, p. 217. 7. Dukhin, S.S., Adv. Colloid Interface Sci., 1995, vol. 61, p. 17. 8. Barany, S., Adv. Colloid Interface Sci., 1998, vol. 75, p. 45. 9. Grigorov, O.N., Koz’mina, Z.P., Markovich, A.V., and Fridrikhsberg, D.A., Elektrokineticheskie svoistva kapillyarnykh sistem (Electrokinetic Properties of Capillary Systems), Moscow: Akad. Nauk SSSR, 1956. 10. Bikerman, J.J., Z. Phys. Chem. A, 1932, vol. 163, p. 378. 11. Kijlstra, J., van Leeuwen, H.P., and Lyklema, J., J. Chem. Soc. Faraday Trans., 1992, vol. 88, p. 3441. 12. Van der Wal, A., Minor, M., Norde, W., et al., Langmuir, 1997, vol. 13, p. 165. 13. Van den Hoven, Th.J.J. and Bijsterbosch, B.H., Colloids Surf., 1987, vol. 22, p. 187. 14. Van der Wal, A., Minor, M., Norde, W., et al., J. Colloid Interface Sci., 1997, vol. 186, p. 71. 15. Minor, M., van der Linde, A.J., and Lyklema, J., J. Colloid Interface Sci., 1998, vol. 203, p. 177. 16. Zhukov, A.N., Levashova, L.G., and Evstratova, A.Yu., Kolloidn. Zh., 1981, vol. 43, no. 2, p. 240. 17. Zhukov, A.N., Levashova, L.G., and Men’shikova, A.Yu., Vest. Leningr. Univ., Ser. 4: Fiz., Khim., 1989, vol. 3, no. 18, p. 61. 18. Zhukov, A.N. and Varzhel’, V.I., Kolloidn. Zh., 1990, vol. 52, no. 4, p. 781. 19. Varzhel’, V.I., Zhukov, A.N., Levashova, L.G., and Uspenskaya, S.V., Vest. Leningr. Univ., Ser. 4: Fiz., Khim., 1990, vol. 3, no. 18, p. 61. 20. Grigorov, O.N., Karpova, I.F., Koz’mina, Z.P., et al., Rukovodstvo k prakticheskim rabotam po kolloidnoi khimii (Laboratory Manual on Colloid Chemistry), Moscow: Khimiya, 1964. 21. Wagner, K.W., Die Isolierstoffe der Elektrotechnik, Berlin: Springer-Verlag, 1924. 22. Dukhin, S.S. and Shilov, V.N., Dieletkricheskie yavleniya i dvoinoi sloi v dispersnykh sistemakh i polielektrolitakh (Dielectric Phenomena and Double Layer in Disperse Systems and Polyelectrolytes), Kiev: Naukova Dumka, 1972. 23. Kratochvil, B. and Yeager, H.L., Top. Curr. Chem., 1972, vol. 27, p. 1.
