An experimental study on the influence of a dynamic Stern-layer on the primary electroviscous effect

Size: px

Start display at page:

Download "An experimental study on the influence of a dynamic Stern-layer on the primary electroviscous effect"

Rodger Rodgers
5 years ago
Views:

Colloids and Surfaces A: Physicochemical and Engineering Aspects 159 (1999) 373 379 www.elsevier.

1 Colloids and Surfaces A: Physicochemical and Engineering Aspects 159 (1999) An experimental study on the influence of a dynamic Stern-layer on the primary electroviscous effect F.J. Rubio-Hernández *, E. Ruiz-Reina, A.I. Gómez-Merino Departamento de Física Aplicada II, Uni ersidad de Málaga, E Malaga, Spain Abstract The most recent theory by Watterson and White for the primary electroviscous effect of a suspension of charged spherical particles has been extended by considering the influence of a dynamic Stern-layer. In this work we have tested the theoretical results by measuring the viscosity of polystyrene suspensions in different electrolyte concentrations. Zeta potential values have been obtained by electrophoresis and conductivity experiments using the theoretical approachs by Mangelsdorf and White that include the Stern-layer conductance. In order to obtain the same potential values calculated from these two independent methods, we have fitted the Stern-layer parameters of our systems. These parameters and zeta values have been used to calculate the theoretical viscosity. The theoretical results have been compared with the experimental viscosity data obtained with a semiauthomatic Ubbelohde capillary viscometer. We can conclude that the dynamic Stern-layer model used in this work has only a slight influence on the correction of the primary electroviscous effect theory due to Watterson and White. We suggest to study the correction supplied by another dynamic Stern-layer model due to Dukhin and Semenikhin, considering its success when is applied to electrophoresis Elsevier Science B.V. All rights reserved. Keywords: Electroviscous effect; Electrolyte concentrations; Stern-layer conductance 1. Introduction The same fundamental equations are the basis of the theories of electrophoresis, conductivity and primary electroviscous effect. This suggests that careful experimentation and comparison with the predictions of the so different phenomena theories can serve as a severe test of the fundamental equations and assumptions which underlie the theories of the diverse dynamic behaviour of * Corresponding author. colloidal suspensions. Experimental studies [1,2] showed that there were significant discrepancies between the zeta potentials inferred from measurements of the electrical conductivity and electrophoresis mobility. Specifically, Zukoski and Saville [2] found that the zeta potentials inferred from the suspension conductivity were larger than those derived from electrophoresis. These and another studies [3 5] on the influence of the surface conduction within the Stern-layer, recently led to Mangelsdorf and White [6] to extend the theory for electrophoresis /99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S (99)

2 374 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) Table 1 Surface charge density and particle radius of the latexes Sample L1 L2 Surface charge density 0 ( C/cm 2 ) Particle radius a (nm) and conductivity developed by O Brien and White [7], taking into account the lateral movement of ions within the Stern-layer, which we can called additional surface conductance [8 11]. The experimental verification of this theory is still under age, being necessary to accomplish a profound and extensive experimental work. The effective viscosity of a suspension of particles in a fluid medium is greater than that of the pure fluid, owing to the perturbation of the shear field in the vicinity of the particles and the consequent increase of the dissipation of energy. The theoretical work of Einstein [12] showed the dependence of the viscosity of a suspension on the volume fraction at low concentration of spherical, rigid, uncharged and small particles. When the particles are charged and the fluid is an electrolyte, the flow fields in the vicinity of the particles are further modified due to the presence in the fluid of an electrostatic body force exerted by the particle on the fluid within the double layer of the particle where a non-zero charge distribution exists. This further modification of the local flow fields leads to an increase of the dissipation of energy and a further increase in the effective viscosity. The first-order term is called primary electroviscous effect [13]. Although scarce, the experimental work on the primary electroviscous effect [14 18] shows that the different theories on this phenomenon [19 22] do not agree with the experimental data. Elsewhere [18] we suggested, from the study of the primary electroviscous effect of a polystyrene latex that this mechanism should be incorporated to the theory of the primary electroviscous effect, considering the success to incorporate a dynamic Stern-layer into the theories of electrophoresis and conductivity of a suspension [6,23]. Therefore, following the method by Mangelsdorf and White [6], we have extended the theory developed by Watterson and White [22] for the primary Fig. 1. Electrophoretic mobility of latexes versus electrolyte concentration.

3 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) Fig. 2. Conductivity increment of latexes versus electrolyte concentration. Fig. 3. Reduced -potential versus electrolyte concentration calculated by using electrophoresis and conductivity theories [6] (see text). The same magnitude has been plotted when no surface conductance is taken into account [7] for comparison.

4 376 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) electroviscous effect by considering the mobility of the ions into the Stern-layer [24]. Numerical results have shown [24] that the primary electroviscous coefficient (p) separately depends on the particle radius (a) and on the Debye length ( 1 ), opposite to the electrokinetic radius ( a) dependence considered in the immobile Stern-layer (no additional surface conductance) problem. Moreover, the characteristic p-maximum versus potential found by Watterson and White [22], as a consequence of their numerical calculations, trends to disappear as higher is the particle radius when the Stern-layer conductance is taken into account. 2. Experimental Two negatively charged polystyrene latexes have been prepared according to the method of Kotera et al [25]. Essentially, a portion of the styrene monomer, distilled under nitrogen just Table 2 Stern-layer parameters. N i is the number of sites per unit area for counterions, i / i [ 1 ] the counterion drag coefficient ratio, 1 the inner Stern-layer thickness and pk i the counterion dissociation constant [6] [KCI] (mol dm 3 ) L1 L2 N i ( i / i [ 1 ]) pk i N i ( i / i [ 1 ]) pk i Fig. 4. Prunary electroviscous effect of latex L1 versus electrolyte concentration. Theoretical values have been obtained by using the modified theory [24], p(theo), and Watterson White theory [22] p(no surf.).

5 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) Fig. 5. The same that Fig. 4 for latex L2. prior to use, and an aqueous buffer (KHCO 3 ) solution was mixed and saturated with nitrogen in a bottle at 70 C. The buffer was added in order to suppress the formation of hydroxil groups during the polymerization process. The reaction was subsequently started by addition of a nitrogen-saturated K 2 S 2 O 8 solution. The latexes were cleaned by ion-exchange over a mixed bed [26] and centrifugation. The surface charge density was obtained by conductimetric titration. The average particle radius was obtained by electron microscopy. The results are shown in Table 1. All chemicals were of A.R. quality. All water was purified by reverse osmosis followed by percolation through charcoal and mixed-bed ion exchange resins (Millipore). The viscosity of each suspension was determined with capillary viscometers of Ubbelohde type (Proton and Schott-Gerate) using water at 25 and 30 C for the determination of the calibration constants of the apparatus. As the effect of the presence of the particles on the viscosity of the suspensions is generally low, at these low concentrations, the uncertainties associated with the manual determination of the efflux time in the viscometers may easily mask the actual viscosity variations. For this reason we have used a semi-automatic system for recording the time, based on photoelectric methods (AVS3 10, Schott-Gerate). Electrophoretic mobilities were obtained with a Zetasizer 2000 (Malvern Instruments) by taking the average of at least six measurements at the stationary level in a cylindrical cell. The conductivity of the suspensions was measured with a conductimeter (Crison) at 100 Hz. To obtain dynamic viscosity of a suspension it is necessary to know its density. This magnitude was obtained with a densimeter DMA58 (Anton Paar). All experiments were performed at C. 3. Results and discussion The various equations describing the primary electroviscous effect of dilute suspensions can all be expressed in the form = 0 [1+2.5(1+p) ] (1) where is the viscosity of the suspension, 0 that of the solvent, is the volume fraction of solid particles and p is the primary electroviscous coeffi-

6 378 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) cient which is a function of the charge on the particle (or, more conventionally, the electrostatic potential,, on the slipping plane which defines the hydrodynamic radius of the particle) and the properties of the electrolyte ions (charge, bulk density number and limiting conductance). Several theories have been formulated for the primary electroviscous effect. They supply different expressions for the coefficient p [19 22] being that by Watterson and White [22] the most advanced until now (there are not limits for its field of validity, i.e. it is applied for any a and values, and coincides with the results of that by Booth [19] when this limited theory is valid). Consequently we started from the theory of the primary electroviscous effect formulated by Watterson and White. In this work an experimental test of Watterson- White theory on the primary electroviscous effect [22] extended by including a dynamic Stern-layer [24] has been made. Details on the mathematical development of the extended theory should be found elsewhere [24]. From a physical point of view the theory presents an unsatisfactory aspect: their results markedly depends upon the values that different properties of ions take into the Stern-layer. The Sternlayer parameters must be fitted because they are not known a priori. To accomplish this task we have taken into account the cross-correlation of independent transport properties according to which the same -potential value should be calculated from different experimental data obtained by measuring different electrokinetic properties of the same system. Therefore, we have measured the electrophoretic mobility and the conductivity increment of the same systems (Figs. 1 and 2). These experimental data have been used to calculate -potential by applying Mangelsdorf White theory [6]. A pair of values for every suspension can be obtained, one applying the theory of electrophoresis ( E ), and the other one by applying the theory of conductivity ( C ) A computer program has been designed to calculate the Stern-layer parameters which make equal both magnitudes. This condition supposed, in all cases, that E increases and C decreases with regard to their initial values in line with the results by Zukoski and Saville [21]. Fig. 3 shows the reduced potential obtained in this way, for every latex. The same calculations were made by using the theories which do not consider the presence of a dynamic Stern-layer [7] and they are also plotted for comparison. In Table 2 we present the Sternlayer parameters that have been obtained from the condition E = C. It can be observed that as higher is the electrolyte concentration lower is the value of these parameters. Considering that as higher is the electrolyte concentration the relative influence of the Stern-layer is less important as a consequence of the double layer compression, this is an expected result. It must be note that the parameters referring to the co-ion have not been obtained. This is due to that the variation of these data have not any influence on the results. On the other hand, modifying the outer Stern-layer capacitance we did not found important modifications of the final results; therefore, a constant value of this magnitude was taken. The dependence of the viscosity of the suspensions with the solid volume fraction was measured at different electrolyte concentrations. A linear dependence was found (0 0.01) which permit us to affirm that only electroviscous effect of first order appears in our experiments. In Figs. 4 and 5 experimental and theoretical values of the primary electroviscous coefficient have been plotted against the electrolyte concentration. The theoretical values obtained by using Watterson-White theory have been also plotted for comparison. Clearly the quantitative discrepancy between experiment and theory is maintained in spite of the extended theory supplies slight larger values for the primary electroviscous coefficient. This result would permit us to conclude that a dynamic Stern-layer has not so high influence on the primary electroviscous effect as was expected. However, another possible interpretation of these results consists in to affirm that the dynamic Stern-layer model here used is not really right. There are other models that consider the movement of ions in the region near the particle surface. One of these [27] supplies alternative -potential values from electrophoresis data, which is in agreement to the expected behaviour [28]. Therefore, as a future work, we will study this possibility in order to solve this uncertain state of the subject.

7 F.J. Rubio-Hernández et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 159 (1999) Acknowledgements This research work was supported by DGI- CYT, project PB and JA, project FQM E. Ruiz-Reina expresses his gratitude to JA for the conceded FPDI-96 grant. We express our gratitude to Dr J.M. Peula, University of Malaga, to supply the latex L1. References [1] R.W. O Brien, W.T. Perrins, J. Colloid Interface Sci. 99 (1984) 20. [2] C.F. Zukoski, D.A. Saville, J. Colloid Interface Sci. 107 (1985) 322. [3] A.G. Van der Put, B.H. Bijsterbosch, J. Colloid Interface Sci. 75 (1980) 512. [4] S.S. Dukhin, N.M. Semenikhin, Kolloidn. Zh. 32 (1970) 366. [5] J. Lyklema, S.S. Dukhin, V.N. Shilov, J. Electroanal. Chem. 143 (1983) 1. [6] C.S. Mangelsdorf, L.R. White, J. Chem. Soc. Faraday Trans. 86 (1990) [7] R.W. O Brien, L.R. White, J. Chem. Soc. Faraday Trans. II 74 (1978) [8] S.S. Dukhin, Adv. Colloid Interface Sci. 44 (1993) 1. [9] J. Lyklema, Colloids Surfaces A 92 (1994) 41. [10] S.S. Dukhin, Adv. Colloid Interface Sci. 61 (1995) 17. [11] J. Lyklema, Fundamentals of Interface and Colloid Science, Academic Press, New York, [12] A. Einstein, Ann. Phys. 19 (1906) 289; 34 (1911) 591. [13] R.J. Hunter, Zeta Potenetial in Colloid Science, Academic Press, New York, [14] J. Stone-Masui, A. Watillon, J. Colloid Interface Sci. 28 (1968) 187. [15] Y.L. Wang, J. Colloid Interface Sci. 32 (1970) 633. [16] E.J. Schaller, A.E. Humphrey, J. Colloid Interface Sci. 22 (1966) 573. [17] A. Delgado, F. Gonzalez-Caballero, M.A. Cabrerizo, I. Alados, Acta Polymerica 38 (1987) 66. [18] F.J. Rubio-Hernandez, A.I. Gomez-Merino, E. Ruiz- Reina, C. Carnero-Ruiz, Colloids Surfaces A 140 (1998) 295. [19] F. Booth, Proc. R. Soc. A 203 (1950) 553. [20] W.B. Russel, J. Fluid Mech. 85 (1978) 209. [21] I.D. Sherwood, J. Fluid Mech. 101 (1980) 609. [22] I.G. Watterson, L.R. White, J. Chem. Soc. Faraday Trans. II 77 (1981) [23] C.F. Zukoski, D.A. Saville, J. Colloid Interface Sci. 114 (1986) 45. [24] F.J. Rubio-Hemandez, E. Ruiz-Reina, A.I. Gomez- Merino, J. Colloid Interface Sci. 206 (1998) 334. [25] A. Kotera, K. Furusawa, V. Takeda, Kolloid Z.Z. Polym. 239 (1976) 677. [26] H.J. Van den Hul, J.W. Vanderhoff, J. Colloid Interface Sci. 28 (1968) 336. [27] S.S. Dukkin, N.M. Semenikhin, Kolloidn. Zh. 31 (1970) 36. [28] F.J. Rubio-Hemandez, J. Non-Equilib. Themmodyn. 21 (1996) 30..

Primary Electroviscous Effect with a Dynamic Stern Layer: Low κa Results

Journal of Colloid and Interface Science 226, 180 184 (2000) doi:10.1006/jcis.2000.6804, available online at http://www.idealibrary.com on Primary Electroviscous Effect with a Dynamic Stern Layer: Low