Aggregation and Charging of Colloidal Silica Particles: Effect of

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Aggregation and Charging of Colloidal Silica Particles: Effect of Particle Size Motoyoshi Kobayashi,† Fre´de´ric Juillerat,‡ Paolo Galletto,† Paul Bowen,‡ and Michal Borkovec*,† Laboratory of Colloid and Surface Chemistry, Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, Sciences II, Quai Ernest Ansermet 30, CH-1211 Geneva 4, Switzerland, and Laboratory of Powder Technology, Institute of Materials, Ecole Polytechnique Fe´ de´ rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland Received December 21, 2004. In Final Form: April 25, 2005 We studied systematically aqueous suspensions of amorphous well-characterized silica particles by potentiometric titration, electrophoretic mobility, and time-resolved light scattering. Their charging behavior and aggregation rate constants were measured as a function of pH and ionic strength in KCl electrolytes for three types of particles of approximately 30, 50, and 80 nm in diameter. The charging behavior was consistent with the basic Stern model; the silica particles carry a negative charge, and its magnitude gradually increases with increasing pH and ionic strength. On the other hand, their early-stage aggregation (or coagulation) behavior is complex. The aggregation of the largest particles shows features resembling predictions of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory. On one hand, the rate constant decreases sharply with increasing pH at low ionic strengths and attains fast aggregation conditions at high ionic strengths. On the other hand, we observe a characteristic slowing down of the aggregation at low pH and high ionic strengths. This feature becomes very pronounced for the medium and the small particles, leading to a complete stabilization at low pH for the latter. Stabilization is also observed at higher pH for the medium and the small particles. From these aggregation measurements we infer the existence of an additional repulsive force. Its origin is tentatively explained by postulating hairy layers of consisting of poly(silicilic acid) chains on the particle surface.

1. Introduction Colloidal silica particles are widely used in many industrial applications, for example, as polishing slurries, catalysts, composite coatings, and adsorbents.1,2 Silicate particles (i.e., quartz, feldspars, clay minerals) further play an important role in determining the fate of nutrients and contaminants in subsurface environments, be it as adsorbents or as mobile carriers.3,4 In all these processes, colloidal stability of silica particles is of major importance, and for this reason it is essential to properly understand the aggregation properties of these systems in aqueous suspensions. The famous theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO) represents the classical framework to discuss the stability of colloidal suspensions.5-9 The theory treats the particle interactions as a superposition of repulsive double-layer overlap forces and an attractive dispersion (van der Waals) force. The aggregation rate constant is in turn evaluated from the steady-state solution of the diffusion equation, where the interaction potential †

University of Geneva. ‡ Ecole Polytechnique Fe ´ de´rale de Lausanne. * Corresponding author. E-mail: [email protected]. (1) Iler, R. K. The Chemistry of Silica; John Wiley: New York, 1979. (2) Castelvetro, V.; De Vita, C. Adv. Colloid Interface Sci. 2004, 108109, 167. (3) Ryan, J. N.; Elimelech, M. Colloids Surf. A 1996, 107, 1. (4) Kretzschmar, R.; Borkovec, M.; Grolimund, D.; Elimelech, M. Adv. Agronomy 1999, 66, 121. (5) Derjaguin, B. W.; Landau, L. Acta Physicochim. URRS 1941, 14, 633. (6) Verwey, E. J.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (7) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (8) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1991. (9) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry; Marcel Dekker: New York, 1997.

and the mutual diffusion coefficient enter.7,9-12 The DLVO theory predicts a well-defined critical coagulation concentration (CCC), which separates the regimes of slow and fast aggregation. Furthermore, the theory suggests an increase of the suspension stability with increasing surface charge and with decreasing salt levelstrends which are observed in most suspensions of charged particles. In the fast regime, the aggregation rate constants are predicted reasonably well, typically within a factor of 2 or better.12-17 As shown recently, the theory can also quantify the aggregation rate constants in the slow regime for some systems, for example, carboxylated latex,18,19 weakly charged sulfate latex,20 and negatively charged hematite.19,21 In the slow regime, however, the validity of the DLVO theory is restricted to systems, where the potential barrier is located at distances exceeding a few nanometers. This condition limits the validity of DLVO theory to weakly charged systems, which have the CCC at low salt levels. For highly charged systems, the CCC is located at higher salt concentrations, and the barriers (10) von Smoluchowski, M. Z. Phys. Chem. (Munich) 1917, 92, 129. (11) Fuchs, N. Z. Z. Phys. 1934, 89, 736. (12) Adachi, Y. Adv. Colloid Interface Sci. 1995, 56, 1. (13) Lips, A.; Willis, E. J. Chem. Soc., Faraday Trans. 1 1973, 69, 1226. (14) Van Zanten, J. H.; Elimelech, M. J. Colloid Interface Sci. 1992, 154, 1. (15) Higashitani, K.; Kondo, M.; Hatade, S. J. Colloid Interface Sci. 1991, 142, 204. (16) Holthoff, H.; Egelhaaf, S. U.; Borkovec, M.; Schurtenberger, P.; Sticher, H. Langmuir 1996, 12, 5541. (17) Holthoff, H.; Schmitt, A.; Fernandez-Barbero, A.; Borkovec, M.; CabrerIzo-Vilchez, M. A.; Schurtenberger, P.; Hidalgo-Alvarez, R. J. Colloid Interface Sci. 1997, 192, 463. (18) Behrens, S. H.; Christl, D. I.; Emmerzael, R.; Schurtenberger, P.; Borkovec, M. Langmuir 2000, 16, 2566. (19) Behrens, S. H.; Borkovec, M.; Schurtenberger, P. Langmuir 1998, 14, 1951. (20) Behrens, S. H.; Semmler, M.; Borkovec, M. Prog. Colloid Polym. Sci. 1998, 110, 66. (21) Schudel, M.; Behrens, S. H.; Holthoff, H.; Kretzschmar, R.; Borkovec, M. J. Colloid Interface Sci. 1997, 196, 241.

10.1021/la046829z CCC: $30.25 © 2005 American Chemical Society Published on Web 05/24/2005

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move to sub-nanometer distances. In this case, one observed deviations from DLVO theory, which are probably related to surface roughness and/or discreteness of charge.18,21-25 The stability of silica particles has been repeatedly reported to disagree with DLVO theory.1,15,26-31 Silica particles are claimed to be stable at low pH, where silica has basically no charge.26,28,32-35 Under such conditions, the DLVO theory incorrectly predicts that silica particles should be unstable. Other silica systems show a minimum in the CCC as a function of pH.26,28,30 Again, this minimum cannot be reconciled with DLVO theory, which predicts a continuous increase of the CCC due to the increase of the magnitude of surface charge with increasing pH. Such anomalies have been mainly reported for nanosized silica particles,1,15,26-30 while sub-micrometer silica particles seem to behave DLVO-like.15,24,29,36-38 We find many of these experimental findings difficult to judge. In many studies, the suspension stability was assessed only in a qualitative fashion by visual observation, sedimentation tests, or turbidity measurements.26,28-30 While such assays are easy to perform, the results are difficult to compare with the DLVO theory quantitatively. Stability studies were sometimes not carried out on wellcharacterized samples, and the particle size, pH, and ionic strength were not always varied systematically.15,24,36-38 For these reasons, we have systematically studied wellcharacterized spherical silica particles by means of potentiometric titration, electrophoretic mobility, and light scattering techniques. We present results concerning the particle charge and aggregation rate constants as a function of ionic strength and pH for particles of different particle size. We find that submicron-sized silica particles aggregate in a fashion, which is similar to predictions of the DLVO theory, while for nanometer-sized particles substantial deviations are observed. 2. Experimental Section Materials. This study used three different batches of commercial colloidal Klebosol silica particles supplied by the manufacturer (Clariant), namely large (150H50), medium (150835), and small (20H12) particles. The large particles were washed three times with 0.1 M HCl and rinsed with deionized water by repeated centrifugation and decantation until the electrical conductivity of supernatant dropped below 2 µS/cm.39 Deionized water was prepared with the Milli-Q A10 UV/UF (Millipore) system and used throughout. The small and medium particles were suspended in 0.1 M HCl solution, dialyzed against three times exchanged 1 mM HCl solution, and finally extensively dialyzed against pure water. (22) Cooper, W. D. Kolloid Z. Z. Polym. 1972, 250, 38. (23) Prieve, D. C.; Lin, M. M. J. J. Colloid Interface Sci. 1982, 86, 17. (24) Kihira, H.; Ryde, N.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1992, 88, 2379. (25) Hiemstra, T.; van Riemsdijk, W. H. Langmuir 1999, 15, 8045. (26) Allen, L. H.; Matijevic, E. J. Colloid Interface Sci. 1969, 31, 287. (27) Allen, L. H.; Matijevic, E. J. Colloid Interface Sci. 1970, 33, 420. (28) Depasse, J.; Watillon, A. J. Colloid Interface Sci. 1970, 33, 430. (29) Harding, R. D. J. Colloid Interface Sci. 1971, 35, 172. (30) Depasse, J. J. Colloid Interface Sci. 1999, 220, 174. (31) Milonjic, S. K. Colloids Surf. 1992, 63, 113. (32) Bolt, G. H. J. Phys. Chem. 1957, 61, 1168. (33) Yates, D. E.; Healy, T. W. J. Colloid Interface Sci. 1976, 55, 9. (34) Hiemstra, T.; van Riemsdijk, W. H.; Bolt, G. H. J. Colloid Interface Sci. 1989, 133, 91. (35) Borkovec, M.; Jonsson, B.; Koper, G. J. M. Colloids Surf. Sci. 2001, 16, 99. (36) Chang, S. Y.; Ring, T. A.; Trujillo, E. M. Colloid Polym. Sci. 1991, 269, 843. (37) Killmann, E.; Adolph, H. Colloid Polym. Sci. 1995, 273, 1071. (38) Barany, S.; Cohen Stuart, M. A.; Fleer, G. J. Colloids Surf. A 1996, 106, 213. (39) de Keizer, A.; van der Ent, E. M.; Koopal, L. K. Colloids Surf. A 1998, 142, 303.

Kobayashi et al. Particle Size Measurements. Particle morphology and the size distribution were assessed by electron microscopy. For transmission electron microscopy (TEM) normal-resolution and high-resolution microscopes (Philips CM20 and CM430) were used. Scanning electron microscopy (SEM) was carried out with a high-resolution instrument (Philips XL-30SFEG). A few microliters of dilute particle suspensions at particle concentrations of around 0.2-0.4 g/L was allowed to air-dry slowly on carbon-coated copper grids for TEM and on glass slides for SEM. The samples were imaged without any metal coatings. For the medium and large particles, the number-averaged radius 〈r〉 and

the coefficient of variance CV ) x〈r2〉/〈r〉2-1 were evaluated by measuring 500-1000 particles on the micrographs. For the small particles only 100 were counted due to difficulties in obtaining sharp focus. Particle size was further measured on two light scattering instruments. First, a multiangle goniometer (ALV CGS-8, Langen) with ALV-5000 correlators and a 532 nm solid-state laser as light source was used. Second, the ZetaPALS instrument (Brookhaven) equipped with a BI-9000AT digital correlator and a 661 nm solid-state laser was utilized. Dynamic light scattering (DLS) was performed in stable dilute suspensions and 0.1 mM KCl at pH around 8 at 25 °C and a scattering angle of 90°. From dynamic light scattering data the number-averaged radius 〈r〉 and CV were obtained with regularized least-squares deconvolution (CONTIN),40 while from second-order cumulants the hydrodynamic radius, rh, was evaluated. The radius remained constant within 2 nm, and we could not detect any systematic dependence on pH or the ionic strength. The latter was compared with the TEM data using the relationship rh ) 〈r6〉/〈r5〉. The higher moments were estimated by assuming a Schultz distribution. Angle-dependent static light scattering was interpreted with the Rayleigh-Gans-Debye (RGD) theory,41 from which an apparent radius rS was extracted, which can be compared with the TEM data by rS ) x〈r8〉/〈r6〉. Centrifugal sedimentation was performed with an X-ray disk centrifuge (XDC, Brookhaven). For such measurements, the suspensions were initially diluted in deionized water down to a concentration of 20 g/L and dispersed with a 150 W ultrasonic horn for 15 min. From the measured sedimentation distribution, the particle densities and CV were obtained on the basis of the particle radii known from TEM. Density and Surface Area Measurements. Density measurements of the particles were performed in suspensions by standard water pycnometry and after drying by helium pycnometry (Microline 380, Micromeritics). The specific surface area of the silica particles, a, was determined with nitrogen adsorption BET measurements9 performed with a Gemini 2375 (Micromeritics) on air-dried and freeze-dried samples (Alpha 1-4, Christ). The specific surface area was compared with the TEM measurements with the relation a ) (3/F)〈r2〉/〈r3〉, where F is the particle density. Potentiometric Acid-Base Titration. The surface charge density of silica particles was measured with acid-base potentiometric titrations. They were carried out on a home-built computer-controlled instrument with four automatic burets containing 0.25 M HCl, 0.25 M CO2-free KOH (Baker Dilut-It), 3.0 M KCl, and pure water. All solutions were freed of CO2 by boiling. The potential between a glass electrode (6.0123.100, Metrohm) and a separate Ag/AgCl reference electrode (6.0733.100, Metrohm) was measured by a high-impedance voltmeter. The titrations were carried out at 25 °C, and the vessel was continuously flushed with moist CO2-free nitrogen gas. Acidified silica suspensions with particle concentrations around 5.5, 32, and 54 g/L for small, medium, and large particles were titrated at constant ionic strength constant from pH 3.5 to 9 and back. The pH range was chosen in order to minimize effects of silica dissolution and to ensure an experimental error below 5%. After such a run, the overall ionic strength was increased, and the procedure was repeated. Electrodes were calibrated with blank titrations, which also served to determine the exact base concentration and the activity coefficients. The surface charge was obtained from the difference between the titration curves (40) Provencher, S. W. Comput. Phys. Commun. 1982, 27, 229. (41) Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969.

Colloidal Silica Particles

Langmuir, Vol. 21, No. 13, 2005 5763 not show any systematic variations with the solution composition. The suspension pH was determined with a combination microelectrode (6.0234.110, Metrohm) in the cuvette right after the measurement. In the case of the small- and medium-sized particles, the cuvette was inserted in the vat, and the suspension was injected with a pipet, mixed, and monitored by DLS. The particle concentrations were in the range 8-60 mg/L (7 × 1016 and 7 × 1018 m-3). In the case of fast aggregation, the smallest time resolution chosen was 1 s, and the experiment was carried out for a few minutes. This procedure permits us to keep the rate increase of the hydrodynamic radius with time sufficiently small. By extrapolating to the initial time, the radius of the particles in a stable suspension could be recovered (see Figure 1). In this way it was assured that the early stages of the aggregation were monitored even for the small particles. The absolute aggregation rate constant k was extracted from the apparent initial DLS rate based on the RGD approximation and the relative hydrodynamic radius of the doublet R ) 1.39 with the relation16,17

[

]( )

sin (2rq) 1 1 drh(q,t) | ) 1+ 1 - kN0 2rq R rh(q,0) dt tf0

Figure 1. Determination of aggregation rates by time-resolved light scattering. (a) Temporal increase of the apparent DLS hydrodynamic radius for the small silica particles in 1 M KCl solution at different pH values. Linear extrapolations to short times in the early stage of the aggregation are shown as solid lines. The intercept is the hydrodynamic radius of isolated particles of 18 nm. (b) Scatter plot of the apparent static and dynamic aggregation rates obtained from an SSDLS experiment. The data are fitted to a straight line, whose intercept gives the absolute aggregation rate constant. with and without the sample and normalized to the BET surface area. Details on the technique are given elsewhere.21,34,35 Electrophoretic Mobility. A laser Doppler velocimetry instrument (Zeta Sizer 2000, Malvern) was used to carry out electrophoretic mobility measurements at 25 °C as a function of pH and at different ionic strength. Samples were prepared from silica suspensions diluted with water and by adding appropriate volumes of stock solutions of KCl, HCl, or KOH to adjust the ionic strength and pH. A combination electrode (6.0234.110, Metrohm) was used to measure the suspension pH. Particle concentrations were around 0.1, 1, and 2 g/L for large, medium, and small particles, respectively. Mobility values were found to be insensitive to changes in particle concentrations within a factor of 4. Aggregation Rate Constants. Time-resolved static and dynamic light scattering was used to determine aggregation rates with the ALV multiangle goniometer (see above). The hydrodynamic radius rh(q,t) was measured as a function of time t and given magnitudes of the wave vector q from second-order cumulant analysis. The DLS measurement were carried out at 90° with a time resolution between 1 and 20 s. Simultaneous static and dynamic light scattering (SSDLS) measurements16,17 were performed for the largest particles only, and in addition to rh(q,t), the scattering intensity I(q,t) was measured as well. The angular resolution improved by repositioning the detectors during the run, typically leading to an angular resolution of 8°. The sample temperature was kept at 25 °C. Quartz or borosilicate glass cuvettes used were cleaned by soaking in a hot 3:1 mixture of concentrated sulfuric acid and 30% hydrogen peroxide and rinsed extensively with water. Prior to experiments, the necessary amounts of stock solutions of KCl, HCl, or KOH were mixed with water in the cuvette. In the case of large silica particles, the stable silica suspension was added, shaken with a vortex mixer, and monitored by DLS or SSDLS light scattering during up to 60 min with a time resolution of 20 s. The particle concentration was chosen around 0.5 mg/L (1015 m-3), which leads to an increase of the hydrodynamic radius of about 2-50% during the measurement. The initial radius did

(1)

where r is the (number-averaged) particle radius and N0 is the particle number concentration. This equation has been shown to be reliable for small particles.16,17,42,43 For the largest particles, the values of the absolute rate constants were verified with SSDLS. This method requires besides the apparent DLS rate also the apparent static light scattering rate as a function of the angle. The quantities are plotted in a scatter plot and fitted to the linear equation16,17

1 dI(q,t) 1 drh(q,t) R - kN0 (2) |tf0 ) | I(q,0) dt rh(q,0) dt tf0 R - 1

(

)

This method makes no assumptions about the optical and hydrodynamic properties of the particle dimers. Representative data and this fit are shown in Figure 1. In the pH range 7-11 and in 1 M KCl, we have performed five independent measurements with DLS and SSDLS. The average rate constant of (1.5 ( 0.2) × 10 - 18 m3 s-1 obtained from DLS is in very good agreement with the SSDLS value of (1.6 ( 0.2) × 10-18 m3 s-1. The latter technique also gives a relative hydrodynamic ratio of R ) 1.38 ( 0.03, which is close to the theoretical value stated above.

3. Modeling Surface Charge. The classical 1 - pK basic Stern model is used to evaluate the surface charge density as a function of pH and ionic strength. This model has been successfully applied to silica and other oxides previously.34,35,44 Surface charge of silica is assumed to originate from the deprotonation of silanol groups according to the reaction

SiOH T SiO- + H+

(3)

The site densities of both surface groups ΓSiOH and ΓSiOobey the mass action law

ΓSiO-aH ) K exp(βeψ0) ΓSiOH

(4)

where aH is the activity of the protons (with pH ) - log aH), K the intrinsic equilibrium constant (with pK ) -log K), ψ0 the surface potential, e the elementary charge, and β the inverse thermal energy. The total number density of these sites is given by (42) Yu, W. L.; Borkovec, M. J. Phys. Chem. B 2002, 106, 13106. (43) Lin, W.; Galletto, P.; Borkovec, M. Langmuir 2004, 20, 7465. (44) Hiemstra, T.; de Wit, J. C. M.; van Riemsdijk, W. H. J. Colloid Interface Sci. 1989, 133, 105.

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Γ0 ) ΓSiOH + ΓSiO-

(5)

V(h) ) VvdW(h) + Vdl(h)

while the surface charge density is

σ ) -eΓSiO-

(6)

The surface charge density is related to the potential drop over the Stern layer

σ ) CS(ψ0 - ψd)

(7)

where CS is the Stern layer capacitance and ψd the diffuse layer potential. The charge potential relationship of the diffuse layer (so-called Grahame equation)

σ)

assumed to be

( )

βeψd 20κ sinh βe 2

(8)

(13)

where VvdW(h) and Vdl(h) are the interaction potentials due to van der Waals and double-layer overlap forces. By invoking the Derjaguin approximation, we can write

VvdW(h) ) -

Ar 12h

(14)

where A is the Hamaker constant across the liquid. The double-layer overlap potential Vdl(h) is obtained within the Derjaguin approximation from a numerical solution of the Poisson-Boltzmann equation including full regulation.48 The solution in use is equivalent to the results based on elliptic functions.18,49

Within the DLVO theory, the interaction potential is

4. Results and Discussion Morphology and Particle Size. The SEM and TEM micrographs for the three silica batches are shown in Figures 2 and 3. The photographs illustrate the spherical shape and the narrow size distributions of the larger particles. The average number-weighted radii 〈r〉 and the coefficients of variation (CV) are summarized in Table 1. The most reliable results are obtained from TEM, giving particle radii of 10, 23, and 38 nm for the small, medium, and large particles, respectively. The large- and mediumsized particles are spherical and monodisperse, with a CV in the range 0.10-0.15. The small particles are sometimes ellipsoidal and much more polydisperse (CV ≈ 0.4). The SEM and light scattering (DLS and SLS) lead to consistent results, indicating only marginal swelling of the particles in water. The particle densities are summarized in Table 2. Air pycnometry gives a value near 2.2 g/cm3, as expected for an amorphous precipitated silica.50 From water pycnometry and XDC,51 one infers densities in the range 1.7-2.2 g/cm3, which indicate porosity or swelling of the surface layer. The BET specific surface areas are listed in Table 2 as well. They are consistently higher than the geometrical surface areas calculated from the TEM data, irrespective of the drying method. This difference represents an additional indication of particle porosity or surface roughness. Surface Charge Density. Figure 4 shows the surface charge density as a function of pH at different ionic strengths in KCl electrolytes measured with potentiometric titrations. The silica particles have a negative charge, the magnitude of which increases with increasing pH and increasing ionic strength. The solid lines are results of calculations based on the 1 - pK basic Stern model with a total site density Γ0 ) 8 nm-2, a Stern capacitance CS ) 2.9 F/m2, and an ionization constant pK ) 7.6. The model predicts a saturation of the surface charge at very high pH, but this saturation cannot be observed within the accessible pH range. The parameters used give adequate fits to the experimental data for the data at lower ionic strengths but give inferior fits at 1 M, probably due to neglect of specific binding of potassium ions. The same values for the site density and the Stern capacitance were proposed previously for silica, while the intrinsic constant was estimated to be pK ) 7.5 on the basis of the multisite surface

(45) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (46) Honig, E. P.; Roeberse, G. J.; Wiersema, P. H. J. Colloid Interface Sci. 1971, 36, 97. (47) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation; Butterworth: Oxford, 1995.

(48) Pericet-Camara, R.; Papastavrou, G.; Behrens, S. H.; Borkovec, M. J. Phys. Chem. B 2004, 108, 19467. (49) Behrens, S. H.; Borkovec, M. J. Phys. Chem. B 1999, 103, 2918. (50) Jelinek, L.; Kovats, E. S. Langmuir 1994, 10, 4225. (51) Staiger, M.; Bowen, P.; Ketterer, J.; Bohonek, J. J. Dispersion Sci. Technol. 2002, 23, 619.

closes the system of equations, whereby 0 is the total permittivity of water, and the Debye length is given by

κ-1 )

x

0

(9)

2βe2NAI

where NA is Avogadro’s number and I the ionic strength. Equation 8 is valid when rκ . 1, which is a good approximation in most situations discussed here. Curvature corrections are considered by using the corresponding charge-potential relationship for a sphere obtained from the numerical solution of the PoissonBoltzmann equation. Electrophoretic Mobility. The standard electrokinetic model due to O’Brien and White is used to evaluate the electrophoretic mobility.45 The model takes into account the double-layer relaxation and retardation effects and uses the potential at the shear plane (so-called ζ potential) as input. We calculate this potential in an approximate fashion from the potential profile of the diffuse layer18

ζ)

[

( )]

βeψd 4 arctanh exp(-κd) tanh βe 4

(10)

where d is the distance of the shear plane from the surface, and the diffuse layer potential is calculated from the 1 pK model discussed above. Aggregation Rate Constants. The steady-state solution of the diffusion equation in a force field leads to the classical expression of the aggregation rate constant7,9,18

k)

{

B(h)

}

∫0∞ (2r + h)2 exp[βV(h)] dh

8 2r 3βη

-1

(11)

where η is the viscosity of solution, h the distance between particle surfaces, V(h) interaction potential, and B(h) the dimensionless hydrodynamic resistance function. The latter is approximated by46,47

B(h) )

6(h/r)2 + 13(h/r) + 2 6(h/r)2 + 4(h/r)

(12)

Colloidal Silica Particles

Figure 2. Scanning electron micrographs (SEM) of the silica particles: (a) large (bar 200 nm), (b) medium (bar 200 nm), and (c) small (bar 100 nm) particles. The results of their particle size analysis are given in Table 1.

complexation (MUSIC) model.34,35,44 With the latter value, a slightly inferior fit of the experimental data is obtained. Electrophoretic Mobility. Figure 5 shows the experimental results for the electrophoretic mobilities as a function of pH at different ionic strengths. In line with their negative charge, the particles exhibit negative mobility, and its magnitude increases with increasing pH. The solid lines are calculations based on the standard electrokinetic model using the diffuse layer potential from the 1 - pK basic Stern model as input. In the calculation, we assume that the position of the shear plane is located at 0.5 nm from the surface. This shift reduces the magnitude of the mobility at higher pH at 100 mM but does not much affect the results otherwise. The model calculations agree reasonably well with the experimental results, particularly when one realizes that the model contains only one adjustable parameter. Note that although the mobility approximately saturates to a common value at pH > 9, the surface potential keeps increasing with increasing pH. This phenomenon is related to the existence of a mobility maximum, which is predicted by

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the standard electrokinetic model.45 Moreover, the model correctly captures the intersections of the mobility curves for 3 and 10 mM, occurring for the large- and mediumsized particles. The shear plane is located twice as far from the surface than the distance of 0.25 nm proposed previously for carboxylated latex particles.18 Aggregation Rate Constants. Before we discuss the experimental results, let us briefly review the predictions of DLVO theory. With the known charging behavior, the DLVO theory can be used to calculate the aggregation rate constants. The only additional parameter is the Hamaker constant of silica across water. Its value is known fairly accurately, and we use A ) 8.3 × 10-21 J reported earlier.8,52 Figure 6 shows the calculated aggregation rate constants for the large particles as a function of pH for different ionic strengths. At low pH, the rate constant is close to diffusion-controlled value, and with increasing pH the aggregation rate decreases sharply beyond a critical pH, due to the buildup of charge on the silica surface. The rate constant also increases with increasing ionic strength, due to screening of the electrostatic interactions. Because of this effect, the critical pH moves toward higher pH values, until the aggregation rate constant remains diffusion-controlled through the whole accessible pH. This transition is predicted to happen at high salt concentrations near 4 M. The predictions of DLVO theory are very similar for the smaller particles, with the exception that the decrease of the rate constant with pH is less pronounced. Note that similar pH dependencies for the aggregation rates were experimentally confirmed for carboxylated latex and negatively charged hematite particles.18,19,21 Let us now discuss the measured absolute aggregation rate constants as a function of pH at different ionic strengths (see Figure 7). The rate constants were obtained with time-resolved light scattering, mostly with DLS and verified with SSDLS for the largest particles. We are thus confident that the rate constants correspond to the absolute rate constants of dimer formation and that they are measured in the early stages of aggregation even for the smallest particles (see section 2). Focus now on the data for the large silica particles shown in Figure 7a. The observed aggregation rate constants show a more complex behavior than what is predicted by the DLVO theory (see Figure 6). Nevertheless, several important features are reproduced, the least in a semiquantitative fashion. At high salt levels and high pH, the aggregation rates are fast and close to the diffusioncontrolled value. At lower salt levels, one observes a rapid decrease of the rate constants with increasing pH, which is also in line with the DLVO theory. However, there are several important differences to the DLVO predictions. The first difference is the lower value of the fast aggregation rate constant, the second is the marked decrease of the rate constant at high ionic strengths with decreasing pH, and the third reflects an increase in the rate constant at pH > 11. Let us now discuss these three differences. However, we do not attempt to model these differences quantitatively. The first difference to DLVO theory is a lower fast aggregation rate constant around 2 × 10-18 m3/s, while the theory predicts 8 × 10-18 m3/s. While the use of the Derjaguin approximation in the calculation leads to a slightly (say 10-20%) larger rate constant, this difference of a factor of 4 is hard to reconcile. Comparable values for the fast aggregation rate constant have been reported for submicron-sized silica particles in the range (2-10) × 10-18 (52) Hough, D. B.; White, L. R. Adv. Colloid Interface Sci. 1980, 14, 3.

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Figure 3. Transmission electron micrographs (TEM) of silica particles for small (left) and large (right) magnification: (a) large, (b) medium, and (c) small particles. Table 1. Particle Size and Polydispersity 〈r〉

(nm)a

CVb

rh (nm)c

rs (nm)d

silica particles

TEM

SEM

CON

TEM

SEM

CON

XDC

CUM

TEM

CON

SLS

TEM

CON

large (150H50) medium (1508-35) small (20H12)

38 23 10

36 24 10

39 25 13

0.11 0.15 0.37

0.11 0.13 0.15

0.06 0.16 0.23

0.18 0.20 0.27

47 28 18

40 26 17

39 28 16

49 28 17

40 26 19

40 29 17

a Number-weighted particle diameter 〈r〉 determined by transmission electron microscopy (TEM), scanning electron microscopy (SEM), and CONTIN deconvolution of dynamic light scattering data (CON). b Coefficient of variation (CV) obtained by the same methods and by X-ray disk centrifugation (XDC). c Apparent hydrodynamic radius rh obtained by cumulant (CUM) analysis of dynamic light scattering data and calculated from TEM and CONTIN data. d Intensity-weighed radius rs obtained from the static light scattering data and calculated from TEM and CONTIN data. Experimental errors are (1 nm in the radii and (0.02 in the CVs.

m3/s for other silica systems.15,36-38 For other systems, fast aggregation rate constants of about factor 2-3 below the DLVO predictions have been noted,12-15,18,19,21 while other studies have reported good agreement between experimentally measured rate constants and DLVO theory in the fast regime.7,47,53 In any case, this difference is not enormous but points toward an additional repulsion or drag force.

The second difference to DLVO theory is a marked decrease of the rate constant with decreasing pH at high ionic strengths. The theory, on the other hand, predicts at high ionic strengths a constant rate which is determined by diffusion control and independent of pH. Necessarily, an additional repulsive force must cause this decrease. This force sets in rather abruptly below pH < 6 and remains roughly constant at lower pH.

Colloidal Silica Particles

Langmuir, Vol. 21, No. 13, 2005 5767 Table 2. Particle Densities and Specific Surface Areas particle density F (g/cm3)a

specific surface area a (m2/g)b

silica particles

helium

water

XDC

air-dry

freeze-dry

TEM

CON

large (150H50) medium (1508-35) small (20H12)

2.20 2.20 2.19

2.14 2.27

1.7 1.7 1.7

51 77 228

52 80 227

36 57 104

35 53 95

a Particle density measured by helium and water pycnometry (errors (0.01 g/cm3) and X-ray disk centrifugation (XDC, errors (0.1 g/cm3). b Measured specific surface area by nitrogen adsorption on air-dried and freeze-dried samples and compared with calculated values based on TEM and CON data with a particle density of F ) 2.2 g/cm3 (see Table 1, errors are (1 m2/g).

Figure 4. Surface charge of silica particles as a function of pH different ionic strengths adjusted with KCl. The data points are obtained by potentiometric titrations, while the solid lines are the results of the basic Stern model with a total site density of 8 nm-2, a Stern capacitance of 2.9 F/m2, and an ionization constant pK ) 7.6. (a) Large, (b) medium, and (c) small particles.

The third difference to DLVO theory reflects an increase in the rate constant at pH > 11. Note that the observed aggregation rate constants are in closer agreement to values in the fast aggregation regime in other systems.18,19,21 We suspect that this acceleration is related to silica dissolution (see below). Turning toward the results for the medium size particles shown in Figure 7b, we find substantial differences with respect to the larger particles. The diffusion-controlled plateau at high pH can be still identified, but only for high ionic strengths. The decrease around pH 6 is much more (53) Lichtenfeld, H.; Knapschinsky, L.; Sonntag, H.; Shilov, V. Colloids Surf. A 1995, 313.

Figure 5. Electrophoretic mobility of silica particles as a function of pH at different ionic strengths adjusted with KCl. The data points are obtained by electrophoresis, and the solid lines are the results of the basic Stern model together with the standard electrokinetic model. The plane of shear is located at 0.5 nm from the surface. The other parameters are the same as in Figure 4. (a) Large, (b) medium, and (c) small silica particles.

pronounced than for the larger particles, and one cannot identify a constant plateau at lower pH any longer. A decrease of the aggregation rate with increasing pH is only visible at 0.6 M. Furthermore, a minimum in the rate constant at an ionic strength of 0.8 M appears around pH 10. The rate constant increases at pH > 11 similar to the larger particles. For the small particles, as shown in Figure 7c, no aggregation could be detected below an ionic strength of 0.5 M and for pH < 6. The latter feature is analogous to the slowdown of the aggregation at pH < 6, as observed

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Figure 6. Theoretical predictions of DLVO theory of aggregation rate constants of large silica particles plotted as a function of pH for different ionic strengths adjusted with KCl. The Hamaker constant was chosen as 8.3 × 10-21 J.

Kobayashi et al.

Figure 8. Hydrodynamic radius measured by the dynamic light scattering as a function of time for the medium-sized silica particles for different pH values in a 0.1 mM KCl solution. The lines correspond to constant dissolution rates of 10-7, 10-8, and 10-9 mol m-2 s-1.

by various authors and were found to vary about 1-2 orders of magnitude depending on the silica type (e.g., quartz, tridymite, cristobalite, amorphous silica).1,54,55 The dissolution rate strongly increases with increasing pH. At pH 12, dissolution rates in the range of 10-11-10-9 mol m-2 s-1 have been reported.33,54-57 The dissolution rate of amorphous silica is close to the fastest rates observed. We have assessed silica dissolution by time-resolved DLS performed on the medium-sized particles at different pH in 0.1 mM KCl. The results are shown in Figure 8. At pH < 11 we see basically no decrease of the particle size as a function of time, while at pH 12.1 a clear decrease is observed. The rate of decrease of the particle radius can be expressed as

M dr ) - kdis dt F

(15)

where kdis is the dissolution rate, M ) 60.1 g/mol the molecular mass of silica, and F ) 2.2 g/cm3. When one assumes a constant dissolution rate, the observed decrease agrees reasonably well with eq 15 for the dissolution rate of kdis ) 10-9 mol m-2 s-1 at pH 12.1. However, the observed decrease is not consistent with a constant dissolution rate, but one observes faster dissolution initially, which then slows down for longer times. In general, the effect of dissolution is small, and a substantial decrease in the particle size can be only observed at pH > 12. We thus conclude that for most conditions the effect of silica dissolution is small. Hairy-Layer Hypothesis. The observed anomalies of silica aggregation can be possibly reconciled with the existence of a hairy (or gel) layer. Such a layer has been proposed by various authors,58-63 and it might be pictured as consisting of short flexible polymer-like segments of poly(silicilic acid) anchored to the surface. The clearest Figure 7. Experimental results of the aggregation rate constants for silica particles as a function of pH at different ionic strength: (a) large, (b) medium, and (c) small silica particles. The lines serve to guide the eye.

for the medium and large particles. The rate at very high ionic strength of 2 M remains about constant for pH > 6 but is substantially slower than the diffusion-controlled rate observed in the previous two cases. The rate constants show a minimum near pH 10 at ionic strengths of 1.2 M and below. This minimum is similar, but more pronounced, to the one observed for the medium-sized particles. Silica Dissolution. At sufficiently high pH, silica dissolves. Dissolution rates of silica have been measured

(54) Hiemstra, T.; van Riemsdijk, W. H. J. Colloid Interface Sci. 1990, 136, 132. (55) House, W. A.; Orr, D. R. J. Chem. Soc., Faraday Trans. 1992, 88, 233. (56) Brady, P. V.; Walther, J. V. Chem. Geol. 1990, 82, 253. (57) van Lier, J. A.; De Bruyn, P. L.; Overbeek, J. T. G. J. Phys. Chem. 1960, 64, 1675. (58) Kitchener, J. A. Faraday Discuss. 1971, 59, 379. (59) Vigil, G.; Xu, Z.; Steinberg, S.; Israelachivili, J. J. Colloid Interface Sci. 1994, 165, 367. (60) Israelachvili, J.; Wennerstrom, H. Nature (London) 1996, 379, 219. (61) Tadros, T. F.; Lyklema, J. J. Electroanal. Chem. 1968, 17, 267. (62) Frens, G.; Overbeek, J. T. G. J. Colloid Interface Sci. 1972, 38, 376. (63) Churaev, N. V.; Sergeeva, I. P.; Sobolev, V. D.; Derjaguin, B. V. J. Colloid Interface Sci. 1981, 84, 451.

Colloidal Silica Particles

evidence for the existence this layer is based on observations of short-range repulsive forces between silica surfaces, suggesting a thickness below a few nanometers.59,64,65 More indirect indications of the existence of this layer are the relatively large value of the Stern layer capacitance with respect to other metal oxides66 and the large distance of the shear plane of 0.5 nm needed to fit the present electrophoresis data. The hairy-layer hypothesis explains the additional repulsive forces, which are clearly established on the basis of direct force measurements59,64,65 and the present stability data. This hypothesis can be reconciled with the observed particle size dependence, since its relative influence decreases with increasing particle size. Therefore, we expect smaller deviations from the DLVO behavior for larger particles than for the smaller ones. The acceleration of the rate around pH 12 might be related to the dissolution of the hairy layer, similarly as the fast initial decrease in the dissolution experiment (see Figure 8). A similar mechanism was suggested on the basis of earlier reflectometry measurements.67 The fact that this layer induces a stronger repulsion at lower pH is probably related to the deprotonation of the silanol groups around pH 7, and differences in the interaction forces could be (64) Zhmud, B. V.; Meruk, A.; Bergstrom, L. J. Colloid Interface Sci. 1998, 207, 332. (65) Adler, J. J.; Rabinovich, Y. I.; Mouldgil, B. M. J. Colloid Interface Sci. 2001, 237, 249. (66) Hiemstra, T.; van Riemsdijk, W. H. Colloids Surf. 1991, 59, 7. (67) van Duijvenbode, R. C.; Koper, G. J. M. J. Phys. Chem. B 2001, 105, 11729.

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related to surface charge heterogeneities,22-25 hydration forces,60 or effects of hydrogen bonding.1,15,26,27 5. Conclusions We have presented extensive set of experimental data on charging and aggregation rate constants as a function of pH and ionic strength of well-characterized silica particles of approximately 30, 50, and 80 nm in diameter. We found the charging behavior to be consistent with the basic Stern model, where the particles are neutral at low pH and their surface charge decreases with increasing pH and increasing ionic strength. Their aggregation behavior, on the other hand, is complex. Only the aggregation of the largest particles exhibits features similar to predictions of the DLVO theory. The smaller particles, on the other hand, aggregate much more slowly at higher pH and are completely stable at low pH. Additional non-DLVO repulsive forces must be present. We propose that the repulsive forces originate from the overlap of hairy layers on the silica surface. Acknowledgment. This research was supported by the University of Geneva, by grants from the Swiss National Science Foundation, and by the Commission for Technology and Innovation, Switzerland, Research Program TOP NANO 21. M.K. is grateful for the Postdoctoral Fellowship for Research Abroad (2003-2005) from the Japan Society for the Promotion of Science. LA046829Z