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Langmuir 1997, 13, 4574-4582
Low-Shear Viscosities of (Semi-)Dilute, Aqueous Dispersions of Charged Boehmite Rods: Dynamic Scaling of Double Layer Effects Anieke M. Wierenga and Albert P. Philipse* Van’t Hoff Laboratory for Physical and Colloid Chemistry, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands Received January 16, 1997. In Final Form: June 2, 1997X Low-shear viscosities were measured of dilute aqueous dispersions of charged boehmite rods with an average aspect ratio of 22.5 as a function of the Debye length κ-1 and the particle volume fraction Φ. It is found that the low-shear viscosity of the dispersions scales with the effective overlap concentration ν/ν1*, where ν1* is the minimum overlap concentration of rods with an effective length L* ) L + 5κ-1. This dynamic scaling is also valid for low-shear viscosity data of FD-virus solutions (Graf et al. J. Chem. Phys. 1993, 98, 4920). The rescaled relative viscosity curves can be described by the (Maron-Pierce) equation ηr ) (1 - (ν/ν1*)/(ν/ν1*)max)-2. The effective overlap concentration at which the low-shear viscosity diverges, (ν/ν1*)max, is much lower for the boehmite rods than for the semiflexible FD-virus and hard rods without electric double layers. Extrapolation of the reduced viscosity to ν/ν1* ) 0 yields an unrealistic high intrinsic viscosity [η]. Possibly the relative viscosity of dilute dispersions at very low ionic strength shows a nonanalytical concentration dependence, which renders the definition of [η] for colloids with thick double layers questionable.
1. Introduction
Abstract published in Advance ACS Abstracts, August 1, 1997.
In technological applications or biological systems, colloidal particles are often both anisotropic and charged. Due to the lack of a theoretical description of the buildup of the shear stress in those dispersions, it is not possible to predict quantitatively the effects of the anisotropy and the double layer interactions on the low-shear viscosity of such systems. At the same time, experimental studies of these effects are often complicated by a large polydispersity in particle shape and size, rod flexibility, and contamination of the studied dispersions. The boehmite dispersions in this work hardly contain contaminants, and the rods are fairly monodisperse (standard deviation in both length and diameter is 25%). Furthermore, boehmite needles are rigid, in contrast to many rodlike macromolecules or viruses. Also the particles are small enough to exhibit Brownian motion. This renders the dispersions useful model systems to study the electroviscous effects in the low-shear rheology of colloidal rod dispersions. The main aim of this work is to investigate experimentally the effect of the presence of electric double layers and double layer interactions in dispersions of Brownian rods on the low-shear viscosity. From the experimental data we will try to establish a (scaling) relation between the electric double layer thickness, the particle volume fraction, and the low-shear viscosity. Before we report and discuss the results in section 4 and section 5, the synthesis of the rods and the rheology experiments are described in section 2. The experimental conditions are interpreted in terms of the competition between Brownian motion, shear flow, and double-layer forces in section 3. This enables us to assess the relative importance of the several contributions to the bulk stress, which is directly related to the dispersion viscosity.
(1) Buining, P. A.; Pathmamanoharan, C.; Jansen, J. B. H.; Lekkerkerker, H. N. W. J. Am. Ceram. Soc. 1991, 74, 1303. (2) Wierenga, A. M.; Philipse, A. P.; Lekkerkerker, H. N. W.; Boger, D. V. To be submitted. (3) Stone-Masui, J.; Watillon, A. J. Colloid Interface Sci. 1968, 28, 187-202. (4) Russel, W. B. J. Fluid Mech. 1978, 85, 209-232. (5) Russel, W. B. J. Colloid Interface Sci. 1976, 55, 590-604. (6) Wierenga, A. M.; Philipse, A. P. J. Colloid Interface Sci. 1996, 180, 360-370. (7) Berry, D. H.; Russel, W. B. J. Fluid Mech. 1987, 180, 475-494. (8) Brenner, H. Int. J. Multiphase Flow 1974, 1, 195.
2.1. The Colloidal System. Synthesis and Characterization. Following Buining et al.,1 boehmite rods (code ASP3) were prepared by hydrothermal treatment (150 °C, 22 h) of a solution of aluminum isopropoxide (15.2 g/L), aluminum secbutoxide (20 g/L), and HCl (0.86 M) in water. After the hydrothermal treatment, the dispersions were dialyzed in cellophane tubes against a continuous flow of deionized water for a week, after which a highly viscous dispersion was obtained.
Boehmite rods can be synthesized from aluminum alkoxide precursors, following Buining.1 At low ionic strength, aqueous dispersions of these colloidal rods show interesting low-shear rheology. Already at very low particle volume fractions ( 0.995. At a given LiCl concentration the relative viscosity (within experimental error) increases linearly with the particle volume fraction, as is shown in Figure 3.1 for three LiCl concentrations. The slope of a linear fit through the ηr-Φ curves (Figure 3) is the reduced viscosity (ηr - 1/Φ) at constant LiCl concentration. Note that because of the presence of ions other than the added LiCl, this reduced viscosity does not equal the intrinsic viscosity at constant κ-1. For dispersions with particle volume fractions of 7.2 ((0.1) × 10-4, 1.07 ((0.05) × 10-3, and 1.43 ((0.05) × 10-3, the low-shear viscosities were measured as a function of the LiCl concentration. Figure 4 shows the dependence of the reduced viscosities on the LiCl concentration.
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Figure 5. Without preshearing, dilute boehmite dispersions (Φ e 0.143%) with LiCl concentrations higher than approximately 0.2 mM show time-dependent behavior at low shear rates ∼0.2 mM. This flocculation concentration is much lower than that expected from the interaction potential curves in Figure 2. Furthermore, after preshearing the sample, the apparent viscosity of the dispersion is reduced but is still higher than the viscosity of the solvent. It therefore seems likely that the orthokinetic flocculation only affects a fraction of the rods and that during the preshearing the flocs sediment. The flow curve measured after preshearing is then the flow curve of a dispersion with a slightly lower particle volume fraction, which explains the decrease of the apparent viscosity. Possibly the sensitivity to salt addition is due to a heterogeneous charge distribution on the colloids. Charge (31) Jones, G.; Dole, M. J. Am. Chem. Soc. 1929, 51, 2950. (32) Jones, G.; Talley, S. K. J. Am. Chem. Soc. 1933, 55, 4124. (33) Falkenhagen, H. Theorie der Elektrolyte; Hirzel, S., Ed.; Verlag: Stuttgart, 1971; p 256. (34) Thies-Weesie, D. M. E.; Philipse, A. P.; Na¨gele, G.; Mandl, B.; Klein, R. J. Colloid Interface Sci. 1995, 176, 43-54. (35) Fuoss, R. M. Discuss. Faraday Soc. 1951, 11, 125-134.
Charged Boehmite Rods
inhomogeneities on one rod can be related to surface irregularities of the polycrystalline boehmite. Furthermore, incomplete conversion of bayerite to boehmite during synthesis may lead to differences in the surface chemistry of several particles. It is conceivable that upon increasing the ionic strength of the dispersion, rods that contain a relatively large part of weakly charged “patches” will flocculate first. If the number of “unstable” rods is very small compared to the stable rods and the only collision mechanism is Brownian motion, the dispersion may remain stable over a period of weeks. However if the collision frequency is increased, for instance by applying a shear rate, the flocculation will become visible on much shorter time scales. This explanation is confirmed by the observation of some flocculation in a quiescent dispersion flocculation is also observed which only affected a small portion of the particles, even after 8 months. In that case the collision frequency is increased by sedimentation of some large flocs with respect to nonsedimenting singlets. Beattie et al.36 report an anomalous stability for boehmite with chloride salts up to concentrations of 0.1 M. They measured the stability over a period of at most 2 h, while the work described in this paper indicates that the flocculation of unsheared boehmite dispersions with low chloride concentrations takes place on time scales of months and, furthermore, that the visible aggregates make up only a very tiny fraction of the total boehmite concentration. However, we also found that instantaneous gelation2 takes place in our dispersions at LiCl concentrations as low as 0.04 M, still much lower than the values Beattie et al. reported. 6. Summary and Conclusions We measured the low-shear viscosity of dispersions (0.005% e Φ e 0.143%) of colloidal boehmite rods with 〈L〉 ) 173 nm and aspect ratio 〈r〉 ) 22.5 as a function of the added LiCl concentration (0-0.3 mM). The low-shear viscosity of charged boehmite rods (r ) 22.5) in water is much higher than for hard rods. The magnitude of the reduced viscosity strongly depends on the ionic strength of the dispersion. Addition of only a small amount of lithium chloride (0.025 mM) to the boehmite dispersions reduces the low-shear viscosity significantly, especially at high particle volume fractions. Using an estimate of the concentration of nonadded electrolyte, the low-shear viscosities can be interpreted in terms of the Debye length κ-1. The relation between the reduced viscosity and κ-1 strongly depends on the particle volume fraction Φ. The particle concentration can be rescaled on the minimum effective overlap concentration ν1* ) (L + 5κ-1)-3, which takes into account both the rod shape of the particles and the presence of the electric double layer. In terms of the effective overlap concentration ν/ν1* all measured viscosity curves fall onto one single master curve. The same dynamic scaling applies for low-shear viscosity data of FD-virus solutions as reported by Graf et al.24 The master curves of both ASP3 rods and FD-virus obey a Maron-Pierce28 equation, also valid for suspensions of non-Brownian fibers.26,27 The (ν/ν1*)max for ASP3 dispersions corresponds to the rod concentration at which the isotropic rods and their electric double layers form a self-sustaining gel, with a “packing fraction” which is severely reduced compared to hard rods because of the electric double layers. The effective overlap concentration at which η diverges is much higher for FD(36) Beattie, J., K.; Cleaver, J. K.; Waite, T. D. Colloids Surf., A 1996, 111, 131-138.
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Figure 9. Electric conductivity measurements of the supernatant of a ASP3 dispersion of Φ ) 0.172%.
virus than for boehmite due to the flexibility of the virus, which reduces the entanglement of the particle significantly. For ASP3, extrapolation of the reduced viscosity data to infinite dilution yields [η] ≈ 500-750, which corresponds to rods that are much longer than the used particles. In analogy with the viscosity of (poly-)electrolyte solutions31-33 and sedimentation of charged colloidal spheres at low ionic strength,34 it is well possible that for dilute colloidal dispersions at extremely low ionic strength, the relative viscosity shows a nonanalytical concentration dependence. This renders the definition of [η] questionable for colloids with thick double layers. Further research is needed to quantify the ηr-Φ relation for colloidal dispersions with very low particle and electrolyte concentrations. We observed orthokinetic flocculation in the dispersion with [LiCl] g 0.25 mM, while interaction energy calculations predict a stable boehmite dispersion for such low ionic strengths. Inspection of the flow curves and analysis of long-standing dispersions revealed that only a fraction of the rods was involved in this flocculation. Appendix: Estimate of the Ionic Strength in a Supernatant Following the Debye-Onsager law,10 the electric conductivity of a dilute solution with electrolyte concentration cs can be written as
K/cs ) Λ0 - (aΛ0 + b)xcs
(A.1)
where Λ0 is the average molar conductivity of the dissolved ions and a and b are parameters which depend on the ion valence. If the electrolyte composition is unknown, it is possible to determine the product csΛ0 by measuring the electric conductivity of a dilution series of the original solution. The electric conductivity of a diluted sample can be written in terms of the volume fraction of the original solution (Φs) in the diluted sample (with c ) Φscs)
K/Φs ) Λ0cs - (aΛ0 + b)xcsΦs
(A.2)
The product csΛ0 can thus be obtained from the intercept of a plot of K/Φsversus Φs1/2 as shown for the supernatant (with Φ ) 0.172%) of ASP3, in Figure 9. For the supernatant of ASP3, this procedure gave csΛ0 ) 34 × 10-4 S/m. It is possible to estimate the electrolyte concentration in the supernatant with an assumption about the character of ions present.
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For instance, if it is assumed that the main part of the conductivity is due to HCl (which is present during and after the synthesis of boehmite), the HCl concentration in the supernatant is 7.9 ((0.2) × 10-5 M. As the pH of the supernatant was 5.5, it is not likely that all electric conductivity is indeed caused by HCl ions. However if only monovalent ions with a lower mobility than H+ ions are present, e.g., with an average mobility u ) 7 × 10-8 V-1 m-2, the salt concentration in the supernatant of a 0.172% boehmite dispersions would be 2.5 ((0.1) × 10-4 M. According to Freier,23 the solubility of boehmite at 25 °C and pH ) 6.1 is 6 × 10-7 mol/L, a value that is not conflicted by our experiments. If it is assumed that the dissolved aluminum ions are mostly three-valent, the contribution of aluminum ions to the electric conductivity is negligible. As no more detailed information about the composition of ions in the boehmite dispersions is known, we assume
Wierenga and Philipse
that all ions in the dispersion are monovalent and not H+ or OH- ions. This approximation yields c ) 0.15Φ. It is likely that neither H+ nor OH- ions are present at all; hence this value overestimates the concentration of monovalent ions. Nonetheless, the presence of any ions with higher valencies than 1 will compensate for this effect. Acknowledgment. We thank Dr. J. K. G. Dhont and Dr. A. van Blaaderen for valuable discussions and comments and Dr. J. Sherwood (Schlumberger Cambridge Research) for his comments on the primary electroviscous effect. This work was supported by The Netherlands Organization for Chemical Research (SON) with financial aid from The Netherlands Organization for Scientific Research (NWO). LA9700477
