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Effect of Counterion Size on Short Range Repulsive Forces at High Ionic Strengths Miroslav Colic,* George V. Franks, Matthew L. Fisher, and Fred F. Lange Materials Department, University of California at Santa Barbara, Santa Barbara, California 93106 Received October 7, 1996. In Final Form: April 7, 1997X The influence of counterion size on short range repulsive forces at high salt concentrations was investigated with Al2O3 slurries at pH 12 coagulated with the chlorides of Li+, Na+, K+, Cs+, and TMA+ (tetramethylammonium)(1+). Measurements of viscosity, shear modulus, and yield stress of slurries, as well as the relative density and flow stress, of saturated, consolidated bodies were performed. The results clearly show that the range of the repulsive forces correlated with the size of the unhydrated ion; namely, stronger particle networks are achieved with smaller bare counterions. Our findings are contradictory to the widely accepted hydration force model, which attributes short range repulsive forces to the desorption of fully hydrated cations as surfaces are pushed together. However, the results are consistent with recently developed statistical mechanics models describing the interaction of ions of different sizes with surfaces and their hydration layers.
Introduction The effect of ions on the forces between particles in aqueous media is described by the classical DerjaguinLandau-Verwey-Overbeek (DLVO) theory.1,2 According to DLVO theory, the total interaction energy between two particles is obtained by summing the interaction energies due to the van der Waals attraction and the electrostatic double layer (EDL) repulsion. The surfaces of oxide particles in water have either a positive or negative surface charge due to the reaction of neutral surface sites with either H+ or OH-; the surface is neutral at a pH called the isoelectric point. Counterions (oppositely charged ions in solution) form a “cloud” around each particle to neutralize the surface. When two particles are forced together, their respective counterion clouds overlap, increasing the concentration of counterions between them and giving rise to an osmotic pressure, and thus a repulsive force. The separation distance at which particles become strongly repulsive depends on the thickness of the counterion cloud. The Debye length is a measure of the counterion cloud thickness and decreases with increasing electrolyte concentration. The counterion concentration is increased by adding salt to the aqueous slurry. At low salt concentrations the Debye length is sufficiently large such that the EDL repulsion exceeds the magnitude of the van der Waals attraction, causing particles to repel one another, producing dispersed slurries. DLVO theory predicts that when the salt exceeds a critical concentration, the Debye length is decreased, the double-layer repulsion is reduced and the van der Waals potential causes the particles to form a touching network. Surface forces between two bodies in close proximity are important in ceramic powder processing, adhesion, wetting, friction, biology, pharmaceutical chemistry, petroleum production, and many other important areas of science and technology.3 Significant improvement in understanding these forces can be attributed to direct observations with the surface force apparatus (SFA),4 and * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, May 15, 1997. (1) Derjaguin, B.; Landau, L. Acta Physiochim. URSS 1941, 14, 633. (2) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyphobic Colloids; Elsevier: Amsterdam, 1948. (3) Horn, R. G. J. Am. Ceram. Soc. 1990, 73, 1117. (4) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975.
S0743-7463(96)00965-1 CCC: $14.00
more recently the atomic force microscope (AFM).5 These instruments directly measure the force between two surfaces as a function of their separation distance at molecular levels. The effect of added salt on the surface forces between two mica plates immersed in water was studied by Israelachvili, Pashley, and co-workers using the SFA.6-8 They discovered an unanticipated, short range oscillatory force at high ionic strength in addition to the expected van der Waals and electrostatic double layer forces. This “third force” was named the hydration force because it was theorized to originate from the dehydration of cations at the mica surface, as the surfaces are pushed together.7 According to the concept developed by these investigators, smaller, more strongly hydrated ions would produce a larger short range repulsive force because of the greater energy required to dehydrate the smaller cations. Velamakanni and co-workers9 studied the effect of surface forces by measuring the rheology and particle packing density of alumina powders in aqueous suspensions. It was discovered that alumina slurries dispersed at low pH coagulated when salt was added and exhibited a 1 order of magnitude lower viscosity and significantly higher packing densities relative to slurries formulated at the isoelectric point (iep). Because the behavior of the slurry at low pH and high salt concentration was different than the flocculated slurry (at the iep), it was theorized that a new force9 was produced in the slurry with added salt. On the basis of the conclusions reached by Israelachvili6 and Pashley,7 Velamakanni et al.9 speculated that the short range repulsive potential might originate from the dehydration of counterions that crowd the particle surfaces at high ionic strength. Using the surface force apparatus (SFA), Ducker et al.10 confirmed the existence of a short range repulsive force between basal sapphire plates when excess salt was added (up to 0.1 M). It has been known for some time that there are limitations to the DLVO equations for calculating the EDL (5) Ducker, W. A.; Senden, T. J.; Pashley, R. N. Langmuir 1992, 8, 1831. (6) Israelachvili, J. N. Adv. Colloid Interface Sci. 1982, 16, 31. (7) Pashley, R. M. Adv. Colloid Interface Sci. 1982, 16, 57. (8) Israelachvili, J. N.; Pashley, R. M. Nature 1983, 306, 249. (9) Velamakanni, B. V.; Chang, J. C.; Lange, F. F.; Pearson, D. S. Langmuir 1990, 6, 1323. (10) Ducker, W. A.; Xu, Z.; Israelachvili, J. A.; Clarke, D. R. J. Am. Ceram. Soc. 1994, 77, 437.
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repulsion.11 Several reasons invalidate this continuum approach at small separation distances and high electrolyte concentrations. Traditional EDL equations are based on the assumption that ions are point charges, and specific ion-solvent interactions (e.g., hydration) are neglected. The Poisson Boltzmann equation can also be in error for high concentrations of electrolytes. Recent work addresses these issues. Yanez and Lange12 have argued that due to the finite size of the counterions, the Debye length cannot decrease to zero as suggested by classical DLVO equations. Recent elastic modulus and yield stress measurements of weakly attractive alumina slurries have suggested that the DLVO theory can explain the effect of added salt provided that the Debye length remains finite and the double layer collapses to approximately the size of the counterion. No additional interparticle force (such as a hydration force) was needed to explain the rheological data. Statistical mechanics models have recently been developed to describe the effect of finite ion size on the EDL repulsion13 and the structure of the solvent and counterions near the surface.14 Feller and McQuarrie13 have shown that at small separation distances the double layer repulsion is underestimated when the ions are assumed to be point charges. The calculations indicate that the additional repulsion is due to the finite size of the ions and might have been the origin of the non-DLVO forces observed in the SFA and attributed to hydration.6,7 Furthermore, this work13 shows that the range of the repulsion is proportional to the size of the counterion. That is, larger counterions produce short range repulsions of greater extent as compared to smaller counterions. Torrie et al.14 have shown that smaller ions tend to adsorb in higher concentrations at the surface than larger ions. In this way, small ions with a high affinity for water do not perturb the bulk water structure since the interfacial water is already highly ordered and polarized. Dumont and co-workers15 studied the influence of various ions on the critical coagulation concentration (ccc) of rutile (TiO2). At low volume fractions, both lyotropic sequences were observed for rutile depending on the isoelectric point. For rutile powders with low isoelectric points (pH < 4), cesium adsorbs more strongly than lithium. Consequently, the ccc is lower when cesium is added than when lithium is added to the dispersed suspension. For rutile powders with isoelectric points above pH 4 (similar to alumina), lithium was found to adsorb more strongly than cesium; correspondingly, a lower ccc was seen for lithium. It was proposed15 that structure-making ions preferentially adsorb on structuremaking surfaces and vice versa. Leong et al.16 reported the effects of specifically adsorbed anions (ions that change the isoelectric point of the particles) on the yield stress of zirconia slurries at or near the isoelectric point (iep). Their results indicate that the bare, specifically adsorbed anion produces a steric barrier equivalent to the size of the ion when the surface charge is neutralized (at the isoelectric point). Leckie and coworkers17 showed that specifically adsorbed selenate (11) Overbeek, J. Th. G. Adv. Colloid Interface Sci. 1982, 16, 17. (12) Yanez, J. A.; Lange, F. F. Submitted for publication to J. Am. Ceram. Soc. (13) Feller, S. E.; McQuarrie, D. A. J. Phys. Chem. 1993, 97, 12083. (14) Torrie, G. M.; Kusalik, P. G.; Patey, G. N. J. Chem. Phys. 1989, 91, 6367. (15) Dumont, F.; Warlus, J.; Watillon, A. J. Colloid Interface Sci. 1990, 138, 543. (16) Leong, Y. K.; Scales, P.; Healy, T. W.; Boger, D.; Buscall, R. J. Chem. Soc., Faraday Trans. 1993, 89, 2473. (17) Hayes, K. F.; Roe, A. L.; Brown, G. E., Jr.; Hodgson, K. O.; Leckie, J. O.; Parks, G. A. Science 1987, 238, 783.
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anions were directly bound to the surface while some hydration water was present between the surface sites and indifferent electrolyte ions such as selenite ions adsorbed on the surface. Recently, Israelachvili and Wennerstrom18 suggested that monotonic repulsive hydration forces may not exist. Several examples are cited in which no hydration force is needed to explain the short range repulsive force. In one such example,19 SFA measurements of mica in tetraalkylammonium bromide solutions exhibited non-DLVO short range repulsive forces. Modeling the system by displacing the plane of charge a distance of one counterion diameter from the surface of the mica (while the van der Waals attraction continued to act from the surface) produced a good fit to the experimental data. Although it was possible to push the surfaces into contact when large counterions were used, the “steric” effect of the ions was not explicitly discussed in the model. The interparticle pair potential is a convenient way to view the interaction of particles in suspension and describe certain properties of particle networks. Many of the properties of particle networks are controlled by the depth of the potential well in which the particles reside. The depth of the potential well is controlled by the van der Waals attraction and the extent of the short range repulsion. When the range of the repulsion is very short, the potential well will be deep, and when the range of the repulsion is greater, the potential well will be more shallow. For a given combination of powder and solvent, where the van der Waals potential does not change, the depth of the potential well is controlled by the properties of the counterion cloud, i.e. its density and thickness. When the extent of the counterion cloud is small (short Debye length), the interparticle potential well is located at a small equilibrium separation distance between the particles. In this case, the potential well will be deep and the particles are attracted to one another. When the range of the counterion cloud is greater than the extent of the van der Waals attraction (large Debye length), the particles are repulsive (dispersed). The relation between interparticle potential and the rheological behavior of slurries has received considerable attention.20 The viscosity, shear modulus, and apparent yield stress have been measured and related to21,22 the potential between particle pairs. These rheological results can be correlated to the strength of the particle network which is controlled by the interparticle pair potential as well as the volume fraction of particles within the liquid. Suspensions with repulsive interparticle potentials exhibit nearly shear rate independent (Newtonian) viscosities, while attractive particle networks exhibit shear thinning behavior (viscosity decreases with increasing shear rate). The viscosity of attractive particle networks, as well as the shear rate dependence, increases with the depth of the potential well. The force between the particles at any separation is the negative derivative of the potential with respect to distance. The force between particles is zero at the equilibrium separation distance, whereas the maximum force required to pull particles apart occurs at the inflection point beyond the equilibrium separation. The yield stress of the network is related to the force needed (18) Israelachvili, J. N.; Wennerstrom, H. Nature 1996, 379, 219. (19) Claesson, P.; Horn, R. G.; Pashley, R. M. J. Colloid Interface. Sci. 1984, 100, 250. (20) Bergstrom, L. Surface and Colloid Chemistry in Advanced Ceramic Processing; Surfactant Science Series Vol. 51; Marcel Dekker Inc.: New York, 1994. (21) Yanez, J. A.; Shikata, T.; Pearson, D. S.; Lange, F. F. J. Am. Ceram. Soc. 1996, 79, 2917. (22) Goodwin, J. W.; Hughes, R. W.; Partridge, S. J.; Zukoski, C. F. J. Chem. Phys. 1986, 85, 559.
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Table 1. Counterions Used in This Study as Soluble Chlorides (Taken from Ref 26) cation
bare radius (Å)
hydrated radius (Å)
Li+ Na+ K+ Cs+ TMA+
0.60 0.95 1.33 1.69 2.56-3.47
3.82 3.58 3.31 3.29 N/A
to pull particles apart. The second derivative of the potential versus distance relationship at the equilibrium separation is proportional to the spring constant between the particles, which is related to the modulus of the network. As expected, interparticle potentials with deeper secondary minima produce higher shear moduli, yield stresses, and viscosities. The consolidation behavior of slurries and the flow stress of the consolidated bodies are also a function of the interparticle pair potential.23-25 For a given powder, the packing densities of bodies consolidated from dispersed slurries are the highest and are relatively insensitive to the applied pressure. The densities of bodies consolidated from flocculated slurries (at the isoelectric point where only the attractive van der Waals forces exist) are low and strongly dependent on the applied pressure.24,25 For bodies consolidated from slurries possessing weakly attractive interparticle potentials (short range repulsive potentials), the packing density is intermediate to that of well dispersed and flocculated. Increasing the depth of the potential well results in slurries behaving more like flocculated networks, with lower and more pressure sensitive packing densities and higher flow stresses. Particles that form networks due to attractive interparticle potentials25 must rearrange to increase their packing density under an applied pressure. This process is believed to be correlated to the repulsive interparticle force and interparticle friction.9 Deep interparticle potential wells result in greater friction, making it more difficult for particles to rearrange and pack efficiently.23-25 In the current work, the authors use results from studies on concentrated, aqueous suspensions and saturated, consolidated bodies to determine the effect of high concentrations of different ions on the interparticle pair potential. As discussed below, all data suggest that the observed short range repulsion is due to counterions acting as a physical barrier to keep particles apart, where the size of the bare ion is the dominant feature that controls the extent of the repulsion at high ionic strength. The observed short range repulsions were of greatest extent for slurries containing large, poorly hydrated cations such as cesium and tetramethylammonium and of smallest extent with small, strongly hydrated cations such as lithium or sodium. It is believed this is influenced by the difference in the depth of penetration of various ions into the primary hydration layer of the surface. Therefore, it is the size of the bare ion, as well as its position relative to the surface, that controls the depth of the potential well. The cations used in this study and their sizes are listed in Table 1. Experimental Procedure Aqueous slurries of R-Al2O3 powder (Sumitomo Chemical Co., New York, AKP-50 Grade, d50 ) 0.25 µm) were prepared at pH 12 containing between 0.10 and 0.475 volume fraction of powder. (23) Bergstrom, L.; Schilling, C. H.; Aksay, I. A. J. Am. Chem. Soc. 1992, 75, 3305. (24) Franks, G. V.; Lange, F. F. J. Am. Chem. Soc. 1996, 79, 3161. (25) Lange, F. F. in Powders and Grains 93; Balkema Press: Amsterdam, 1993; p 187. (26) Conway, B. E. Ionic Hydration in Chemistry and Biophysics; Elsevier Science Publishing Co.: Amsterdam, New York, 1981.
Li, Na, K, Cs, and tetramethylammonium (TMA) chlorides (Sigma Chemical, St. Louis, MO, analytical grade) were added to the dispersed suspension to create a weakly attractive network. Flocculated slurries were also formulated by changing the pH to 9, the isoelectric point, to create a strongly attractive network. The pH was adjusted ((0.1 pH units) with analytic grades of either HNO3 or the corresponding metal hydroxide (LiOH to (TMA)OH). All slurries were mixed overnight on a roller to allow equilibration, and the pH was then readjusted if necessary. ζ potential measurements (ZetaMeter 3.0 electrophoretic mobility measurement system) of alumina suspensions (20 mg/L ) 5 × 10-6 volume fraction) were performed at ionic strengths between 0.001 and 0.1 M after equilibration at pH 4. Electrophoretic light scattering (Malvern ZetaSizer 3) and electroacoustophoretic (Matec Applied Sciences AcoustoSizer) measurements were performed at pH 12 with 0.5 M salt solutions. Viscosity measurements of 0.20 volume fraction slurries were made with a dynamic stress rheometer (Rheometrics DSR) using a couette type measuring cell (29.5 mm diameter, 44.0 mm long). Slurries were subjected to a high shear rate, which was decreased until the measured torque was below the sensitivity of the instrument (0.1 g cm). Shear modulus and yield stress measurements of 0.30 volume fraction were made using a vane tool (16.0 mm diameter, 31.0 mm long) in an oscillatory mode, as described elsewhere.27 Two sets of dynamic experiments were performed to determine the elastic (storage) modulus (G′) and apparent yield stress values for the attractive slurries. In the first experiment, an oscillatory strain of increasing amplitude was applied at a fixed frequency (stress sweep), and in the second an oscillatory strain of increasing frequency was applied at constant stress (frequency sweep). The stress sweep experiments were used to determine the range of stress, at a fixed frequency, where the response of the slurry was elastic, i.e. when the phase angle, δ, between stress and strain is small, and invariant. With the stress fixed within the elastic region, the frequency sweep experiments were used to determine the storage modulus of the network. At high frequencies, G′ was invariant over a large range of frequencies; this plateau value of G′ was taken as the shear modulus of the network. The phase shift (δ) between stress and strain in a stress sweep was used to determine the apparent yield stress of the network.28 The apparent yield stress was defined as the point of upswing in the tan(δ) curve (concurrently, as tan(δ) increases, G′ decreases from its relatively constant value) when the stress/strain response becomes nonlinear. The shear modulus (G′) and yield stress were measured at volume fractions ranging from 0.10 to 0.30 for slurries containing 0.5 M LiCl and from 0.20 to 0.475 for slurries containing 0.5 M CsCl. Consolidated bodies (2.5 cm diameter, 1.5 cm height) were formed from the 0.20 volume fraction slurries at pressures between 2.5 and 100 MPa using a pressure filtration device described elswhere.24 The filtration pressure was maintained until an apparent equilibrium packing density was reached, which was recognized when the movement of the die plunger ceased. The relative density of the consolidated bodies was determined using the weight difference method. Weight measurements of saturated, dried, and pyrolized bodies as well as the densities of water, salt, and the powder were used to calculate the volume fraction of the components. Load-displacement measurements were performed on the saturated, consolidated bodies using a servo-hydraulic mechanical test frame (MTS Model 850, Minneapolis, MN). The saturated, cylindrical specimens, contained within a plastic bag, were deformed in uniaxial compression using the displacement control mode of the testing machine. Each experiment consisted of applying a compressive strain of 0.20 at a loading rate of 1 mm/min, while the load was recorded. The specimen was then unloaded and reloaded to an additional strain of 0.10 to measure the flow stress of the plastic bodies.
Results The isoelectric point of the alumina powder used in the investigation is pH 9.0 ( 0.1, and at pH 12 the ζ potential is -35 ( 2 mV (with 0.01 M KCl), which is consistent with (27) Fisher, M. L.; Lange, F. F. Manuscript in preparation. (28) Yoshimura, A. S.; Prud’homme, R. K. Rheol. Acta 1987, 26, 428.
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Figure 1. Viscosity versus strain rate for alumina slurries (0.20 volume fraction solids) formulated at pH 9 (the iep) without salt and with the addition of 0.5 M of various chlorides, as labeled.
the data previously reported.29 The isoelectric point did not change for salt concentrations up to 0.1 M, indicating that the counterions were not specifically adsorbing. ζ potentials of suspensions formulated with different counterions at pH 12 were somewhat different. The ζ potential of alumina suspensions formulated at pH 12 with 0.01 M lithium chloride was -29 mV, with sodium chloride was -29 mV, with cesium chloride was -35 mV, and with TMA chloride was -37 mV. Electrophoretic light scattering and electroacoustophoretic measurements at 0.5 M of different salts showed zero ζ potential with lithium and sodium, -2 mV with potassium -5 mV with cesium, and -6 mV with TMA chloride. The viscosities of pH 12 slurries prepared with LiOH and NaOH, without added salt, containing 0.20 volume fraction of alumina powder were slightly shear thinning, indicative of an attractive particle network. These observations strongly suggest that the amount of counterions introduced by adjusting the pH of the slurries to 12 and producing the surface charge was sufficient to produce a weakly attractive particle network. For dispersed suspensions prepared with the hydroxides of the larger cations, the viscosities were Newtonian, indicating that the amount of counterions produced was less than that required to coagulate the slurry. The flocculated slurries (formulated at the isoelectric point, pH 9) had the highest viscosities at all shear rates. Figure 1 shows that the viscosities of 0.20 volume fraction slurries formulated at the isoelectric point with 0.5 M additions of different salts. The viscosities of slurries (pH 12, 0.20 volume fraction of powder) formulated with 0.5 M of the different salts are shown in Figure 2. The results show that at any given shear rate, the viscosity decreased as the counterion was changed from Li+ to TMA+. It is clear that the viscosity decreased with increasing size of the bare ion (see Table 1). Figure 3 shows the effect of the different counterions on the storage modulus of alumina slurries (0.30 volume fraction) prepared at pH 12 with 0.5 M salt. It is evident that the elastic modulus is relatively independent of frequency of the range shown. The slurry formulated at the isoelectric point (pH 9) had the highest modulus, whereas the modulus of the weaker, coagulated networks decreased with increasing bare ion size (Table 1). Table 2 shows the yield stress of the same slurries. The flocculated slurry has the highest yield stress, while the (29) Velamakanni, B. V.; Lange, F. F. J. Am. Ceram. Soc. 1991, 74, 166.
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Figure 2. Viscosity versus strain rate for alumina slurries (0.20 volume fraction solids) formulated at pH 12 with 0.5 M chlorides (as labeled) compared to the flocculated slurry formulated at the iep (pH 9) with no added salt.
Figure 3. Shear moduli of 0.30 volume fraction alumina slurries at pH 12.0 with 0.5 M of various chlorides compared to the flocculated slurry at the iep (pH 9). Table 2. Apparent Yield Stresses of 0.30 Volume Fraction Alumina Slurries Flocculated at pH 9 and Coagulated at pH 12 with Various Chlorides
slurry
yield stress (Pa)
slurry
yield stress (Pa)
flocculated (pH 9) pH 12, 0.5 M LiCl pH 12, 0.5 M NaCl
495 320 180
pH 12, 0.5 M KCl pH 12, 0.5 M CsCl pH 12, 0.5 M (TMA)Cl
100 30 4
yield stresses of the slurries coagulated with the different chlorides decreased with increasing size of the bare ion. Figure 4 shows that the shear modulus and yield stress were found to vary as power law functions of the volume fraction (exponent ) 4.5 ( 0.20 for the shear modulus and 3.1 ( 0.10 for the yield stress) for slurries formulated at pH 12 and containing 0.5 M LiCl. For slurries formulated at pH 12 and containing 0.5 M CsCl, the exponents were 3.7 ( 0.25 (elastic modulus) and 3.2 ( 0.15 (yield stress). At least three experiments were run for each test condition. The effect of applied pressure on the relative density of alumina bodies consolidated by pressure filtration from coagulated slurries (0.20 volume fraction, pH 12, 0.5 M different chlorides) is shown in Figure 5. The lowest packing density and strongest pressure dependence were observed for bodies consolidated from slurries coagulated with LiCl. Bodies consolidated from slurries coagulated with CsCl and (TMA)Cl exhibit the highest relative densities.
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Figure 6. Flow stresses of bodies consolidated from slurries at pH 12 coagulated with 0.5 M of the chlorides (as labeled). The bodies were consolidated at 10 MPa and have relative densities as in Figure 5. The bodies were compressed to a strain of 0.2 to ensure all particles are in the secondary minimum24 prior to obtaining the data shown above.
for bodies consolidated from slurries coagulated with LiCl, whereas the lowest flow stress was observed for bodies consolidated from slurries coagulated with CsCl and (TMA)Cl (flow stress too low to be seen on the plot). Discussion
Figure 4. Volume fraction dependence of the (a) shear modulus and (b) yield stress for slurries containing 0.5 M LiCl and 0.5 M CsCl at pH 12. The shear modulus and yield stress were found to vary as power law functions of the volume fraction (exponent ) 4.5 ( 0.20 for the shear modulus and 3.1 ( 0.10 for the yield stress) for slurries containing LiCl. For slurries containing CsCl, the exponents were 3.7 ( 0.25 (elastic modulus) and 3.2 ( 0.15 (yield stress).
Figure 5. Relative density versus applied filtration pressure for alumina compacts consolidated from coagulated slurries (0.20 volume fraction, pH 12, different chlorides) compared to the flocculated slurry at pH 9.
Consolidated bodies tested in uniaxial compression typically exhibited a high peak stress on initial loading, followed by a lower flow stress; the reasons for this are reported elsewhere.24 Upon reloading, no peak stress was observed and the specimen deformed at the flow stress. As shown in Figure 6, the highest flow stress was observed
The collective results overwhelmingly show that the strength of the attractive particle networks follow the sequence from strongest to weakest as flocculated (at iep) then coagulated with Li+, Na+, K+, Cs+, and TMA+. Relative to the sequence of counterions, these results indicate that the Li+ counterions produce the deepest potential well, whereas the counterions Cs+ and TMA+ produce more shallow potential wells. In addition, with the assumption that the van der Waals potential is identical for all slurry formulations, the depth of the potential well must correlate to the extent of the short range repulsion. Deeper potential wells are produced by short range repulsions of lesser extent, while shallower potential wells are produced by repulsions of greater extent. Therefore, the extent of the repulsion is the least for Li+-coagulated slurries and becomes greater as the bare ion size is increased to TMA+. Thus the equilibrium separation distance appears to be correlated to the size of the bare ions. Since the smallest cation (Li+) is the most highly hydrated, it is clear the physical barrier of the condensed counterion clouds creates the short range repulsion and not the water of hydration, as was previously suggested by Pashley7 and Israelachvili et al.6 The results presented here are the opposite of what would be observed if the short range repulsion were due to hydration forces. Thus, the current results are not consistent with the hypotheses of Pashley7 and Israelachvili et al.,6 which attribute the difference in short range repulsion created by various ions to the differences in the binding energy of the water molecules hydrating the ions. That is, the higher the binding energy, the more difficult it is to dehydrate the counterions and “squeeze” the water molecules away as particles are pushed together. If this hypothesis held true, the strongest network would be formed with the weakly hydrated Cs+ ions and the weakest network produced with the strongly hydrated Li+ counterions. In fact the results presented here are opposite to those predicted by the hydration force theory. Instead, it appears the present results are consistent with recently developed statistical mechanics models.13,14
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Figure 7. Schematic representation of the structure of oxide/ water interface at pH 12 with various counterions adsorbed to the surface. Small counterions with greater affinity for water penetrate deeper into the surface hydration layer than large ions.
According to the model of Torrie et al.,14 smaller counterions perturb the structure of bulk water more efficiently. The layer of structured water molecules at the particle surface is more favorable for the accommodation of small ions that prefer to be surrounded by organized water. Thus, it is possible for smaller counterions to become partially embedded “inside” the layer of structured water at the particle surface. In this way, ions embedded within the hydration layer may not additionally influence the structure of water in the bulk. However, for larger ions, penetration becomes less likely because the ions do not favor the highly structured water environment near the interface, such that they tend to lie farther from the surface. Figure 7 is a schematic representation of the proposed structure of the oxide/water interface for the various cations at high concentrations. This schematic suggests that the counterion cloud simply acts as a physical barrier to keep particles separated, thus allowing particles to reside in potential wells determined by the thickness of the barrier layer and the van der Waals attraction. Thus, the current authors concur with the Torrie et al. result and propose that the short range repulsive potential observed in the current work is caused by the reduction of the electrical double layer to a thickness that is proportional to the size of the unhydrated counterion. The results presented here also follow the same trend as previously reported for the influence of the point of zero charge on the adsorption sequence of various ions.15 Small ions which promote structuring of water (structuremakers) would be expected to adsorb closer to the surface of a high isoelectric point material such as alumina than larger structure-breaker ions. Because of their greater affinity for the surface, the small ions such as lithium and sodium adsorb in higher concentrations and thus produce counterion clouds of smaller extent. The previous results by Dumont and co-workers15 suggest that at low ionic concentration and volume fractions the adsorption sequence is influenced by the iep. However, our preliminary unpublished results with different powders including silica (with low iep), zirconia, rutile, and mullite, and silicon nitride show that at high volume fraction and high ionic strength the lyotropic sequence is identical to that reported here for alumina. More work on the microscopic mechanism of indifferent electrolyte adsorption at the solid/ liquid interface should be performed to further resolve this apparent paradox. It is important to recognize that the results presented here and those of Leong and co-workers16 show the same trend regarding the effects of bare ion size on surface forces
Colic et al.
in concentrated suspensions; that is, larger ions produce longer range repulsions than smaller ions. Leong and co-workers studied specifically adsorbed ions, which according to the surface ionization and complexation model,17 are adsorbed inside the inner Helmholtz layer, without hydration water. On the other hand, indifferent electrolytes are expected to adsorb in the fully hydrated form according to both the surface ionization and complexation17 and the hydration force models.4 Our results do not support these models. ζ potential measurements indicated the absence of specific adsorption in our measurements. In addition, other surface charge and adsorption studies30,31 also report no specific adsorption of alkali metal cations at the alumina/water interface. In the present study (see Figure 1), as well as in a previous study,21 the addition of salt did not significantly influence the viscosity or other rheological properties of the system at the isoelectric point (pH 9) of alumina. The viscosity of slurries formulated with 0.5 M lithium chloride at the isoelectric point was somewhat higher than that of alumina at the isoelectric point with no added salt. Possible causes of this effect will be discussed later in this section. It is clear that a charged surface and counterions are required to produce the short range repulsion observed. It is expected that the rheological properties of the system depend on both the strength of the interparticle bonds and the structure of the network. The dependence of the shear modulus and yield stress on the volume fraction is a measure of the network structure.32,33 The modulus and yield stress were measured at different volume fractions for slurries containing LiCl and CsCl. The power law behavior for the modulus and yield stress versus volume fraction was similar for both LiCl and CsCl and in agreement with theoretical34 and experimental21,32,33,35,36 results on colloidal networks, suggesting that both networks have similar structures. As detailed elsewhere,37 sedimentation velocity was measured at different volume fractions using the method of Hunter and Ekwadi38 and it was found that the transformation from the fast to the slow sedimentation regime occurs at approximately 2.5 vol % for all cations studied. This result indicates that a space-filling network is formed at the same volume fraction for all salts investigated and suggests that the structure of the network is similar for all of the counterions studied here. The current study suggests the minimum thickness of the counterion cloud to be proportional to the size of the bare (unhydrated) counterion, but the results do not define the minimum thickness itself. The minimum equilibrium separation distance between identical particles is thus undefined but known to depend on the bare counterion size. Surface force apparatus measurements on molecularly smooth surfaces of mica8 and alumina10 have shown that the force versus separation function contains large oscillations, which were attributed to the sequential removal of layers of water as the surfaces are brought into contact. We propose that these oscillations at high ionic strength (>0.1 M) may be caused by the sequential (30) Sprycha, R. J. Colloid Interface. Sci. 1989, 127, 12. (31) Jafferzic-Renault, N.; Karisa, N.; Trang, D. R. J. Radioanal. Chem. 1982, 72, 515. (32) Chen, M.; Russel, W. B. J. Colloid Interface. Sci. 1991, 141, 564. (33) Shih, W.; Shih, W. Y.; Kim, S.; Liu, J.; Aksay, I. A. Phys. Rev. A 1990, 42, 4772. (34) Feng, S.; Sen, P. Phys. Rev. Lett. 1984, 52, 216. (35) Potanin, A. A.; DeRooij, R.; Van den Ende, D.; Mellema, J. J. Chem. Phys. 1995, 102, 5845. (36) Sonntag, R. C.; Russell, W. B. J. Colloid Interface Sci. 1987, 116, 485. (37) Colic, M.; et al. To be submitted for publication to Science. (38) Hunter, R. J.; Ekwadi, N. Colloids Surf. 1986, 18, 325.
Counterion Size Effect on Repulsive Forces
removal of layers of either dehydrated or partially hydrated counterions as the surfaces are pushed together. In fact, the experiments of Ducker et al.10 show that the periodicities of the oscillations near the alumina/water interface did not correspond with the size of a water molecule but to the size of the partially hydrated counterions used in the study. As mentioned earlier, it was observed that the viscosity of slurries formulated at the isoelectric point of alumina (pH 9) with 0.5 M lithium chloride was somewhat higher than that of slurries prepared at the iep with no salt or the addition of the other cations studied. At the iep and higher ionic strength, namely 4 M of lithium, sodium, potassium, and cesium chlorides, all cations studied increased the viscosity as compared to that of the slurry formulated at the iep without added salt. The viscosity of the lithium chloride containing slurries was always the highest and that of the cesium chloride containing slurries the lowest. Similar behavior was also observed with silica and zirconia slurries. It is possible that the indifferent electrolyte ions are adsorbing at the iep to some extent. Alternatively, the observed behavior may be due to cation penetration inside the hydration layer of alumina or the removal of hydration water from the alumina surface. Since the viscosity is increasing with the addition of high amounts of salt, the removal of some water molecules from the hydration layer of the alumina particles seems a more plausible explanation. Spectroscopic measurements are currently underway in order to shed more light on this unexpected behavior. Specific ion adsorption cannot explain the observed behavior. It is well-known that at silica at low volume fraction, cesium adsorbs stronger than lithium,39 yet we observed the same lyotropic sequence in our rheological measurements with silica and (39) Allen, L. H.; Matijevic, E. J. Colloid Interface Sci. 1969, 31, 287.
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alumina at different pH values, including the iep. Chapel40 also observed the same trend with surface force apparatus measurements on silica; namely, short range repulsions with the shortest extent were observed with lithium as the counterion, and with the longest extent with cesium as the counterion. Miller and and co-workers41 also observed the same trend with direct force measurements between alumina and silica at 4 M of different salts. Conclusions Experimental results on alumina slurries coagulated at high ionic strengths clearly show that Li+ counterions produce an interparticle pair potential with the deepest potential well and thus the strongest particle network. Larger counterions, such as Cs+ or TMA+, produce shallow potential wells and short range repulsions that extend farther from the surface of particles. All evidence suggests that the size of the bare, adsorbed ion as well as the depth to which the ion penetrates into the surface hydration layer are responsible for the minimum thickness of the collapsed double layer and the resulting short range repulsion. This concept is contradictory to the widely accepted hydration force theory6,7 but consistent with statistical mechanics models13,14 that describe the interaction of counterions with surfaces at high ionic strength. Acknowledgment. The authors would like to acknowledge the Office of Naval Research for supporting this work under contract No. N00014-92-J-1808. We would also like to thank J. N. Israelachvili, R. M. Pashley, L. Bergstrom, J. A. Yanez, P. Scales, and G. Sposito for useful discussions. LA960965P (40) Chapel, J. P. Langmuir 1994, 10, 4237. (41) Miller, J. D.; et al. Colloids Surf., in press.
