Heteroflocculation of Particle Mixtures by a Coacervation Mechanism

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Heteroflocculation of Particle Mixtures by a Coacervation Mechanism. A Rheological Study Pierre Starck and Brian Vincent* School of Chemistry, UniVersity of Bristol, Bristol BS8 1TS, United Kingdom ReceiVed February 1, 2006. In Final Form: March 21, 2006 In most of the classical studies of heteroflocculation two sets of oppositely charged particles are mixed. In this current study, a somewhat different mechanism of heteroflocculation is described. Two sets of concentrated dispersions of polyacrylate latex particles (having the same surface-charge sign) have been mixed, where the surface of one set had been functionalized with methacrylic acid (MAAc) groups and the second set with poly(ethylene oxide) (PEO) chains. The resultant heteroflocculation has been investigated as a function of the number fraction (F) of MAAcfunctionalized particles, the size ratio (R) of the two sets of particles (R ) dMMAc/dPEO), the background electrolyte concentration (0-0.2 M KCl), the pH (3 or 9), and the order of mixing of the particles. The relative extent and strength of flocculation were assessed using two basic rheological techniques: (i) the plastic viscosity (ηpl) and the Bingham yield stress (σB) were determined from steady-state shear experiments, (ii) the modulus (G) and the viscosity (η) (both at a given applied stress) and the actual yield stress (σY) were determined from creep-recovery experiments. Heteroflocculation was observed at a pH value of 3, where the carboxylic groups at the surface of the MAAcfunctionalized particles remain largely undissociated. However, no flocculation was observed at pH 9, where the COOH groups dissociate to become COO-. The aggregation mechanism is, therefore, believed to be due to hydrogenbonding between the hydrogens of the carboxylic acid groups and the ether oxygens present on the surface of the PEO-functionalized particles. To this extent, this mechanism of heteroflocculation resembles the coacervation of mixtures of solutions of two H-bonding polymers, for which aqueous mixtures of PMAAc and PEO (at low pH) are a well-known example. Because both sets of particles carried negative surface charge groups, arising from the polymerization initiator used in their preparation, a minimum concentration of added electrolyte (KCl) was needed before any heteroflocculation between the two sets of particles was observed. However, this minimum KCl concentration for the onset of heteroflocculation was significantly lower than the concentration of KCl required to induce homoflocculation of either set of latex particles separately. At an R value of 1.3, all the rheological parameters passed through a maximum value at F ) 0.5, whereas when R was 6.2 the maximum occurred at a value of F ) 0.018 or F ) 0.025, depending on the order of mixing.

Introduction Heteroflocculation in mixtures of particulate dispersions has been widely studied. The topic has been reviewed by Islam et al.1 In general, the dispersions studied have contained oppositely charged particles. Napper2 was probably the first person to suggest the possibility of heteroflocculation between two types of sterically-stabilized particles. He considered in some detail the necessary thermodynamic conditions for selective homoflocculation and selective heteroflocculation in such mixtures, and suggested, to observe selective heteroflocculation, using mixtures of particles carrying poly(acrylic acid) (PAAc) and others carrying poly(ethylene oxide) (PEO) chains. As far as we are aware, there have been no detailed experiments to investigate this suggestion. We address this anomaly in this paper. Previous studies from this group3,4 have been concerned with the addition of PAAc chains to dilute, aqueous dispersions of polystyrene latex particles, carrying terminally anchored PEO chains. In that work we showed, using turbidity measurements, that, at low pH values, the added polymer chains led to bridging flocculation of the particles, at low added polymer concentrations. The acrylic acid groups were in the undissociated form, and hydrogen bonds were formed between the -COOH groups and (1) Islam, A. M.; Chowdhry, B. Z.; Snowden, M. J. AdV. Colloid Interface Sci. 1995, 62, 109. (2) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983; p 314. (3) Cawdery, N.; Milling, A.; Vincent, B. Colloids Surf. 1994, 86, 239. (4) Cawdery, N.; Vincent, B. In Colloidal Polymer Particles; Goodwin, J. W., Buscall, R., Eds.; Academic Press: London, 1995; p 245.

the ether oxygen atoms of the PEO chains on the particles, leading to adsorption of the PAAc chains onto the particles. At high pH values, no such H-bonding is possible, because of dissociation of the carboxylic acid groups, so the PAAC chains cannot adsorb onto the particles. Under those conditions depletion flocculation of the particles was observed at higher PAAC concentrations. Liang et al.5 subsequently carried out rheological experiments on essentially similar systems. Therefore, the work presented in this paper is in many ways a direct extension of those earlier studies. Experimental Section Materials. Water was “MilliQ” grade. Potassium chloride (KCl), sodium hydroxide (NaOH), hydrochloric acid (HCl), methyl methacrylate (MMA), butylacrylate (BA), methacrylic acid (MAAc), ammonium persulfate (APS), tert-butyl hydroperoxide (TBHP), sodium metabisulfite (SMBS), and Nonylphenol 20 (NP20) were all obtained from Aldrich (U.K.) at 99% or better purity. Atpol E1234 was kindly supplied by ICI Paints plc, U.K. Preparation and Characterization of the Latex Dispersions. All the latex dispersions were prepared, under a nitrogen atmosphere and with continuous stirring, using a standard emulsion polymerization apparatus, equipped with a temperature control facility.6,7 pH adjustments were made using 0.1 M solutions of HCl or NaOH, as necessary. After preparation, all the latices were cleaned by (5) Liang, W.; Bognolo, G.; Tadros, Th. F. Langmuir 1994, 10, 441. (6) Blackley, D. C. Polymer Latices: Fundamental Principles; Chapman and Hall: London, 1997. (7) Van Herk, A. M.; Gilbert, R. In Chemistry and Technology of Emulsion Polymerisation; Van Herk, A. M., Ed.; Blackwell: Oxford, 2005; p 46.

10.1021/la060314l CCC: $33.50 © 2006 American Chemical Society Published on Web 05/09/2006

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Table 1. Composition and Properties of the Individual Latices type of [MMa]/ [BA]/ [MAAc]/ % solids d(pH 3)/ code surface wt % wt % wt % stock nm A B C D

MMAc PEO MMAc PEO

69 41 43 41

21 59 27 59

10 30

30 50 30 40

Tg/ °C

380 ( 20 60 290 ( 15 -10 430 ( 20 60 69 ( 5 -10

exhaustive dialysis against numerous changes of water. The wt % particle concentration in each of the final stock latex dispersions was estimated by drying a known weight of dispersion in an oven. The average hydrodynamic diameters (d) of the particles were determined using dynamic light scattering (Brookhaven Instruments Zeta Plus apparatus). The glass transition temperatures (Tg) of the particles were kindly determined at ICI Paints Division (Slough) using thermal gravimetric analysis (TGA). Two sets of particles were prepared. (1) MAAc-Functionalized Particles (A and C).8Mixtures of three monomers (MMA + BA + MAAc) were polymerized in water at 80 °C, using APS as the initiator. An anionic surfactant (Atpol E1234) was present to help maintain particle stability during the polymerization. Details of the monomer compositions are given in Table 1. From evidence described previously8 it would seem that particles of this type have cores comprised essentially of the hydrophobic monomer(s), while the surfaces are enriched with the more hydrophilic monomer. Hence, these particles would have a shell surrounding their (MMA + BA) cores, which is rich in COOH groups arising both from the MAAc moeities and the surfactant (Atpol E1231) headgroups. (2) PEO-Functionalized Particles (B and D).9Mixtures of two monomers (MMA + BA) were polymerized in water at 60 °C, using a TBHP plus SMBS mixture as a redox initiator system. A nonionic surfactant (NP20) was present as a stabilizer. The core of these particles is composed of MMA and BA, as for the MAAcfunctionalized particles. The particles are thought to have a shell of PEO chains from the NP20 surfactant incorporated in the synthesis. However, electrophoretic mobility measurements10 indicated that the particles also had a negative surface charge, presumably arising from initiator fragments present at their surface. Preparation of Samples for Rheological Measurements. In all the cases the single or mixed dispersions were allowed to stand for at least 24 h, at room temperature, after the particle concentration, the pH, and the electrolyte concentration were adjusted, before any rheological measurement was made, to ensure that the extent of any flocculation had been maximized. As well as the rheological properties of the four individual latices, those of two sets of mixtures (A + B and C + D) were studied. Two parameters may be defined for the mixtures, the particle size ratio (R) and the particle number fraction (F), as follows: R ) dMMAc/dPEO

(1)

F ) NMMAc/(NMMAc + NPEO)

(2)

where dPMMAc and dPEO are the hydrodynamic diameters and NMMAc and NPEO are the number concentrations of the MMAc-functionalized latex particles and the PEO-functionalized latex particles, respectively. In all the experiments, unless otherwise stated, the total particle concentration (i.e., NMMAc + NPEO) was always kept fixed. Rheological Measurements. Shear Stress-Shear Rate Measurements. A Bohlin CVO constant-stress rheometer, thermostated at 25 ( 1 °C and incorporating the bob and cup (C14) geometry, was used for these measurements. All the samples were presheared, at a fixed stress (σ ) 5 Pa) for 60 s, and then left to equilibrate for 300 s. During an experiment the applied stress was increased from an initial (8) Lee, C. F.; Young, T. H.; Huang, Y. H.; Chiu, W. Y. Polymer 2000, 41, 8565. (9) Bromley, C. W. A. Colloids Surf. 1986, 17, 1. (10) Starck, P. Ph.D. Thesis, University of Bristol, 2005.

low value (σ ) 0.075 Pa) to a value of the stress corresponding to a shear rate (γ˘ ) approaching 600 s-1. The total time of each experiment was ∼120 s. A Bingham model,12,13 developed for shear-thinning systems, such as weakly aggregated, concentrated dispersions, was used to analyze the σ versus γ˘ data, where σ ) σB + ηplγ˘

(3)

The Bingham yield stress (σB) was obtained by extrapolation of the linear portion of the σ versus γ˘ plot to γ˘ ) 0; the plastic viscosity (ηpl) was obtained from the slope of this linear portion of the curve.14,15 Creep-RecoVery Measurements. A Bohlin CS50 rheometer, incorporating the parallel plate (PP20) geometry, was used for these measurements, in particular, for those mixtures which appeared to be more strongly aggregated, as it offered manual gap-setting. In a creep-recovery experiment,13,15 a constant stress is applied to the sample for a certain time (t1) and the change in strain (the creep) is monitored. In general, in this work t1 ) 20 s. Creep data are generally described in terms of the creep compliance function: J(t) ) γ/σ

(4)

Here, γ is the measured strain or relative deformation and σ is the constant stress applied to the sample during the creep time. When the stress is then released, some recovery may be observed as the system attempts to return to its original state. The recovery time (t2) was, in general, set at 40 s. For each system, a series of such creeprecovery experiments was carried out, starting at a chosen low σ value and then gradually increasing the value of σ applied during t1 until the yield stress (σY) was surpassed. The determination of various rheological parameters from a creeprecovery experiment12 is best described by reference to some actual experimental data. Figure 1 shows the effect of increasing stress on the creep-recovery behavior for a typical, concentrated mixture of two of the functionalized latex particles which have flocculated. For σ values up to 550 Pa the J(t) plots show very similar behavior. During the period t1, while the constant stress is applied (i.e., for the first 20 s), the rate of increase of J decreases with time. This is typical for a system showing viscoelastic behavior, such as flocculated dispersions. Information about the elastic and steady-shear viscous components, at a given applied stress value, can be obtained from analyzing the linear portion of the J(t) plot: the modulus (G0) of the dispersion is the value of 1/J obtained by extrapolating J(t) to t ) 0, and the viscosity (η0) is given by the reciprocal of the slope of J(t) in the linear region. For σ ) 550 Pa, the following values are obtained: G0 ) 104 Pa and η0 ) 2.3 × 105 Pa s. Again, for σ values up to 550 Pa, the J(t) plots show very similar behavior during period t2, when the stress is removed. The systems more-or-less recover to their original (flocculated) state, although this is not quite achieved before the experiment is stopped in the case of σ ) 550 Pa. For σ ) 600 Pa a dramatic, fundamental change takes place. The system now only shows viscous behavior, indicating that the flocs have been broken down. This occurs after an initial period while the structure is breaking (note the difference in the ordinate scale between the two diagrams). After this time J increases linearly, and η is 1.5 Pa s, i.e., orders of magnitude lower than for the (flocculated) systems at the slightly lower σ value of 550 Pa. Moreover, once the stress is removed the compliance remains constant, indicating no recovery, which is what one would expect for a system showing a purely viscous response. Thus, the yield stress for this system lies between 550 and 600 Pa. Since, for the purposes of this paper, we are only interested in semiquantitative comparisons, the value for σY would be quoted as 600 Pa. (11) Liang, W.; Bognolo, G.; Tadros, Th. F. Langmuir 1995,11, 2899. (12) Pal, R. Colloid Polym. Sci. 1999, 277, 583. (13) Goodwin, J. W.; Hughes, R. W. Rheology for Chemists; Royal Society of Chemistry: London, 1999. (14) Luckham, P. F.; Vincent, B. Colloids Surf. 1982, 6, 101. (15) Gabriel, C.; Kaschta, J. Rheol. Acta 1998, 37, 358.

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Figure 1. Example of a creep-recovery experiment and yield stress determination for a mixture between latex C and latex D. F ) 0.04 at [KCl] ) 0.1 M and pH 3.

Results and Discussion Properties of Individual Latices. Some physical properties of the four latex systems are shown Table 1. The Tg values of the MMAc-functionalized latex particles suggest that these particles have a “hard” core, while those for the PEOfunctionalized latex particles indicate a “soft” core. There is evidence for this from scanning electron micrograph pictures (not shown here) of the PEO-functionalized latex particles on drying, which show that they film-form.10 The diameter (d) values for the four latices are the values determined at pH 3, the pH value at which most of the significant rheological experiments were carried out. The MMAc-functionalized latex particles do show evidence of swelling when the pH is raised to 9, as the carboxylic acid rich shell then forms a polyelectrolyte layer. A fuller description of the variations in the particle diameter and the electrophoretic mobility of these particles, as function of pH (including reversible “sweeps” of pH), is given elsewhere.10 At a KCl concentration of 0.2 M and pH 3, all the individual latex systems (A-D) showed very similar rheological behavior, as illustrated for latex A in Figure 2. The creep-recovery results (Figure 2A) indicate that, during the period up to 20 s, while a very small stress (0.013 Pa) is applied, the dispersion shows a steadily decreasing, but relatively small viscosity value (given by the reciprocal slope), reaching a limiting steady shear value of 0.023 Pa s at this applied stress. This is indicative of some slight shear-thinning, possibly due to a very small amount of weak flocculation. This conclusion is supported by the continuous shear data shown in Figure 2B. The Bingham yield stress (σB)

Starck and Vincent

Figure 2. Creep recovery (A) at σ ) 0.013 Pa and continuous shear (B) experiments for latex A. [KCl] ) 0.2 M and pH is 3.

for this latex is 3.2 Pa, and the plastic viscosity (ηpl) is 5 × 10-3 Pa s. These are very small values, indicating again that any flocculation is very slight. It would seem that the addition of 0.2 M KCl to the individual latex dispersions causes only very small (barely detectable) levels of weak homoflocculation, so that any substantial flocculation found in the mixed dispersions, at KCl concentrations up to 0.2 M, must be largely due to heteroflocculation. Mixtures of Latex A and Latex B. For this mixture R ) 1.3. The value of F was varied between 0.1 and 0.9. Figure 3 shows the creep-recovery curves for pH 3 and for a KCl concentration of 5 × 10-3 M. The plots are all very similar to that shown in Figure 2A for the individual, stable latex A particles, implying that very little, if any flocculation, has occurred in the mixture. Although there is no systematic trend in the plots with F, the η values are all very low and in the range 3 × 10-3 to 10-2 Pa s. No recovery after removal of the stress is observed. A somewhat different picture emerges when the KCl concentration is increased to 0.08 M (at pH 3). The results for the F ) 0.5 system are shown in Figures 4 and 5, for the creeprecovery and continuous shear experiments, respectively. Now one is definitely detecting some, albeit weak, flocculation, with clear evidence of a (very low) yield stress (σY ≈ 0.75 Pa, Figure 4) and a slightly higher, as expected, Bingham yield stress (σB ≈ 1.7 Pa, Figure 5). The steady-state viscosity is ∼200 Pa s at σ ) 0.013 Pa (Figure 4), while the plastic viscosity is ∼0.08 Pa s (Figure 5). Since one would not expect to see any homoflocculation at 0.08 M KCl, one must be observing heteroflocculation. The values of σB and σY are plotted as a function of F in Figure

Heteroflocculation of Particle Mixtures

Figure 3. The compliance as a function of time for mixtures of latex A and latex B, for different F values, as indicated. σ ) 0.013 Pa, [KCl] ) 0.005 M, and pH is 3. F ) 0.1 to F ) 0.9.

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Figure 5. Continuous shear experiment for a mixture of latex A and latex B. F ) 0.5 at [KCl] ) 0.08 M and pH 3. The continuous line is a theoretical fit (eq 3).

Figure 6. Yield stress (0) and Bingham yield stress (O) values for mixtures of latex A and latex B. [KCl] ) 0.08 M and pH is 3.

Figure 4. Creep-recovery experiment for mixtures of latex A and latex B at different σ values. F ) 0.5, [KCl] ) 0.08 M, and pH is 3.

Figure 7. Zero shear viscosity (O) and shear modulus (b) as a function of F for mixtures of latex A and latex B. σ ) 0.1 Pa, [KCl] ) 0.08 M, and pH is 3.

6. Similar plots for G0 and η0, derived from the creep-recovery experiments, are shown in Figure 7. All these rheological parameters pass through a maximum value at F ≈ 0.5. This condition is to be expected for mixtures of particles of about the same size, as here, and has commonly been found for mixtures of equally sized, but oppositely charged particles.1 An even more dramatic effect is observed when the KCl concentration is increased to 0.15 M (at pH 3). Very strong flocculation is now evident. Since, as has been demonstrated

earlier, only very weak homoflocculation occurs at a KCl concentration of 0.2 M, this must be essentially heteroflocculation. Because of the strong nature of the flocculation, only creeprecovery experiments are now possible. The results are shown in Figure 8 for F ) 0.6. The yield stress has now increased to ∼350 Pa, compared to ∼0.2 Pa for 0.08 M KCl (Figure 6). Plots of G0 and η0, derived from the creep-recovery experiments, are shown as a function of F in Figure 9. The maximum for both parameters at F ) 0.5 is again apparent.

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Figure 8. Creep-recovery experiment for mixtures of latex A and latex B at various σ values. F ) 0.6, [KCl] ) 0.15 M, and pH is 3.

Figure 9. Zero shear viscosity (O) and shear modulus (b) as a function of the number fraction. σ ) 200 Pa, [KCl] ) 0.15 M, and pH is 3.

Figure 10. Yield stress as a function of F, for three different electrolyte concentrations, as indicated. pH is 3.

The values of σY, as a function of F, for the three KCl concentrations studied (at pH 3), are summarized in Figure 10. The explanation of why the heteroflocculation increases so strongly between 0.005 and 0.15 M KCl can be interpreted, at least semiquantitatively, in terms of the Debye thickness (κ-1) of the particle electrical double layers at these KCl concentrations: κ-1 decreases from about 4.4 nm at 0.005 M KCl to about 0.8 nm at 0.15 M KCl. For H-bonding to occur between an MAAc-functionalized particle and a PEO-functionalized particle (at pH 3) the two particles have to approach so that they are

Starck and Vincent

Figure 11. Yield stress as a function of F for mixtures of latex A and latex B, for pH 3 (O) and pH 9 (0). [KCl] ) 0.15 M.

effectively “touching”. Because both types of particle are charged (even at pH 3),10 there is a mutual electrostatic repulsion keeping them separated. The effective range of this repulsion is ∼2/κ, so that at 0.005 M KCl this distance is ∼9 nm, preventing close contact. However, at 0.15 M KCl this has been reduced to ∼1.5 nm, so that intimate interparticle contact may now occur readily. An interesting feature of Figure 10 is why no heteroflocculation is apparently observed for F < 0.25 and F > 0.75. The explanation has to do with the fact that, upon mixing at these extreme values of F, the particles present at low concentration very quickly become surrounded by a single sheath of the other particles, present in abundance, so any further aggregation is prevented. Another way of testing the H-bonding hypothesis underpinning the heteroflocculation mechanism would be to investigate the effect of pH on the extent of heteroflocculation. At high pH there should be no H-bonding (the pKA of -COOH groups is ∼4.8).16 In Figure 11σY values are shown as a function of F, for mixtures of latices A and B, at a KCl concentration of 0.15 M, for two pH values: 3 and 9. At pH 9 the extent of heteroflocculation is clearly negligible (σY is only ∼0.25 Pa at F ) 0.5). Mixtures of Latex C + Latex D. For this mixture R ) 6.2. The value of F was again varied, but in addition, in this case, the order of mixing of the two latex dispersions and the total particle concentration were also considered. Figure 12 shows σY, as a function of F (log scale), at pH 3, for two KCl concentrations, 0.01 and 0.1 M, in which the smaller latex particles (D) are added to the larger ones (C). No flocculation is apparent at 0.01 M KCl, but very strong heteroflocculation occurs at 0.1 M KCl. The explanation of this strong electrolyte concentration effect is essentially the same as that proposed for mixtures of latices A and B, discussed above, namely, the closer approach of the particles which can occur at the higher KCl concentration, allowing heteroflocculation to take place, at pH 3. Figure 13 shows the corresponding plots of G0 and η0, for a KCl concentration of 0.1 M at pH 3, as a function of F (linear scale), also derived from the creep-recovery experiments. The main difference between the mixtures of latices C and D, compared to mixtures of latices A and B, has to do with the value of F where the rheological parameters are maximum. This is now at F ) 0.025 (rather than at F ) 0.5). This corresponds to ∼40 small particles to every large particle. Essentially, one can think of the small particles “bridging” the large particles, and building up a three-dimensional network of bridged large particles. If each large particle were to be surrounded by a hexagonally close(16) Ayward, G. H.; Findlay, T. J. V. S.I. Chemical Data; John Wiley: Australia, 1974; p 90.

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Figure 12. Yield stress as a function of F for mixtures of latex C and latex D at different [KCl] values as indicated. pH is 3, and latex D is added to latex C. Figure 14. Yield stress as a function of F for mixtures of latex C and latex D, for different total particle concentrations and orders of mixing. [KCl] ) 0.1 M.

Figure 13. Zero shear viscosity (O) and shear modulus (b) as a function of F for mixtures of latex C and latex D. σ ) 1000Pa, [KCl] ) 0.1 M, pH is 3, and latex D is added to latex C.

packed layer of small particles, this would require 140 of the small particles for each large one. Returning to Figure 12, it is instructive to investigate the N values where the ratio of small to large particles is 1 and where it is 140, as these might be considered to be the limiting range of values where any flocculation could possibly occur. The former occurs at N ) 0.5 and the latter at N ) 0.007. At both these values the value of σY is reduced effectively to zero, implying that indeed no flocculation has occurred outside this range of N values. The magnitude of the maximum value of σY for mixtures of latices C and D (2200 Pa; see Figure 12) is larger than for mixtures of latices A and B (750 Pa; see Figure 10), at pH 3 and high KCl concentrations. This is partly due to the fact that, at the same total particle concentration, there are more contacts to be broken in the mixture of latices C and D, but also that latex C has a higher MAAc content (30 wt %) compared to latex A (10 wt %); see Table 1. This could mean that the hydrophilic shell around the C particles is more dilated (even at pH 3) than that around the A particles, allowing greater contact with the PEO chains from the PEO-functionalized D latex particles. Figure 14 shows the effect of changing the order of mixing of latices C and D, and increasing the total particle concentration, on σY versus F (log scale), at a KCl concentration of 0.1 M and pH 3. The effect of increasing the total particle concentration (by ∼50%) is to increase the maximum value of σY (by ∼20%); this trend is as expected, simply because more H-bonds have to be broken if more particles are present in a given volume of the

Figure 15. Zero shear viscosity (O) and shear modulus (b) for mixtures of latex C and latex D. σ ) 500 Pa, [KCl] ) 0.1 M, pH is 3, and latex C is added to latex D.

mixture. The effect of the order of mixing is more intriguing: if the large particles are added to the small ones, the maximum value of σY decreases, compared to the other way around (Figure 14). Before attempting an explanation, it is useful to see where the maximum in the rheological parameters occurs. This is more obvious from the plots of G0 and η0, as a function of F (linear scale), at a KCl concentration of 0.1 M and at pH 3, shown in Figure 15. The maximum occurs at F ) 0.18. This corresponds to ∼55 small particles for every large particle. It would seem that, on adding the large particles to the small ones, each large particle, on average, becomes surrounded by a greater number of smaller particles, than the other way around. This makes sense on purely statistical grounds, given that the mixing is nonuniform initially. Because there are more small particles per large particle, presumably the network buildup is not as efficient as when the small particles are added to the large ones, so the various rheological parameters are smaller in magnitude (σY, Figure 14; G0 and η0, compare Figures 13 and 15).

Conclusions The rheological experiments reported here have shown that heteroflocculation occurs between MMAc-functionalized particles and PEO-functionalized particles, through H-bonding between the -COOH moeities of the former and the ether oxygens

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of the latter. Such H-bonding only occurs at low pH values. There is a strong effect of electrolyte concentration, as a minimum electrolyte concentration is required to sufficiently reduce the mutual electrostatic repulsion between the two sets of negatively charged particles, so that they may come into close contact. There are also strong effects of the particle size ratio (R), particle number fraction, and order of mixing (when R is very different from 1). Heteroflocculation does not take place at high pH values, when the H-bonding can no longer occur. In some experiments (reported elsewhere10) it has been shown that increasing temperature also leads to weaker heteroflocculation, as H-bonding breaks down. In ref 10 some other, related experiments are reported, including (i) optical and scanning electron microscope studies of some of the heteroflocculated mixtures discussed in

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this paper and (ii) depletion flocculation studies of mixtures of latex B plus latex D, where the particles are of the same type, but differ in size ratio (R ) 4.2). Acknowledgment. We thank ICI for the provision of an ICI Science Research Fellowship to fund P.S. to carry out these experiments as part of his Ph.D. program. We also thank various ICI Paints Division personnel (in particular Dr. Simon Emmett and Dr. Steve Downing) for guidance with the preparation of the latex dispersions and for many other helpful discussions. Special thanks are also due to Dr. Cheryl Flynn, of the Bristol Colloid Centre, for her guidance in carrying out the rheology experiments and for helping to interpret the data. LA060314L