Flocculation Mechanism Induced by Cationic Polymers Investigated

Monodisperse spherical silica particles were obtained from Nissan Chemical ...... Geoffrey S. Simate , Sunny E. Iyuke , Sehliselo Ndlovu , Mike Heyden...
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Langmuir 2006, 22, 6775-6786

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Flocculation Mechanism Induced by Cationic Polymers Investigated by Light Scattering Ying Zhou and George V. Franks*,† Chemical Engineering and the Centre for Multiphase Process, The UniVersity of Newcastle, Callaghan, NSW 2308 Australia ReceiVed January 29, 2006. In Final Form: April 23, 2006 Three cationic polymers with molecular weights and charge densities of 3.0 × 105 g/mol and 10%, 1.1 × 105 g/mol and 40%, and 1.2 × 105 g/mol and 100% were chosen as flocculants to aggregate silica particles (90 nm), under various conditions, including change in polymer dosage, particle concentration, background electrolyte concentration, and shear rate. The size and structure of flocs produced were determined using the static light scattering technique. On the basis of measurements of polymer adsorption and its effect on the zeta potential and floc properties, it has been found that the polymer charge density plays an important role in determining the flocculation mechanism. Polymers with a 10% charge density facilitate bridging, 40% charged polymers bring about either a combination of charge neutralization and bridging or bridging, depending on the polymer dosage, and polymers with the charge density of 100% induce electrostatic patch flocculation mechanism at the optimum polymer dosage and below but bring about bridging mechanism at the polymer dosage approaching the adsorption plateau value. Bridging aggregation can readily be affected by the particle concentration, and an increase in particle concentration results in the formation of larger but looser aggregates, whereas electrostatic patch aggregation is independent of particle concentration. The addition of a background electrolyte aids in bridging aggregation while it is detrimental to electrostatic patch aggregation. It has also been found that the effect of shear rate on the mass fractal dimension depends on polymer charge density.

1. Introduction Polyelectrolyte flocculants can significantly enhance solidliquid separation processes and are increasingly being used in a wide range of industries, such as minerals recovery, industrial tailings dewatering, paper manufacturing, and water and wastewater treatment. When polyelectrolytes are added to oppositely charged particles, electrostatic attraction is believed to be the main driving force for adsorption and the postulated mechanisms by which polyelectrolytes can bring about flocculation are bridging, charge neutralization, or electrostatic patch models.1 Bridging flocculation occurs when segments of the same polymer molecule are attached to more than one particle, thereby linking the particles together. This type of flocculation mechanism has been found to be very efficient. Charge neutralization is caused by the reduction in the electric double layer repulsion between particles due to adsorption of highly charged polyelectrolytes on oppositely charged particles. It is generally believed that low molecular weight polymers tend to adsorb and neutralize the opposite charges on the particles. The electrostatic patch flocculation is thought to be operative for polymers of very high charge density interacting with oppositely charged particles of low charge density. The net residual charge of the polymer patch on one particle surface can attach to the bare part of an oppositely charged particle. Several studies on polymer flocculation have been published in the literature,2-6 the choice of polymer in any particular case * Corresponding author. E-mail: [email protected]. † Current address: Department of Chemical and Biomolecular Engineering, The University of Melbourne, VIC 3010 Australia. (1) Gregory, J., Flocculation by Polymers and Polyelectrolyte. In Solid/liquid dispersions; Tadros, T. F., Ed.; Academic Press: London, 1987. (2) Gregory, J. J. Colloid Interface Sci. 1973, 42, 448-56. (3) Yan, Y. D.; Glover, S. M.; Jameson, G. J.; Biggs, S. Int. J. Miner. Process. 2004, 73, 161-75. (4) Thomas, D. N.; Judd, S. J.; Fawcett, N. Water Res. 1999, 33, 1579-92. (5) Gregory, J. J. Colloid Interface Sci. 1976, 55, 35-44. (6) Mabire, F.; Audebert, R.; Quivoron, C. J. Colloid Interface Sci. 1984, 97, 120-36.

still has to be made on a largely empirical basis, which is primarily due to two reasons. One is that, flocculation is a very complicated process involving the following stages:7 (a) particle-polymer mixing, (b) attachment of the polymer molecules onto the particle surface, (c) reconformation of the polymer molecules on the particle surface, (d) particle flocculation, and (e) floc breakup due to shear mixing. These processes can take place concurrently and are often competing. Therefore, to understand the flocculation mechanisms, it is crucial to gain fundamental knowledge of the key parameters which can significantly influence the time scale of a particular stage. Polymer molecular weight,6,8,9 charge density,6,8,10 dimensions in solution,11 polymer concentration,8,12,13 background electrolyte concentration,8,14 and particle concentration13-16 are among some of these parameters. The other reason might be that usually indirect methods, such as turbidity, sedimentation rate, or visual observation, are applied to monitor the flocculation progress. In this way, only some overall parameters are measured and no information is obtained on floc properties, especially the floc structure. This was despite the fact that knowledge of floc properties can lead to better understanding and control of many industrial separation processes. It is wellknown that different industrial applications require aggregates (or flocs) of different properties.17,18 For example, in filtration (7) Elimelech, M. Particle Deposition and Aggregation: Measurement, Modelling, and Simulation; Butterworth-Heinemann: Oxford, 1995. (8) Graham, N. J. D. Colloids Surf. 1981, 3, 61-77. (9) Gill, R. I. S.; Herrington, T. M. Colloids Surf. 1987, 25, 297-310. (10) Gill, R. I. S.; Herrington, T. M. Colloids Surf. 1987, 28, 41-52. (11) Mpofu, P.; Addai-Mensah, J.; Ralston, J. J. Colloid Interface Sci. 2004, 271, 145-156. (12) Bratskaya, S.; Schwarz, S.; Liebert, T.; Heinze, T. Colloids Surf. A 2005, 254, 75-80. (13) Pelssers, E. G. M.; Stuart, M. A. C.; Fleer, G. J. Colloids Surf. 1989, 38, 15-25. (14) Wagberg, L.; Inger, A. Colloids Surf. A 1995, 104, 169-84. (15) Pelssers, E. G. M.; Cohen Stuart, M. A.; Fleer, G. J. J. Chem. Soc., Faraday Trans. 1990, 86, 1355-61. (16) Gregory, J. Colloids Surf. 1988, 31, 231-53. (17) Moudgil, B. M.; Behl, S. Flotation Sci. Eng. 1995, 415-39. (18) Gregory, J. Filtr. Sep. 1998, 35, 367-71.

10.1021/la060281+ CCC: $33.50 © 2006 American Chemical Society Published on Web 07/08/2006

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processes, strong but porous flocs are often preferred. The aggregate size and its size distribution are clearly important, because it will determine whether the flocs are suitable for a particular separation process such as filtration or sedimentation. The advent of fractal mathematics in the mid 1970s led to significant advancement in our understanding of the complex structure of particle aggregates.19,20 It is now known that aggregates formed from random aggregation processes, in dilute suspensions, possess mass fractal characteristics.7,19-23 This means that the structure of the aggregates is self-similar at different length scales or scale invariance. For a mass fractal aggregate, its mass, M(R), is proportional to its radius, R, raised to power Df

M(R) ∝ RDf

(1)

Table 1. Charge Densities and Molecular Weights of Three Cationic Polymers Used in This Study polymer

charge density %

molecular weight g/mol

D6010 D6040 D6099

10 40 100

3.0 × 105 1.1 × 105 1.2 × 105

Table 2. Hydrodynamic Diameters of Three Cationic Polymers at Different Concentrations of NaCl hydrodynamic diameter, nm polymer

0.01 M NaCl

0.03 M NaCl

0.06 M NaCl

0.1 M NaCl

D6010 D6040 D6099

66 55 68

63 53 65

59 50 62

55 n.a.a n.a.

a

where Df stands for the mass fractal dimension and is not limited to integer values. Df can further be used to characterize the mass density of the aggregate, F(R), i.e.

F(R) ∝ RDf-3

(2)

Therefore, the mass fractal dimension is a powerful measure of the structural compactness or the space filling capacity of an aggregate. In three-dimensional Euclidean spaces, Df ranges from 1 to 3. An entirely compacted object such as a solid sphere has a Df of 3, whereas aggregates with an open configuration of particles are characterized by smaller fractal dimensions. Static light scattering has been extensively used in the measurement of the size of particles and aggregates as well as in the study of aggregating and aggregated colloidal systems.24,25 However, it is surprising that this technique has not, to our knowledge, yet been widely applied to flocs induced by polyelectrolytes. In a static light scattering experiment, a beam of light is directed onto a sample and the scattered light intensity is measured as a function of the magnitude of the scattering vector, Q. For a mass fractal aggregate consisting of monodisperse primary particles and satisfying the criteria of the RayleighGans-Debye regime, there is the following relationship between the scattered intensity from the aggregate, I(Q), and the scattering wave vector, Q.24,25

I(Q) ∝ Q-Df

(3)

where

Q)

πn sin(θ/2) λ

(4)

and n is the refractive index of the fluid, λ, the wavelength in vacuo of the laser light used, and θ, the scattering angle. Since 1/Q is the length scale probed in a scattering experiment, the low and high regions of Q reveal the overall structure of the aggregates and the structure of the primary particles, respectively. The Q-Df dependence with the scattered intensity is valid in a range of (19) Mandelbrot, B. B. The Fractal Geometry of Nature; W. H. Freeman: New York, 1983. (20) Stanley, H. E.; Ostrowsky, N. On Growth and Form: Fractal and NonFractal Patterns in Physics; M. Nijhoff: Dordrecht, The Netherlands, 1986. (21) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. ReV. Lett. 1985, 54, 1416-19. (22) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360-2. (23) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Phys. ReV. A 1990, 41, 2005-20. (24) Schaefer, D. W.; Martin, J. E.; Wiltzius, P.; Cannell, D. S. Phys. ReV. Lett. 1984, 52, 2371-4. (25) Bushell, G. C.; Yan, Y. D.; Woodfield, D.; Raper, J.; Amal, R. AdV. Colloid Interface Sci. 2002, 95, 1-50.

n.a. ) not available.

length scales much larger than the primary particles and much smaller than aggregates.22

1 1 ,Q, R r0

(5)

where r0 is the radius of the primary particle and R stands for the aggregate radius. The measure of fractal dimension can be estimated from the absolute slope of log I(Q) versus log Q by fitting a straight line through the fractal regime section of the scattering plot. In this study, we used three cationic polymers with various charge densities as flocculants to aggregate model silica particles (90 nm) and investigated the effect of aggregation conditions, including polymer dosage, particle concentration, background electrolyte concentration, and shear rate, on the flocculation mechanism. Silica particles of 90 nm were chosen because they tend to form relatively small flocs whose size and structure are suitable for characterization by the static light scattering technique. The aim of the current research is to gain an improved understanding of the relationship between polymer characteristics, aggregation conditions, and flocculation mechanism as well as the aggregate characteristics such as size and structure. 2. Experimental Section 2.1. Materials. Monodisperse spherical silica particles were obtained from Nissan Chemical America Corporation, with a BET surface area of 30 m2 g-1, a mean particle diameter of 90 nm, and a density of 2.2 g cm-3. The silica was supplied as aqueous suspension with a concentration of 40.5% w/w and a pH of 10. Prior to use, pH was adjusted to 5.5 at which the silica is negatively charged. Two cationic copolymers of acrylamide/diallyldimethylammonium, chloride (D6010 and D6040) and one cationic homopolymer of diallyldimethylammonium, chloride (D6099) were received as gift from SNF Floerger. The molecular weights of these polymers in 0.01 M NaCl solution were determined by static light scattering at pH 5.5 and 25 °C on Zetasizer Nano ZS (Malvern Instruments, U.K.) and are listed in Table 1. The hydrodynamic diameters of these polymers at different NaCl concentrations were measured by dynamic light scattering at pH 5.5 and 25 °C on Zetasizer Nano ZS and are presented in Table 2. The supplied liquid solutions of polymers were diluted using gentle stirring for 1 h to produce solutions of 0.1% w/w polymer concentration which were then adjusted to pH 5.5, the same as that of silica suspensions. Reagents used to adjust the pH of the suspensions and solutions were analytic grade HCl and NaOH. The background electrolyte used throughout this work was NaCl. Distilled water was used in all experiments. 2.2. Minithickener and Aggregation Conditions. Figure 1 is a drawing of the minithickener fabricated for the production of aggregates. A 35 L PVC column was flange connected with a large

Flocculation Mechanism Induced by Cationic Polymers

Langmuir, Vol. 22, No. 16, 2006 6777 flowed through the cell in the course of sizing measurement. This setup can prevent aggregates from producing networks and at the same time bring about negligible shear and disruption to their size and structure. 2.4. Zeta Potential Measurement. The zeta potential measurements were performed with a Colloidal Dynamics, Acoustosizer (Warwick, RI). A concentration of 2 vol % solids were chosen for this investigation as it is within the range of the volume fractions which (1) are high enough to produce a signal from the particles that is large relative to the signal from the polyelectrolyte and electrolyte ions and (2) are low enough so that the particle-particle interaction does not significantly affect the signal. The measurements were carried out on agitated suspensions at 22 ( 0.1 °C and pH 5.5. The conductivity, temperature, and pH of the slurry were continuously monitored in situ using probes attached to the instrument. 2.5. Polymer Adsorption Experiments. A 100 mL aliquot of the supernatant above the settled flocs was removed from the minithickener 1 h after flocculation and then centrifuged at 3500 rpm for 25 min to remove any residual particles. The residual polymer concentration was determined by total organic carbon analysis for the supernatant obtained by centrifugation. The TOC analysis was carried out using TOC-5000 (Total organic carbon analyzer, Shimadzu). It should be pointed out that adsorption experiments were just performed over the polymer dosage at which flocculation occurs in this study.

3. Results and Discussion

Figure 1. Drawing of the mini-thickener fabricated for the production of aggregates (not to scale). Perspex funnel with another flange attached to the bottom. A removable, clear Perspex cup was fastened with screws and a gasket onto the bottom of this flange. Four steel baffles were inserted along the inner diameter of the cylindrical section. The baffles extended 3 cm into the vessel. Mixing within the mini-thickener was achieved with a Shelton mixer having a 15 cm diameter 6 bladed Rushton impeller in the cylindrical section, and a 7.5 cm diameter 6 bladed Rushton impeller in the conical section on the same shaft. All flocculation experiments were conducted at 25°C. A volume of 25 L suspension of silica particles was flocculated at pH 5.5 in all flocculation experiments. The silica particles were allowed to flocculate for 90 s after addition of polymer and were stirred continuously at the same shear rate during this time. Unless stated otherwise, the silica particle concentration used was 0.16% w/w and the mixing speed was kept at 142 rpm for all flocculation experiments undertaken. 2.3. Characterization of Aggregate Size and Structure. Small angle static light scattering was employed to study the size and structure of the silica particle aggregates. The instrument used was a Mastersizer S (Malvern Instruments, U.K.), which has a 633 nm He-Ne laser as the light source. The Mastersizer simultaneously measures scattered intensities at a range of scattering angles from 0 to 46ο. It also provides a direct measure of the average size distribution of the material in the scattering cell using full Mie theory. It should be noted that most aggregates induced by polymers throughout this work can grow very rapidly and form networks in 3-5 min. To minimize the effect of these aggregate networks, samples were taken from the bulk suspensions in a 250 mL beaker immediately after mixing was completed. It took about 3 min to carry the samples to the room with the light scattering instrument where they were subsequently diluted 20 to 1 in a 2 L beaker with dispersion medium at the same pH and salt concentration as in the minithickener to produce optimum obscuration. The samples were then gravity fed into the light scattering cell from the connected 2 L beaker and

3.1. Effect of Polymer Dosage on the Aggregate Size and Structure. Preliminary experiments suggested that 10% charged polymers are not able to flocculate 90 nm silica particles even at polymer doses as high as 50 mg/g silica. This is presumably due to the fact that the segments of the low charged polymer layer that protrude from the particle surface, even before flattening, cannot overcome the distance of closest approach between two silica particles. This distance is, at an estimated 1-1 electrolyte concentration, about 10-5 M, well above 200 nm, since under this condition the reciprocal double layer thickness is about 100 nm. The effective thickness of the electric double layer reduces to 1.8 nm at 0.03 M NaCl. The polymer hydrodynamic diameter listed in Table 2 is 63 nm, much larger than ∼ 2κ-1 (3.6 nm). Therefore, 0.03 M NaCl was added to decrease the electric double layer distance when 10% charged polymers were used as flocculants. The optimum polymer dosages in terms of the best supernatant clarity for 10% at the background salt concentration of 0.03 M NaCl, 40% and 100% charged polymers were visually determined to be 12, 12 and 2 mg/g silica, respectively. Figure 2 presents the volume average aggregate diameter (D [4, 3]) and size distribution with polymer dosage for 10%, 40%, and 100% charged polymers used as flocculants, respectively. It can be seen from Figure 2a,b that the average aggregate size (diameter, D [4, 3]) increases with the increase in polymer dosage for the 10% and 40% charged polymers. At the optimum dosages, the average aggregate size is 49 and 36 microns for 10% and 40% charged polymers, respectively. Figure 2c indicates that, in the case of 100% charged polymers, the typical aggregate diameter (D [4, 3]) attains the maximum value, 20 microns, at its optimum dosage, below and above which the average aggregate size decreases. It is worth noting that there should be some uncertainty in the absolute aggregate size information obtained from the Mastersizer due to the fact that the commercial data analysis program used treats any scattering object as a solid sphere rather than a porous object such as an aggregate. However, we are confident that our observed trend in the average aggregate size as a function of the polymer dosage is reliable. Figure 3 shows log I(Q) versus log Q with polymer dosage for 10%, 40% and 100% charged polymers used as flocculants,

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Figure 2. Typical floc size distribution and volume average (D [4, 3]) floc sizes of silica flocculated with (a) 10% charged polymers at [NaCl] ) 0.03 M, (b) 40% charged polymers, and (c) 100% charge polymers, respectively, at various polymer dosages.

respectively. For the purpose of clarity, the scattering curves of all scattering figures in this paper are shifted vertically with respect to one another. As shown in Figure 3a, for the aggregates induced by 10% charged polymers, the mass fractal dimension is 2.4 at the polymer dosages of 4 and 12 mg/g silica while 2.5 at the dosages of 6 and 8 mg/g silica. In the case of aggregates induced by 40% charged polymers, as shown in Figure 3b, the slopes reveal a mass fractal dimension of 2.6 at all polymer dosages applied. When aggregates are induced by 100% charged polymers (see Figure 3c), the mass fractal dimension is 2.6 at the highest polymer dosage, 12 mg/g silica, and 2.7 at the other three polymer dosages. The most noticeable distinction observed from Figures 2 and 3 is that, at the optimum dosage, aggregates produced by 10% charged polymer possess large average sizes and relatively low mass fractal dimensions, whereas aggregates induced by 100% charged polymer attain small average sizes and high mass fractal

Zhou and Franks

Figure 3. Typical scattering patterns of silica flocculated with (a) 10% charged polymers at [NaCl] ) 0.03 M, (b) 40% charged polymers, and (c) 100% charge polymers, respectively, at various polymer dosages.

dimensions. This seems to indicate that the two polymers induce flocculation by different mechanisms and the difference in flocculation mechanism is responsible for the difference in the size and mass fractal dimension of flocs observed. If the same flocculation mechanism resulted for each polymer at its optimum dosage, the average size and mass fractal dimension of flocs should be very similar. To better understand the flocculation mechanism operating for each charged polymer, it is essential to study the zeta potential and polymer adsorption of the flocculated particles as a function of polymer dosage. The zeta potential of silica particles with polymer dosages is shown in Figure 4. The magnitude of the negative zeta potential slightly decreases with increasing the dosage of 10% charged polymers (D 6010) at the background salt concentration of 0.03 M NaCl over lower polymer dosages, whereas over high polymer dosages, the negative zeta potential nearly levels off with changes in the polymer dosage. The zeta potential does not reach the isoelectric point even at the polymer dosage much higher than the optimum dosage of 12 mg/g silica. The charge of 10% charged polymer under 0.03 M NaCl, to

Flocculation Mechanism Induced by Cationic Polymers

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Figure 4. Electrokinetic zeta potential of silica particles as function of the polymer dosages.

Figure 5. Adsorbed amounts of three cationic polymers on silica particles as a fuction of the polymer dosage.

some extent, should be screened by salt ions. So the reduction in zeta potential by the 10% charged polymers is not simply due to charge neutralization but also the adsorption of a layer of polymer chains at the silica particle surface causes the shear plane to shift farther from the surface of the particle, reducing the measured zeta potential.26 In fact, Mpofu et al. 27 found that the adsorption of nonionic poly(ethylene oxide) (PEO) polymer gives rise to the reduction in the magnitude of the zeta potential when they investigated the zeta potential of kaolinite dispersions as a function of PEO dosage. The zeta potential varied from negative to positive values with increasing dosages of 40% charged polymers (D6040) and 100% charged polymers (D6099). The zeta potential value is more positive for silica particles flocculated by 100% charged polymers than by 40% charged polymers at the same polymer dosage. The isoelectric point is attained at 4.5 mg/g silica for 100% charged polymers and at 8.2 mg/g silica for 40% charged polymers. This is in agreement with the larger cationic charge density of 100% charged polymers. The adsorbed amounts of 10% charged polymers (D6010) at the background salt concentration of 0.03 M NaCl, 40% charged polymers (D6040) and 100% charged polymers (D6099) onto the silica particles are shown in Figure 5. The adsorbed amount increases with increasing equilibrium concentrations of polymers for three charged polymers. It can be seen that for 100% charged polymers the adsorbed amount nearly reaches the maximum plateau value at the equilibrium concentration of 6.7 mg dm-3, which corresponds to the polymer dosage of 12 mg/g silica, whereas for 40% and 10% charged polymers, the adsorbed amounts are far from approaching the maximum plateau values at equilibrium concentrations of 4.9 and 4.0 mg dm-3, corresponding to the optimum polymer dosages of 12 and 12 mg/g silica. The Langmuir adsorption isotherm model 28 is applied to analyze the adsorption of the three charged polymers onto silica and is given by

Figure 6. Langmiur plot of the adsorption of three cationic polymers.

Ceq (x/m)

)

Ceq 1 + K((x/m))max ((x/m))max

(6)

where Ceq (mg dm-3) is the equilibrium concentration of polymer, x is the amount of polymer adsorbed (mg dm-3), m is the total (26) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: London, 1981. (27) Mpofu, P.; Addai-Mensah, J.; Ralston, J. Int. J. Miner. Process. 2003, 71, 247-68. (28) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990.

Table 3. Maximum Value of Adsorbed Amount of Three Cationic Polymers maximum value of the adsorbed amount (mg m-2)

a

polymer

absolute

DADMAC

D6010a D6040 D6099

1.49 0.314 0.126

0.149 0.125 0.126

At the background salt concentration of 0.03 M NaCl.

solid particle surface area per unit volume (m2 dm-3), K is the langmuir adsorption constant (dm3 mg-1), and (x/m)max is the maximum amount of polymer adsorbed per unit solid surface area. The model assumes that the solute (polymers) and solvent (water) have equal molecular cross-sectional surface areas and that there is no net solute-solvent interaction. Although this assumption may not be totally valid in the case of polymer adsorption, the use of the model in the context of this study allows a direct and consistent comparison between three charged polymers. A plot of Ceq/(x/m) against Ceq should yield a linear relationship if the Langmiur model is followed. The value of (x/m)max can be determined from the slope of such a plot. A plot of Ceq/(x/m) as a function of Ceq for three charged polymers is shown in Figure 6, which indicates that the isotherms conform to a langmuir type of adsorption as depicted by the linearity of the plots. Values of (x/m)max are given in Table 3. It can be seen that (x/m)max (the maximum value of adsorbed amount) increases

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Table 4. Number of Adsorbed Polymer Molecules Per Particle at Different Polymer Dosages for Three Cationic Polymers number of adsorbed polymer molecules per particle polymer a

D6010 D6040 D6099

1 mg/g

2 mg/g

4 mg/g

6 mg/g

8 mg/g

12 mg/g

n.ab

n.a n.a 3

6 10 n.a.

8 15 n.a.

11 18 12

16 25 13

n.a 2

a At the background salt concentration of 0.03 M NaCl. b n.a. ) not available.

with decreasing the charge densities of polymers. However, the maximum values of adsorbed amounts expressed in terms of charged DADMAC segments are almost the same for 40% and 100% charged polymers (shown in Table 3). This is consistent with the finding of Bauer et al.,29 who observed that the large electrostatic attraction between the copolymers of diallyldimethylammonium-chloride and N-methyl-N-vinyl-acetamide with different charge densities and the silica surface leads to the same number of adsorbed charges of the copolymers and therefore to a corresponding increase of the adsorbed amounts with decreasing charge density of the copolymers at pH 5.8. Interestingly, the maximum values of adsorbed amounts expressed in terms of charged DADMAC segments for 10% charged polymers is higher than those for 40% and 100% charged polymers (Table 3). This is likely attributed to screening of the charge of 10% charged polymers by 0.03 M NaCl and formation of more loops and tails. It can be concluded that the lower the charge density of the polymers, the more loops and tails the polymers have, and the adsorption is dominated by the strong electrostatic attraction between the positive segment charges and the negative silica particle surface charges. The number of adsorbed polymer molecules per silica particle is also calculated and given in Table 4. To better understand the conformations of polymer molecules on the silica particles, it is necessary to calculate the number of polymer molecules required if a silica particle is fully covered by three charged polymers with a flat conformation (polymer patch), respectively. The size or conformation of the three charged polymer molecules in solution can give an indication of the patch size formed by three charged polymers when they are adsorbed on the particle surface. Here we can establish the relationship between polymer hydrodynamic diameter and patch area as a first approximation. Assuming that the patch consists of only one adsorbed polymer molecule and is circular with a polymer hydrodynamic diameter in solution then the patch area is 3115 nm2 for 10% charged polymers at the background salt concentration of 0.03 M NaCl, 2374 nm2 for 40% charged polymers, and 3630 nm2 for 100% charged polymers. The surface area of a sphere of 90 nm is 25434 nm2. So the number of polymer molecules required to fully cover a silica particle with flat patch conformations is 8 for 10% charged polymers under 0.03 M NaCl, 10 for 40% charged polymers, and 7 for 100% charged polymers, respectively. In comparison with these values, it is clear that 10% charged polymers at the polymer dosages of 6, 8, and 12 mg/g silica, 100% charged polymers at the polymer dosage of 8 and 12 mg/g silica, and 40% charged polymers at all four polymer dosages applied in flocculation cannot adopt flat conformations on the silica particle surface, since the number of adsorbed polymer molecules per silica particle is equal to or larger than that required to fully cover one silica particle with flat patch conformations. This implies that in these cases, polymer molecules can only adopt extended conformations on the particle surface with loops (29) Bauer, D.; Buchhammer, H.; Fuchs, A.; Jaeger, W.; Killmann, E.; Lunkwitz, K.; Rehmet, R.; Schwarz, S. Colloids Surf. A 1999, 156, 291-305.

and tails protruding away from the particle surface. However, for 100% charged polymers, it is very likely that adsorbed polymer molecules adopt flat configurations at the polymer dosages of 1 and 2 mg/g silica, since the silica particle surface is far from being fully covered. We suggest that the flocculation of silica particles with 10% charged polymers at the background salt concentration of 0.03 M NaCl was most likely attributed to bridging, since the relatively large aggregates were formed at the optimum dosage. At low polymer dosage, the polymer molecules adopt a relatively flat conformation on the particle surface, so few at most polymer chains can extend beyond the range of the electric double layer repulsion. At high dosage, a more extended configuration of the polymer chains result 30 so that bridging flocculation can result as the polymer chains extend beyond the range of the double layer. Therefore, at the optimum polymer dosage of 12 mg/g, flocs with large size are formed due to the increased polymer loops and tails protruding from the particle surfaces and extending beyond the influence of the electric double repulsion. The number of adsorbed polymer molecules per silica particle and the adsorbed polymer amount do confirm the formation of polymer loops and tails. The zeta potential value in Figure 4 does not support the charge neutralization mechanism at this polymer dosage. These provide extra evidence that flocculation is a bridging mechanism. In comparison, below the optimum polymer dosages, small flocs are produced. The relatively smaller aggregates obtained at the polymer dosage of 6 and 8 mg/g silica should be attributed to the ineffective flocculation, since not many loops and tails of adsorbed polymers were able to extend beyond the electric double layer to invoke the efficient bridging. This is supported by the smaller number of the adsorbed polymer molecules per silica particle (Table 4) and the relatively lower adsorbed polymer amount (Figure 5). We suggest that the lower mass fractal dimension of aggregates at the polymer dosage of 4 mg/g silica mainly results from the strong particles’ electric double layer repulsion due to the low particle surface coverage. The zeta potential value in Figure 4 confirms that the silica is still highly charged. Moreover, the adsorbed polymer amount and the number of adsorbed polymer molecules per particle both indicate that the polymer surface coverage is low. Flocculation induced by the 100% charged polymers is caused by the electrostatic patch mechanism1 at the polymer dosages of 1 and 2 mg/g silica. It can be seen from Figure 4 that the zeta potential value is -48.3 mV at the polymer dosage of 1 mg/g silica and -36.75 mV at 2 mg/g silica. This suggests charge neutralization is not the operating flocculation mechanism at these two polymer dosages. The polymer adsorbed amount of 0.0233 mg m-2 at the dosage of 1 mg/g silica and 0.0273 mg m-2 at 2 mg/g silica is below 50% of the maximum value of adsorbed amount of 0.126 mg m-2 in Table 3. Moreover, as discussed previously, the number of adsorbed polymer molecules per particle at these two polymer dosages indicates that this highly charged polymer can readily be adsorbed with a very flat conformation and form the positive polymer patch on the silica particle surface, since this process is energetically most favorable. As shown previously (Figures 2c and 3c), flocculation induced by 100% charged polymers forms aggregates with high mass fractal dimension and the size of the aggregates produced at the optimum dosage is small. The formation of flocs with high mass fractal dimension by 100% charged polymers is in agreement with the finding by Wong et al.,31 that is, the more charges that (30) Bremmell, K. E.; Jameson, G. J.; Biggs, S. Colloids Surf. A 1998, 139, 199-211. (31) Wong, K.; Cabane, B.; Duplessix, R. J. Colloid Interface Sci. 1988, 123, 466-81.

Flocculation Mechanism Induced by Cationic Polymers

the macromolecules carry, the shorter the distance of separation between neighboring spheres within a floc. At the polymer dosage of 8 and 12 mg/g silica, the number of adsorbed polymer molecules per silica particle (Table 4) indicates that polymer molecules can only adopt extended conformations with loops and tails protruding away from the particle surface. The large positive zeta potential values at the polymer dosage of 8 and 12 mg/g silica also provide additional supporting evidence that flocculation at these two polymer dosages is by the bridging mechanism. The lower mass fractal dimension and the minimum size of flocs at the polymer dosage of 12 mg/g should be attributed to the high particle surface coverage, since the adsorbed polymer amount of 0.107 mg m-2 shown in Figure 5 nearly reaches the maximum value of the adsorbed amounts of 0.126 mg m-2. Flocculation mechanisms induced by 40% charged polymers could be either bridging or a combination of charge neutralization and bridging, depending on the polymer dosage. At higher polymer dose such as the optimum, the adsorbed polymer molecules tend to adopt more extended configuration,26 and more polymer loops and tail can extend beyond the influence of the electric double layer repulsion, invoking quite efficient bridging aggregation. This is consistent with the experimental observation that relatively large flocs are produced at the optimum dosage, as shown in Figure 2b. The number of adsorbed polymer molecules per silica particle confirms the bridging mechanism, since the polymer molecules can only adopt extended conformations with loops and tails protruding away from the particle surface at the optimum polymer dosage. The positive zeta potential value of 9.9 mV at the polymer dosage of 12 mg/g silica also provides supporting evidence that the flocculation mechanism is bridging. At a polymer dosage of 8 mg/g silica, charge neutralization is supposed to be the dominant flocculation mechanism, since the zeta value in Figure 4 is close to 0. However, it is worth noting that the number of adsorbed polymer molecules per silica particle (Table 4) provides evidence that the adsorbed polymers adopt extended conformations with the formation of the loops and tails. This implies that bridging should still be operating mechanism concurrently. The number of adsorbed polymer molecules per silica particle (Table 4) at polymer dosage of 4 or 6 mg/g silica indicates the adsorbed polymers should adopt extended rather than flat conformations on the particle surface. Although the particles are negatively charged (zeta potential value of - 23.3 and - 9.4 mV respectively) at the polymer dosage of 4 and 6 mg/g silica, it is likely that charge neutralization would still be the operating mechanism since this polymer is moderately charged. So a combination of charge neutralization and bridging should be the operating flocculation mechanism at the polymer dosage of 4, 6, and 8 mg/g silica. Since 40% and 100% charged polymers have approximately the same molecular weights (of 40% (1.1 × 105 and 1.2 × 105 g/mol, respectively), we suggest that the difference in charge density of these polymers should be responsible for the difference in the properties of flocs formed and flocculation mechanisms induced. Compared to 40% and 100% charged polymers, 10% charged polymers possess lower charge density and higher molecular weight (3.0 × 105 g/mol), both of which can facilitate bridging flocculation. However, we believe that the low charge density of 10% polymers plays a more important role. Otherwise, we would expect that 40% charged polymers should bring about electrostatic patch flocculation rather than typical bridging at its optimum dosage. Our suggestion is also supported by DurandPiana et al.,32 who believed that, of all the parameters that (32) Durand-Piana, G.; Lafuma, F.; Audebert, R. J. Colloid Interface Sci. 1987, 119, 474-80.

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Figure 7. Effect of particle concentration on typical floc size distributions and volume average (D [4, 3]) floc sizes of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g silica and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

determine flocculation mechanisms, the most important one is the number of charges brought to the oppositely charged particle surface by the cationic polymers. 3.2. Effect of Particle Concentration on the Aggregate Size and Structure. Figure 7 shows the volume average aggregate diameter (D [4, 3]) and size distribution at two different particle concentrations for aggregates induced by 10% polymer at the background salt concentration of 0.03 M NaCl, 40% and 100% charged polymers under their own optimum dosage. As shown in Figure 7a,b, increasing concentrations of particles results in a dramatic increase in the average aggregate size for 10% and 40% charged polymers, whereas it has little effect on aggregate size for 100% charged polymer. Figure 8 shows log I(Q) versus log Q with the particle concentration for aggregates induced by three polymers under the optimum dosage conditions. It can be seen from Figure 8 that an increase in particle concentration leads to a decrease in mass fractal dimension of aggregates induced by 10% and 40% charged polymers. For aggregates induced by 100% charged polymers, the mass fractal dimension does not change with particle concentration.

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Zhou and Franks

The model predicts that the aggregate size should be larger at higher initial particle concentration as we find for the 10% and 40% charged polymers. On the other hand, we find that when 100% charged polymers are used the size of flocs is constant regardless of the solid concentration. In an aggregation process involving adsorbing polymers, there are two important time scales: the polymer adsorption time (tA) and the particle collision time (tC). As a first approximation, one can treat both the polymer adsorption and subsequent particle flocculation processes as simple bimolecular reactions. Under orthokinetic conditions as used in this study, the rate of collision, Jij, between i (silica) particles and j (polyacid) species is given by7

Jij ) kijninj

(7)

where kijcan be calculated from (ignoring hydrodynamic effects)

kij )

4G (a + aj)3 3 i

(8)

in the above equations, ni and nj are the respective number concentrations of particle and polymer in solution. Their respective radii are ai and aj. G is the mean shear rate of mixing, which can be calculated from the power input per unit mass of fluid. It is about 1000 s-1 in this experiment. Note that, by setting j equal to i, eqs 7 and 8 can also be used to describe the collision process between the silica particles. As has been pointed out by Gregory,1 it is usually necessary for a substantial fraction of the added polymer to be adsorbed before particles are sufficiently destabilized for flocculation to occur. It has been shown that the time required to adsorb a fraction f of the initial concentration can be calculated from7

tA ) -

Figure 8. Effect of particle concentration on typical scattering patterns of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g silica and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

According to conventional aggregation theory, a higher concentration of particles will yield larger aggregates,33-35 which has been confirmed by numerous experimental studies and field investigations. However, this is not always true since many researchers have reported that an increase in the particle concentration could result in a lower aggregate size in some cases36-38 or have little or no impact.39 In our case, the particle concentrations ( tA and tr > tC, a polymer molecule will adopt a more extended conformation on the silica particle owing to the shorter time between particle collisions, resulting in very efficient bridging flocculation.13,16 Such a process is not second order (as commonly acknowledged), but strongly biased toward larger aggregates.13 3.3. Effect of Background Electrolyte Concentration on the Aggregate Size and Structure. Strong electrolytes are always present in industrial suspension. Thus it is important to understand the influence of background salt on flocculation induced by polyelectrolytes. It is well-known that the addition of background electrolyte can influence aggregation induced by polymers. This is because it can (1) screen the particles’ surface charge by counterion binding; (2) reduce the double layer range; (3) decrease the mean extension of the polymer; (4) affect polymer adsorption; (5) decrease the polymer effective charge. For example, the effective thickness of the electric double layer is about 1000 nm in salt free suspension, and it reduces to 100 nm at an estimated 1-1 electrolyte concentration about 10-5 M. The effective thicknesses of the electric double layer are only 1.8, 1.2, and 1 nm at 0.03, 0.06, and 0.1 M NaCl, respectively. The variation of polymer hydrodynamic diameter with background NaCl is shown in Table 2. However, it is not clear if the addition of background salt can influence aggregation induced by a different mechanism to the same extent. Figure 9 shows the volume average aggregate diameter (D [4,3]) and size distribution as a function of the background electrolyte concentration for flocs induced by 10%, 40%, and 100% charged polymers under the optimum dosage conditions. As can be seen from Figure 9a,b, the increase in NaCl concentration initially results in a dramatic increase in floc size, followed by the slight increase in floc size, for 10% and 40% charged polymers, whereas Figure 9c show the increase in NaCl

Figure 9. Effect of background electrolyte concentration on typical floc size distributions and volume average (d [4, 3]) floc sizes of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g silica and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

results in a steady reduction in aggregate size for 100% charged polymer. The former is consistent with the findings of Graham, who found that modest increase in ionic strength can enhance flocculation rates during bridging flocculation of amorphous silica particles by cationic polyelectrolytes,8 whereas the latter is in agreement with the findings of Gregory who observed a systematic reduction in the peak-flocculation rate with increasing salt concentration for the electrostatic patch mechanism.2 Figure 10 shows log I(Q) versus log Q with the background electrolyte concentration for aggregates induced by 10%, 40%, and 100% charged polymers under the optimum dosage conditions. For flocs induced by 10% and 40% charged polymers, as shown in Figure 10a,b, the mass fractal dimension decreases with an initial increase in NaCl concentration, and remains relatively constant with further increase in NaCl concentration, whereas for flocs induced by 100% charged polymers, the mass fractal dimension remains constant with the increase in NaCl concentration (Figure 10c). The dramatic increase in aggregate size and the reduction in mass fractal dimension of aggregates for 10% and 40% charged polymers at the optimum dosage with the initial increase in background NaCl concentration should be attributed to the enhanced bridging aggregation by the compression of the electric

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Figure 10. Effect of background electrolyte concentration on typical scattering patterns of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

double layer and the screening of both the particles’ surface charge and polymer charge. The latter can effectively reduce the electrostatic attraction between silica and polymer, and thus the polymers can adopt a more extended configuration with more loops and tails protruding away from the particle surface. More polymer loops and tails passing through the relatively narrower extent of the double layer can predominantly facilitate the flocculation induced by the bridging mechanism. The slight increase in aggregate size and the relatively constant floc structure of aggregates with further increase in NaCl concentration for 10% and 40% charged polymers at the optimum dosage imply that the positive effect of the background salt on the bridging flocculation is only limited to a certain NaCl concentration. However, the formation of aggregates with large size and low mass fractal dimension with the increased background salt in the case of 10 and 40% charged polymers suggest that the reduced polymer molecule extension (shown in Table 2) upon the addition of NaCl does not play an important role in the enhanced bridging aggregation. The slight decrease in aggregate size for 100% charged polymers at the optimum dosage upon the addition of

Zhou and Franks

Figure 11. Effect of shear rate on typical floc size distributions and volume average (D [4, 3]) floc sizes of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g silica and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

background NaCl should mainly result from the reduction in both the mean extension (shown in Table 2) of polymer molecule and the charges on the patch. Such reduction can lead to the polymer patch with decreased size and charge, thereby diminishing the attraction between the patch and the bare area of the oppositely charged particles whose charges are also screened by the counterions of the background salt. Therefore, it is not difficult to comprehend why the addition of NaCl causes the slight reduction in aggregate size. However, the effect of the addition of NaCl on the mass fractal dimension of aggregates induced by 100% charged polymers is inappreciable, because the slight change of the mass fractal dimension with NaCl concentration lies in the uncertainty arising from fitting the straight line through the fractal regime section of the scattering plot and thus cannot be determined more accurately than about 0.1. 3.4. Effect of Shear Rate on the Aggregate Size and Structure. Almost all applications of polymeric flocculants are operated under conditions where a suspension is subjected to shear. When flocculation occurs by bridging or electrostatic patch

Flocculation Mechanism Induced by Cationic Polymers

Langmuir, Vol. 22, No. 16, 2006 6785 Table 6. Polymer Adsorption Time and Particle Collision Time at Different Shear Rate for Three Cationic Polymers tA (s) polymer

142 rpm

318 rpm

82 rpm

142 rpm

318 rpm

D6010a D6040 D6099

6.9 3.5 6.2

3.0 1.5 2.7

0.89 0.45 0.81

5.3 5.3 5.3

2.3 2.3 2.3

0.68 0.68 0.68

a

Figure 12. Effect of shear rate on typical scattering patterns of silica flocculated with (a) 10% charged polymers under the optimum polymer dosage of 12 mg/g and at [NaCl] ) 0.03 M, (b) 40% charged polymers under the optimum polymer dosage of 12 mg/g silica, and (c) 100% charge polymers under the optimum polymer dosage of 2 mg/g silica, respectively.

mechanisms, the conformation of polymer chains may be considerably affected by the applied shear. Figure 11 shows the volume average aggregate diameter (D [4,3]) and size distribution of aggregates induced by 10% at the background salt concentration of 0.03 M NaCl, 40% and 100% charged polymer at the optimum dosage conditions. As illustrated in this figure, the increased shear rate results in a decrease in aggregate size for all three charged polymers. A higher shear rate can increase the aggregation rate by increasing mixing and particle collision, but on the other hand, it also increases aggregate breakage to a much greater extent.16 As a result, aggregate breakage at higher rates prevails, resulting in a drop in the aggregate size in this work. Figure 12 presents log I(Q) versus log Q with the shear rate for flocs induced by 10% charged polymers at a background salt concentration of 0.03 M NaCl, 40% and 100% charged polymers under the optimum dosage conditions. As shown in Figure 12a, the mass fractal dimension of flocs from 10% charged polymers invariably increases with shear rate, whereas the mass fractal

tC (s)

82 rpm

At background salt concentration of 0.03 M NaCl.

dimensions of flocs from 40% and 100% charged polymers remain constant, being 2.6 and 2.7, respectively. It is expected that polymer reconformation rate at its own optimum dosage follows the trend: 100% > 40% > 10%, since the electrostatic attraction is the main driving force for polymer adsorption. From eqs 8-10, the polymer adsorption time (tA) and particle collision time (tC) can be calculated, as listed in Table 6. It should be pointed out that the shear rates of 82 and 318 rpm are estimated as 430 and 3333 s-1, respectively, in his study. We can see that lowering the shear rate will lead to an increase in the polymer adsorption time (tA) and particle collision time (tC). This will in turn allow more time for a polyelectrolyte molecule to adopt a much flatter conformation on the silica surface before encountering another silica particle and hence causing aggregation. A flatter polymer conformation on the particle surface favors aggregation induced by the charge neutralization and electrostatic patch mechanisms. In contrast, the increase in the shear rate can aid a polymer molecule to adopt a more extended conformation on the particle surface before encountering another silica particle, which can greatly improve the flocculation induced by the bridging mechanism. However, it should be pointed out that more polymer tails and loops can be permanently broken if flocculation is via a bridging mechanism.16 In all, our results suggest that flocculation induced by 10% charged polymers at its optimum dosage should be via bridging. The slight increase in aggregate mass fractal dimension with shear rate is possibly attributable to the floc breakup and partial reflocculation after the shear force is removed. Under high shear conditions, the flocs are broken either by disruption of the attachment point on a particle surface or by the scission of covalent bonds with the bridging polymer chains, followed by reconformation of the polymer to form a flatter configuration on the particle surface. As a result, the denser flocs were produced at higher shear rate. Flocculation induced by 40% charged polymers is likely to exhibit a changover from a combination of charge neutralization and bridging mechanism at low shear rate to bridging mechanism at higher shear rate. Flocculation induced by 100% charged polymers occur via an electrostatic patch mechanism. It is likely that 100% charged polymers are initially adsorbed with a very flat conformation and induce electrostatic patch flocculation regardless of shear rate. Although the flocs which are initially formed via the electrostatic patch mechanism can be broken by shear, the floc structure is not influenced due to the flat conformation of this highly charged polymer on the particle surface.

4. Conclusions The flocculation of 90 nm diameter silica particles by the addition of differently charged cationic polymers results in the formation of flocs with distinctive characteristics determined by the flocculation conditions, including polymer dosage, solid concentration, background electrolyte concentration, and shear rate. Lower charged polymers are prone to produce flocs with smaller mass fractal dimension than the higher charged one in

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the range of polymer dosages used. Furthermore, lower charged polymers favor the production of larger flocs at the optimum dosage than the higher charged ones. This is possibly due to the fact that 10% and 100% charged polymers induce bridging and electrostatic patch flocculation, respectively, whereas 40% charged polymers induce either a combination of charge neutralization and bridging or bridging, depending on the polymer dosage and shear rate. Bridging aggregation induced by 10% and 40% cationic polymers at their optimal dosages can readily be affected by the particle concentration. Increasing particle concentration results in the formation of larger aggregates. Electrostatic patch aggregation induced by 100% charged polymers is not influenced by the solids concentration. The addition of background electrolyte aids in bridging aggregation induced by 10% and 40% charged cationic polymers at their optimal dosages, whereas it is detrimental to electrostatic patch aggregation induced by 100% charged polymers. The

Zhou and Franks

addition of the background electrolyte leads to the production of large aggregates for 10% and 40% charged polymers, whereas the increase in background electrolyte results in the formation of smaller aggregates for 100% charged polymers. The increase in shear rate results in a reduction of floc size for all three charged polymers. However, the effect of shear rate on mass fractal dimension is greatly dependent on polymer charge density. Acknowledgment. Y.Z. thanks the Australian government for the award of an IPRS and the University of Newcastle, Australia, for the award of UNRS Central. Thanks are also due to SNF for the provision of cationic polymers. The authors acknowledge financial support from the Australian Research Council (in particular, Discovery Grant 0209669 and the Special Research Centre for Multiphase Processes). LA060281+