Mechanism of Polyelectrolyte Transfer during Heteroflocculation

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Mechanism of Polyelectrolyte Transfer during Heteroflocculation Tom Asselman and Gil Garnier* Department of Chemical Engineering and Paprican Pulp and Paper Research Centre, McGill University, 3420 University Street, Montreal, Quebec, Canada H3A 2A7 Received November 10, 1999. In Final Form: February 29, 2000 The flocculation kinetics of colloids (fines) on polymer-coated collectors (fibers) was quantified. The variables of interest include shear rate, salt concentration, and polymer chemistry. After an initial deposition on the collector surface, the colloids slowly detach to form a stable suspension. This is caused by polymer transfer. A theoretical model describing the simultaneous kinetics of colloid deposition on polymer-coated surfaces and polymer transfer was developed and validated. The flocculation is characterized by three rate constants: k1 (deposition), k2 (detachment), and β (polymer transfer coefficient). Two limiting cases were identified in the colloids detachment/polymer transfer behavior, which correspond to flocculation mechanisms by bridging and by charge reversal. Low-MW, highly charged polyelectrolytes provide weak bonds (high detachment rates) and a low transfer coefficient. Contrarily, high-MW, weakly charged PAMs provide stronger bonds (low detachment rates) but are more efficiently transferred. The different behavior was explained by the different layer conformations of both cases.

Introduction Polyelectrolytes are used as flocculants for various applications including water purification, food processing, and pharmaceuticals. In paper making they are used to deposit colloids (fines, fillers) onto collectors (fibers) in turbulent flow. Three main principles are believed to cause aggregation:1 bridging, charge neutralization, and patch flocculation. In bridging, a polymer forms a link between two surfaces by adsorbing on both. In the other mechanisms, a polyelectrolyte compensates (neutralization) or locally reverses the surface charge (patch flocculation), which induces aggregation by van der Waals and electrostatic attraction forces. The kinetics governing the flocculation behavior are rather complex and still not fully understood. The polymer coils adsorb from solution onto the surface and can deform to achieve a thermodynamically favorable conformation.2-5 This generally flattens the adsorbed layer and can occur on a time scale of seconds.4,5 Once adsorbed, the polymer molecule can encounter another surface and induce aggregation. This can only take place if the loops and tails of the polymer layer protrude sufficiently far into the solution to overcome the electrostatic repulsion between the surfaces. One can distinguish between active and inactive bridging sites,6 depending on the polymer conformation. In the presence * Corresponding author. Phone: +1 (514) 398-1367. Fax: +1 (514) 398-8254. E-mail: [email protected]. (1) Adachi, Y. Dynamic aspects of coagulation and flocculation. Adv. Colloid Interface Sci. 1995, 56, 1-31. (2) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London, 1993. (3) Cohen Stuart, M. A.; Fleer, G. J. Adsorbed polymers in nonequilibrium situations. Annu. Rev. Mater. Sci. 1996, 26, 463-500. (4) Wågberg, L.; O ¨ dberg, L.; Glad-Nordmark, G. Conformation of adsorbed polymers and flocculation of microcrystalline cellulose and pulp suspensions. The fundamentals of papermaking materials. Transactions of the 9th Fundamental Research Symposium; Cambridge, U.K.; Baker, C. F., Puncton, V. W., Eds.; Mechanical Engineering Publications, Ltd.: London, 1989; Vol. 1, pp 413-435. (5) Pelssers, E. G. M.; Cohen Stuart, M. A.; Fleer, G. J. Kinetics of bridging flocculation. J. Chem. Soc., Faraday Trans. 1990, 86 (9), 13551361. (6) Moudgil, B. M.; Shah, B. D.; Soto, H. S. Collision efficiency factors in polymer flocculation of fine particles. J. Colloid Interface Sci. 1987, 119, 466-473.

of shear, the formed bond can break up and polymer transfer between the surfaces can occur.7-10 The polymer transfer eventually leads to restabilization of the aggregated system and reduces the bridging ability of the resulting polymer layers.10 Therefore, the flocculation is transient. A kinetic model, assuming that a bridging polymer layer is ruptured upon particle detachment, resulting in inactive sites on both surfaces was developed but not validated experimentally.11 The purpose of this study was to model the simultaneous particle deposition and polymer transfer kinetics and to elucidate the governing phenomena of polymer transfer by using this model to correlate experimental results. The variables of interest polymer chemistry, polymer molecular weight, electrolyte concentration, and shear rate were studied for PAM and PEI. A suspension of wood fibers and fines was used, in which the fibers were first coated in an excess solution of polymer. The flocculation kinetics was measured by following the fines concentration in the supernatant. The surface chemistry of colloids and collectors is similar. Experimental Section Materials. Dried unbleached thermomechanical pulp (Black Spruce) was soaked for 24 h and disintegrated. The pulp was separated over a 200-mesh screen, resulting in a long fiber fraction (cylinders with an average length of 2 mm and a diameter of 20 µm) and a fines suspension (colloids with a diameter of approximately 50 µm). Cationic poly(acrylamides) of different molecular weight and degrees of substitution were supplied by Allied Colloids (Percol) (7) O ¨ dberg, L.; Tanaka, H.; Swerin, A. Kinetic aspects of the adsorption of polymers on cellulosic fibres. Nordic Pulp Paper J. 1993, 1, 159-166. (8) Tanaka, H.; O ¨ dberg, L. Transfer of cationic polymers from cellulose fibers to polystyrene latex. J. Colloid Interface Sci. 1992, 149 (1), 4048. (9) Tanaka, H.; Swerin, A.; O ¨ dberg, L. Cleavage of polymer chains during transfer of cationic polyacrylamide from cellulose fibres to polystyrene latex. J. Colloid Interface Sci. 1992, 153 (1), 13-20. (10) Asselman, T.; Garnier, G. Dynamics of polymer-induced coflocculation of wood fibres and fines. Submitted for publication in Colloids Surf. A. (11) Pelton, R. H. A model for flocculation in turbulent flow. Colloids Surf. A 1981, 2, 277-285.

10.1021/la991479f CCC: $19.00 © 2000 American Chemical Society Published on Web 04/21/2000

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Table 1. Characteristics of the Poly(acrylamides)a charge density (%) PAM0.4/100 PAM5/25 PAM9/25 PAM9/40 PAM15/5

100 25 25 40 5

[η] (dL/g)

MW (g/mol)

〈R2g〉1/2 (nm)

1 6 10 10 14

0.4 × 4.6 × 106 9.3 × 106 9.3 × 106 15 × 106

50 180 260 260 340

106

(hydrodynamics), γ the deposition efficiency (chemistry), and k1 the collision rate constant (m3 s-1). k2 is the detachment rate constant (s-1), nj is the collector number concentration (m-3), and n0 is the ratio of available colloids compared to the maximum coverage on the collectors, given by

n0 )

a

Charge density and intrinsic viscosity (η) were measured by the manufacturer. Molecular weight and radius of gyration Rg were calculated according to ref 11.

n0,i Γmaxnj

(2)

with n0,i the initial concentration of family i (m-3) and Γmax the maximal coverage of family i on collector family j. Initially, i.e., at low surface coverage, eq 1 simplifies to

[ ] dni dt

t)0

) -Rγk1ni,0nj

(3)

For shear-induced collisions, the collision rate constant can be calculated from the Smoluchowski theory

1 k1 ) G(di + dj)3 6 Figure 1. Experimental setup. and used as received. Solutions of 1 g/L were prepared by first wetting the polymer with 5 mL/g of ethanol and mixing with deionized water. This stock solution was stirred for 30 min before adsorption on the fibers. The characteristics of these PAMs supplied by the manufacturer are listed in Table 1 as PAMX/Y. X denotes the estimated molecular weight (106 D), and Y represents the degree of subsitution (%). The MW and radius of gyration were calculated according to ref 12. PEI (Polymin P, BASF) was used as received. It is a highly branched polymer containing primary, secondary, and tertiary amine groups in the approximate ratio 1:2:1.13 It is polydisperse with MW = 600 000 and Mn = 36 000 measured from vapor osmometry.13 Branching is believed to occur every 3-3.5 amino groups.13 The polymer was received as a 50% solution and was diluted immediately before the experiments. Methods. Full polymer coverage was achieved by stirring the fibers in a polymer solution for 5 min, at a ratio of 50 mg of polymer per gram of fiber. The suspension was then filtered over a 200-mesh screen, and the fibers were washed twice with distilled water in order to remove the excess polymer. The heteroflocculation kinetics was studied by adding 2 g of coated fibers to a stirred fines suspension of 0.28 g/L (pH ) 6.5). The fines concentration was determined by continuously pumping a fines flow via a 200-mesh filter using a peristaltic pump through a spectrophotometer cell (Varian CARY 1E UV/vis spectrophotometer), measuring the absorbance at 300 nm. The experimental setup is illustrated in Figure 1. The electrophoretic mobility of fines was measured in a Rank Bros particle electrophoresis apparatus (Cambridge, U.K.) equipped with a flat cell.

Theory Deposition of Colloids on Collectors. The deposition kinetics of colloids (family i) on a collector (family j) can be described by the Langmuir equation, where the particle coverage of i on j is expressed by14

dθ ) Rγk1nj(n0 - θ)(1 - θ) - k2θ dt

(1)

with θ the surface coverage of i on j, R the capture efficiency (12) Mabire, F.; Audebert, R.; Quiveron, C. Synthesis and solution properties of water soluble copolymers based on acrylamide and quartenary ammonium acrylic comonomer. Polymer 1977, 25, 13171322. (13) Horn, D. Polyethylenenimine-Physicochemical Properties and Applications. In Polymeric Amines and Ammonium Salts; Goethals, E. J., Ed.; Pergamon Press: Oxford, 1980.

(4)

with G the effective shear rate (s-1), and di and dj the equivalent spherical particle diameters (m). The deposition rate constant can be derived from the following expression

katt )

[ ]

1 dCf CFC0,f dt

t)0

(5)

with Cf and CF, respectively, the fines and fiber concentrations (g/L), C0,f the initial fines concentration (g/L), and katt the deposition rate constant (L/g‚s). This apparent deposition rate constant relates to the theoretical collision rate as follows:

katt )

Rγk1nj CF

(6)

Polymer Transfer between Collectors and Colloids. We will only consider the case of polymer transfer from collectors to colloids; the opposite case is symmetrical and follows the same argumentation. Polymer is transferred in this system when particles detach from the surface. Therefore, it is assumed that the polymer transfer rate is proportional to the detachment rate of the colloids and to the fractional coverage of polymer on the colloids. The detachment of polymer from the surface to the solution is neglected. This yields the following equation

dQp ) ktk2θΓmaxnj(1 - π) dt

(7)

with Qp the amount of transferred polymer (g/m3), kt the polymer transfer rate, and π the fractional polymer coverage of the colloids. This equation can be normalized by dividing by the colloid concentration ni and the maximal polymer coverage on the colloids Γpol,i and substituting eq 2:

ktk2θ dπ ) (1 - π) dt Γpol,in0

(8)

(14) van de Ven, T. G. M. The capture of colloidal particles on surfaces and in porous material: basic principles. Colloids Surf. A 1998, 138, 207-216.

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Figure 2. Typical evolution of the fines concentration. At t ) 0, polymer-coated fibers are mixed with fines. G ∼ 50 s-1. CF ) 2 g/L, C0,f ) 0.28 g/L.

Figure 3. Time dependence of the electrophoretic mobility of fines (m2/V s) for PAM5/25 (b) and PEI (O).

It is convenient to define a polymer transfer coefficient β as

β)

kt Γpol,i

(9)

Only interactions between polymer-coated and bare surfaces are considered; consequently, the deposition efficiency can be expressed as follows

γ ) φ(1 - π) + π(1 - φ)

(10)

with φ the polymer coverage on the collectors. We assume, however, that φ ) 1 at all times, which means that the collectors remain completely covered with polymer. Hence, the deposition kinetics can be described by the following set of equations:

dθ ) Rk1nj(1 - π)(n0 - θ)(1 - θ) - k2θ dt

(11)

dπ βk2θ ) (1 - π) dt n0

(12)

Upon mixing the polymer-coated collectors with the bare colloids, there are no colloids deposited on the collectors and no polymer transfer has occurred; therefore, the initial conditions are the following:

θt)0 ) 0

(13)

πt)0 ) 0

(14)

Results Characterization of the Flocculation Behavior. A typical fines concentration curve after mixing polymercoated fibers with bare fines is shown in Figure 2. After the initial (fast) deposition, the fines concentration in the supernatant rises back to the original concentration. We have attributed this behavior to polymer transfer.10 The transferred polymer creates an electrosteric barrier on the originally bare surface, which inhibits redeposition and eventually leads to a complete restabilization of the system. It was shown that the deposition rates in this system are consistent with the Smoluchowksi kinetics for orthokinetic collisions.10 In Figure 3, the electrophoretic mobility (EM) of the fines as a function of time is compared for PAM5/25 and PEI. Charge reversal occurs in both cases, which indicates that cationic polymer is transferred. The effect is faster for PEI since its charge is much higher than PAM5/25. In comparison, the EM’s of fully coated fines from an excess

Figure 4. Comparison between the experimental kinetics (dotted curve) and the model calculations (solid curve) (eqs 1114). The difference is 8% in this case.

polymer solution are 2.3 × 10-8 and 8.8 × 10-9 m2 V-1 s-1 for PEI- and PAM-covered fines, respectively. The model described by eqs 11-14 was used to determine k2 and β from experimental data. katt was measured according to eq 5. Rk1nj was then calculated from eq 6. The differential equations were solved with a classical Runge-Kutta 4-5 algorithm. A multipleparameter optimization method implemented in the MATLAB package was used to correlate k2 and β during the first 5 min of the experiment. Γmax is 0.25 (g/g), which was determined from adsorption experiments at low shear rates. The agreement between experiments and model was in the range of 2-10%. The model was further validated by varying the fiber concentration (n0). Figure 4 illustrates the results of a typical experiment with the fitted data curve. Influence of Shear Rate. The influence of shear was studied by depositing fines on polymer-coated fibers for stirring rates ranging between 100 and 300 rpm. Figure 5 shows the detachment rate constant k2 as a function of the stirring rate for both polymers. The detachment rate constant for PEI is clearly much more shear-dependent than for PAM, which indicates a lower bond strength. The polymer transfer coefficient β as a function of shear is shown in Figure 6. The transfer coefficient is much higher for PAM and increases with shear. For PEI, β can be considered to be shear-independent in this interval. Influence of Electrolyte Concentration. The deposition kinetics of fines was measured at four NaCl concentrations. Figure 7 shows the influence of salt on the deposition rate constant katt for both PAM and PEI. The detachment rate constant k2 is shown in Figure 8. The reduction in k1 and increase in k2 with salt concentration can be attributed to charge screening, which

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Figure 5. Influence of stirring rate on the detachment rate constant k2 (min-1) for PAM5/25 (b) and PEI (O).

Asselman and Garnier

Figure 8. Influence of salt concentration on the detachment rate constant k2 (min-1) for PAM5/25 (b) and PEI (O). Table 2. Effect of Polymer Chemistry on the Flocculation Kinetics. Summary of the Detachment Rate (k2) and Polymer Transfer Coefficient (β)a PAM0.4/100 PAM5/25 PAM9/25 PAM9/40 PAM15/5 PEI

k2 (min-1)

β

33.8 2.4 3.8 6.0 2.1 7.0

0.1 0.3 0.2 0.2 1.1 0.08

a Results from curve fitting using eqs 11-14. 0.28 g of fines, 2 g of fibers. Stirring rate 200 rpm; no salt added.

Figure 6. Influence of stirring rate on the polymer transfer coefficient β for PAM5/25 (b) and PEI (O).

Figure 7. Influence of salt concentration on the deposition rate constant katt (L/min‚g) for PAM5/25 (b) and PEI (O).

reduces the positive attraction between the cationic polyelectrolytes and the negative cellulosic surfaces. Since PEI is highly charged and is believed to act by charge reversal rather than by bridging,15 the screening effect is much more pronounced. Salt has two effects on polyelectrolytes: it screens both the attractive surface-polymer charges and the repulsive segment-segment charges. It was shown that this leads to an expansion of a PAM layer,16,17 which should increase its bridging ability. On the other hand, screening the surface-segment interac(15) Pfau, A.; Shrepp, W.; Horn, D. Detection of a single molecule adsorption structure of poly(ethyleneimine) macromolecules by AFM. Langmuir 1999, 15, 3219-3225. (16) Shubin, V.; Linse, P. Effect of electrolytes on cationic polyacrylamide on silica: Ellipsometric study and modeling. J Phys Chem. 1995, 99, 1285-1291. (17) O ¨ dberg, L.; Sandberg, S.; Welin-Klintstro¨m, S.; Arwin, H. Thickness of adsorbed layers of high molecular weight polyelectrolytes studied by ellipsometry. Langmuir 1995, 11, 2621-2625.

tions leads to weaker adhesion. It is clear that this phenomenon dominates the effect of the layer expansion in the reduced bridging efficiency. The trend for PAM corresponds to observations reported in ref 18. For both polymers, no influence of salt on the polymer transfer coefficient was observed. This means that the transfer coefficient is chiefly governed by hydrodynamic forces. Influence of Molecular Weight and Charge Density. The kinetic constants k2 and kt for five different polyacrylamides are listed in Table 2. Two extremes are of particular interest: the low molecular weight, highcharge PAM and the high molecular weight, low-charge PAM. The first gives roughly the same results as the studied PEI: a high detachment rate and a low polymer transfer coefficient. The second provides a low detachment rate and a very high transfer coefficient. All other cases fall between those extremes. Discussion Polymer Transfer. The main advantage of the proposed flocculation model is that it distinguishes the particle detachment from the polymer transfer. However, the cause-effect relationship between the two phenomena is yet to be elucidated. Physically, it is indeed difficult to distinguish both from a mechanistic point of view. Let us consider the deposition of a colloid on a polyelectrolytecoated surface, with subsequent particle detachment and polymer transfer. When an aggregate is formed between the colloids and the polymer-coated collectors, three different bond types are present (Figure 9): (1) the polymer-collector bonds between the surface on which the polymer is adsorbed originally, (2) the covalent bonds forming the macromolecule, and (3) the bonds between the adsorbed polymer layer and the colloids. When the (18) Pelton, R. H.; Allen, L. H. The effects of some electrolytes on flocculation with a cationic poly(acrylamide). Colloid Polym. Sci. 1983, 261, 485-492.

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Figure 9. Different bonds between colloids and collectors.

bonds of type 1 and 2 break up, under the influence of hydrodynamic forces, particle detachment and polymer transfer occur simultaneously. A breakup of type 3 bonds only leads to particle detachment. Thus, polymer transfer can only occur with particle detachment, but particle detachment can occur without polymer transfer. Bond of type 1 are stronger than those of type 3, even though the surfaces are chemically identical. This is due to the density profile of polymers segments in an adsorbed layer. Van de steeg et al. modeled the density of polyelectrolyte segments as a function of the distance from the adsorbate surface by extending the Scheutjens-Fleer theory to charged macromolecules.2,19 These calculations show that the segment density near the surface is much larger than at the outer plane of the adsorbed layer. Hence, the number of potential polymer-surface contacts or bonds is much lower on the “outer” polymer layer surface, causing a weaker bond. We have previously presented indirect evidence of this phenomenon by comparing bridging configurations with both PAM and highly anionic microparticles.20 Therefore, when a deposited particle is subjected to hydrodynamic forces, the most likely bonds to break up are those of type 3. However, polymer transfer does occur, which implies that bonds of type 1 and 2 also break up. This leaves us with the probability of cleaving interchain or C-C bonds. It was shown both theoretically21 and experimentally9 that cleavage can occur. Indeed, the lifting force acting on a particle deposited on a flat surface in laminar flow is given by22

F ) 32ηGr2

(15)

with r the particle radius (m) and η the viscosity (Pa‚s). For a particle with a radius of 25 µm and a shear rate of 100 s-1, this force becomes 2 nN. The force required to break a C-C bond is roughly 1-10 nN,23,24 which is of the same order of magnitude. Tanaka et al.9 showed that a significant reduction in molecular weight occurs during polymer transfer, especially for higher molecular weight PAMs. The fact that the electrolyte concentration does not influence the transfer coefficient β for PAM supports this cleavage mechanism. Since charge screening decreases the polymer-surface affinity, it favors only the breakage of bonds of type 1 and 3. The transfer coefficient of PAM increases with shear. The greater hydrodynamic forces facilitate the breakup of all bonds with increasing shear. Therefore the chain cleavage is intensified, which increases the amount of polymer transferred per detached particle. Hence, β is increased. (19) van de Steeg, H. G. M.; Cohen Stuart, M. A.; de Keizer, A.; Bijsterbosch, B. H. Polyelectrolyte adsorption: A subtle balance of forces. Langmuir 1992, 8, 2538-2546. (20) Asselman, T.; Garnier. G. The role of anionic microparticles in a poly(acrylamide)-montmorillonite flocculation aid system. Colloids Surf. A., in press. (21) van de Ven, T. G. M. Effects of bridging on selective shear flocculation. J. Colloid Interface Sci. 1981, 81 (1), 290-291. (22) Goldman, A. J.; Cox, R. G.; Brenner, H. Slow viscous motion of a sphere parallel to a plane. Chem. Eng. Sci. 1967, 22, 653. (23) Goldacre, R. J. Nature 1954, 174, 732. (24) Goren, S. J. J. Colloid Interface Sci. 1971, 36, 94.

The polymer transfer coefficient β is about 10 times larger for the low-charge, high-MW PAM than for the highcharge, low-MW one. β is the ratio between the transfer rate constant and the maximum amount of polymer on the colloids. Since this amount increases with molecular weight and decreases with charge density,2,25 the trend in the actual transfer rate kt is probably even stronger. This can be understood from the polymer conformation on the adsorbate surface. The high-charge, low-MW polymer adopts a very flat conformation, with few protruding loops and tails. Consequently, when a colloid detaches from this layer, the polymer-colloid bond is the most likely to be broken; hence, less polymer transfer occurs. Contrarily, the low-charge, high-MW chains adsorb in thicker layers with more protruding loops and tails. Therefore, the force exerted by the particle is distributed over these protruding chains, which can lead to cleavage (type 2) or polymer detachment (type 1). The fact that β is independent of shear in the case of PEI supports this mechanism. Particle Detachment. The decreasing detachment rate constant with higher molecular weight PAM can be explained by the higher elongation of the longer chains. Since the particles are subjected to shear fluctuations, due to turbulent eddies,26 longer chains allow for longer elongation during such fluctuations. Hence, more kinetic energy can be stored before one of the bonds is broken. This result is in agreement with ref 27. Mu¨hle showed that the adhesion of latexes on surfaces coated with cationic PAM rises significantly between molecular weights of 106 and 107 g/mol. For particles with a diameter of 5 µm, adhesion forces between 1 and 7 nN for this MW range were reported. This increase in adhesion force corresponds to the 10-fold increase in detachment rate observed in our experiments over the same MW range. Pelton and Allen28 measured adhesion forces on the order of 1-2 nN for 5-µm polystyrene spheres deposited on PEI-coated (Polymin P) glass. This is again comparable to the data of Mu¨hle for cationic PAM with a MW of 105-106, as is the case for our results for the lower MW PAM and the PEI. It should be noted that all these adhesion forces are comparable to the strength of a C-C bond. The high detachment rate of PEI can be attributed to its branched structure, which reduces its flexibility compared to the linear PAMs and to the flat layer conformation. Stabilization by Polymer Transfer. From first principles it is not obvious that the system eventually stabilizes completely. Indeed, polymer transfer between surfaces should lead to a redistribution of the coverage. When a polymer coil or fragment is transferred, a bare spot can be created on the original surface. Transferred polymer could then again form a bridge with those bare spaces. However, several other phenomena have to be considered to explain this stabilization. First, reconformation can occur for PAM. When the polymer is adsorbed on the surface from an excess solution, the surface is quickly covered with polymer coils, and limited time and space are available for reconformation. Upon polymer (25) Durand-Piana, G.; Lafuma, F.; Audebert, R. Flocculation and adsorption properties of cationic polyelectrolytes toward Na-montmorillonite dilute suspensions. J. Colloid Interface Sci. 1987, 119 (2) 474480. (26) Wågberg, L.; Lindstro¨m, T. Kinetics of polymer-induced flocculation of cellulosic fibres in turbulent flow. Colloids Surf. A 1987, 27, 29-42. (27) Mu¨hle, K. Floc stability in laminar and turbulent flow. In Coagulation and flocculation. Theory and applications; Surfactant Science Series, 47; Dobia´s, B., Ed.; Marcel Dekker: New York, 1993; p 356. (28) Pelton, R. H.; Allen, L. H. Factors influencing the adhesion of polystyrene spheres attached to pyrex by polyethlyeneimine in aquous solution. J. Colloid. Interface Sci. 1984, 99, 387-398.

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transfer, the space originally occupied by the transferred chain becomes available for reconformation of neighboring chains. Transferred chains initially encounter an empty surface and have sufficient time to relax in a flat conformation. Therefore, both transferred and depleted layers will flatten and lose their bridging ability. Chain cleavage likewise increases the space occupied by polymer. Similarly, the depleted chain is flattened and the transferred chain is shortened, which leads to flatter chains. Finally, a redistribution of the positive charge leads to electrostatic repulsion between the surfaces (especially for the highly charged polymers). This repulsion also contributes to the stabilization. Consequently, the hypothesis used in the model that the collector surface remains completely coated is justified. Conclusions The flocculation kinetics of colloids (fines) on polymercoated collectors (fibers) of similar surface chemistry was characterized experimentally and theoretically. The variables of interest include shear rate, salt concentration, and polymer chemistry. After an initial deposition on the collector surface, the colloids slowly detach to form a stable suspension. This is caused by polymer transfer. A theoretical model describing the simultaneous kinetics of colloid deposition on polymer-coated surfaces and polymer transfer was developed and validated. The flocculation is characterized by three rate constants: k1 (deposition), k2 (detachment), and β (polymer transfer coefficient). This

Asselman and Garnier

model was used to study the influence of shear, electrolyte concentration, and polymer chemistry on the particle detachment and polymer transfer kinetics. Shear increased the detachment rate constant for both PAM and PEI, which is expected. The polymer transfer coefficient increases with shear for PAM, presumably due to increased polymer chain cleavage. Electrolytes screen attractive forces, favoring the detachment of colloids and limiting the deposition. The polymer transfer coefficient was not affected by salt. Two limiting cases were identified in the detachmentpolymer transfer behavior, which correspond to flocculation mechanisms by bridging and charge reversal. LowMW, highly charged polyelectrolytes provide weak bonds (high detachment rates) and are less efficiently transferred. Contrarily, high-MW weakly charged PAMs provide stronger bonds (low detachment rates) but are more efficiently transferred. This was explained by the different layer conformations of both cases. The stabilizing effect of polymer transfer was attributed to reconformation effects of both transferred and depleted polymer layers and to the buildup of electrostatic repulsion by polymer transfer. Acknowledgment. The authors thank Dr. T. G. M. van de Ven for fascinating discussions. Financial contributions from NSERC for T.A.’s PGS scholarship and for R&D Grant 601-110 1195 are kindly acknowledged. LA991479F