Adsorption of Polyampholytes on Polystyrene Latex: Effect on Colloid Stability

Adsorption of Polyampholytes on Polystyrene Latex: Effect on Colloid Stability

JOURNAL OF COLLOID AND INTERFACE SCIENCE 176, 86–94 (1995) Adsorption of Polyampholytes on Polystyrene Latex: Effect on Colloid Stability S. NEYRET,...

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JOURNAL OF COLLOID AND INTERFACE SCIENCE

176, 86–94 (1995)

Adsorption of Polyampholytes on Polystyrene Latex: Effect on Colloid Stability S. NEYRET, L. OUALI, F. CANDAU,

AND

E. PEFFERKORN 1

Institut Charles Sadron, 6, rue Boussingault, 67083 Strasbourg Cedex, France Received December 12, 1994; accepted May 2, 1995

aggregation processes have been determined to be reactionlimited, with the limitation corresponding to the possibility of interparticle bridging (3). The present study addresses polyampholytes which are terpolymers bearing at the same time uncharged, positively, charged, and negatively charged chain segments, with the density of the charged chains being relatively low. The samples were prepared using a microemulsion polymerization process which was shown to lead to copolymers more homogeneous in composition than those prepared in solution (4). This class of polymers presents unusual solubility properties which can be summarized as follows (5–7). Ion-pairing between positively and negatively charged chain segments belonging to the same polymer, which is induced in the absence of electrolyte, confers poor solubility in aqueous solution. Dissolution is favored in the presence of electrolyte; the small ions are counterions of the two dissociated groups. Therefore polyampholytes are expected to display unusual interfacial properties. In fact, charged colloids in salt-free solutions may play a role similar to that of electrolytes insofar as the negative surface charges of the colloid may interact with the positively charged chain segments of the polymer (8, 9). This confers a true polyelectrolytic behavior to the nonbounded negatively charged chain segments. Therefore terpolymers of different stoichiometry have been synthesized to determine the extent of this charge segregation. To determine the charge characteristics of the resulting polymer layer we measured the electrophoretic mobility of the polyampholyte–colloid complexes at partial and full surface coverage. At the same time, we determined the stability domain of these systems at different polymer dosages and the kinetics of aggregation in the instability domain.

The interfacial characteristics of low-charge-density polyelectrolytes and polyampholytes synthesized by a microemulsion polymerization technique have been investigated. Terpolymers of acrylamide (AM, neutral segment), [2-(methacryloyloxy)ethyl] trimethylammonium chloride (MADQUAT, positively charged segment), and sodium 2-(acrylamido)-2-methyl propanesulfonate (NaAMPS, negatively charged segment) and copolymers of AM and MADQUAT as well as of MADQUAT and NaAMPS were adsorbed on a negatively charged polystyrene latex. The zeta potential at full surface coverage was determined and analyzed as a function of the surface charge excess of the colloid–polymer complex. The domains of colloidal instability were determined and the rate of destabilization was studied for the different systems at the optimum flocculation concentration. A deviation from the usual polyelectrolyte behavior was found for the copolymers and the terpolymers, which may be attributed to the reversible character of the aggregation processes resulting from a progressive modification of the characteristics of the adsorbed layer. q 1995 Academic Press, Inc.

Key Words: polyampholyte adsorption; colloid stabilization by polyampholytes; surface charge of adsorbed terpolymers.

INTRODUCTION

Polyelectrolytes are used as destabilizing agents in a great number of industrial applications, and it has been shown that the most common mechanism of destabilization involves the establishment of polymer bridges between the elementary particles (1). The optimum polymer dosage inducing a fast flocculation usually corresponds to a degree of surface coverage between one-third and one-half (2). In this situation doublet formation can be viewed as the encounter of two identically polymer covered colloids, with the chain adsorbed on the first colloid particle colliding with a portion of the polymer free area of the second particle. In the final state the two colloids share the chain segments of a polymer and at each stage of the process, all particles share a great number of polymer chains. The resulting aggregate is characterized by an unusual internal stability. The kinetics of such 1

MATERIALS AND METHODS

Terpolymers. Acrylamide (AM) from Aldrich and 2(acrylamido)-2-methylpropanesulfonic acid (AMPS, neutralized at pH 9) from Casella were purified by recrystallization before use. [2-(Methacryloyloxy)ethyl]trimethylammonium chloride (MADQUAT) was supplied by ElfAtochem as a 75% (w/w) aqueous solution and used without

To whom correspondence should be addressed.

0021-9797/95 $12.00 Copyright q 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

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further purification. The terpolymers and polyacrylamide were prepared by means of a microemulsion polymerization procedure described elsewhere (10). The MADQUAT/ AMPS sample with a stoichiometric composition was prepared in homogeneous aqueous solution. The microemulsion polymerization method was shown to provide polymers more homogeneous in composition (monomer distribution not far from random) than those prepared in solution, which have a great tendency to alternation (4). A direct consequence of this difference in microstructure is that the sample synthesized in homogeneous aqueous solution is soluble in pure water, making the adsorption experiments possible even in the absence of salt, whereas the sample of similar stoichiometry prepared in microemulsions is insoluble in water and requires a large amount of electrolyte to become soluble (11, 12). We note also that all copolymers have been dialyzed against water, which allows them to self-neutralize almost completely. The terpolymer composition in neutral AM, negatively charged AMPS, and positively charged MADQUAT chain segments is indicated by T[x/ f /g], where x, f, and g are the percentages of neutral, negatively charged, and positively charged groups, respectively. The interfacial properties of these terpolymers were compared to those of AM–MADQUAT copolymers whose molar composition is similarly indicated by C[x/00/g] and one AMPS–MADQUAT copolymer C[00/50/50]. Polyacrylamide (PAM) was used to determine the interfacial behavior of the acrylamide chain segments which are present at relative concentrations of 80 and 92% in the terpolymers and copolymers. The weight average molecular weights Mw of the different polymers were determined with the AMTEC MM1 SM200 apparatus in 1 M NaCl solution and found to be on the order of 10 7 except for the C[00/50/50] sample prepared in solution, for which Mw is equal to 3 1 10 6 . Latex. Monosized spherical polystyrene latex particles of 1.06-mm diameter bearing sulfate surface groups at a density of 8.50 mC/cm2 were obtained from IDC (Portland). Their density of 1.055 enabled the preparation of nonsedimenting suspensions using a mixture of water and deuterium oxide as suspending liquid phase for the determination of the aggregation rate. Stability domain. Polyethylene cylindrical tubes were used to determine the sediment height because the colloid– polymer complex adsorbs onto glass tubes. The concentration of the latex was 2 g/liter. The height of the settled latex was recorded at maximum compactness. Electrophoretic mobility. The Malvern Zetasizer III was used to determine the electrophoretic mobility of the bare colloid and colloid–polymer complexes in 10 03 M NaCl aqueous medium and at a latex concentration of 7 mg/liter. Equilibrium characteristics of the latex–polymer complexes were determined in the presence of polymers at concentra-

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tions between 0.1 and 4 1 10 05 g/ml. For experiments carried out at the optimum flocculation concentration (ofc) a small sample of the suspension at a concentration of 0.1 g/ liter was diluted with the supernatant liquid phase recovered after centrifugation to obtain a latex concentration of 7 mg/ liter. Aggregation kinetics. Aggregation was carried out using a latex suspension at a concentration of 0.1 g/liter. The mass of polymer initially added to the latex was calculated on the basis of the dosage which led to the maximum height of sediment, the underlying assumption being that the polymer added to the colloid is effectively fully adsorbed. After mixing by gentle tumbling, the test tubes were left at rest during perikinetic aggregation. Aliquots of 1 ml were taken from the aggregating suspension at different time intervals to determine the progress of the aggregation. A particle counter (Coulter counter) was used to determine the concentration c(n, t) of aggregates composed of n elementary particles at time t. The analysis procedure has been detailed elsewhere (13, 14). All experiments were performed at 207C and at pH 5.5 in water without addition of buffer. THEORETICAL

Adsorption of a Polyampholyte Chain on a Negatively Charged Surface Recently Joanny studied the adsorption of a single polyampholyte chain on a solid charged surface (15). He established that for long-range interactions, the adsorption is monitored by the electrical field gradient existing in the vicinity of the surface. Adsorption of a polymer bearing a net negative charge on a negatively charged surface is expected to occur only under certain conditions. For a polyampholyte composed of N monomers distributed among a fraction x of neutral segments, a fraction f of negatively charged segments, and a fraction g of positively charged segments, the criterion for adsorption is f 0 g ú ( f / g) 3 / 2 IB /a,

[1]

where IB Å e 2 /4pDkT is the Bjerrum length, e the elementary charge, D the dielectric constant of the solvent, and a the monomer size. From Joanny’s theory we retain the situation where all the chain segments feel the decaying electric field imposed by the surface. It is concluded that the energy field is larger close to the surface, and energy can be gained by distributing the charges in such a way that the repelled negative charges are away from the surface and the attracted positive charges are closer to the surface (15). It is possible to correlate the excess of charges within the polyelectrolyte layer to the surface potential existing at the boundary between the polymer layer and the surrounding

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solution (16, 17). Since the zeta potential may be related in the same way, a correlation can be established between the values of the zeta potential and the net excess charge ( f 0 g) of the polymer. The existence of an anisotropic distribution of positively and negatively charged chain segments inside the layer should be evident in this way. Dynamic Laws of the Aggregation Kinetics In the irreversible reaction-limited aggregation of a latex in the presence of an electrolyte, an energy barrier is crossed when an interparticle collision succeeds in a sticking. This energy Vh combines repulsive VR and attractive VA terms (18, 19),

t Å 2 0 (w/z),

[6]

where t represents the slope of the size frequency curve in the domain of the small aggregates, and z and w are the exponents of the power laws S(t) É t z;

N(t) É t w .

[7]

The number N(t) and weight S(t) average sizes were calculated on the basis of the aggregate size distribution c(n, t) vs n using the usual relationships N0 Å ∑ nc(n, t);

S(t) Å ∑ n 2 c(n, t)/N0;

n

n

N(t) Å N0 / ∑ c(n, t).

[8]

n

VR Å (Dac 2 /2) ln[1 / exp( 0 kh)]

[2]

VA Å 0Aa/12h,

[3]

and

where a is the radius of the spherical latex particle, D the dielectric constant of the double layer, h the distance between the surfaces of the spheres, c the surface potential, k the Debye–Hu¨ckel reciprocal screening length, and A the effective Hamaker constant. The term ‘‘reaction’’ should be taken as in a chemical reaction where the chance of success is given by (20) WÅ

*

`

h 02 exp(Vh /kT )dh.

[4]

0

In aggregation processes involving polymers, the situation may be more complex because, as indicated by La Mer, the success of the interparticle collision P( u ) depends on the encounter of portions of free and polymer-coated areas (2), P( u ) Å 2u (1 0 u ),

[5]

where u represents the fraction of polymer-coated surface area. The situation is more complex because only encounters between free and covered areas lead to particle sticking. The system merely resembles a statistical problem which can be numerically solved by Monte Carlo techniques. This similarity may explain why computer simulations have been successful in the prediction of dynamic scaling laws for aggregation processes induced by interparticular bridging (3). Pefferkorn and Varoqui found evidence for the validity of the scaling laws determined by simulation to characterize the aggregate size distribution and the temporal evolution of the weight S(t) and number N(t) average sizes of aggregates in colloid–polymer systems (14). They found valid the relationship

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When aggregation is induced by interparticle bridging, the aggregate size distribution usually decreases continuously so that elementary particles and small colloids are present at a high concentration during aggregation. A variation with time of the exponents w and z, as observed for some systems, may result from restructuring processes inside the aggregates (21) and/or the appearance of a different destabilizing phenomenon (22). The relative variation of S(t) and N(t) may be indicative of the nature of the rate-limiting process: a fast increase in S(t) such as S(t) É N 2 (t) indicates that the aggregation develops mainly by collisions involving aggregates of large sizes, whereas a similar increase in S(t) and N(t) is characteristic of a diffusion-limited process. Departure from these limiting rates has not been found in polymeric systems until now. Elaissari and Pefferkorn have determined that t has two values for polymer–colloid systems. t Å 01.50 was found at small values of the degree of surface coverage u, while t Å 01.65 was found at larger values (23). The threshold was on the order of 0.6 for flexible polymers (14) and 0.3 for globular polymers (23). We know that a universal value of 01.5 should characterize reaction-limited processes (24). The higher absolute value of 1.65 is, however, indicative of a lower reactivity of aggregates toward aggregation, which is supposed to result from a concomitant adsorption of solute polymer chains, insofar as polymer chains already attached on other colloids and nonadsorbed chains compete for the same free surface sites. This interpretation agrees with the fact that the adsorption rate is very fast at low degrees of surface coverage but strongly decreases when the adsorption tends to completion. To avoid such complications, the aggregation experiments were performed at the optimum flocculation concentration. RESULTS AND DISCUSSION

Characteristics of the Bare Latex The electrophoretic mobility of the bare latex was determined as a function of pH, and the zeta potential was calcu-

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lated via Smoluchowski’s formula. A constant value of 080 mV was found for pH values between 5.5 and 10. Below pH 5, the absolute value decreased and became positive below pH 3, indicating the presence of protonated hydroxyl surface groups. The experiments were performed at pH 5.5 to avoid ion-pairing of sulfonate groups of AMPS with these groups. Surface Modification Induced by the Homopolymer Acrylamide The assumption of the presence of hydroxyl groups is confirmed by our observation that at pH 5.5, the addition of polyacrylamide promotes a drop in the zeta potential to 0 mV if the latex is treated as a rigid particle. Since in saltfree solution PAM may adsorb via formation of hydrogen bonds with isolated hydroxyl groups (25, 26), this leads us to envisage weak adsorption of the homopolymer on the polystyrene latex although we and others have established that polyacrylamide has no effect on latex stability (27). Since the adsorbed neutral chain segments shift the shear plane far from the surface plane, we can conclude that the electrophoretic mobility of the latex–polymer complex is indicative of the electrical characteristics of the polymer layer. Electrophoretic Mobility of the Colloid–Polymer Complexes The electrophoretic mobility of a polyelectrolyte-coated particle cannot be expressed simply by considering the rigid particle model. Calculation of the zeta potential in this way ignores the effects of the Debye–Hu¨ckel parameter and the Donnan potential in the polyelectrolyte layer and, as a result, overestimates the surface potential at the boundary between the polyelectrolyte layer and the surrounding solution (16, 17). Nevertheless, in an attempt to compare the electrical characteristics of different polymer layers, let us assume that the liquid flow undergoes similar frictional forces in all situations, which allows us to correlate the zeta potential of the polymer-coated latex and the excess charge ( f 0 g) of TABLE 1 Zeta Potential and Charge Characteristics of the Latex–Polymer Complexes Polymer

( f 0 g)

T[80/16/04] T[80/12/08] T[80/08/12] T[80/04/16] C[80/00/20] C[92/00/08] C[00/50/50] PAM

12 4 04 012 020 08 0 0

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Zeta potential (mV) 036.3 033.7 021.7 /24.3 /19.5 /6.2 022.1 0

{ { { { { { { {

Ref. in Fig. 1

4.3 2.5 3.9 2.2 1.7 1.3 0.5 2

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FIG. 1. Zeta potential (mV) of the latex–polymer complex as a function of the excess ( f –g) of the electrical charges of the polymers. The numbers placed in the open squares correspond to the different polymers and refer to the numbers in the last column of Table 1. The top and bottom lines describe the polyelectrolyte and polyampholyte behaviors, respectively.

the adsorbed polyelectrolyte. The limiting values of the zeta potential determined at full surface coverage are represented in Table 1. Figure 1 shows the zeta potential as a function of ( f 0 g). The experimental values fall on two lines: one corresponding to polyelectrolyte–latex complexes and one to polyampholyte–latex complexes. For large negative values of ( f 0 g) the interfacial behavior of the polyampholyte 7 in Fig. 1) corresponds to that of the polyelectrolytes, (see h thus indicating that the presence of a small fraction of negatively charged chain segments is not expected to contravene the usual polyelectrolyte behavior in colloid destabilization. The zeta potential of 022.1 mV resulting from adsorption 3 ) is unexpected, as of the copolymer C[00/50/50] (see h the average net charge of the polyelectrolyte is equal to zero. If the charge balance were zero at each level of the interface, the zeta potential would be equal to that of the polyacryl5 ). The difference observed may result amide shell (see h from the anisotropic distribution of the chain segments in the diffuse layer. A given number of positively charged chain segments are attracted by the negative surface charges of the latex so that the outer zone of the layer may be negatively charged on the average. This scheme is also valid for the symmetrical terpolymers T[80/16/04] and T[80/04/16] 1 and h 7 ) characterized by net charges of 12 and 012, (see h which should display asymmetrical surface charge densities as indicated by the zeta potentials of 036.6 and 24.3 mV, 4 ) respectively. Finally, the terpolymer T[80/08/12] (see h bearing a net positive electrical charge is expected to develop a positive zeta potential. The comparison between the zeta

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FIG. 2. Representation of an adsorbed terpolymer showing the segregation between positively and negatively charged chain segments imposed by the negatively charged adsorbent.

potential of 021.7 mV determined for this polymer and the 8 ) value of /19.5 mV determined for C[80/00/20] (see h leads us to conclude that a maximum of roughly 13 positive polymer charges may be involved in the neutralization of the negative surface charges using the simple assumption of the charge–charge annihilation. Obviously, fewer positive charges are engaged when the total charge g is less than 13 as positive zeta potentials are nevertheless determined for 6 ). The description of the less charged polyelectrolyte (see h the anisotropic charge distribution inside the adsorbed layer depicted in Fig. 2 is in agreement with the conclusion of Joanny (15). On the basis of this information on the fully coated latex, we assume that such a charge segregation may exist even at smaller degrees of surface coverage for which the latex– polymer complexes are unstable.

same number of free and polymer-coated surface portions ( u Å 0.5). The system latex–polyampholyte. Different situations can be observed depending on the net charge of the polyampholytes and copolymers. Polyampholytes characterized by an excess of negatively charged chain segments such as T[80/16/04] do not induce flocculation. When positively charged chain segments are in excess such as for the polymer T[80/04/16], flocculation immediately starts after mixing and develops in a way similar to flocculation induced by adsorption of polyelectrolytes. The sedimentation behavior of the terpolymers T[80/08/ 12] and T[80/12/08] is different from that of the polyelectrolytes. The settling takes weeks to be clearly visible, and we observed a settled bed at the bottom of the test tube, a turbid gel phase in the middle, and a clear supernatant. The values of HS shown in Fig. 4 correspond to the heights of the settled bed. The curves of HS vs polymer dosage for T[80/08/12] and T[80/12/08] are similar in shape, while that of T[80/04/16] shows behavior closer to that of the polyelectrolytes bearing a fraction g of 8 and 20 positively charged chain segments, respectively. The copolymer C[00/50/50] does not flocculate the latex because the outer zone of the adsorbed layer is characterized by a zeta potential of 022 mV, thus promoting an efficient electrosteric repulsion between two approaching colloids. Mechanism and Kinetics of Aggregation of the Latex– Polymer Complexes The system latex–polyelectrolyte. Figure 5a shows the temporal variation in the weight S(t) and number N(t) aver-

Sedimentation Behavior of the Latex–Polymer Complexes The system latex–polyelectrolyte. The copolymers C[80/00/20] and C[92/00/08] induce a fast destabilization of the latex, and a constant height HS of settled beds is obtained within 24 h. As shown in Fig. 3, the shape of the curve HS vs polymer concentration expressed in g/cm3 for C[80/00/20] is high-peaked while that of C[92/00/08] is rounded off, and the optimum flocculation concentration roughly varies by a factor of 8/20. This may be interpreted by considering that the positively charged chain segments of the two polyelectrolytes are in the ratio 20/8. The symmetrical shape of the curves of HS vs polymer concentration shows that the optimum flocculation requires roughly the

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FIG. 3. Height of the settled bed (mm) as a function of polymer concentration for the latex–polyelectrolyte systems: ( l ) C [80/00/20] and ( s ) C[92/00/08].

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lead to different heights of the settled beds as shown in Fig. 3. An increase in the aggregation rate is observed, however, when the residual zeta potential is decreased to a value close to 016 mV after 340 min as shown in Fig. 7. The system latex–polyampholyte. In the presence of T[80/12/08], the aggregation displays unusual kinetic characteristics. Figure 8a shows the temporal variation in S(t) and N(t). In the long initial phase the average aggregate sizes increase according to t 0.04 . The sizes abruptly increase after 50 h and thereafter the variation in S(t) É t 1.2 is equal to that determined in the presence of C[92/00/08]. The lower variation in N(t) is scaled by t 0.12 . The rapid increase in S(t) while the total number of colloids in the suspension slowly decreases may indicate that the aggregates are formed by collisions between large particles and that elementary particles are poorly involved in the process. This interpretaFIG. 4. Height of the settled bed (mm) as a function of polymer concentration for the latex–polyampholyte systems: ( l ) T[80/04/16]; ( s ) T[80/ 12/08]; and ( h ) T[80/08/12].

age sizes of the aggregates formed in the presence of C[92/ 00/08]. Figure 5b shows that the reduced size distributions of the aggregates determined at different times lie on the same curve, thus indicating self-similarity of the size frequency (28–34). From the typical variations in S(t) É t 1.12 and N(t) É t 0.53 and from Eq. [6], we obtain t Å 01.53, a value equal to the slope of the reduced size distribution at small values of the variable n/S(t), which characterizes this class of irreversible processes induced by adsorbed polyelectrolytes (14). Figure 6a shows the temporal variation in the weight S(t) and number N(t) average sizes of the aggregates formed in the presence of C[80/00/20]. Figure 6b shows that the reduced size distributions of the aggregates determined at different times also fall on the same curve. From the variations in S(t) É t 0.40 and N(t) É t 0.16 and from Eq. [6], we obtain t Å 01.60. This value is smaller than the slope 02.2 of the initial variation of the reduced size distribution. The main difference between the two colloid–polymer systems is that the zeta potential displayed at full surface coverage by the adsorbed layer of C[80/00/20] is equal to /19.5 mV while that of C[92/00/08] is equal to /6.2 mV and leads to a rapid aggregation at the optimum flocculation concentration. A zeta potential of 027.8 mV is initially determined at the optimum flocculation concentration for C[80/00/20] indicating the existence of residual net repulsive forces exerting between the half-coated latexes, thus inducing (i) a slowing of the process at the aggregation rate level, (ii) a possible reversibility of the colloid sticking, leading to an increase in the concentration of isolated colloids and aggregates of small sizes, and (iii) a different particle compactness inside the aggregates, which would

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FIG. 5. (a) System latex–C[92/00/08]: weight S(t) ( h ) and number N(t) ( s ) average size of aggregates as a function of the aggregation period (min) (log–log scale). (b) Reduced size distribution of aggregates c(n, t) S 2 (t)/N0 as a function of the reduced variable n/S(t) for the total period of flocculation.

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ation of colloids may be complex. However, we determined that a modification of the temporal variation of the average sizes may result from reconformation of the adsorbed polymer, which established successively the conditions of a reaction- and a diffusion-limited process (22). Redistribution of the charge distribution in the adsorbed layer was found to be responsible for the large delay preceding aggregation (35). Moreover, no size fractionation would arise when reconformation occurs, and charge distribution should similarly modify the reactivity of the polymer groups. This leads us to envisage that the aggregation may be reversible and that a concomitant fragmentation accompanies the slow progress of the aggregation. In this situation, since the colloid–polymer complex initially displays a zeta potential of 041.6 mV and a value close to 030 mV after a period of 1500 min, as shown in Fig. 7, an important fragmentation may result from strong internal repulsive forces below 1500 min and progressively decrease with the progress of the charge redistribution. This situation has been studied by Stoll and Pefferkorn, who showed that for aggregates formed in a diffusion-limited process, fragments of very small sizes are produced when internal repulsive forces emerge suddenly (36, 37). The existence of a bell-shaped curve for the aggregate size distribution is compatible with a reaction-limited process where aggregate restructuring is expected to occur during the aggregation (21). In this case, compacting of aggregates with time would favor the formation of aggregates of typical size even under conditions of a reaction-limited process. Our assumption of reversibility agrees with the variation of N(t) with time, which indicates

FIG. 6. (a) System latex–C[80/00/20]: weight S(t) ( h ) and number N(t) ( s ) average size of aggregates as a function of the aggregation period (min) (log–log scale). (b) Reduced size distribution of aggregates c(n, t) S 2 (t)/N0 as a function of the reduced variable n/S(t) for different periods of flocculation in the rapid regime.

tion is confirmed by the reduced size distribution determined for times between 3800 and 12,800 min, as shown in Fig. 8b. The characteristic curves of Figs. 5b and 6b, valid for times less than 2500 min, are progressively modified by the disappearance of aggregates of size S(t) while the concentration of elementary particles decreases according to S 02 (t). Aggregates of size close to S(t) disappear at a higher rate. The phenomenon responsible for this evolution thus contributes to the emergence of aggregates with a bell-shaped size frequency curve and a typical size of 3 1 S(t). We note that the bell-shaped size distribution is rather self-similar, while that of the smallest aggregates is far from being selfsimilar. The phenomenon inducing the abrupt increase in the aggregation rate after 50 h and the concomitant size fraction-

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FIG. 7. Zeta potential (mV) of the latex–polymer complexes as a function of time (min) for the systems C[80/00/20] ( s ) and T[80/12/ 08] ( l ).

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duces flocs of very large sizes. In the range of latex concentrations between 1 and 2 g/liter, immediately after initial mixing we observed the formation of very small aggregates whose size distribution could not be reproduced. No progress in aggregation was noted for a week. It is conjectured that the initial mixing process is only poorly reproducible and that orthokinetic aggregation is induced by gentle mixing. For latex concentrations below 1 g/liter, the initial size distribution of the latex was recovered after mixing. CONCLUSION

FIG. 8. (a) System latex–T[80/12/08]: weight S(t) ( h ) and number N(t) ( s ) average size of aggregates as a function of the aggregation period (min) (log–log scale). (b) Reduced size distribution of aggregates c(n, t) S 2 (t)/N0 as a function of the reduced variable n/S(t) for different periods of flocculation (min): ( h ) 3855; ( n ) 5410; ( L ) 6810; ( s ) 8490; and ( 1 ) 12,720.

that the number of colloids in the suspension decreases only very slowly, despite the strong increase in S(t). The turbid gel phase observed in the sedimentation experiments obviously contained aggregates of sizes smaller than S(t), while the settled bed was formed of aggregates of average size equal to 3 1 S(t). It is therefore easy to separate small aggregates from those of a given size by centrifugation of the suspension. In the presence of T[80/04/16] bearing an excess of positively charged chain segments, which confers on the 7 in Fig. terpolymer a typical polyelectrolyte character (see h 1), the aggregation was only poorly reproducible in a range of polymer dosages between 0.1 and 14 1 10 06 g/cm3 . For instance, for a latex concentration higher than 2 g/liter, we observed that the aggregation is quite instantaneous and pro-

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The adsorption of terpolymers bearing neutral, positively charged, and negatively charged chain segments and that of copolymers bearing neutral and positively charged chain segments on model colloids bearing negative surface charges lead to colloid–polymer complexes of well-differentiated surface characteristics. All polymers may be classified in two groups on the basis of the zeta potential of the colloid– polymer complexes. All copolymers and terpolymers having an excess of positively charged chain segments adsorb on the latex as usually observed for polycations. Terpolymers characterized by a small excess of negatively charged chain segments adsorb on negatively charged colloids as theoretically predicted. Adsorption induced a redistribution of the chain segments so that, on average, positively charged chain segments were concentrated in the inner interfacial zone while negatively charged ones were concentrated in the outer zone. The importance of the charge distribution anisotropy is revealed by the fact that adsorption of a neutral copolymer bearing positively and negatively charged chain segments in equal concentration and almost alternatingly distributed along the chain backbone conferred a zeta potential of 020 mV on the latex–polymer complex. This value must be compared to the zero potential determined in the presence of polyacrylamide. At the optimum flocculation concentration, terpolymers and copolymers play the role of destabilizing agents although with very different efficiencies. The excess of surface charge constitutes the most indicative parameter. The existence of internal repulsive interactions at large distances usually slows the aggregation rates by inducing a partial reversibility in the process. The electrostatic origin of the internal fragmentation was confirmed by the correlation between the magnitude of the zeta potential of the colloid–polymer complex and the relative extent of the fragmentation process. Likewise, the evolution with time of the zeta potential could be correlated to the evolution of the colloid stability. ACKNOWLEDGMENTS The authors thank J. F. Joanny for helpful discussions. The financial assistance of the Elf Atochem group is gratefully acknowledged.

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AP: Colloid