8626
J. Phys. Chem. B 2007, 111, 8626-8633
Charging and Aggregation of Positively Charged Latex Particles in the Presence of Anionic Polyelectrolytes† Graeme Gillies, Wei Lin,‡ and Michal Borkovec* Laboratory of Colloid and Surface Chemistry, Department of Inorganic, Analytical, and Applied Chemistry, UniVersity of GeneVa, Sciences II, 30 Quai Ernest Ansermet, 1211 GeneVa 4, Switzerland ReceiVed: December 29, 2006; In Final Form: March 16, 2007
Charging behavior and colloidal stability of amidine latex particles are studied in the presence of poly(sodium styrene sulfonate) (PSS) and KCl. Detailed measurements of electrophoretic mobility, adsorbed layer thickness, and aggregation (or coagulation) rate constant on varying the polymer dose, molecular mass of the polymer, and ionic strength are reported. Polyelectrolyte adsorption leads to the characteristic charge reversal (or overcharging) of the colloidal particles at the isoelectric point (IEP). In accordance with classical DerjaguinLandau-Verwey-Overbeek (DLVO) theory, uncharged particles tend to aggregate because of van der Waals attraction, whereas charged particles are stabilized by electrical double layer repulsion. Attractive patchcharge interactions originating from the laterally inhomogeneous structure of the adsorbed polymer substantially decrease the suspension stability or even accelerate the aggregation rate beyond diffusion control. These electrostatic non-DLVO forces become progressively important with increasing molecular mass of the polymer and the ionic strength of the solution. At higher polymer dose of typically 10 times the IEP, one observes the formation of a saturated layer of the adsorbed polymer with a thickness of several nanometers. Its thickness increases with increasing molecular mass, whereby the layer becomes increasingly porous. This layer does not seem to be involved in the suspension stabilization, since at such high polymer doses the double layer repulsion has attained sufficient strength to stabilize the suspension.
1. Introduction The addition of polyelectrolytes to aqueous suspensions of charged colloidal particles drastically modifies their properties, for example, their stability, rheology, flotability, or deposition characteristics to surfaces.1-10 Colloidal particles encountered in practice are mostly negatively charged, and therefore cationic polyelectrolytes are frequently used as additives in industrial processes, most importantly, in papermaking and wastewater treatment. Therefore, many studies focused on systems containing negative particles and cationic polyelectrolytes.1-8 On the other hand, relatively few studies deal with positive particles and anionic polyelectrolytes.8-10 The latter systems are relevant in natural waters, where positively charged iron oxide particles interact strongly with negatively charged humic acids, which are anionic, highly branched polyelectrolytes.11,12 The stability of a colloidal suspension in the presence of oppositely charged polyelectrolytes is governed by the adsorption process of the polyelectrolyte and the resulting charge reversal. At low polymer dose, the magnitude of the particle charge is reduced, leading to a decrease in the suspension stability. At a certain polymer dose, the particle charge is neutralized by the adsorbed polyelectrolyte. In the neighborhood of this isoelectric point (IEP), the aggregation process is fast and similar to diffusion-controlled aggregation. At higher polymer dose, the particle charge is reversed and results again † Part of the special issue “International Symposium on Polyelectrolytes (2006)”. * To whom correspondence should be addressed. E-mail:
[email protected]. ‡ Present address: Key Laboratory of Leather Chemistry and Engineering of Ministry of Education, Sichuan University, Sichuan, Chengdu, P. R. China.
in suspension stabilization. By now, this characteristic behavior of charged particles in the presence of oppositely charged polyelectrolytes is well established.1-5,8-10 Accepting the fact that polyelectrolyte adsorption leads to a charge reversal, this stability behavior is expected on the basis of the theory of Derjaguin, Landau, Verwey, and Overbeek (DLVO).13,14 This classical theory stipulates a competition between attractive van der Waals forces and repulsive diffuse layer overlap forces. The fact that negatively charged particles in the presence of cationic polyelectrolytes behave similarly to positively charged particles in the presence of anionic polyelectrolytes strongly supports the DLVO charge reversal mechanism. However, this classical theory was developed for ideally smooth and homogeneous spherical particles, and therefore its applicability to a system containing polymers is somewhat surprising. Indeed, the existence of additional attractive non-DLVO forces is suggested on the basis of the two following phenomena. The first phenomenon, originally reported by Gregory,1 is that polyelectrolytes lead to aggregation rates of oppositely charged colloidal particles larger than those observed in concentrated salt solutions, where electrical double layer interactions are negligible. This acceleration, which happens near the IEP, can be interpreted because of additional attractive forces acting between oppositely charged patches on the surface. These patches originate from the individual adsorbed polymers and result in a nonuniform charge distribution on the surface. The heterogeneous charge distributions induce attractive electrostatic forces.15-17 Besides the originally studied system containing a sulfate latex and a cationic linear polyamine,1 similar acceleration was observed for sulfate latex particles and poly(ethylene imine) (PEI) and poly(vinyl amine) (PVA), as well as for amidine latex
10.1021/jp069009z CCC: $37.00 © 2007 American Chemical Society Published on Web 04/28/2007
Charging and Aggregation of Latex Particles particles in the presence of poly(styrene sulfonate) (PSS).4,8 In a system containing sulfate latex particles and poly(amido amine) (PAMAM) dendrimers, it was shown that this acceleration becomes increasingly important with increasing molecular mass, again hinting toward patchlike attraction.3 For low molecular mass, the effect is weak since the patches are small and the surface charge distribution appears to be more homogeneous. For high molecular mass, the effect is more important since the patches are larger and thus the distribution is more heterogeneous, as demonstrated by direct imaging by atomic force microscopy (AFM).18 The second phenomenon, through which additional attractive non-DLVO forces become apparent, is the weak dependence of the aggregation rate on the polymer dose in the slow aggregation regime.3,8 DLVO theory predicts a very strong dependence of the aggregation rate on the surface charge density, particularly, at low ionic strengths as confirmed by experiments in well-defined model systems.19-21 In the presence of polyelectrolytes, the aggregation rate depends only weakly on the charge density, which is controlled by the polymer dose. This unusually weak dependence is particularly pronounced at low polymer dose. Again, patch-charge attraction can be invoked to explain this phenomenon as the attraction between oppositely charged patches leads to an acceleration of the aggregation rate, and this effect becomes important when the size of the patches becomes large compared to the Debye length. This point was demonstrated convincingly in a system containing sulfate latex and PAMAM dendrimers, where the molecular mass of the dendrimers was systematically varied over a wide range.3 Indeed, for low molecular mass, the resulting patches are small and the aggregation rate was very sensitive to the polymer dose. However, for high molecular mass, the patches are much larger and the additional attractive forces lead to an acceleration of the rate and to a less pronounced dependence on the dose. These findings suggest that only electrostatic forces dictate the stability of the charged particle suspension. However, besides the classical double layer repulsive forces, electrostatic patch-charge attraction must be equally considered. This point of view is consistent with recent theoretical work that suggests that the adsorption of charged polyelectrolytes to oppositely charged surfaces is largely governed by electrostatic forces but that effects beyond conventional DLVO theory must be taken into account.22-26 The characteristic charge reversal (or overcharging) is explained by the formation of correlated surface structures during the adsorption process, whereby the adsorption to the bare patches continues beyond the charge neutralization point. Furthermore, between such heterogeneously charged patchlike surfaces, one expects additional attractive forces, which are not considered in the traditional DLVO picture. During the approach of two such surfaces, the mutual particle orientations will choose those configurations where a charged patch will be facing a patch on the oppositely charged surface, leading to additional attractive forces.15-17,26 When neutral polymers in good solvents adsorb to particle surfaces, steric repulsion forces can become very important, and they are often responsible for the substantial stability of colloidal systems in the presence of polymers.6,27-30 Water is generally a good solvent for polyelectrolytes mainly because of the strongly solvated charged groups on the somewhat hydrophobic backbone. Therefore, one expects that steric stabilization may contribute to the stabilizing mechanism in such systems. Several studies point toward the possibility of the formation of polyelectrolyte layers adsorbed on oppositely charged particles with substantial thickness in the range of several nanometers,
J. Phys. Chem. B, Vol. 111, No. 29, 2007 8627 sometimes, even up to a few tens of nanometers.6-8,31-34 These conclusions are corroborated by hydrodynamic layer thickness measurements by dynamic light scattering6-8,31,32 and direct force measurements.33,34 Information on polyelectrolyte monolayers is also available from studies of polyelectrolyte multilayers obtained by the sequential layer-by-layer deposition technique.35-38 These systems consist of many alternating layers of cationic and anionic polyelectrolytes, and one finds that the mean thickness of such a polyelectrolyte monolayer is just a few nanometers. This quantity can be estimated from the number of individual layers and the total layer thickness obtained by neutron scattering, reflectometry, ellipsometry, or AFM. In this context, one important question concerning the stabilization of charged particles in the presence of oppositely charged polyelectrolytes arises: Are electrostatic forces solely responsible for the stabilization, or could steric forces due to the overlap of the adsorbed polyelectrolyte layers be equally important? This paper addresses this question by investigating the charge reversal and stability of positively charged amidine latex particles and negatively charged PSS. The measurements were carried out by different light-scattering techniques. One knows that the stability behavior of this system is similar to the case of negatively charged colloidal particles and positively charged polyelectrolyte.8 Thus, it seems that electrostatic forces are indeed dictating the stability behavior. However, the formation of relatively thick adsorbed layers was reported in a similar system, making them potential candidates for steric stabilization.31 The present stability studies are thus accompanied by detailed layer thickness measurements to address the importance of the steric stabilization mechanism. The thickness of these layers is known to increase with the molecular mass, and thus one would expect that steric stabilization should also become important. The other possibility is, however, that the electrostatic forces prevail and the system behaves similarly to the system containing PAMAM dendrimers.3 These questions will be clarified in this paper, whereby insight is gained by systematically varying the molecular mass of the polymer over a wide range. We shall further argue that depletion forces do not play any important role in the discussed phenomena. 2. Experimental Section Materials. Positively charged amidine-terminated surfactantfree polystyrene latex particles were purchased from Interfacial Dynamics Corporation (IDC, Portland). The mean diameter of 210 nm determined by transmission electron microscopy by the supplier was in good agreement with the hydrodynamic diameter of 220 nm measured by dynamic light scattering (DLS) in our laboratory. The particles are in effect monodisperse, possessing a polydispersity characterized by a coefficient of variation of 0.08. The particles have a surface charge density of about 100 mCm-2 as determined by conductivity measurements by the supplier and which is largely independent of the pH. More details on the characterization of the same batch of these particles are given elsewhere.39 Prior to use, all suspensions were dialyzed against Milli-Q water in a stirred ultrafiltration cell (Millipore, Amicon 8010) until the specific resistance of the filtrate reached the value of 18.2 MΩcm of the Milli-Q water. Negatively charged sodium poly(styrene sulfonate) (PSS) with molecular masses of 2.2, 29, 323, and 2260 kDa was supplied by Polymer Standards Service (Mainz, Germany) and was used as received. Being a strong polyelectrolyte, PSS is fully charged over a wide pH range. The gyration radius Rg of PSS of molecular mass of 1000 kDa has been reported as 51 nm in 0.1 M NaCl.40 The radius increases with decreasing monovalent
8628 J. Phys. Chem. B, Vol. 111, No. 29, 2007
Gillies et al.
salt concentration c as Rg ∝ c-0.2, and its hydrodynamic radius is a factor of about 0.6 smaller. At high salt levels, the radii scale with the molecular mass M as Rg ∝ M0.6 similarly to neutral polymers.41 All solutions used were prepared in Milli-Q water, were adjusted to pH 4.0, and were given ionic strength by adding HCl and KCl. Particle suspensions in the presence of polyelectrolytes were prepared by diluting the concentrated particle suspension with the appropriate electrolyte. After an equilibration time of a few minutes, a comparable volume of a similarly pre-equilibrated solution of PSS was added. Rate constant and layer thickness investigations commenced immediately after mixing. All experiments were carried out at a temperature of 25.0 ( 0.2 °C. Electrophoretic Mobility. The particle suspensions were investigated with Doppler velocimetry (Zeta Sizer 2000, Malvern) at field strengths of 125 V/cm and a frequency of 250 Hz. Electrophoretic mobilites were recorded after a 1-2 h equilibration time. The reported electrophoretic mobilities were determined at a particle concentration of 10 mg/L (volume fraction 10-5, number density of 2 × 1015 m-3). No significant differences were observed at other particle concentrations (150 mg/L). Layer Thickness Measurements. The hydrodynamic thickness of adsorbed layers was determined by DLS at 90° with an ALV/CGS-8 goniometer system (Langen, Germany). The instrument uses a solid-state laser of a wavelength of 532 nm (Verdi V2, Coherent, Inc.) operated at 400 mW. Glass cuvettes were cleaned for 30 min in a boiling mixture of hydrogen peroxide (30%), concentrated ammonia, and water in a ratio 1:1:5. The hydrodynamic layer thickness was determined from the difference in hydrodynamic radii of lattices with and without PSS under otherwise identical conditions. To circumvent any influence arising from aggregation, hydrodynamic radii were determined as a function of time over 8 h in very dilute suspension conditions at particle concentrations near 0.04 mg/L (volume fraction 4 × 10-8, number density 8 × 1012 m-3). The hydrodynamic radius of both bare and coated particles is determined by extrapolating to zero time. When extrapolating to time zero for samples with added polymer, the initial transient in hydrodynamic radius is ignored. When observed, the time constant of this initial transient was at least 1 order of magnitude larger than the one expected from fast aggregation. The extreme dilution reduces the particle aggregation rate to the point that the time scale of polymer adsorption is fast with respect to the characteristic time of the aggregation. Particle Aggregation. The aggregation of amidine latex suspensions was investigated with DLS at 90° with ALV-CGS3 (Langen, Germany). This system uses a 20 mW He-Ne laser of a wavelength of 633 nm. The aggregation rates were determined at a particle concentration of 1.0 mg/L (volume fraction 10-6, number density 2 × 1014 m-3) by time-resolved DLS measurements. During a typical measurement of 20-90 min, the hydrodynamic radius did not increase more than 20%, indicating that the aggregation remains in its early stages and primarily particle doublets are being formed. Aggregation rate constants, k, were determined from the relative rate of change of the apparent hydrodynamic radius, rh(q,t), which depends on time t and the magnitude of the scattering vector q, from the relation42
(
)
1 drh(q,t) rh(q,0) dt
tf0
(
) kN0 1 -
)
rh,1 I2(q) rh,2 2I1(q)
(1)
Figure 1. Electrophoretic mobility of amidine latex particles as a function of the dose of poly(styrene sulfonate) (PSS) relative to the particle concentration at pH 4. (a) Dependence on the PSS molecular mass at an ionic strength of 1 mM in KCl and (b) dependence on the ionic strength for PSS of 2260 kDa.
where N0 is the initial particle number concentration, and rh,1 and rh,2 are the respective hydrodynamic radii of the singlets and doublets with corresponding scattering intensities of I1(q) and I2(q). The scattering intensities are known from the theory of Rayleigh, Debye, and Gans, and the ratio of the hydrodynamic radii rh,2/rh,1 ) 1.39 is known from hydrodynamics.42,43 Aggregation rates are commonly reported as the dimensionless stability ratio defined as28
W)
kfast k
(2)
where kfast is the rate constant determined in the fast aggregation regime in the absence of polyelectrolytes at high salt concentrations. In the present case, kfast ) 3.3 × 10-18 m3 s-1 as determined by simultaneous static and dynamic light scattering39 in KCl solutions well above the critical coagulation concentration (CCC). For these particles, the CCC is situated around 0.33 M KCl at pH 4. 3. Results and Discussion Aqueous suspensions of positively charged amidine latex particles were investigated in the presence of negatively charged PSS by different light scattering methods. Electrophoretic mobility, adsorbed layer thickness, and aggregation rate measurements were carried out as a function of the polymer dose, ionic strength, and molecular mass. Electrophoretic Mobility. The charge reversal of the positively charged particles with increasing dose of negatively charged PSS at pH 4 is illustrated in Figure 1. The variation of
Charging and Aggregation of Latex Particles the molecular mass of the PSS in the range from 2.2 to 2260 kDa at an ionic strength of 1 mM in KCl is shown in Figure 1a, while the dependence on the ionic strength is shown in Figure 1b. The electrophoretic mobility is insensitive to both molecular mass and ionic strength. The charge reversal originates from the adsorption of the polyelectrolyte to the particle surface, and similar behavior was reported in other systems earlier.2-6,8-10 At low polymer dose, the mobility is unaffected by the presence of the polymer. Increasing the dose above 2 mg PSS/g latex results in a noticeable decrease in the mobility owing to a compensation of the latex charge by adsorbed PSS. Upon further addition of PSS, the mobility of the latex continues to decrease past the isoelectric point (IEP) located at 6.3 mg/g. Further decrease of the mobility indicates that PSS continues to adsorb to the particles despite both possessing a net negative surface charge. At higher doses around 10 mg/g, the mobility reaches a plateau indicating that maximum surface coverage has been reached. Increasing the polymer dose above this value, the adsorbed amount remains constant near the saturation value of 0.6 ( 0.1 mg/m2, while the rest of the polymer remains in the dissolved state in the bulk solution. The saturation value decreases somewhat with decreasing ionic strengths, but only weakly. For smaller polymer doses, the polymer is completely adsorbed, and only trace amounts of the polymer are dissolved in solution.5 For the system investigated here, the latter point is evidenced by the lack of a particle concentration dependence of the electrophoresis mobility data. The current belief is that the adsorption of polyelectrolytes to an oppositely charged interface is largely electrostatic in origin, even beyond the charge reversal point.23-26 The charge reversal (or overcharging) is explained by the buildup of heterogeneous patchlike surface structures. Adsorption proceeds until the empty surface patches are filled, and this point can be located far beyond the IEP. However, the discussion continues to which extent additional forces such as van der Waals or hydrophobic interactions might be important as well. The position of the IEP is independent of the molecular mass and the ionic strength, in spite of the substantial range in both quantities. Generally, one observes that the IEP shifts to larger polymer doses with increasing ionic strength.5 This variation can be explained by coadsorption of the polyelectrolyte counterions originating from the dissolved salt. With increasing salt level, bound counterions decrease the effective polyelectrolyte charge,44 and consequently more polyelectrolyte is needed to neutralize the particle charge. However, the data reported here and elsewhere8 show that PSS is an exception to this rule. This unusual behavior can be explained by the fact that most studies on charge reversal investigate negatively charged particles and cationic polyelectrolytes, to which the anions are expected to bind strongly.1-5,8 In the presently investigated system involving amidine particles and PSS, the signs of the charges are reversed. We surmise that cations bind only weakly to the negatively charged polyelectrolyte, and thus the shift of the IEP is less pronounced. Cations are known to interact more weakly with surfaces than anions, whereby the effect is mainly caused by the larger polarizability of the latter.37,45,46 The lack of molecular mass dependence of the location of the IEP in the present system is consistent with the findings on positively charged hematite particles and poly(acrylic acid) (PAA)9 but is in sharp contrast with the pronounced shift toward higher polymer dose in the systems involving sulfate latex particles and poly(amido amine) (PAMAM) dendrimers.3 In the latter case, the counterion binding is strongly dependent on the
J. Phys. Chem. B, Vol. 111, No. 29, 2007 8629
Figure 2. Hydrodynamic layer thickness of adsorbed poly(styrene sulfonate) (PSS) for different molecular mass on amidine latex at pH 4. The solid lines serve to guide the eye. (a) Thickness as a function of the PSS dose relative to the particle concentration in 300 mM KCl and (b) as a function on the ionic strength at a polymer dose of about 600 mg/g corresponding to about 100 times the IEP.
molecular mass because of the highly branched dendrimer architecture. This effect is absent for a linear polyelectrolyte, such as PSS and PAA, and probably for polyamines too.1,9 An interesting quantity to consider at IEP is the charging ratio (CR). This parameter states how many polyelectrolyte charges are necessary to neutralize one charge on the particle surface. The dose of 6.3 mg/g latex corresponds to a CR of 1.6, which is comparable to values of 1.3-3.2 reported elsewhere.5,8 One observes that adsorption of PSS to amidine latex is nearly stoichiometric, meaning that roughly one charge on the particle surface is neutralized by one polyelectrolyte charge. In this case, no coadsorption of polyelectrolyte counterions accompanies the charge neutralization process. Kleimann et al.5 have suggested that the CR is determined by the ratio of the nearest neighbor distances between the charged groups on the polymer backbone and on the particle surface and that stoichiometric adsorption is expected when these two distances are comparable. From the molecular structure of PSS, one infers that the distance between the anionic sulfonate groups is about 1.0 nm, while the distance between cationic amidine groups on the latex can be estimated from the known charge density to be 1.3 nm. These two distances are quite similar, and thus a CR near unity is expected. Hydrodynamic Layer Thickness. At higher polymer dose, the thickness of the adsorbed PSS layer becomes measurable. The data are shown in Figure 2. The dependence of the layer thickness on the polymer dose is shown in Figure 2a, while the dependence on the ionic strength is shown in Figure 2b. The
8630 J. Phys. Chem. B, Vol. 111, No. 29, 2007 thickness of the layer increases with increasing molecular mass. In the case of the lowest molecular mass of 2.2 kDa, the layers were too thin to be reliably detected by DLS, and therefore the corresponding data are not reported. The layer thickness as a function of the polymer dose at an ionic strength of 300 mM in KCl is shown Figure 2a. For a polymer dose up to the IEP, the adsorbed layer is not detectable by DLS, although its presence can be clearly inferred from electrophoresis. Under these conditions, the layer remains very thin, typically having a thickness below 0.2 nm. At higher doses of about 10 times the IEP, the layer thickness increases strongly and reaches a plateau value, approximately at the same dose where the plateau in the electrophoretic mobility is reached. The layer thickness at the plateau increases with the molecular mass, being approximately 1.0, 3.5, and 5.7 nm for 29, 323, and 2260 kDa, respectively. These data tentatively suggest a square root dependence on the molecular mass. The ratio of the layer thickness to the gyration radius of the polymer is about 0.15 ( 0.04, and this ratio is quite independent of the molecular mass. This observation suggests strong flattening of the polymer upon adsorption, which is consistent with the substantial train fraction of the adsorbed polymer.47 This behavior is in contrast to the adsorption of neutral water-soluble polymers, such as poly(ethylene oxide). In this case, the adsorbed layer thickness is comparable to the gyration radius of the polymer.29,30 The hydrodynamic layer thickness of adsorbed PSS was further investigated as a function of KCl concentration for different molecular masses at a dose 100 times larger than the IEP. The data are shown in Figure 2b. When PSS is adsorbed at low ionic strength, the layer remains thin, indicating that the polymer is adsorbed almost entirely in trainlike configurations. Increasing the ionic strength above 10 mM, the layer thickness increases rapidly and appears to reach a plateau above 100 mM. This increase in layer thickness and its characteristic dependence on the molecular mass suggest that increasing the electrolyte concentration increases the fraction of loops and tails, but a high concentration of polymer trains remains. At high ionic strength, the layer swells progressively with increasing molecular mass. This progressive swelling can be surmised by combining the latter observation with the fact that the adsorbed amount remains roughly constant, as evidenced from the electrophoresis data. We suspect that the layer has low porosity for the low molecular mass PSS, but the layer porosity exceeds 0.9 for the highest molecular mass investigated. Similar increase in layer thickness with electrolyte concentration has been reported for other polyelectrolytes adsorbed on oppositely charged particles.6,7 In particular, the thickness of poly(diallyl-dimethylammonium chloride) (DADMAC) layers on silica was shown to increase strongly with increasing ionic strength and with increasing molecular mass.6 On the other hand, the adsorbed amount depends on the molecular mass only weakly. Combining these observations, one may again conclude that at high salt levels the porosity of the adsorbed layers increases with increasing molecular mass. A similar, but less complete, data set was published for poly(lysine) layers on negatively charged latex.7 In all these studies, however, the reported values of the layer thickness exceed the present ones. It is difficult to ascertain whether these effects are real or whether experimental artifacts come into play. While it is conceivable that the hydrophobic effect compresses the PSS layer, it is essential to note that reliable layer thickness measurements are difficult to carry out in these systems. Care must be exercised to properly separate the layer formation from particle aggregation, as these two effects are not easily distin-
Gillies et al. guished by DLS. Relatively large hydrodynamic thickness of 10 nm and more have further been reported for adsorbed poly(ethylene imine) (PEI) of high molecular mass on sulfate latex particles.8,32 However, this system might not be directly comparable to the present case of linear polyelectrolytes, since PEI is highly branched. The observed increase of the layer thickness is readily rationalized.22,23,33,48 At low ionic strength, the interactions between the polymer segments are screened only weakly. The polymer adopts a more rigid conformation leading to strong attractive segment-surface interactions and flat adsorbed configurations. At higher ionic strengths, the segment-segment interactions are progressively screened, leading to more coiled conformations and thicker adsorbed layers. Nevertheless, the situation is probably dominated by kinetic effects. Initially, the polyelectrolytes adsorb in a flat configuration, and at later stages only few adsorption sites separated by large distances remain. The later stages of the adsorption are dominated by those sites that lead to long loops and a substantial layer thickness.49 Suspension Stability. The stability ratio versus the polymer dose is shown in Figure 3. One observes the characteristic “U” shaped plots with the minimum located at the IEP. The variation of the stability with the molecular mass is shown in Figure 3a at an ionic strength of 1 mM. Figure 3b and 3c illustrates the dependence on the salt concentration for the molecular mass of 2260 kDa and 29 kDa, respectively. In general, the stability decreases with increasing molecular mass and ionic strength and is accompanied by a decrease of the slope in the stability plot in the slow regime (i.e., widening of the U). The U shaped stability plot has been reported for several particle systems containing oppositely charged polyelectrolytes.1-6,8-10 The effect can be qualitatively rationalized with the DLVO theory.13,14 Particles are highly charged above and below the IEP and repulsive forces due to the overlap of the diffuse layers lead to slow aggregation between the particles and a larger stability ratio. Near the IEP, attractive van der Waals forces dominate the interaction profile and lead to rapid aggregation. Figure 3a reveals the primary finding of this paper, namely, the strong decrease of the stability with increasing molecular mass of PSS. The region of fast aggregation widens, and at the same time the slope of the stability plot decreases, in particular, at polymer doses below the IEP. To the best of our knowledge, this is the first time where this effect has been reported for an anionic polyelectrolyte. The widening of the stability plot with increasing molecular mass was reported for cationic polyelectrolytes earlier.1,3 In particular, quite similar trends of the stability plot with increasing molecular mass were observed for sulfate latex particles in the presence of PAMAM dendrimers.3 The close similarity between the anionic and the cationic polyelectrolytes strongly indicates that the observed phenomena are only governed by electrostatic forces between heterogeneous patchlike charge distributions. The major difference between these two systems is that the IEP shifts toward higher polymer dose with increasing molecular mass for the PAMAM dendrimers, while the position of the IEP is independent of the molecular mass in the PSS system discussed here. The present finding is similar to the case of negative latex particles and a linear polyamine, where the position of the fast aggregation region does not shift when the molecular mass was varied.1 In a system containing positively charged hematite particles and negatively charged poly(acrylic acid) (PAA), only a minor shift upon a substantial molecular mass variation was observed.9 The pronounced shift in the
Charging and Aggregation of Latex Particles
Figure 3. Stability ratio of amidine latex as a function of the dose of poly(styrene sulfonate) (PSS) relative to the particle concentration at pH 4. The solid lines serve to guide the eye. (a) Dependence on the molecular mass of PSS at an ionic strength of 1 mM in KCl. Dependence on the ionic strength for PSS of molecular mass of (b) 2260 kDa and (c) 29 kDa. Inset on the top shows schematically the envisaged structure of the adsorbed layers for high molecular mass PSS.
PAMAM dendrimer system originates from the fact that the amount of counterions bound to the dendrimers increases with the molecular mass.3 For a linear polyelectrolyte, this effect seems to be absent. Recall that the IEP always lies within the fast aggregation region,1-3,5,6,8-10 and thus any shift in the IEP
J. Phys. Chem. B, Vol. 111, No. 29, 2007 8631 is always accompanied by a corresponding shift of the instability region. The decrease of the suspension stability with increasing molecular mass has been attributed to increasing strength of attractive electrostatic interactions between oppositely charged patches.1,3 At low surface coverage, the oppositely charged PSS chains adsorb individually, leading to isolated negatively charged patches on the positively charged latex surface depicted in Figure 3 (top). With increasing adsorption density, the layers will still remain heterogeneous, but a layer formed of low molecular mass polymer will be less heterogeneous than a layer formed with a polymer of high molecular mass. The more heterogeneous layer will lead to stronger attractive interactions. These interactions will be important once the characteristic size of the patches exceeds the Debye length. This point is the likely reason why the low molecular mass polymers of 2.2 and 23 kDa show almost no difference in stability, while a substantial decrease in stability is observed for the molecular masses of 323 and 2260 kDa. Only the gyration radii of the polymers with the latter two molecular masses substantially exceed the Debye length, in this case, being around 10 nm. For the largest molecular mass, only about 12 polymer chains are adsorbed to a single particle, and considering the known gyration radii, one concludes that the surface coverage is likely to be rather high. A very similar onset was observed in the system containing sulfate latex and PAMAM dendrimers.3 This striking similarity between the present PSS data and the formerly published PAMAM dendrimer data3 suggests that the patch-charge attraction mechanism is the important one, while polymer bridging is irrelevant. While polymer bridging cannot be excluded on the basis of the present data alone, this mechanism cannot be operational in the case of highly branched dendrimers. The variation of the stability plots with the ionic strength is very similar to the variation with the molecular mass. Indeed, the same patch-charge attraction mechanism can be invoked to rationalize the salt dependence shown in Figure 3b and c. With increasing ionic strength, the Debye length decreases and the heterogeneous surface is probed on increasingly smaller length scales. Thus, patch-charge attraction becomes increasingly important and leads to a decrease in the suspension stability. Similar salt dependence of the suspension stability has been observed in other charged particle systems in the presence of oppositely charged polyelectrolytes1,3-6,8 and has been interpreted in terms of patch-charge attractions. In this context, the DLVO theory predicts extremely steep stability profiles, similar to those for low molecular mass PSS and low ionic strength shown in Figure 3c. While such narrow U shaped stability profiles are expected for homogeneous surfaces, wider stability profiles with more moderate boundary slopes are observed for more heterogeneous surfaces, like those shown for high molecular mass in Figure 3b. We note another characteristic feature in the stability plots, which strongly supports the electrostatic patch attraction mechanism. The data shown in Figure 3 reveal that the stability ratio decreases at the IEP with decreasing ionic strength. However, the effect is not easily recognized on the scale of Figure 3. For this reason, the stability ratio at IEP is reported as a function of the ionic strength in Figure 4. One observes that the stability ratio decreases with decreasing ionic strength and that the effect becomes increasingly important with increasing molecular mass. This acceleration at the IEP has been already observed in other systems1-4,8 and has been explained in terms of attractive patchcharge interactions. At the IEP, the repulsive component of the electrostatic double layer overlap force is absent, but the patch-
8632 J. Phys. Chem. B, Vol. 111, No. 29, 2007
Gillies et al. It is less obvious to firmly exclude the role of the forces due to the adsorbed polymers, but we suspect that neither attractive bridging nor steric repulsion forces are important. Bridging forces can be excluded, since very similar features are observed in a dendrimer-containing system, where this mechanism is certainly not operational.3 While we have clearly established that a saturated layer of the adsorbed polymer with a thickness of several nanometers is formed at a polymer dose of typically 10 times the IEP, this layer does not seem to be involved in the suspension stabilization. At this point, the electrostatic repulsive forces have attained sufficient strength to stabilize the suspension completely. Whether this observation is generic or whether this layer may contribute to suspension stabilization in other systems remains an open question.
Figure 4. Stability ratio of amidine latex as a function of the ionic strength with adsorbed PSS within the fast aggregation regime for different molecular mass at pH 4. The solid lines serve to guide the eye. Schematic structure of the particles with adsorbed PSS near the IEP for different molecular mass are represented on the top.
charge attractive force remains present. With decreasing ionic strength, the patch-charge attraction becomes more important and thus leads to a more pronounced acceleration of the rate constant. The structure of the adsorbed layers is schematically depicted in Figure 4 (top). 4. Conclusions Poly(sodium styrene sulfonate) (PSS) adsorbs strongly on amidine latex particles, leading to a charge reversal and a subsequent formation of a saturated polymer layer. We argue that the suspension stability is mainly governed by electrostatic interactions. Repulsive forces between overlapping diffuse layers are capable of stabilizing the suspensions away from the IEP, and they are absent in its vicinity where attractive van der Waals forces destabilize the suspension. Attractive patch-charge interactions substantially decrease the suspension stability and originate from the laterally inhomogeneous structure of the adsorbed polymer surface layers. Patch-charge effects become increasingly important with increasing molecular mass of the polymer and increasing ionic strength. In light of similar results existing in the literature for cationic polyelectrolytes,1,3 the presently described influence of the molecular mass and ionic strength can be considered as established and applicable to any oppositely charged polyelectrolyte-particle system. In particular, the similarities between the anionic and cationic systems strongly indicate that the observed trends are governed by electrostatic interactions between patchlike charge heterogeneities. One might suspect that polymer-induced interactions could be also relevant in the present system. First of all, it is important to realize that depletion interactions are irrelevant within the entire concentration range considered. While depletion interactions have been observed in polyelectrolyte solutions,50,51 these effects are important at much higher polymer concentrations and especially at low salt levels. In the present case, depletion forces become important in salt-free PSS solutions at concentrations of 10 mg/L and higher,50 while the concentrations used here are about 3 orders of magnitude smaller. In the present system, the monovalent salt ions are, moreover, in excess with respect to the counterions originating from the polyelectrolyte or the particles.
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