Super-Stoichiometric Charge Neutralization in ParticleâPolyelectrolyte

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Super-Stoichiometric Charge Neutralization in Particle-Polyelectrolyte Systems Jo¨rg Kleimann,† Ce´cile Gehin-Delval,†,‡ Helmut Auweter,§ and Michal Borkovec*,† Department of Inorganic, Analytical, and Applied Chemistry, University of Geneva, Science II, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland, and Department of Polymer Physics, BASF AG, Ludwigshafen, Germany Received December 15, 2004. In Final Form: January 31, 2005 The adsorption of poly(vinylamine) (PVA) on poly(styrene sulfate) latex particles is studied, and its consequences on the charging behavior and suspension stability are investigated. The adsorption process is assessed by batch depletion experiments and time-resolved electrophoretic mobility measurements. The adsorption of PVA appears to be basically irreversible. The rate of adsorption decreases with decreasing polymer dose. At low polymer dose, the polymer coverage corresponds to the amount of the polyelectrolyte added, while at high polymer dose, the polymer coverage saturates the surface. Stability ratios are determined by dynamic light scattering, and strongly depend on the polymer dose and salt level. The aggregation is rapid near the isoelectric point (IEP), and it slows down when moving away from it. The charge neutralization is highly nonstoichiometric with charging ratios (CR) larger than unity, meaning that several charges on an adsorbed polyelectrolyte chain are necessary to neutralize a single charge on the particle surface. By comparing the IEP for particles and polyelectrolytes of different charge densities, we find a strong dependence of the CR on the mismatch between the average distances between individual charges on the surface and on the polyelectrolyte. A simple model is proposed to explain this trend.

1. Introduction Aqueous dispersions of solid particles in the nanometerto-micrometer size range represent an important class of chemical products, such as, for example, paints, glues, cosmetics, or food additives.1-3 The colloidal stability of such dispersions is seldom guaranteed by pure electrostatic repulsion, as stipulated by the classical theory put forward by Derjaguin, Landau, Verwey, and Overbeek (DLVO).4-6 This theory explains the stability of suspensions of weakly charged particles in the presence of indifferent electrolytes quantitatively.7,8 For highly charged particles, however, the theory is applicable only semiquantitatively, as various short-range forces become important. Stabilization of industrially relevant aqueous suspensions is typically achieved with polyelectrolytes. Suitably chosen, they provide excellent dispersion properties, but they may also give rise to particle aggregation.9-12 Cationic polyelectrolytes are particularly important, as they are normally oppositely charged to the frequently occurring negatively charged surfaces. Adsorption of polyelectrolytes * Author to whom correspondence should be addressed. Phone: +41 22 379 6045. E-mail: [email protected]. † University of Geneva. ‡ Present Address: Nestle ´ Research Center, Nestec Ltd, Verschez-les-Blanc, P.O. Box 44, CH-1000 Lausanne 26, Switzerland. § Polymer Physics Laboratory. (1) Tadros, T. F. Adv. Colloid Interface Sci. 1993, 46, 1. (2) McKay, R. B. E. Technological applications of dispersions; Marcel Dekker: New York, 1994; Vol. 52. (3) Kissa, E. Dispersions; Marcel Dekker: New York, 1999; Vol. 84. (4) Derjaguin, B. V.; Landau, L. Acta Physicochim. U.S.S.R. 1941, 14, 633. (5) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (6) Israelachvili, J. Intermolecular & Surface Forces, 2nd ed.; Academic Press: London, 1991. (7) Behrens, S. H.; Borkovec, M.; Schurtenberger, P. Langmuir 1998, 14, 1951. (8) Behrens, S. H.; Christl, D. I.; Emmerzael, R.; Schurtenberger, P.; Borkovec, M. Langmuir 2000, 16, 2566.

to oppositely charged particles initially leads to a decrease of the overall particle charge. At a certain polymer dose, the particle charge is neutralized. This neutralization results in an isoelectric point (IEP) and rapid aggregation of the colloidal particles. Upon further polyelectrolyte addition, the adsorption continues beyond the IEP, leads to a charge reversal of the particle, and a restabilization of the particle suspension.13-16 The charge reversal phenomenon (“overcharging”) is largely of electrostatic origin.17,18 The overcharging is caused by the electrostatic attraction of the polyelectrolyte to the particle surface, which remains attractive even when the diffuse layer charge of the particle is of equal sign as the polyelectrolyte charge.19,20 Thereby, the repulsion between adsorbed polyelectrolytes is reduced due to strong mutual lateral correlations. Several studies have already focused on the interaction between charged particles and oppositely charged polyelectrolytes. Some authors have investigated the adsorption process,21-25 while others have considered the charge (9) Gregory, J. J. Colloid Interface Sci. 1973, 42, 448. (10) Walker, H. W.; Grant, S. B. Colloids Surf., A 1996, 119, 229. (11) Auweter, H.; Andre, V.; Horn, D.; Luddecke, E. J. Dispersion Sci. Technol. 1998, 19, 163. (12) Fritz, G.; Schadler, V.; Willenbacher, N.; Wagner, N. J. Langmuir 2002, 18, 6381. (13) Killmann, E.; Bauer, D.; Fuchs, A.; Portenla¨nger, O.; Rehmet, R.; Rustemeier, O. Prog. Colloid Polym. Sci. 1833, 111, 135. (14) Bouyer, F.; Robben, A.; Yu, W. L.; Borkovec, M. Langmuir 2001, 17, 5225. (15) Ashmore, M.; Hearn, J.; Karpowicz, F. Langmuir 2001, 17, 1069. (16) Radeva, T. Colloids Surf., A 2002, 209, 219. (17) Grosberg, A. Y.; Nguyen, T. T.; Shklovskii, B. I. Rev. Mod. Phys. 2002, 74, 329. (18) Quesada-Perez, M.; Gonzalez-Tovar, E.; Martin-Molina, A.; Lozada-Cassou, M.; Hidalgo-Alvarez, R. ChemPhysChem 2003, 4, 235. (19) Nguyen, T. T.; Shklovskii, B. I. Phys. Rev. Lett. 2002, 89, 0181011. (20) Nguyen, T. T.; Shklovskii, B. I. J. Phys. IV 2002, 12, 215. (21) Kokufuta, E.; Takahashi, K. Macromolecules 1986, 19, 351. (22) McCarron, A. M.; Crispo, S.; Smith-Palmer, T. J. Appl. Polym. Sci. 2002, 83, 2382.

10.1021/la046911u CCC: $30.25 © 2005 American Chemical Society Published on Web 03/03/2005

Charge Neutralization in Particle-Polyelectrolyte Systems

reversal with electrokinetic techniques,26-30 and finally, some studies have focused on the aggregation kinetics.29-35 By now it is well established that charge reversal governs the colloidal stability of such systems, which also strongly depends on the salt level.9,14 Near the charge neutralization point, the aggregation rate is typically accelerated due to attractive interactions induced by surface charge heterogeneities. The fast aggregation regime has also been shown to widen with an increase of the molecular mass of the polyelectrolyte, presumably also due to increasing importance of surface charge heterogeneities.36 Aggregation and charging behavior of sulfate latex particles in the presence of poly(vinylamine) (PVA) was already investigated.37 That study indeed confirms the general patterns of charge reversal, particularly, by investigating the effects of the charge variation of PVA as a function of pH. On the other hand, the data indicate that depending on ionic strength about 2-5 charges on the polyelectrolyte are necessary to neutralize one particle charge. This charging ratio (CR) is naı¨vely expected to be unity, as confirmed in a system containing a cationic polysaccharide, chitosan, and sulfate latex particles.15 In the PVA system, the CR could be eventually larger due to incomplete adsorption of the polyelectrolyte. More recently, however, in systems containing poly(amido amine) (PAMAM) dendrimers, a CR as high as 40 was reported.36 Such widely varying CRs are surprising, but could be eventually caused by incomplete polymer adsorption too. The authors have argued that adsorption is quantitative but presented no experimental adsorption data. This study aims to shed light on this point. We present experimental adsorption, electrophoresis, and stability data for the system containing PVA and sulfate latex in order to clarify whether the polyelectrolyte is completely adsorbed near the IEP. We conclude that adsorption is indeed complete, but this point raises the question why the CRs vary so much from system to system. For this reason, we present further data on different types of PVA and sulfate latex particles. Comparison of these results with additional available literature data leads to the conclusion that CRs vary widely and that these variations are related to co-adsorption of the counterions of the polyelectrolytes. 2. Experimental Section Polyelectrolytes. PVAs were synthesized at BASF, Ludwigshafen, Germany. The polyelectrolytes consist of two types of monomer units in random sequence, namely of positively (23) Farrokhpay, S.; Morris, G. E.; Fornasiero, D.; Self, P. J. Colloid Interface Sci. 2004, 274, 33. (24) Bob, M.; Walker, H. W. Colloids Surf., A 2001, 191, 17. (25) Bauer, D.; Killmann, E.; Jaeger, W. Colloid Polym. Sci. 1998, 276, 698. (26) Fuchs, A.; Killmann, E. Colloid Polym. Sci. 1998, 279, 53. (27) Radeva, T.; Petkanchin, I. J. Colloid Interface Sci. 1997, 196, 87. (28) Walker, H. W.; Grant, S. B. Langmuir 1996, 12, 3151. (29) Zhang, J.; Huguenard, C.; Scarnecchia, C.; Menghetti, R.; Buffle, J. Colloids Surf., A 1999, 151, 49. (30) Ashmore, M.; Hearn, J. Langmuir 2000, 16, 4906. (31) Walker, H. W.; Grant, S. B. J. Colloid Interface Sci. 1996, 179, 552. (32) Rustemeier, O.; Killmann, E. J. Colloid Interface Sci. 1997, 190, 360. (33) Fuchs, A.; Killmann, E. Colloid Polymer Sci 2001, 279, 53. (34) Ferretti, R.; Zhang, J. W.; Buffle, J. J. Colloid Interface Sci. 1998, 208, 509. (35) Ferretti, R.; Stoll, S.; Zhang, J. W.; Buffle, J. J. Colloid Interface Sci. 2003, 266, 328. (36) Lin, W.; Galletto, P.; Borkovec, M. Langmuir 2004, 20, 7465. (37) Yu, W. L.; Bouyer, F.; Borkovec, M. J. Colloid Interface Sci. 2001, 241, 392.

Langmuir, Vol. 21, No. 8, 2005 3689 charged vinylamine, -CH2CH(NH3+)-, and vinyl formamide, -CH2CH(NHCHO)-, units. The experimental conditions of pH 4.0 ensure that >90% of the primary amine groups are protonated.38 The vinyl formamide units, which originate from the incomplete hydrolysis of the polyelectrolyte precursor, remain neutral. By using a fully hydrolyzed PVA-94 with a degree of hydrolysis (DH) of 94.3% and a molecular mass of 520 kg/mol and partially hydrolyzed PVA-32 with DH 32.1% and a molecular mass of 470 kg/mol, two different charge densities can be investigated. The degree of hydrolysis is determined by polyelectrolyte titrations with potassium poly(vinyl sulfate) at pH 2.0 in the absence of background electrolyte and o-toluidine blue as indicator.39 The molecular mass was determined by static light scattering and differential refractometry. Polyelectrolyte solutions were extensively dialyzed in a cellulose ester membrane (cutoff ) 500 g/mol) against deionized water (Milli-Q, filter cutoff ) 0.22 µm) until there was no difference between the conductivities of the surrounding water and of fresh water. Polyelectrolyte concentrations after dialysis were determined by total organic carbon and nitrogen analysis (TOC-V, Shimadzu, Japan). Polyelectrolyte solutions are always pre-equilibrated at pH 4.0 and KCl at concentrations required for the experiments. Particles. Surfactant-free poly(styrene sulfate) latex (SL) particles are purchased from Interfacial Dynamics Corporation, Portland, OR. Highly charged SL-67 particles have a surface charge density of 67 mC/m2, as determined by conductometric titrations by the manufacturer. Their mean diameter of 120 nm and the coefficient of variation of 8.4% are measured by transmission electron microscopy (TEM). From this information and the density of 1.05 g/cm3, the specific surface area of 48 m2/g can be estimated reliably, as demonstrated earlier for similar latex particles.40 The weakly charged SL-12 particles bear a surface charge of 12 mC/m2. Their mean diameter is 190 nm, the coefficient of variation is 3.1%, and the specific surface area is 30 m2/g. In both cases, the particle diameter is in excellent agreement with static and dynamic light scattering measurements. The SL-12 particles were used for similar studies previously.36 The suspensions are extensively dialyzed in deionized water with cellulose ester membranes (cutoff ) 300 kg/mol). Total organic carbon analysis and static light scattering are used to determine the particle concentrations in stock solutions after dialysis. All experiments are carried out at pH 4.0 and a temperature of 25 °C. The ionic strengths in the range of 1-100 mM are adjusted with KCl. Adsorption Measurements. The amount of adsorbed polyelectrolyte is determined by batch depletion experiments from solution.41,42 Particle suspensions are shaken for 24 h in the presence of PVA and KCl at pH 4.0. The particle concentrations are between 30 mg/L and 15 g/L, and concentrations of PVA are above 0.3 mg/L. The sample is subsequently centrifuged for 4 h at 105g, and the supernatant is filtered through a syringe filter (Millipore, 0.1 µm). The concentration of PVA is determined in the supernatant by total nitrogen and carbon analysis. The C/N ratio serves as a reliability check. The procedure was tested in blank experiments with pure salt solutions, with particle solutions without PVA, and PVA solutions without particles. The detection limit of PVA in the supernatant was about 10 µg/L. The maximum PVA concentrations were limited to about 20 mg/L due to difficulties to measure accurately the adsorbed amounts at higher concentrations. Electrophoretic Mobility. Laser Doppler velocimetry is used to measure electrophoretic mobilities (Zetasizer 2000, Malvern). The applied voltage in the 1 cm quartz cell is between 75 and 150 V, and the modulation frequency is set to 1 kHz. For SL-12 particles, the lowest concentration is 0.38 mg/L. Neutral attenuator plates of several optical densities serve to optimize the count rate for particle concentrations up to 380 mg/L. (38) Katchalsky, A.; Mazur, J.; Spitnik, P. J. Polymer Sci. 1957, 23, 513. (39) Horn, D. Prog. Colloid Polym. Sci. 1978, 65, 251. (40) Gisler, T.; Schulz, S. F.; Borkovec, M.; Sticher, H.; Schurtenberger, P.; D’Aguanno, B.; Klein, R. J. Chem. Phys. 1994, 101, 9924. (41) Tartakovsky, A.; Drutis, D. M.; Carnali, J. O. J. Colloid Interface Sci. 2003, 263, 408. (42) Atkin, R.; Craig, V. S. J.; Wanless, E. J.; Biggs, S. Adv. Colloid Interface Sci. 2003, 103, 219.

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Light Scattering Experiments. Particle aggregation is monitored by time-resolved dynamic light scattering (DLS). The measurements are performed on a light scattering goniometer with an optical fiber pseudo-cross-correlation detector (ALVCGS8F, Langen, Germany) and a solid-state laser (Verdi V-2, Coherent, Santa Clara, USA) as the light source (532 nm). Borosilicate glass cuvettes were cleaned in a boiling mixture of hydrogen peroxide (30%, 1 volume share) and sulfuric acid (96%, 4 volume shares) and rinsed with deionized water. The samples were prepared by mixing the PVA solution with the particle suspension, which was followed by shaking the mixture. Concentrations and volumes are chosen to avoid high local particle concentrations. The final particle number concentration is 1.0 × 1015 m-3 (3.8 mg/L SL-12). All measurements are carried out at a scattering angle of 90°. Correlation functions are typically recorded for 15 s, and the apparent hydrodynamic radius, rh, is evaluated from a second-order cumulant fit. The aggregation rate constant, k, is obtained from the initial relative rate of change of the hydrodynamic radius from the relation43

(

)

drh(t,q) 1 dt rh(0,q)

tf0

[

) kN0 1 +

]( )

sin(2aq) 1 12aq R

(1)

where N0 is the initial particle number concentration, a is the particle radius, q is the magnitude of the wave vector, and R ≈ 1.39 is the relative hydrodynamic radius of the dimer. This equation invokes the Rayleigh-Gans-Debye (RGD) approximation for the particle dimer, which is applicable for sufficiently small particles as the ones used here.44 The aggregation rate is reported in terms of the stability ratio

W)

kfast k

(2)

where k is the aggregation rate constant measured and kfast is the fast aggregation rate constant in a polymer-free reference system containing an excess of inert salt. In the latex particle suspensions considered, we have found critical coagulation concentrations of 0.2 and 0.3 M for the weakly charged SL-12 and highly charged SL-67. The fast aggregation rate constants are (3.5 ( 0.2) × 10-18 and (3.2 ( 0.4) × 10-18 m3/s for SL-12 and SL-67, respectively.

3. Results and Discussion Adsorption. The adsorption process of highly charged cationic poly(vinylamine) (PVA-94) onto weakly charged negative sulfate latex (SL-12) particles is investigated with batch depletion experiments and through electrophoretic mobility measurements. Batch depletion experiments are carried out at an ionic strength of 10 mM in KCl at pH 4.0, where the PVA is fully charged.38 The particle concentration is varied between 30 mg/L and 15 g/L (corresponding to number concentrations between 8.0 × 1015 and 4.0 × 1018 m-3). Polyelectrolyte doses below 0.01 mg/g result in free polymer concentrations, which are below the detection limit, even at the highest particle concentrations. Experiments with doses above 20 mg/g are also unreliable due to difficulties in determining the adsorbed amount accurately. Figure 1 shows the adsorbed amount as a function of polymer dose. At low polyelectrolyte dose, complete adsorption of polymer from solution onto the particles can be observed. At high polymer dose, the adsorbed amount shows saturation at the adsorption plateau at (0.13 ( 0.05) mg/m2, which is reached above a polymer dose of (3.90 ( 0.05) mg/g (arrows). The solid lines in Figure 1 are calculated under the assumption of complete adsorption (43) Holthoff, H.; Egelhaaf, S. U.; Borkovec, M.; Schurtenberger, P.; Sticher, H. Langmuir 1996, 12, 5541. (44) Bohren, C. F.; Huffmann, D. R. Adsorption and Scattering of Light by Small Particles; Wiley-Interscience: New York, 1983.

Figure 1. Adsorbed amount of cationic polyelectrolyte PVA94 on negatively charged latex particles SL-12 as a function of polymer dose by batch depletion experiments in 10 mM KCl and pH 4.0 at different particle concentrations in semilogarithmic representation. Solid lines refer to a complete polymer adsorption up to a maximum coverage of 0.13 mg/m2. The inset shows the same data in a doubly logarithmic representation.

until the limiting coverage is reached, and the simple model fits the data within experimental error. The amount adsorbed plotted as a function of the polymer dose is entirely independent of the particle concentration, which is varied over several orders of magnitude (see Figure 1). When the data would be plotted as a function of the free polymer concentration, as is customary for adsorption isotherms, only the constant adsorption plateau would be observed, and no dependence on the free solution concentration can be established. Due to the facts that an adsorption plateau exists and that below the plateau the polymer adsorbs completely, we have strong indications that the adsorption is not an equilibrium process but is rather governed by irreversible adsorption kinetics. Similar behavior was also reported for poly(diallyldimethylammonium chloride) (PDADMAC) onto negatively charged particles.45 Therefore, we tentatively conclude that the irreversible adsorption mechanism is generic for the adsorption of polyelectrolytes on oppositely charged particles. Adsorption of polyelectrolytes on oppositely charged particles leads to a charge reversal and, thus, has an important effect on their electrophoretic mobility. Let us now discuss such results for weakly charged SL-12 particles in the presence of PVA-94 at pH 4.0 and in 10 mM KCl as a function of time and particle concentration. Figure 2 depicts the electrophoretic mobility as a function of the polymer dose. Since we have mentioned the importance of kinetic effects, let us first discuss effects of time. The fact that the adsorption is time dependent is best demonstrated by the data shown in Figure 2a, which compares the mobility obtained right after exposing the particles to polyelectrolyte (solid circles) with measurements carried out 1 day after the sample preparation (open circles). The particle concentration is 3.8 mg/L (1.0 × 1015 m-3) in both cases. At low polyelectrolyte dose, the electrophoretic mobility is weakly affected by the addition of polyelectrolyte. Increasing the polyelectrolyte dose leads to an increase of the mobility since the negative particle charge is reduced by adsorption of the positively charged polymer. At (45) Bauer, D.; Buchhammer, H.; Fuchs, A.; Jaeger, W.; Killmann, E.; Lunkwitz, K.; Rehmet, R.; Schwarz, S. Colloids Surf., A 1999, 156, 291.


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Figure 3. Electrophoretic mobility measurements of SL-12 particles in the presence of PVA-94 polyelectrolyte as a function of time at pH 4.0 and in 10 mM KCl. A particle concentration of 3.8 mg/L (1.0 × 1015 m-3) is kept constant at various polyelectrolyte doses (solid symbols). The effect of different particle concentrations on the adsorption process is investigated at a polymer dose of 1.1 mg/g (open symbols).

Figure 2. Electrophoretic mobility of SL-12 particles as a function of PVA-94 polymer dose in 10 mM KCl and pH 4.0. (a) Comparison between measurements right after exposing particle suspension to polyelectrolyte (b) and 1 day later (O) at a concentration of 3.8 mg/L (1.0 × 1015 m-3). The solid line is a linear function of the adsorbed mass. (b) Electrophoretic mobilities obtained right after sample preparation for different particle concentrations.

intermediate polymer dose, the mobility vanishes at the isoelectric point (IEP, arrow). Further increase of the polymer dose leads to an increase of the electrophoretic mobility, and beyond five times the IEP dose, the mobility levels off (adsorption plateau, arrow). Although the general trends are preserved, mobility data obtained right after sample preparation are lower than the ones measured 1 day later. As a result, the IEP shifts toward lower polyelectrolyte doses with time, from (1.3 ( 0.1) mg/g right after adding polyelectrolyte to the suspension to (1.0 ( 0.1) mg/g after 1 day. To clarify the origin of this aging effect, the electrophoretic mobility is measured as a function of time (see Figure 3). Solid symbols refer to the particle concentration of 3.8 mg/L (1.0 × 1015 m-3) for different polymer doses. The electrophoretic mobility increases initially with time, which indicates an increase in the polymer coverage, and then reaches a saturation plateau at longer times. Additionally, results at particle concentrations 0.38 and 38 mg/L (1.0 × 1014 and 1.0 × 1016 m-3) are compared with the particle concentration of 3.8 mg/L for the polymer dose of 1.1 mg/g. The adsorption rate increases with increasing particle concentration (i.e., with increasing polymer concentration at a given dose), but the plateau value remains the same for all concentrations. This observation strongly suggests a transport-limited adsorption process of the polymer to the particle surface. The polymer might consequently rearrange on the surface. However, the latter effect cannot affect the electrophoretic

mobility, as its kinetics has to be independent of the polymer concentration, which is in contradiction to the experiment. When the electrophoretic mobility is measured right after mixing, a very weak dependence on the particle concentration is observed. The results shown in Figure 2b can be understood in terms of the kinetics of the adsorption process. Since the adsorption plateau is reached more quickly at higher particle concentrations, the electrophoretic mobility will increase with increasing particle concentration after a finite measurement time. At high particle concentrations, the adsorption plateau is reached quickly and the electrophoretic mobilities will collapse on a common master curve. For high particle concentrations, the IEP lies at (0.95 ( 0.1) mg/g. This value is identical to the IEP in the limit of long exposure time at lower particle concentration. This loading corresponds to about six adsorbed polymer chains per particle. On the other hand, however, the dependence of the electrophoretic mobilities on the particle concentration is very weak indeed (see Figure 2b). While the particle concentration is varied over 3 orders of magnitude, the IEP shift by a mere factor of 2. This weak dependence of the electrophoretic mobilities on the particle concentration is indicative for complete adsorption of the polymer onto the particles. If the polymer would partition between the adsorbed and dissolved states, a strong dependence of the IEP on particle concentration would be observed. In the case of a linear adsorption isotherm, for example, the IEP should decrease in the polymer dose by the same factor by which the particle concentration is being increased, which is in complete contradiction to the data. A similar argument has been used to confirm that PAMAM dendrimers are normally fully adsorbed on sulfate latex particles, with the exception of the lowest-generation dendrimer G0.36 The irreversible nature of the adsorption can be also confirmed by dilution experiments. Dilution of suspensions with of 10 mg/g PVA-94 and particle concentrations of 38 mg/L by a factor of 50 leads to no appreciable changes in the mobility over 24 h. Let us now relate the adsorption and electrophoresis data. Figures 1 and 2 reveal an increase in the electrophoretic mobility with increasing amount of absorbed polymer. Once the adsorption plateau (arrow) is reached, further polymer addition does not lead to higher polymer

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adsorption, and accordingly, the mobility remains constant at its highest value of 4 × 10-8 m2/(Vs). The standard electrokinetic model predicts that, near the IEP (arrow), the mobility is a linear function of the surface potential and, consequently, of the surface charge density. With increasing charge densities, one expects a mobility maximum as a function of the surface potential, as discussed by O’Brien and White.46 While the presence of the adsorbed polyelectrolyte does modify the potentialmobility relationship, the O’Brien and White model can be used to obtain a reasonable estimate. When this model is applied to the SL-12 particles in 10 mM KCl, the electrophoretic mobility is approximatively proportional to the surface charge density up to mobilities of about 5 × 10-8 m2/(Vs) in magnitude. In the experimentally accessible range, the electrophoretic mobility is therefore a linear function of the adsorbed amount to a good degree of approximation (see solid line in Figure 2a). The mobility plateau thus signals the adsorption maximum, and it is unrelated to a nonlinearity within the standard electrokinetic model. This behavior is also likely to be generic, as a similar relation between the mobility plateau and the adsorption maximum was observed in similar systems of sulfate latex particles in the presence of PDADMAC.47 We conclude this subsection by reiterating that the adsorption of PVA onto latex particles cannot be understood as an equilibrium process but can be only rationalized as rapid, irreversible adsorption. At low and intermediate polymer doses, the polymer adsorbs to the particles quantitatively, and only traces remain in solution. Above a certain polymer dose, which is (0.13 ( 0.05) mg/m2 in the present case, the adsorbed amount remains constant, and any further added polymer is dissolved in solution. The electrophoretic mobility can be used to probe this adsorption process, as it increases approximately linearly with increasing polymer dose and levels off when the adsorption maximum is reached. The IEP is reached well below this dose, which is 0.03 mg/m2 here. While the adsorption process is relatively rapid at high particle concentrations, its kinetics can be observed at lower polymer concentrations at a given dose. The rate of adsorption is found to increase with increasing polymer concentration. A similar irreversible adsorption process was observed for PAMAM dendrimers on mica.48 Charging and Aggregation. Figure 4 shows the close relationship between charging and aggregation for the weakly charged SL-12 particles in the presence of highly charged PVA-94 polyelectrolyte for different KCl concentrations at pH 4.0. The data were measured at a particle concentration of 3.8 mg/L (corresponding to 1.0 × 1015 m-3) immediately after sample preparation. Recall that the adsorption of PVA is not complete and that a kinetic transient influences the suspension stability. From the data shown in Figure 2b, we suspect that this effect will not modify the stability behavior substantially in the present situation. The characteristic U-shaped plot of the stability ratio as a function of the polymer dose is given in Figure 4a. This appearance is typical for systems of particles and polyelectrolytes bearing opposite charges.9,10,14 Regions of high suspension stability enclose a fast aggregation regime at intermediate polymer dose. The electrophoretic mobility increases with increasing polymer dose, as illustrated in Figure 4b. As discussed above, the mobility (46) O’Brien, R.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 77, 1607. (47) Rehmet, R.; Killmann, E. Colloids Surf., A 1999, 149, 323. (48) Pericet-Camara, R.; Papastavrou, G.; Borkovec, M. Langmuir 2004, 20, 3264.

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Figure 4. Stability and electrophoresis of weakly charged SL-12 particles as a function of the dose of highly charged polyelectrolyte PVA-94 at different ionic strengths and pH 4.0. Solid lines serve to guide the eye only. (a) Stability and (b) mobility measurements.

passes through the isoelectric point (IEP) and levels off at the maximum in the adsorbed amount. The IEP lies within the fast aggregation regime. The coincidence between the IEP and the fast aggregation regime was reported in many other similar systems and can be understood on the basis of DLVO theory.9,14,49,50 This theory stipulates that interactions between particles are governed by repulsive electrostatic double-layer forces and by attractive dispersion interactions. At IEP, the particles are uncharged, double layer forces are largely absent, and attractive dispersion interactions induce fast aggregation. If one moves away from the IEP, repulsive double layer forces set in and lead to a stabilization of the suspension. The suspension stability is most sensitive to the presence of salt, a feature that underlines the importance of electrostatic interactions in the process (see Figure 4a). The widening of the fast aggregation region with increasing salt levels can be explained with DLVO theory qualitatively. With increasing salt level, the electrostatic double-layer potential decreases. Consequently, the repulsive electrostatic double-layer force decreases in magnitude and the width of the fast aggregation regime increases. At low salt concentrations, fast aggregation proceeds more rapidly in the presence of PVA-94 than without (i.e., W < 1). This feature is again most charac(49) Schudel, M.; Behrens, S. H.; Holthoff, H.; Kretzschmar, R.; Borkovec, M. J. Colloid Interface Sci. 1997, 196, 241. (50) Borkovec, M.; Behrens, S. H. In Encyclopedia of colloid and surface science; Hubbard, A., Ed.; Dekker Publishers: New York, 2002; pp 4795.


teristic but cannot be rationalized in terms of DLVO theory. Surface charge heterogeneities are the most likely explanation of this phenomenon. These heterogeneities are due to the positively charged patches originating from the polyelectrolyte molecules adsorbed to the negatively charged latex surface. When a positively charged patch approaches the negatively charged uncovered surface, an additional attractive electrostatic force results, and this force leads to an acceleration of the aggregation rate. These salt dependencies are generic, and they have been observed in similar systems as well.9,14,36,37 In contrast to the suspension stability, the electrophoretic mobilities are relatively insensitive to salt. However, an important feature is the shift of the IEP toward higher polymer doses with increasing salt level. In the previous section, we have argued that all added polymer is adsorbed near IEP. On the basis of this premise, one immediately concludes that a larger amount of polymer is needed to reach the IEP at higher salt level, as the charge of the polyelectrolyte is partially neutralized through bound anions. With increasing salt level, we must therefore progressively co-adsorb anions with the polymer, and the adsorbed anions contribute to the charge neutralization process. By analyzing literature data in the next subsection, we shall see that this co-adsorption mechanism seems to be generic. The importance of salt anions in the charge neutralization of sulfate latex particles by PVA can be also inferred by calculating the charging ratio (CR). This quantity represents the ratio between the number of charges on the polyelectrolyte and the opposite charges on the particle surface. At the first sight, one expects a CR of unity, as each charge on the polyelectrolyte should be capable of neutralizing a charge on the particle. We refer to such behavior as stoichiometric charge neutralization (CR ) 1). In the example of the weakly charged SL-12 particles and highly charged PVA-94 polyelectrolyte, the polymer dose at IEP is 1.3 mg/g at 10 mM. With the known line charge density of PVA-94 of 2.5 nm-1 and the surface charge density of SL-12 of 12 mC/m2, CR ) 7.3 is found. This value means that about seven elementary charges on the polymer are necessary to neutralize one charge on the particle. We shall refer to such a situation, which turns out to be typical, as super-stoichiometric charge neutralization (CR > 1). Three explanations for this super-stoichiometric charge neutralization come to mind. (i) The adsorption of the polyelectrolyte could be accompanied by the adsorption of its counterions (i.e., anions). (ii) Only a fraction of the polymer might be adsorbed, and the rest of the polymer could be dissolved. (iii) PVA is a weak polyelectrolyte, and it might be only partially charged. We now put forward arguments in favor of explanation (i). However, let us first argue why (ii) and (iii) are incorrect. Explanation (ii) of partial adsorption was already ruled out in the last subsection. On the basis of the adsorption experiments, it was shown that the polymer is completely adsorbed at IEP. Eventually, traces of polymer might be present in solution due to kinetic effects, but a factor of 10 can be ruled out. Explanation (iii) of partial protonation is equally unlikely. For the present experimental conditions at pH 4.0, PVA-94 is fully charged.38 However, one might suspect that the degree of protonation might be modified upon adsorption. While such a modification can be expected in the general case, no effect of this kind is expected here. Adsorption of a weak cationic polyelectrolyte to a negatively charged

Langmuir, Vol. 21, No. 8, 2005 3693

Figure 5. Stability and electrophoresis of weakly charged SL-12 particles as a function of the dose of weakly charged polyelectrolyte PVA-32 at different ionic strengths and pH 4.0. Solid lines serve to guide the eye only. (a) Stability and (b) mobility measurements.

surface is likely to increase the charge of the polymer.51 In our case, PVA is already fully charged in solution and cannot be charged further upon adsorption. For these reasons, we conclude that the PVA is completely adsorbed and fully charged and the explanation of the deviations of the CR from unity must be sought in the co-adsorption of counterions. In solution, the highly charged PVA-94 is associated with anions, and there is no reason to believe that these anions will be fully released upon adsorption to the surface. A very similar effect was observed with PAMAM dendrimers adsorbing on negatively charged latex particles, where CR up to 40 were observed.36 Coadsorption of anions was equally the only sensible explanation of these surprising numbers. If the ion co-adsorption hypothesis is correct, it follows that the CR should vary for different line charge densities of the polymers and/or for different surface charge densities of the particles. Let us first focus on results with weakly charged PVA-32, which is obtained by partial hydrolysis of the precursor. The polymer contains only 32% of the charged amine groups, and the remaining ones are uncharged formamide groups. Figure 5 shows the stability and mobility data in the presence of weakly charged PVA-32 polymer for the weakly charged SL-12 particles discussed previously at pH 4.0. The charging and the aggregation behavior is qualitatively very similar to that found for the highly charged polyelectrolyte and indicates that the replacement of the amine groups by formamide does not drastically affect the polyelectrolyte (51) Shubin, V. J. Colloid Interface Sci. 1997, 191, 372.

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Table 1. Charge Neutralization in Polyelectrolyte-Particle Systems of Opposite Charge systema 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

PVA-94 + SL-67 PVA-94 + SL-12 PVA-94 + SL-12 PVA-94 + SL-12 PVA-32 + SL-67 PVA-32 + SL-12 PVA-32 + SL-12 PVA-32 + SL-12 PVA + SL PVA + SL PVA + SL PSS + AL PSS + AL PSS + AL PSS + AL PSS + AL PDADMAC + SL PDADMAC + SL PDADMAC + SL PDADMAC + SL PDADMAC + SL PDADMAC + SL PDADMAC + SL chitosan + SL PEI + kaolin PEI + SL PEI + SL PEI + SL G2 + SL G6 + SL

I ξ σ (mM) pH (nm-1) (mC/m2) CRb refc 10 1 10 100 10 1 10 100 0.1 1 10 0.1 1 10 10 10 1 10 100 1 10 100 10 10 1 0.1 1 10 10 0.1

4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

6.5 6.5 6.5 4.0 2.9 5.0 4.0 4.0 4.0 4.0 4.0

2.5 2.5 2.5 2.5 0.8 0.8 0.8 0.8 2.5 2.5 2.5 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.5 2.5 2.5 2.5 2.5 2.5 2.5

67 10 10 10 67 10 10 10 16 16 16 42 42 42 48 30 71 71 71 71 71 71 44 86 130 16 16 16 12 12

2.8 5.3 7.3 12 3.3 18 23 32 1.8 4.6 5.0 2.2 2.2 2.2 1.3 3.2 0.9 1.3 1.8 0.8 0.9 1.5 2.0 1.0 1.1 6.3 8.5 11 5.1 7.9

37 37 37 14 14 14 61 61 47 47 47 45 45 45 61 15 54 14 14 14 36 36

systema 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

G6 + SL G6 + SL G10 + SL G10 + SL G10 + SL PDADMAC + SiO2 PDADMAC + SiO2 PDADMAC + SiO2 PDADMAC + SiO2 PDADMAC + SiO2 PDADMAC + CL PDADMAC + CL PDADMAC + CL PDADMAC + Al2O3 PD-co-NMVA + SiO2 PM + SiO2 PM + SiO2 PSS + iron oxide PVA + SL PVA + SL PAA + Fe2O3 PAA + Al2O3 PAA + ZrO2 PMAA + ZrO2 PMAA + ZrO2 PMAA + Al2O3 PDMAEMA + SiO2 PDMAEMA + SiO2 HA + Al2O3d FA + iron oxided

I (mM) 1 10 0.1 1 10 10 10 10 10 10 10 10 10 10 10 1 1 1 10 10 1 0.1 10 10 10 10 10 10 1 1

ζ σ (nm-1) (mC/m2) CRb 4.0 4.0 4.0 4.0 4.0 6.0 9.3 5.8 7.8 8.8 4.0 5.7 7.7 11.5 5.8 6.5 9.5 4.0 7.9 9.7 3.0 5.0 4.7 3.4 4.9 4.0 6.0 8.0 5.0 6.6

2.5 2.5 2.5 2.5 2.5 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.6 0.7 0.7 1.0 0.9 0.25 0.1 0.3 0.3 0.4 0.5 0.3 3.3 1.0 0.1 0.1

12 12 12 12 12 15 75 7 32 70 20 90 340 40 7 20 70 280 16 16 280 60 240 250 190 80 20 70 60 100

9.3 11 32 34 35 2.9 1.8 4.9 3.0 2.1 4.5 2.5 1.5 2.3 3.5 4.3 2.0 3.5 4.3 3.0 5.2 10 1.0 1.1 1.0 2.0 4.3 1.3 6.0 1.8

refc 36 36 36 36 36 45 45 45 59 59 59 59 59 60 45 62 62 63 37 37 64 65, 66 67, 68 69 69 70 71 71 65 55

a Systems at reported ionic strength I and pH. The running number refers to Figure 9. The line charge density of the polyelectrolyte, ξ, and surface charge density, σ, of the particles are estimated. The following abbreviations are used: sulfate latex (SL), amidine latex (AL), carboxyl latex (CL), poly(vinylamine) (PVA), poly(styrene sulfonate) (PSS), poly(diallyldimethylammonium chloride) (PDADMAC), poly(ethylene imine) (PEI), poly(amido amine) dendrimers of generation 2, 6, and 10 (G2, G6, G10), poly(diallyldimethylammonium chlorideco-N-methyl-N-vinylactamide) (PD-co-NMVA), poly(methacryloyloxyethyltrimethylammonium chloride) (PM), poly(acrylic acid) (PAA), poly(methacrylic acid) (PMAA), poly(dimethylaminoethyl methacrylate) (PDMAEMA), humic acid (HA), and fulvic acid (FA). b Charging ratio (CR) defined as the polyelectrolyte charge relative to the particle charge of the individual systems at IEP at given ionic strength, I, and pH. c Empty fields refer to the present work. d Corrected for dissolved amount. In all other cases, complete adsorption is assumed.

properties except reducing its line charge density. Consequently, a higher polymer dose is needed to neutralize the particles, and we find the IEP at 16 mg/g for PVA-32 at 10 mM, which is substantially larger than the value of 1.3 mg/g found for the strongly charged PVA-94. However, when these values are converted to the CR, one finds 23 for PVA-32, which must be compared with 7.3 for PVA94. These values are given in Table 1, which will be discussed in greater detail in the next subsection. Thus, the CR is indeed system specific, and this observation provides further support for the co-adsorption hypothesis. In the case of weakly charged PVA-32, fewer charges contribute to charge neutralization. Our interpretation of the larger CR for the PVA-32 system relative to PVA-94 is related to the larger thickness of adsorbed PVA-32 layer. From experiments on multilayer systems, one has strong indications that layers of highly charged polyelectrolytes (i.e., PVA-94) adsorbed to oppositely charged surfaces form extremely thin layers due to strong electrostatic attractions, with a typical thickness of a few nanometers.52,53 In this case, trainlike configurations are frequent and an efficient charge neutralization of the surface charge by the polyelectrolyte is expected (lower CR). With decreasing charge density of the polymer (i.e., PVA-32), a larger amount of the polymer must be adsorbed to achieve an overcharged state, and therefore the layer is expected to be thicker. Within such a layer, loops and tails dominate the conformations and only few

trains are expected. Since the trains are mainly responsible for the neutralization of the surface charge, the chargeneutralization process is less efficient here (higher CR). The effect can be again explained by an increased coadsorption of counterions on loops and tails. Let us point out another interesting difference between the stability plots for the weakly charged PVA-32 (Figure 5a) and strongly charged PVA-94 (Figure 4a). One observes that the regions of fast aggregation are narrower for PVA32 and wider for PVA-94. At the same time, the stability ratio depends on the polymer dose more sensitively for PVA-32 (steeper curves), while the dependence is weaker for PVA-94 (shallower curves). The sensitivity of the stability ratio on the polymer dose or other parameters controlling the surface potential, such as ionic strength or pH, has been suggested to be related to surface charge heterogeneities.14,49 This effect was most clearly demonstrated by studying the stability of colloidal particles in the presence of oppositely charged PAMAM dendrimers.36 For low generations, where the adsorbed layer is relatively homogeneous, the stability of the suspension was highly sensitive to the dendrimer dose. On the other hand, the adsorbed layer is highly heterogeneous for high generations, and accordingly, the dependence of the stability on the dose was much less pronounced. Following the same line of argumentation for the present case, we conclude that the adsorbed layer is more homogeneous for the weakly charged PVA-32 and more heterogeneous for the

(52) Estrela-Lopis, I.; Leporatti, S.; Moya, S.; Brandt, A.; Donath, E.; Mohwald, H. Langmuir 2002, 18, 7861.

(53) Sukhorukov, G. B.; Donath, E.; Lichtenfeld, H.; Knippel, E.; Knippel, M.; Budde, A.; Mohwald, H. Colloids Surf., A 1998, 137, 253.


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Figure 6. Stability and electrophoresis of strongly charged SL-67 and weakly charged SL-12 particles as a function of the dose of highly charged polyelectrolyte PVA-94 at an ionic strength of 10 mM and pH 4.0. Solid lines serve to guide the eye only. (a) Stability and (b) mobility measurements.

Figure 7. Stability and electrophoresis of strongly charged SL-67 and weakly charged SL-12 particles as a function of the dose of weakly charged polyelectrolyte PVA-32 at an ionic strength of 10 mM and pH 4.0. Solid lines serve to guide the eye only. (a) Stability and (b) mobility measurements.

strongly charged PVA-94. To reach charge reversal, more PVA-32 will be adsorbed, and consequently, a thicker and a more homogeneous film will be formed. The IEP dose corresponds to about 80 adsorbed PVA-32 chains per particle. On the other hand, for PVA-94, the adsorbed layers are expected to be thinner and more heterogeneous, corresponding to only about six chains per particle at IEP. Let us now discuss the results for highly charged SL-67 particles for both polymers and compare the results with the more weakly charged SL-12 particles. In Figure 6, we compare stability and electrophoretic mobility data for highly charged SL-67 and weakly charged SL-12 particles in the presence of highly charged PVA-94 at pH ) 4.0 and a salt level of 10 mM KCl. As expected, a higher polymer dose is required for neutralizing the more highly charged SL-67 particles, but the interpretation of the actual amount necessary is nontrivial. For the strongly charged SL-67 particles, the IEP lies at 4.3 mg/g and leads to CR ) 2.8. This value is much lower than CR ) 8.8 observed for the weakly charged SL-12 particles in the presence of PVA-94. Figure 7 depicts the analogous stability and electrophoretic mobility data for different sulfate latex particles and weakly charged PVA-32 at 10 mM KCl. Again, a higher polymer dose is required for neutralizing the more highly charged SL-67 particles. The IEP lies at 22 mg/g for the strongly charged SL-67 particles, leading to CR ) 3.3. This value has to be compared with CR ) 27 for the weakly charged SL-12 particles in the presence of PVA-32. To conclude this subsection, we recall that the presence of cationic PVA influences colloidal stability and electro-

phoretic mobility of anionic colloidal latex particles in a very characteristic fashion. With increasing polymer dose, the mobility goes through an isoelectric point (IEP) and signals a charge reversal. At the IEP, the suspension is unstable and becomes progressively stabilized away from it. The interesting quantity to consider is the charging ratio (CR), which is the number of polyelectrolyte charges dosed relative to the particle surface charges needed to reach the IEP. Depending on the line charge density of the PVA, the surface charge density of the particles, and the salt level, the CRs have been observed to vary from 2.8 to 38, which is more than an order of magnitude. Our interpretation of this super-stoichiometric charge neutralization is that the polymer adsorption is accompanied by co-adsorption of anions. Super-Stoichiometric Charge Neutralization. Table 1 summarizes the CR values for the systems reported here and for similar systems of charged particles and oppositely charged polyelectrolytes from literature. We only consider publications where particles and polyelectrolytes are reasonably well characterized, the salt level is specified, and charge densities are given or can be determined from literature. For each system, we further report the particle surface charge density, σ, given as charge per unit area, and the polyelectrolyte line charge density, ξ, given as number of ionized groups per unit length. The CR is estimated from the IEP obtained from electrophoretic mobility measurements or from the center of the fast-aggregation region in colloidal stability studies. The data are of varying quality, and errors are hard to estimate. One immediately concludes that, for most of

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Figure 8. Charging ratio (CR) as a function of the ionic strengths for various systems. The CR is the number ratio of the polyelectrolyte and particle charges at the IEP. Abbreviations and numbers refer to Table 1.

the systems tabulated, nonstoichiometric charge neutralization is observed and stoichiometric charge neutralization (CR ) 1) is rather the exception.10,54 For most systems, super-stoichiometric charge neutralization (CR > 1), with the largest CR near 40, is observed. Suprastoichiometric charge neutralization (CR < 1) is seldom, with the smallest CR values around 0.8. The CR obviously strongly depends on the type of particles and polyelectrolytes in question. Figure 8 depicts CR as a function of ionic strength for several systems, where the particles have a constant charge and the polyelectrolytes are either strong or fully ionized. Increasing ionic strength leads to an increase of the CR, a trend which is independent of the chemical nature of the system. We suspect that the reason for this characteristic dependence is that the binding of the polyelectrolyte counterions increases with increasing salt level, thereby reducing the effective charge of the polyelectrolyte. When the polyelectrolyte has a lower effective charge, a higher dose is necessary to neutralize the particle charge. For two systems, the CR is basically independent of the ionic strength. PAMAM dendrimers (G6, G10) adsorbed on negatively charged sulfate latex particles show only marginal increase with the ionic strength, which might be related to their globular structures. For poly(styrene sulfonate) (PSS) on highly charged amidine latex (AL), the CR is independent of ionic strength, which might be related to the high charge density of these particles (42 mC/m2). Highly charged particles will also bind counterions to their surface and thereby reduce their effective charge. This effect would lead to a decrease of the CR with increasing ionic strength, and this trend could balance the increase originating from the polyelectrolyte. One might be tempted to argue that the salt dependence of the IEP is related to partitioning of the polymer between the surface and the solution, but this interpretation cannot be maintained. Increasing ionic strength typically leads to an increased polyelectrolyte adsorption at a given polymer dose.45,47 Consequently, a decrease of the CR with increasing salt level would be expected. This fact is in contradiction to the data shown in Figure 8. In any case, we have further shown that at IEP all polymer is adsorbed, and we suspect that this is a general feature in most of these systems. To our knowledge, examples deviating this rule involve molecules of very low molecular mass, such (54) Gill, R. I. S.; Herrington, T. M. Colloid Surf. 1987, 28, 41.

Kleimann et al.

as G0 PAMAM dendrimers (517 g/mol) or humic and fulvic acids (typically below 10 kg/mol).36,55,56 While variations in salt concentration lead to changes of CR by a factor of 2 or less, the CR varies almost over 2 orders in magnitude depending on the nature of the system (see Table 1). To rationalize such large variations, we propose a very simple model of the charge neutralization phenomenon. Consider a surface with unit charges separated by an average distance dS between the nearest neighbors and imagine the polymer to adsorb flatly on the surface, exclusively in trainlike conformations. Suppose that, for an adsorbed charged chain, only one charged site is neutralized by a surface site and the remaining sites are neutralized by salt ions. The end-to-end distance of a subchain between neighboring surface sites has to match the distance between them and thus obeys the scaling relation dS ∝ Nν, where N is the number of charged subunits, with ν ) 1/2 for a Gaussian chain and ν ) 3/4 for the Flory chain in two dimensions.57,58 Within this model, the charging ratio CR is simply given by N; we thus find that CR ∝ dSR where R ) 1/ν. In the special case, when the nearest-neighbor distance between charged groups on the polymer dP equals the distance between the surface groups dS, we have CR ) 1, and for this reason, we propose the simple relation

CR )

() dS dP

R

for CR g 1

(3)

with R ) 2 for the Gaussian chain and R ≈ 1.3 for the Flory chain. Analogous arguments can be given for a stiff chain, and in this case, one obtains R ) 1. The latter exponent is also obtained for the situation dP > dS leading to CR < 1. The model assumes that the polymer adsorbs flatly on the surface exclusively in trainlike conformations and a surface charge can neutralize one charge on the polyelectrolyte. In reality, the charges neutralize only partially due to the competition between specific ion binding and unspecific binding in the diffuse layer, and for this reason, the model cannot account for the increase of the CR with increasing salt levels. The model further neglects loops and tails in thicker adsorbed layers, specific binding of other ions (e.g., protons), or surface curvature effects. For (55) Liang, L.; Morgan, J. J. ACS Symposium Series 1990, 416, 293. (56) Gu, B. H.; Schmitt, J.; Chen, Z. H.; Liang, L. Y.; McCarthy, J. F. Environ. Sci. Technol. 1994, 28, 38. (57) Flory, P. J. Statistical mechanics of chain molecules; Hanser: Mu¨nchen, 1988. (58) Doi, M. Introduction to polymer physics; Clarendon Press: Oxford, 1995. (59) Cakara, D. Thesis in Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 2004. (60) Greenwood, R.; Kendall, K. Powder Technol. 2000, 113, 148. (61) Kleimann, J. unpublished. (62) Schwarz, S.; Lunkwitz, K.; Kessler, B.; Spiegler, U.; Killmann, E.; Jaeger, W. Colloids Surf., A 2000, 163, 17. (63) Sontum, P. C.; Naevestad, A.; Fahlvik, A. K.; Gundersen, H. G. Int. J. Pharmaceutics 1996, 128, 269. (64) Ferretti, R.; Zhang, J. W.; Buffle, J. Colloids Surf., A 1997, 121, 203. (65) Elfarissi, F.; Nabzar, L.; Ringenbach, E.; Pefferkorn, E. Colloids Surf., A 1998, 131, 281. (66) Buleva, M.; Peikov, V.; Pefferkorn, E.; Petkanchin, I. Colloids Surf., A 2001, 186, 155. (67) Wang, J. Ceram. Int. 2000, 26, 187. (68) Tan, Q.; Zhang, Z.; Tang, Z.; Luo, S.; Fang, K. Mater. Lett. 2003, 57, 2375. (69) Shojai, F.; Petterson, A. B. A.; Ma¨ntyla¨, T.; Rosenholm, J. B. J. Eur. Ceram. Soc. 2000, 20, 277. (70) Wei, W.-C. J.; Lu, S. J.; Yu, B.-C. J. Eur. Ceram. Soc. 1995, 15, 155. (71) Shin, Y.; Roberts, J. E.; Santore, M. M. J. Colloid Interface Sci. 2002, 247, 220.


Figure 9. Charging ratio (CR) as a function of the distance mismatch, dS/dP, whereby dP and dS refer to the average distances between charges on the polyelectrolyte and on the particles, respectively. The CR is the number ratio of the polyelectrolyte and particle charges at the IEP. The numbers refer to Table 1.

the PVA systems discussed here, curvature effects are unimportant, as the layers are thin with respect to the particle size. However, such effects are certainly of relevance for nanoparticles. In any case, the model makes considerable simplifications but suggests that the CR should increase with increasing distance mismatch, dS/dP, between the charges on the surface and on the polymer. This model prediction can be easily tested on experimental data summarized in Table 1. Figure 9 presents the CR as a function of the distance mismatch, dS/dP. The nearest-neighbor distance between the groups on the polymer can be obtained from dP ) ξ-1, where ξ is the line charge density, and the nearest-neighbor distance between the surface groups from dS ) (e/σ)1/2, where σ is the surface charge density and e the elementary charge. The solid line is eq 3 with R ) 1. Figure 9a summarizes the fully ionized systems. The polymers and particles considered are either strong electrolytes, or the experimental conditions are such that they are both completely ionized. While the data show substantial scatter, they reveal a clear increase of the CR with the distance mismatch, dS/dP, as suggested by the simple model discussed above. Three obvious outliers are immediately identified (Figure 9a, triangles). Two of them are the systems investigated here, both involving the weakly charged PVA32 (numbers 5 and 7 in Figure 9a). As we have argued above, the adsorbed PVA-32 layer is relatively thick, and consequently, a large fraction of the adsorbed chains protrude into solution in loop (or tail) conformations.

Langmuir, Vol. 21, No. 8, 2005 3697

Charged groups on these polymer segments are mainly neutralized by salt counterions in solution, and thus, they contribute very little to the neutralization of the surface charges. Consequently, a larger CR should be observed. The other system having a large CR is PAMAM G10 dendrimer adsorbed on weakly charged sulfate latex (number 35, Figure 9a). In this case, a similar argument can be used, as the dendrimers do not adsorb flatly on the surface either but have a thickness of around 4 nm.48 These protruding groups will be again neutralized by counterions in solution and do not contribute to the surface neutralization. In general, one would expect that the CR should increase with increasing thickness of the adsorbed polyelectrolyte layer. However, our simple model assumes a flat layer, and therefore, CR is underestimated in these cases. Figure 9b summarizes systems containing partially ionized weakly acidic or basic groups. The CR is calculated from the known protonation equilibrium of the isolated particles and polyelectrolytes at the neutralization point. Similarly, the ratio dS/dP is calculated for isolated particles and polyelectrolytes. When a weak polyelectrolyte adsorbs onto a particle surface of constant opposite charge, generally the line charge density of the polyelectrolyte will increase. Similarly, the charge density of particles with weakly acidic or basic surface groups will increase upon the adsorption of a strong polyelectrolyte. When the polyelectrolyte and the particle surface are both titrating, the ionization equilibria shift on both, leading to a modification of the surface charge in either direction. In the present case of titrating systems, one concludes that the simple model presented fails, as the CR is relatively constant, typically in the range 1-4. The reason for the failure of our simple model is that the ionizable systems shift the ionization states in order to match more closely the stoichiometric charge neutralization condition (CR ≈ 1). Exceptions to this rule of thumb are metal oxides neutralized with weak anionic polyelectrolytes leading to CR values up to 10 (numbers 51, 52, and 59 in Figure 9b). We conclude this subsection by reiterating that neutralization of charged particles with oppositely charged polyelectrolytes is usually super-stoichiometric, meaning that the charging ratio (CR) can be as high as 40. This ratio specifies the number of polyelectrolytes charges, which are necessary to neutralize one charge on the particle. Deviations of the CR from unity are mainly due to the binding of counterions to polyelectrolytes. Counterions neutralize charges on the polyelectrolyte, which cannot be neutralized by the charges on the particle surface. For this reason, the CR increases with the distance mismatch between the distance between the charges on the surface and on the polyelectrolyte. The CR seems also to increase with increasing layer thickness since charges on the loop or tail segments of the polyelectrolyte are neutralized by salt ions. When protons can regulate the charge of the surface and/or the polyelectrolyte, the CR typically remains close to unity. 4. Conclusion Neutralization of charged particles with oppositely charged polyelectrolytes is normally super-stoichiometric and is only rarely stoichiometric. Many charges on the polyelectrolyte are usually necessary to neutralize a single charge on the particle. The remaining polyelectrolyte charges are neutralized by polyelectrolyte counterions, which are co-adsorbed to the particle. We have further shown that this nonstoichiometric process cannot be explained by incomplete polyelectrolyte

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adsorption. Typically, polyelectrolyte is completely adsorbed near the charge neutralization point, and its solution concentration is negligibly small. Polyelectrolyte adsorption does saturate, but normally far above the neutralization point, where the particle charge is reversed. The charge neutralization point can be equally well identified through the isoelectric point measured by electrophoresis, as well as by determining the maximum in the aggregation rate between the colloidal particles. These two points normally coincide. The lack of stoichiometry in polyelectrolyte adsorption raises several interesting questions concerning the role of simple ions in polyelectrolyte adsorption. The importance of protons has been demonstrated by comparing

Kleimann et al.

systems that can regulate their charge through ionization reactions to systems that are fully ionized or bear a constant charge. By the same token, pronounced ionspecific effects are expected, for example, when the nature of the electrolyte is changed, or when strongly complexing ions are added. Acknowledgment. This work has been supported by program TopNano21 administered by Swiss Commission of Technology and Innovation, BASF Aktiengesellschaft, Ludwigshafen, and Swiss National Science Foundation. LA046911U

Super-Stoichiometric Charge Neutralization in ParticleâPolyelectrolyte

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