Controlled Association in Suspensions of Charged Nanoparticles with

The properties of high-pH suspensions of mixtures of silica with low-molecular-weight samples of the water-soluble polymer polyethylenimine (PEI) have...
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Langmuir 2006, 22, 4518-4525

Controlled Association in Suspensions of Charged Nanoparticles with a Weak Polyelectrolyte Andrew M. Howe,* Robin D. Wesley, Magali Bertrand, Marie Coˆte, and Julien Leroy Kodak European Research, 332 Science Park, Milton Road, Cambridge CB4 0BW, U.K. ReceiVed December 8, 2005. In Final Form: March 2, 2006 The properties of high-pH suspensions of mixtures of silica with low-molecular-weight samples of the water-soluble polymer polyethylenimine (PEI) have been studied. At pH > 10 and low ionic strength, silica nanoparticles are stabilized by a negative surface charge, and PEI has only a very low positive charge. The adsorption of PEI induces a localized positive charge on the segments of polymer closest to the silica surface. The parts of the molecule furthest away from the surface have little charge because of the high pH of the medium. The polymer-covered particle remains negatively charged, imparting some electrostatic stabilization. Suspensions of silica and low-molecular-weight PEI are low-viscosity fluids immediately after mixing, but aggregation occurs leading to the eventual gelation (or sedimentation at lower concentrations) of these mixtures, indicating colloidal instability. The gelation time passes through a minimum with increasing surface coverage. The rate of gelation increases exponentially with molecular weight: for molecular weight g10 000 Da PEI, the instability is so severe that uniform suspensions cannot be produced using simple mixing techniques. The gelation rates increase rapidly with temperature, ionic strength, and reduction in pH. The rate of gelation increases with increasing particle concentration at low surface coverage but decreases at high coverage as a consequence of a small increase in pH. Gels are broken by application of high shear into aggregates that re-gel more rapidly than the original discrete coated particles.

Introduction Polyethylenimine (PEI) is a highly branched, weak polyelectrolyte (or polybase). At low pH, PEI has a very high cationic charge density,1-4 but as the pH rises and the ionic strength falls, the charge density drops.5-7 At pH 10, the degree of protonation is 8% at 0.5 M NaCl,2-4 7% at 0.1 M NaCl7 (the same as for comb-PEI8), and 1% at 0.001 M NaCl,7 so the polybase becomes essentially uncharged at pH g10.5 at low ionic strength.7 The high degree of branching means that PEI molecules have a globular structure with relatively little conformational freedom.9 The surface-charge density of silica nanoparticles is also variable with pH,10,11 with the point of zero charge at approximately pH 2.7 Theoretical12 and pH titration7,11 studies indicate that the dissociation of surface silanol groups increases with pH. A Stern model with a total site charge density of 8 nm-2, a Stern capacitance of 2.9 F‚m-2, and an ionization constant pK of 7.6 was found to describe the charging well of particles 30 to 80 nm in diameter at ionic strengths from 10 to 1000 mM.11 A compensating increase in (sodium) counterion condensation within the plane of shear means that the ζ potential of silica remains constant throughout the high-pH range.10 * Corresponding author. E-mail: [email protected]. (1) Ham, G. E. In Polymeric Amines and Ammonium Salts; Gothals, E. J., Ed.; Pergamon Press: Oxford, U.K., 1980. (2) Borkovec, M.; Koper, G. J. M. Macromolecules 1997, 30, 2151. (3) Balif, J. B.; Lerf, C.; Schlapfer, C. W. Chimia 1994, 48, 336. (4) Borkovec, M.; Koper, G. J. M. Prog. Colloid Polym. Sci. 1998, 109, 142. (5) Griffiths, P. C.; Paul, A.; Stilbs, P.; Petterson, E. Macromolecules 2005, 38, 3589. (6) Lindquist, G. M.; Stratton, R. A. J. Colloid Interface Sci. 1976, 55, 45. (7) Me´sza´ros, R.; Thompson, L.; Bos, M.; de Groot, P. Langmuir 2002, 18, 6164. (8) Koper, G. J. M.; van Duijvenbode, R. C.; Stam, D. P. W.; Steurle, U.; Borkovec, M. Macromolecules 2003, 36, 2500. (9) Kobayashi, S.; Hiroshi, K.; Tokunoh, M.; Saegusa, T. Macromolecules 1987, 20, 1496. (10) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; John Wiley & Sons: New York, 1979. (11) Kobayashi, M.; Juillerat, F.; Galletto, P.; Bowen, P.; Borkovec, M. Langmuir 2005, 21, 5761. (12) Behrens, S. H.; Grier, D. G. J. Chem. Phys. 2001, 115, 6716.

Polyelectrolyte adsorption has been the subject of intense study.13,14 The conformation of the adsorbed polyelectrolyte depends both on charge density and ionic strength. Polyelectrolytes adsorb in a flat conformation (trains) on oppositely charged surfaces, provided the charge density is high and ionic strength low. Consequently, the adsorbed amount is low under these conditions. As the ionic strength increases or the charge density decreases, loops and tails may form, enabling an increase in the adsorbed amount. Loops and tails, or an increasing fraction of the charged groups located away from the particle surface, may arise through other configurational arrangements, such as when the charges are well separated by uncharged segments15 or when the polymer has dendrimeric structure.16 For weak polyelectrolytes, the situation is more complex because the charge density on the polymer varies with pH and therefore adsorption is strongly pH-dependent.17,18 It is generally accepted that adsorption decreases as the degree of ionization of the polyelectrolyte increases (although a maximum may be observed): at very low ionization the adsorbed layers are thick, whereas at high ionization the layers are thin and flat. The adsorption of PEI onto silica is an interesting case because the charge of the substrate varies inversely with pH with respect to the charge on the adsorbent. The adsorption of PEI onto graphite,19 aluminum-modified nanoparticulate silica,6 planar glass or silica surfaces,7,20,21 and planar mica22,23 has been studied. As expected, the maximum adsorption occurs at high pH, where (13) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces, 1st ed.; Chapman & Hall: London, 1993; Chapter 2. (14) Cohen Stuart, M. A.; Cosgrove, T.; Vincent, B. AdV. Colloid Interface Sci. 1986, 24, 143. (15) Kleimann, J.; Gehin-Delval, C.; Auweter, H.; Borkovec, M. Langmuir 2005, 21, 3688. (16) Lin, W.; Galletto, P.; Borkovec, M. Langmuir 2004, 20, 7465. (17) Bohmer, M. R.; Efers, O. A.; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. (18) Blaakmeer, J.; Bohmer, M. R.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1990, 23, 2301. (19) Schneider, M.; Brinkmann, M.; Mo¨hwald, H. Macromolecules 2003, 36, 9510.

10.1021/la053327s CCC: $33.50 © 2006 American Chemical Society Published on Web 04/07/2006

Charged Nanoparticles with a Weak Polyelectrolyte

the PEI is essentially uncharged in solution. The plateau value of the adsorbed amount falls as the pH is reduced below 10, a phenomenon that is ascribed to the increase in interpolymer electrostatic repulsion that arises from the increasing charge on the PEI. Me´sza´ros21 showed that there was some hysteresis with pH. The adsorbed amount of PEI introduced to silica at high pH (9.7) was greater than when introduced at intermediate pH (5.8), yet no desorption occurred when PEI was preadsorbed at pH 9.7 and the pH was then reduced to 5.8. At low pH (3.3), the adsorbed amount was always low, regardless of the preparation procedure. Similar pH dependence was reported by Claesson et al.,22 who also investigated surface charge by electro-osmotic measurements. In the absence of PEI, the mica surface was negatively charged, but adsorption of PEI reversed the charge at low pH (5.8-8.8). At the highest pH investigated (pH 9.9, where the maximum adsorbed amount was observed), the surface charge fell to close to zero. Hysteresis in adsorption with pH has been observed with other weak polyelectrolytes, for instance with a hydrophobically modified poly(acrylic acid) on a hydrophobic polystyrene surface.24 Layers of PEI adsorbed to silica surfaces are rather thin. Me´sza´ros,20 in an ellipsometric study, reported a 12-nm-thick layer for a 750 kDa PEI on planar silica at 0.01 M NaCl and high pH. At low pH, the layer decreased to 4 nm in thickness. Thin layers are probably a consequence of the hyperbranched nature of PEI. In the biomedical field, PEI has applications as a gene-transfer agent.25-27 The adsorption of PEI onto surfaces has attracted recent interest as a component of polyelectrolyte multilayer structures.28-33 Such structures may have unusual and useful optical34-36 or biological37-39 properties. In the present article, the rheology of concentrated suspensions of silica nanoparticles with low-molecular-weight PEI will be studied and related to the adsorbed amount and surface charge. Experimental Section Materials. A single type of silica nanoparticle was used in the experimental work. The silica was Ludox PW50, manufactured by Grace Davison. The batch used had an average particle diameter of (20) Me´sza´ros, R.; Thompson, L.; Varga, I.; Gila´nyi, T. Langmuir 2003, 19, 9977. (21) Me´sza´ros, R.; Varga, I.; Gila´nyi, T. Langmuir 2004, 20, 5026. (22) Claesson, P. M.; Paulson, O. E. H.; Blomberg, E.; Burns, N. L. Colloids Surf., A 1997, 123-124, 341. (23) Schneider, M.; Zhu, M.; Papastavrou, G.; Akari, S.; Mo¨hwald, H. Langmuir 2002, 18, 602. (24) Go¨bel, J. G.; Besseling, N. A. M.; Cohen Stuart, M. A.; Poncet, C. J. Colloid Interface Sci. 1999, 209, 129. (25) Nichol, C. A.; Yang, D.; Humphrey, W.; Ilgan, S.; Tansey, W.; Higuchi, T.; Zareneyrizi, F.; Wallace, S.; Podoloff, D. A. Drug DeliVery 1999, 6, 187. (26) Hellweg, T.; Henry-Toulme, N.; Chambon, M.; Roux, D. Colloids Surf., A 2000, 163, 71. (27) Godbey, W. T.; Wu, K. K.; Mikos, A. G. J. Controlled Release 1999, 60, 149. (28) Decher, G.; Schlenoff, J. B. Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials; Wiley-VCH: Weinheim, Germany, 2003. (29) Scheutz, P.; Caruso, F. Colloids Surf., A 2002, 207, 33. (30) Schwarz, S.; Nagel, J.; Jaeger, W. Macromol. Symp. 2004, 211, 201. (31) Chen, J. Y.; Luo, G. B.; Cao, W. X. J. Colloid Interface Sci. 2001, 238, 62. (32) Baba, A.; Kaneko, F.; Advincula, R. C. Colloids Surf., A 2000, 173, 39. (33) Caruso, F.; Schuler, C. Langmuir 2000, 16, 9595. (34) Ma, H.; Peng, J.; Zhou, B.; Han, Z.; Feng, Y. Appl. Surf. Sci. 2004, 233, 14. (35) Jiang, M.; Wang, E.; Wei, G.; Xu, L.; Li, Z. J. Colloid Interface Sci. 2004, 275, 596. (36) Casson, J. L.; Mcbranch, D. W.; Robinson, J. M.; Wang, H. L.; Roberts, J. B.; Chiarelli, P. A.; Johal, M. S. J. Phys. Chem. B 2000, 104, 11996. (37) Trimaille, T.; Pichot, C.; Delair, T. Colloids Surf., A 2003, 221, 39. (38) Etheve, J.; Dejardin, P.; Boissiere, M. Colloids Surf., B 2003, 28, 285. (39) Ram, M. K.; Adami, M.; Paddeu, S.; Nicolini, C. Nanotechnology 2000, 11, 112.

Langmuir, Vol. 22, No. 10, 2006 4519 79 nm (measured with a Malvern Zetasizer 3000HS in PCS mode), and this value was used to calculate the surface area of the particles. The silica suspension was supplied at a pH of 10.2 at 50% w/w in water. The volume fraction of suspensions was calculated assuming a density of amorphous silica of 2.2 g‚mL-1. Several different PEI samples have been studied. Samples with molecular weights (Mn) between 250 and 10 000 Da were obtained from Nippon Shokubai Co. Ltd. under the Epomin trade name. A second Mn ) 1800 Da (Mw ) 2000 Da) sample was obtained from Aldrich. The PEI samples are identified by their manufacturer (E for Epomin, A for Aldrich) and molecular weight. The samples here are essentially oligomeric in nature and have a ratio of close to 1:1:1 for primary/secondary/tertiary amines.40,54 The PEI concentration is usually expressed as micromoles of monomer per square meter of silica (µmol‚m-2) to provide independence from polymer molecular weight and dispersity as well as particle size and concentration. This approach uses an average molecular weight for the PEI monomer of 43 Da. An adsorbed PEI amount of 20 µmol‚m-2 corresponds to 0.86 mg‚m-2. Sample Preparation. The experiments described here require the ability to mix liquids on a 10 to 100 mL scale efficiently and controllably. Equal volumes of the two components (PEI and silica) were combined at equal flow rates from a pair of syringes via a T piece with a 1.6 mm bore. The injection process was quick, taking less than 5 s. For final concentrations of silica above 29% w/w, a 1:1 volume mixture ratio is not possible from a 50% w/w silica stock solution, so a simple addition process was used. PEI and silica are both high-pH liquids, and the samples were usually simply diluted in Millipore water prior to mixing without adjusting the pH or ionic strength. However, on certain occasions the pH was adjusted by adding a small amount of sodium hydroxide or hydrochloric acid to the PEI solution prior to mixing, and the final value of the pH was noted. The ionic strength was adjusted in the same manner with potassium nitrate. Measurements. pH with Time. The device for this experiment comprised a sample container and a pH meter (Fisherbrand Hydrus 200 meter) connected to a data-logging computer. The sample was introduced into the container using the syringes connected via a T piece. The pH meter was calibrated with pH 7 and 10 buffers before starting each experiment. Adsorption Isotherms. Adsorption isotherms were determined by measuring the free concentration of PEI using the colorimetric technique of Perrine and Landis.41 The colored complex formed by PEI and copper (CuSO4‚5H2O) was used to determine the concentration of PEI in solution using an Ocean Optics USB2000 fiber optic spectrometer with a 1-cm-path-length quartz cell. The peak at 635 nm was measured. First, a calibration curve was constructed by measuring the absorption spectra of a series of solutions containing 0.023 M copper sulfate (Aldrich) and up to 0.1% w/w PEI. Next, suspensions were prepared by mixing silica and PEI in the appropriate concentrations without pH adjustment. After equilibration, the suspensions were centrifuged (Centrikon T-42k, A19C rotor) at 25 °C for 80 min at 12 500 rpm. A 3 mL aliquot of the supernatant (40) Epomin literature, supplied by Nippon Shokubai Co. Ltd. (41) Perrine, T. D.; Landis, W. R. J. Polym. Sci., Part A 1967, 5, 1993. (42) Jenkel, E.; Rumbach, B. Z. Electrochem. 1951, 55, 612. (43) Bringley, J. F.; Wunder, A.; Howe, A. M.; Wesley, R. D.; Qiao, T. A.; Liebert, N. B.; Kelley, B.; Minter, J.; Antalek, B.; Hewitt, J. M. Langmuir, submitted for publication, 2005. (44) Ferry, J. D.; Eldridge, J. E. J. Phys. Chem. 1949, 53, 184. (45) Ferry, J. D. J. Am. Chem. Soc. 1948, 70, 2244. (46) Gregory, J. J. Colloid Interface Sci. 1973, 42, 448. (47) Gregory, J. J. Colloid Interface Sci. 1976, 55, 35. (48) Ashmore, M.; Hearn, J.; Karpowicz, F. Langmuir 2001, 17, 1069. (49) Bouyer, F.; Robben, A.; Yu, W. L.; Borkovec, M. Langmuir 2001, 17, 5225. (50) Pericet-Camara, R.; Papastavrou, G.; Borkovec, M. Langmuir 2004, 20, 3264. (51) Robertson, C. G.; Wang, X. Phys. ReV. Lett. 2005, 95, 75703. (52) Behl, S.; Moudgil, B. M. J. Colloid Interface Sci. 1993, 161, 422. (53) Gaudreault, R.; van de Ven, T. G. M.; Whitehead, M. A. Colloids Surf., A 2005, 268, 131. (54) Generally, PEIs of higher molecular weight are quoted to have a 1:2:1 primary/secondary/tertiary ratio.

4520 Langmuir, Vol. 22, No. 10, 2006 was mixed with 3 mL of a 0.046 M copper sulfate solution and one drop of 1 M HCl added to redissolve the precipitate. The absorption spectra of this PEI/Cu solution were recorded, allowing the calculation of the concentration of PEI in the supernatant by reference to the calibration curve. Electrophoresis-ζ Potential. The surface charge of the particles with adsorbed polymer was followed by measurements of the ζ potential made with a Malvern Zetasizer 3000HS instrument. Samples were initially prepared at high concentrations (g15% w/w silica) without pH adjustment. Dilution to 20 µmol‚m-2), where colloidal stability might have been expected. These data were obtained with samples that had not been pH adjusted, so the pH changes with time and with PEI concentration (Figure 1) but is in the range of 10.5-11.7. Thus the ζ potential would be in the range of -20 to -60 mV (Figure 4). The strength of the gels increases with time as the structure develops. At the gel time, the modulus for all samples is similar at ∼0.1 Pa. However, at twice the gel time, the strength of the gels increases very significantly with PEI concentration up to 20 µmol‚m-2. Effect of PEI Molecular Weight. The dependence of the gelation time on the number-mean molecular weight Mn of PEI with silica at a constant PEI concentration of 20 µmol‚m-2 is shown in Figure 8. The gelation time decreases exponentially with increasing Mn. The average degree of polymerization is shown in the upper x axis: a range from 5 to 45 serves as a reminder that the PEI samples used in this study are oligomeric. For PEI samples of molecular weight g10 000 Da, uncontrollable aggregation occurs instantaneously as mixing is attempted. However, if special mixing techniques are employed (as described in reference,43 for example), it is possible to avoid bridging flocculation on initial mixing of suspensions of silica nanoparticles and solutions both of higher-molecular-weight PEI and at lower pH. Effect of Temperature. The structuring of suspensions of PEI and silica is strongly dependent on other factors besides PEI concentration or molecular weight. The gelation time of 15% w/w silica with 20 µmol‚m-2 PEI of different molecular weights is reduced by an order of magnitude on increasing the temperature by 15 °C (Figure 9). The gelation rate has an activation energy of 105 kJ‚mol-1 and increases by a factor of 3.5 with each increasing 600 Da in molecular weight from 600 to 1800 Da (Figure 10). Effect of Ionic Strength. The addition of KNO3 at concentrations between 3 and 1000 mM to 15% w/w silica and 20 µmol‚m-2 PEI leads to a reduction in gelation time by up to a factor of 50 (Figure 11) but has no effect on the network structure (at twice the gelation time). The addition of salt is thought to increase the rate of gelation because screening reduces the electrostatic stabilization of the particles.

Charged Nanoparticles with a Weak Polyelectrolyte

Figure 9. Gelation time of 27.7% w/w silica with 20 µmol‚m-2 PEI of different molecular weights as a function of temperature.

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Figure 12. Gelation time and complex modulus at 2tg for silica with 5.8 µmol‚m-2 PEI (A1800) as a function of silica volume fraction.

Figure 13. Gelation time and complex modulus at 2tg for silica with 20 µmol‚m-2 PEI (A1800) as a function of silica volume fraction. Figure 10. Arrhenius plot of gelation rate versus inverse absolute temperature for 27.7% w/w silica with 20 µmol‚m-2 PEI of different molecular weights. The gelation rate has been multiplied by 3.5 for each reduction in Mn of 600 Da from 1800 Da in order to collapse the data onto a single line.

Figure 11. Gelation time and complex modulus at tg and 2tg for 15% w/w silica with 20 µmol‚m-2 PEI (A1800) at different added salt (KNO3) concentrations.

Effect of pH and Particle Concentration. The gelation of silica and PEI was followed at two levels of PEI coverage, with a range of silica concentrations and on addition of acid (HCl) or base (NaOH). The gelation of suspensions of silica with a constant 5.8 µmol‚m-2 PEI (i.e., near the coverage at which gelation is most rapid (Figure 7)) was studied for samples ranging from 5 to 20% w/w silica without added acid or base. The pH of these suspensions increased from 10.3 to 10.6 over this concentration range. The

values of gelation time decrease and the complex modulus increases by a factor of 20 over this range (Figure 12). In contrast, the gelation times of suspensions of silica with a constant 20 µmol‚m-2 PEI (i.e., near surface saturation) increase by an order of magnitude on increasing concentration from 15 to 48% w/w (Figure 13). The strength of the gels, measured at the gelation time and small multiples of the gelation time, increases with the square of the volume fraction of particles. Such an increase in the modulus with concentration is typical of polymer gels, such as gelatin gels.44,45 The dependence of the gelation time on concentration at high surface coverage seems somewhat counterintuitive: dilute samples gel more quickly than concentrated samples. However, the pH of these samples was not controlled and was found to increase with concentration. The gelation time is very sensitive to pH: tg increases in an exponential fashion by approximately 3 orders of magnitude over a pH range of 0.7 unit (Figure 14). The ζ potential could not be determined with precision over this narrow range of pH, but the ζ potential becomes less negative as the pH is reduced, thus reducing electrostatic interparticle repulsion. The modulus is approximately constant at a given multiple of the gelation time. The pH of the samples plotted in Figure 13 increases with concentration; consequently, the rise in pH drives the increase in gelation time. These data are replotted in Figure 15 as a function of pH along with those measured at a constant silica concentration (27.7% w/w, 14.8% v/v). At the same pH, samples of higher concentration gel more rapidly. The gelation behavior can be compared to the studies of the stability of higher-molecular-weight, highly charged linear

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Figure 14. Gelation time and complex modulus at 2tg for 27.7% w/w silica with 20 µmol‚m-2 PEI (A1800) as a function of pH.

Figure 15. Gelation time for silica with 20 µmol‚m-2 PEI (A1800) as a function of pH. The suspension pH was adjusted by either the addition of acid or base at 27.7% w/w silica or by changing the concentration of silica/PEI.

polyelectrolytes with oppositely charged particles. The rapid flocculation of dilute suspensions of anionic latex particles brought about by a cationic polyelectrolyte was described first by Gregory46,47 and more recently by Ashmore et al.48 and the group of Borkovec.15,16,49 The rate of flocculation of the latex particles showed a maximum at the concentration of cationic polyelectrolytes corresponding to charge neutralization. At this point, the flocculation rate showed relatively little dependence on molecular weight and a small decrease with ionic strength. Interestingly, the rate can be greater than the diffusion-controlled rate measured at high ionic strength in the absence of polymers (i.e., the flocculation rate in the presence of polyelectrolytes can be higher than that brought about by charge neutralization alone). This behavior was ascribed to the polyelectrolytes adsorbing in a patchy conformation,50 leading to an electrostatic enhancement of the flocculation process. Away from the point of charge neutralization, the aggregation rate falls, and the more usual behavior of increasing rate of flocculation with increasing molecular weight and increasing ionic strength is observed. The behavior at compositions away from charge neutralization is consistent with DLVO theory and aggregation via the formation of polyelectrolyte bridges between the latex particles. As the polyelectrolyte concentration was further increased, the particles became stabilized against flocculation, probably because the surface of the particle becomes saturated and the ζ potential becomes strongly positive, preventing the formation of bridges.

Howe et al.

Figure 16. Oscillatory stress-sweep measurement on gelled samples of 27.7% w/w silica with 20 µmol‚m-2 PEI. Filled symbols and the solid line correspond to E1200 after 54 000 s at 25 °C, and the open symbols and dashed line, to E1800 after 14 500 s at 20 °C.

The PEI-silica suspensions studied here are different in a number of respects. Here, the rate of particle aggregation is slowed to such an extent that the gelation of concentrated suspensions can be followed rheologically for molecular weights e1800 Da. The very weak cationic charge of the PEI at high pH prevents charge reversal or even complete neutralization (the ζ potential remains negative, Figure 4). Consequently, increasing the ionic strength increases the rate of gelation. The suspension is not completely restabilized at high polymer levels, suggesting that these low-molecular-weight PEIs do not provide sufficient steric stability to compensate for the localized charge neutralization that occurs on adsorption and that bare patches of the silica surface may be present even at the very high concentrations of PEI (Figure 7) corresponding to the maximum adsorbed amount (Figure 3). Breakage and Reformation of Gels. The strength of the gels at 27.7% w/w silica and 20 µmol‚m-2 PEI were measured by oscillatory stress-sweep studies at a constant 1 rad‚s-1. Typical data are shown in Figure 16 for two molecular weights of PEI at different temperatures in which the structure had been allowed to develop to different extents. The rheological properties were little changed with increasing stress until the sample broke suddenly at a critical stress (σy), when there was a sudden fall in the moduli and the sample became fluid. The PEI molecular weight variations described in Figure 9 were allowed to age at various temperatures for arbitrary times to form gels of different strength before investigating the gel breakdown (Figure 17). As the gels age and reinforce, the stress required to break them (the yield stress, σy) increased with gel stiffness (σy ≈ G/o 0.69), and they became more brittle and broke at lower strain (γy ≈ G/o -0.53, data not shown). These changes were independent of molecular weight and temperature. Thus, there was little dependence of the mechanical energy input at the yield point (σyγy) on the gel strength (inset of Figure 17). The independence of this critical mechanical energy was recently reported for a range of particle gels at different volume fractions.51 The gels were treated as jammed systems, and their stress-induced breakdown from solid to liquid was treated as dejamming. In this study, the volume fraction is constant, but the polymer MW is varied, as is the structuring within the gel by means of aging. After the gel has been broken, it reforms rapidly. This is illustrated in Figure 18 for the samples of 27.7% w/w silica with 20 µmol‚m-2 PEI that were broken in the oscillatory stresssweep measurement shown in Figure 16. After breaking the gels, we then sheared the fluid suspensions for 120 min at 3000 s-1 and followed the regrowth in structure under oscillatory shear

Charged Nanoparticles with a Weak Polyelectrolyte

Figure 17. Yield stress as a function of the zero-stress limiting value of the complex modulus for gels of 27.7% w/w silica with 20 µmol‚m-2 PEI, with samples that are the same as in Figure 9. The inset shows the dependence of the mechanical energy on the limiting modulus.

Figure 18. Low-amplitude oscillatory measurements of fresh and gelled 27.7% w/w silica with the 20 µmol‚m-2 PEI samples described in Figure 16. After gelation, the yield behavior was determined and the samples were then sheared for 120 s at 3000 s-1 before the oscillatory data shown here were recorded. The preshear and oscillation process was repeated twice more for the E1800 sample.

at a stress of 0.04 Pa and a frequency of 1 rad‚s-1. This process of high shear followed by oscillatory shear was repeated twice more for the sample with E1800. The fresh samples formed on mixing silica and PEI have an initial viscosity of 3 mPa‚s, but after gelation and shearing, the viscosity after 10 s is increased to approximately 20 mPa‚s. These sheared samples regel more rapidly: typically the gelation rate is 2 orders of magnitude greater and increases with the stiffness of the gel prior to break up. These findings indicate that shear has not broken the gel into primary particles but instead into aggregates of particles that reassociate more rapidly into a gel.

Conclusions When silica and low-molecular-weight PEI are mixed, the resulting suspension is a low-viscosity opaque fluid that grows in viscosity and eventually gels. On mixing, the pH of the suspension immediately increases to a value significantly higher than that of either of the parent liquids. We ascribe the pH jump

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to an adsorption-induced localized protonation of the PEI at the negative silica surface. Although the parts of the PEI molecule closest to the surface are charged, those segments furthest away remain uncharged because of the high pH of the medium. The maximum number of charged PEI segments occurs at 15 µmol‚m-2, after which a further 5 µmol‚m-2 of polymer is possible through a configurational rearrangement of the PEI molecules. Under these conditions, the surface of the polymer-coated particles is always negatively charged. The gelation of silica-PEI suspensions indicates that they are not colloidally stable under these pH conditions, even at full coverage. As time passes, the particles with adsorbed polymers aggregate to form flocs and eventually a 3D network if the particle concentration is sufficiently high. The relatively long time scale of the aggregation process indicates that there is a delicate balance between the repulsive and attractive forces acting on the particles and polymer. Electrostatic forces provide the repulsion between particles. When the pH is lowered or when the ionic strength is increased, electrostatic repulsion is reduced, which causes an increase in the aggregation rate (i.e., reduction in gelation time). The repulsive forces between the negative silica surfaces may also be decreased when PEI adsorbs, forming patches that are nearly neutral at high pH and that develop an increasing positive charge as the pH is reduced. Adsorbed PEI molecules may form bridges between two (or more) particles at the same time. The efficiency of the bridging process is limited by the rather low molecular weight of the PEI used here, although there is a clear increase in the aggregation rate as the molecular weight increases across the narrow range over which PEI forms uniform suspensions with silica. The ease with which the gels can be broken indicates that the bridges between surfaces are not strong. However, when higher molecular weights of PEI are used or the pH is reduced so that the PEI is strongly charged in solution, bridging becomes so favorable that PEI and silica cannot be mixed easily without uncontrollable aggregation. The efficiency of the bridging process is also affected by the patchy nature of the surface coverage: the minimum in gelation time with PEI concentration is thought to occur where there is the maximum probability that collisions between particles will lead to contacts between patches of adsorbed PEI and the bare surface. The gelation of the suspensions, even at the maximum adsorbed amount of PEI, suggests that the silica surface always retains a degree of patchy character. The low molecular weight and highly branched nature of the PEI molecules are likely to promote a patchy surface because overlap between neighboring molecules is unfavorable. The bridging processes described here occur at much lower molecular weights than those typical for neutral polymers.52,53 Therefore, the sensitivity of the charge on the PEI to the solution pH and local environment (i.e., the fact it is a polybase) is important in promoting the bridging of negatively charged surfaces. Gels of constant composition containing PEI of a range of molecular weights are broken by the application of high shear at a value of the mechanical energy (the product of stress and strain) at a yield point that shows little dependence on the gel strength. The resulting fluids have higher viscosity and gel faster than the freshly mixed silica-PEI suspensions. Acknowledgment. We are very grateful to John Hone (Kodak European Research) for discussions and related experimental studies. We thank Joe Bringley (Eastman Kodak Company) and Peter Griffiths and Sarah Waters (both at Cardiff University) for discussions and the PFGSE NMR datum. LA053327S