Adsorption of Nanolatex Particles to Mineral Surfaces of Variable

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Adsorption of Nanolatex Particles to Mineral Surfaces of Variable Surface Charge David A. Antelmi† and Olivier Spalla* Equipe Mixte CEA/Rhodia, Service de Chimie Mole´ culaire, Baˆ t 125 CEA, Centre d’Etudes de Saclay, 91191 Gif sur Yvette Cedex, France Received December 7, 1998. In Final Form: June 7, 1999

The adsorption of 25-nm-diameter latex particles to flat sapphire (R-Al2O3) and cerium oxide (CeO2) substrates was studied as a function of pH by direct imaging and force measurement. The adsorption density was highest for latex dispersions at low pH and decreased as the pH increased. For the CeO2 substrate, no adsorption of latex was evidenced above the point of zero charge (PZC) of the substrate. In the framework of classical electrostatic interactions, a model was used to describe the adsorption density by taking into account the balance between the surface attraction and the repulsion caused by existing adsorbed particles. On the other hand, classical electrostatic arguments could not account entirely for the adsorption of the latex to the sapphire substrate, because significant adsorption occurred above its PZC. For both substrates, the possibility of lateral migration of the adsorbed particles was examined. Finally, direct force measurements between adsorbed layers of nanolatex particles were performed to quantify the encapsulation layer strength.

1. Introduction Mineral oxide particles have applications in many paint and paper formulations as pigments and fillers. Their stability, in what are often rather complex mixtures of different components, is of importance to the processing properties and the quality of the final products. Great effort has therefore been placed in controlling the interactions between such particles ultimately to prevent them from flocculating or, at least, to control the flocculation. Although the mineral particles may become charged in aqueous dispersions, the electrostatic repulsions are not always sufficient to prevent particle aggregation. This is particularly a problem at high particle volume fraction or upon drying of the formulations where strongly attractive capillary forces begin to act. Adsorption of polymers1 or organic molecules2 to the surfaces of the mineral particles has been used successfully to provide a steric barrier to the flocculation of the particles in such highly attractive regimes. More recently, a study attempted to fabricate a relatively thick steric barrier to aggregation by encapsulating the mineral particles with particles of latex. The latex particles ideally should be of nanometer size for two reasons. First, the attractive forces between mineral particles (van der Waals) have a typical range of the order of a few nanometers and second, the increase in volume fraction of the encapsulated mineral particle dispersion will be kept to a limit. Ideally, a full monolayer of nanolatex would be adsorbed irreversibly to the surface of the mineral particle. Because the nanolatex particles are themselves charged, the stability of the dispersion is preserved. Such a process is then particularly relevant to paint and paper manufacture given that latex forms the base of these formulations. * To whom correspondence should be addressed. † Present address: Ian Wark Research Institute, University of South Australia, Warrendi Road, The Levels, S.A. 5095 Australia. (1) Napper, DH. Polymeric Stabilization of Colloidal Dispersions; Academic Press: New York, 1983. (2) Peyre, V.; Spalla, O. ; Belloni, L.; Nabavi, M. J. Colloid Interface Sci. 1997, 187, 184.

The resistance to flocculation provided by the encapsulating layer depends on the overall surface density of the nanoparticles adsorbed and the strength of that adsorption. A low adsorption density, for instance, will destabilize the dispersion via heterocoagulation or bridging interactions and provide a less efficient steric barrier upon drying of the formulation. A weakly adsorbed monolayer will not withstand the high compressive force on the action of capillary forces in the drying stage. Rupture of the nanolatex layer and subsequent aggregation of the pigment particles may occur. The irreversible adsorption of particles onto solid substrates has been the subject of numerous theoretical3-7 and experimental8-12 studies. The adsorption of noninteracting particles usually is well described by the random sequential adsorption (RSA) model.4,5,9 This model can also account for the adsorption of interacting particles,6 at least for large particles where κa > 1 (κ-1 being the Debye length and a the radius of the particle).3,6,11 Even simple RSA simulations using a renormalized particle radius that takes into account the electrostatic repulsion between two adsorbing particles have been used with great success.6 A more recent theoretical study3 takes into account the balance between the interparticle repulsions and the attraction by the surface. Nanoparticles, however, generally impose a value of κa that is less than unity. From an electrostatic point of view, the spontaneous adsorption of nanoparticles onto a (3) Oberholzer, M. R.; Stankovich, J. M.; Carnie, S.; Chan, D. Y. C.; Lenhoff, A. J. Colloid Interface Sci. 1997, 194, 138. (4) Feder, J. J. Theor. Biol. 1980, 87, 237. (5) Schaaf, P.; Talbot, J. J. Chem. Phys. 1989, 91, 4401. (6) Adamczyk, Z.; Zembala, M.; Siwek, P.; Warszynski, P. J. Colloid Interface Sci. 1990, 140, 123. (7) Wojtaszczyk, P.; Bonet Avalos, J.; Rubi, J. M. Europhys. Lett. 1997, 40 (3), 299. (8) Feder, J.; Giaver, I. J. Colloid Interface Sci. 1980, 78, 144. (9) Onoda G. Y.; Liniger E. G. Phys. Rev. A 1986, 33, 715. (10) Johnson, C.; Lenhoff, A. M. J. Colloid Interface Sci. 1996, 179, 587. (11) Semmler, M.; Mann, E. K.; Ricka, J.; Borkovec, M. Langmuir 1998, 14, 5127 (12) Bo¨hmer, M. R.; van der Zeeuw, E. A.; Koper, G. J. M. J. Colloid Interface Sci. 1998, 197, 242.

10.1021/la9816858 CCC: $18.00 © 1999 American Chemical Society Published on Web 08/26/1999

Nanolatex Particles Adsorbed to Mineral Surfaces

macroscopic substrate is therefore not a classical situation because the Debye length, defining the range of both repulsive and attractive electrostatic interactions, is comparable with the particle size. Monolayer adsorption with surface coverage of 20% or so (the coverage required to create an acceptable encapsulation) imposes a faceto-face distance between adsorbed particles that is also in the nanometer range. The adsorption therefore strongly depends on the solution conditions, because the Debye length is controlled by the amount of salt in the suspension. Furthermore, the pH of the suspension is important, because the charge on both the latex particles and the mineral surfaces is controlled by the protonation of surface acid groups. Our main goal in this work was to quantify, experimentally and theoretically, the effect of pH and ionic strength on the density of particle adsorption to a mineral substrate. The particles used in this study were of nanometer size and hence could be observed directly in their adsorption sites by atomic force microscope (AFM) imaging. Two recent studies10,11 also focused on the adsorption of small latex particles to solid substrates. These authors looked at the effect of salt in detail, while keeping the charge distribution on the two surfaces fixed. In this article, we report experimental results for a system in which the charge on the two components was varied systematically. In practice this was accomplished by varying the pH, which strongly influences the surface charge of the latex and mineral substrates. Furthermore, the charge density and surface potential as a function of pH could be readily characterized (Section 2). The optimum solution conditions for a maximal surface coverage and adsorbed layer stability were then examined using scanning probe microscopy (Section 3.1). The adsorption study was followed by measurements of the force between two layers of nanolatex using the colloidal probe technique13 (Section 3.2). Despite the roughness of nanolatex layers (at a scale of a few nanometers), this technique allowed the direct measurement of the interaction between native latex particles that had not been dried. A similar protocol was used previously for silica particles.14 This approach further provides a strong analogy for the colloidal interactions between the encapsulated mineral particles. In particular, such measurements give insight into the magnitude of the steric barrier provided by the nanolatex layer from measurement of the force required to rupture the adsorbed nanolatex film. A theoretical model was developed to describe the experimentally measured adsorption density taking into account the balance between the direct attraction between the substrate and the latex particles and the repulsion between an approaching particle and the particles already adsorbed (Section 4). Our model is comparable with the 3D RSA model of ref 3 which describes the growth of an energy barrier during adsorption that ultimately gives rise to an adsorption limit. We did not perform Monte Carlo (MC) simulations but rather, in our model, the adsorption terminates when the energy barrier increases beyond a threshold value. The value observed in our calculations was in the range 15-22 kT, which is in the generally accepted “never overcome” limit between two colloids. Because the adsorption densities investigated here were low, a simple analytical method predicting the surface coverage from the known electrostatic charac(13) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (14) Atkins, D. P.; Ke´kicheff, P.; Spalla, O. J. Colloid Interface Sci. 1997, 188, 234.

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Figure 1. Surface charge of the nanolatex particles as a function of pH determined from titration experiments.

teristics of the surfaces was possible without resorting to MC methods. 2. Experimental Section Nanolatex Particles. Nanolatex particles (synthesized by Rhodia Recherches) were obtained by emulsion polymerization using an sodium dodecyl sulfate (SDS) emulsifier and sodium persulfate initiator. The polymer composition was 95% methyl methacrylate and 5% methacrylic acid giving a latex of high Tg (≈100 °C). The nanolatex dispersion was purified using direct ion exchange with a mixed bed of strong anionic (Amberlite IRN78) and strong cationic (Amberlite IRN77) exchange resin. In this procedure 10 g of each resin were mixed together and about 200 mL of 10% nanolatex dispersion was added to the mixture. The nanolatex was left in contact with the resin for 3 h with gentle agitation before filtering and repeating once more with a fresh bed of mixed resin. Both the cationic and anionic resins were conditioned according to ref 15 before use. The technique gave a nanolatex recovery of about 60% and proved to be very efficient for removing the SDS surfactant, as evidenced by the increase in the surface tension of the dispersion (from 56 to 70 mJ‚m-2) and the decrease in the conductivity (from 120 to 20 µS‚cm-1). Transmission electron microscopy and neutron scattering were performed to evaluate the average diameter and polydispersity of the nanolatex dispersion. Both techniques indicated a diameter 2a ) 25 nm with a low degree of polydispersity. Surface Charge and Surface Potential Measurements. The nanolatex particles are stabilized in dispersion mainly because of the presence of surface carboxylate groups (COOH, pKa ) 4) and some stronger acid groups in the form of sulfate groups (SO4H, pKa ) 0.5-1) originating from the persulfate initiator used during the synthesis. The surface charge of particles was determined experimentally by titrating a 2% (by weight) dispersion with 0.1 M sodium hydroxide and monitoring both the conductivity and pH. The maximum surface charge Zmax was 9 µC‚cm-2 (1200 charges per particle or 0.6 e‚nm-2) occurring at pH ) 11. The charging of the latex as a function of pH was calculated from the titration data to give the curve shown in Figure 1 with and without a NaNO3 background electrolyte. The zeta potential of the nanolatex particles was also measured by Doppler electrophoretic light-scattering analysis (Coulter Delsa 440). The results indicated a small negative surface potential (-25 mV), even at pH ) 2.5, which rapidly became more negative as the pH increased. At pH ) 7 a plateau value of approximately -80 mV was reached. The small surface potential even at pH ) 2.5 is consistent with several dissociated sulfate groups and some dissociated carboxylate groups. At such low potentials the surface charge can be related to the surface potential ψ via:16 (15) Van Den Hull, H. J.; Vanderhoff, J. W. J. Electroanal. Chem. 1972, 37, 161. (16) Hunter, R. J. Foundations of Colloid and Interface Science; Oxford University Press: Oxford, 1989; Vol. 1.

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Antelmi and Spalla

}

4 eψ κa2 eψ + tanh 2 sinh LB 2kT κa 4kT

(1)

For 10-4 M salt, eq 1 indicates that the nanolatex particles carry approximately 25 charges each at pH ) 2.5. So few charges cannot maintain the stability of the dispersion, and the dispersion appeared turbid at this pH after several hours. At pH ) 4 the number of charges is about 80 for 10-4 M salt. This value will be used as an offset added to the titratable charge determined from Figure 1 (Section 4). Sapphire (r-Al2O3) Substrates. Flat single-crystal substrates of sapphire were purchased from RSA Le Rubis (Lyon, France). These substrates are made from a pure R-Al2O3 powder which is fused at high temperature and drawn into a cylinder. The resulting cylinder is a single alumina crystal with the crystallographic c-axis parallel to the long axis of the cylinder. Thin disks are then cut from the cylinder and polished so that the c-axis is approximately perpendicular to the plane of the disk. The deviation of the c-axis with respect to the normal was quoted by the manufacturer to be between 5 and 10°. These disks were prepared for the adsorption studies by first washing them in pure ethanol, rinsing with Milli-Q water, and blow-drying with compressed nitrogen. Immediately before use, the sapphire disks were subjected to an H2O plasma for 1 min to remove any remaining chemical contaminants. Imaging of these surfaces by scanning probe microscopy (SPM) showed that they were smooth to (0.5 nm over an area of several micrometers, but on a larger scale, deeper grooves (∼20 nm) resulting from the manufacturer’s polishing process could be evidenced. The point of zero charge (PZC) of the sapphire surfaces was estimated to occur at 5 < pH < 6 by direct force measurements using an atomic force microscope (AFM, Digital Instruments Mk III). In this technique, the deflection of the silicon nitride (Si3N4) probe of the AFM was monitored as it approached a cleaned sapphire substrate while immersed in a solution of known pH.17 As the PZC is approached, the cantilever deflection goes to zero (and may change from repulsive to attractive in some cases) because the electrostatic contribution to the total interaction goes through a minimum. The measurements showed this phenomenon at pH values in the range 5 < pH < 6, and hence we conclude that the PZC also lies in this range. The determined PZC is in agreement with some previous work on similar single alumina crystal substrates,17-19 but other studies have returned a value of about pH ) 9.20 It has been proposed18 that the PZC of an R-alumina surface depends on its degree of hydroxylation. Different substrate preparation and cleaning may thus explain the discrepancy between the different values reported in the literature. In this study, several attempts were made to displace the PZC of the sapphire substrates, including plasma treating the substrates for long periods20 and soaking the sapphire substrates in acidic17 or basic solutions at elevated temperatures. AFM measurements always showed that the substrate had a PZC at about pH ) 5-6 regardless of the treatment. The potential for silica contamination was minimized as much as possible by using polypropylene containers and Teflon plumbing. In fact, the only silica that came in contact with the electrolyte was that from the quartz SPM fluid cell. However, the dissolution of silica should have been negligible over the pH range studied (4-10). Cerium Oxide (CeO2) Substrates. The second substrate used in this adsorption study was fabricated by adsorbing a uniform dense monolayer of CeO2 nanoparticles onto naturally occurring muscovite mica. Preparation and characterization of the CeO2 nanoparticles has been described in detail elsewhere.21 A 20 g/L dispersion of the CeO2 nanoparticles was prepared into which freshly cleaved mica was immersed for approximately 1 h. The CeO2-coated mica disk was then removed and washed in Milli-Q water at pH ) 2 to remove any nonadsorbed particles. In general, the ceria-coated mica substrates were prepared 1 day before use and were left immersed in Milli-Q water at pH ) 2 until ready for nanolatex adsorption. The CeO2 layer had to be aged for at least 12 h to obtain reproducible nanolatex adsorption densities. The monolayer of adsorbed CeO2 particles did not desorb and gave a substrate that was smooth to several nanometers. Previous detailed studies22 have shown that the properties of this adsorbed monolayer reflect the surface properties of the dispersed CeO2

particles. The surface charge of CeO2-coated mica substrate can therefore be taken from surface titration data of the dispersed particles which have been characterized in detail.21 It has been shown further that the PZC of the CeO2 particles may be shifted from 10 to 8.6 when the particles are subjected to conditions of high pH. In this regime the surface-bound nitrates are replaced by OH- groups according to:

Ce-O-NO2 + OH- f Ce-OH + NO3-

(2)

The phenomenon described by eq 2 was used to alter the PZC of the CeO2 layer adsorbed to the mica. After the initial adsorption of the CeO2 nanoparticles was carried out as described above, the mica substrates were immersed in water at pH ) 12 for about 3 h. The substrates were then rinsed and left in a solution of pure water at pH ) 5.6 overnight. Adsorption Method. The nanolatex particles were adsorbed to the mineral surfaces from solution. A purified dispersion of nanolatex was diluted to 1% (by weight) with pure water or an electrolyte solution at a specific concentration. The pH was then adjusted by the addition of 0.1 M NaOH or HNO3. The clean mineral substrates were immersed into the dilute nanolatex dispersion and left for 10 min in an upright position to avoid any influence of sedimentation. The basic model of diffusion-limited adsorption23 indicates that the time required to reach the RSA jamming limit is 32 ms. Even if extra time is required, because of the “blocking factor” for instance, the jamming limit will still be reached long before a 10-min adsorption period. Indeed, the adsorption density did not increase after leaving the substrates soaking for longer times (e.g., overnight). At the end of this period the substrates were carefully removed and washed by immersing them into three separate solutions of particle-free solvent at the same pH and electrolyte strength as the 1% original nanolatex dispersion. If the adsorption was performed at high ionic strength (>10-2 M), then a quick final wash was performed in pure water to avoid the formation of salt crystals upon drying of the substrate. In most of these experiments the substrates were dried and imaged in ambient conditions. To minimize the effects of capillary forces,24-26 most of the solvent that adhered to the substrate after the washing procedure was carefully blown away using compressed nitrogen. The substrates were then left uncovered in a filtered air cabinet for at least 1 h to complete the drying. Imaging of the Adsorbed Particles. SPM was used to directly image the particles adsorbed on the flat mineral substrates. The SPM (Digital Instruments Nanoscope III) was operated in a noncontact TappingMode to reduce the lateral forces exerted on the particles. Several different areas on each substrate were scanned and recorded. A computer program was developed to count the number of particles adsorbed on the surface and also to record their positions. Once the number of particles was determined the fraction surface coverage θ could be deduced as follows:

θ)

Nπa2 Sc

(3)

where N is the number of particles adsorbed over an area Sc of the collector. The projected area of the particles πa2 was calculated from the radius a measured by transmission electron microscopy (17) Larson, I.; Drummond, C. J.; Chan, D. Y. C.; Grieser, F. Langmuir 1997, 13, 3, 2109. (18) Smit, W.; Holten, C. L. M. J. Colloid Interface Sci. 1980, 78, 1. (19) Pedersen, H. G. Ph.D. Thesis, Technical University of Denmark, 1998. (20) Veeramasunemi, S.; Yalamanchili, J. D.; Miller, J. D. J. Colloid Interface Sci. 1996, 184, 594. (21) Nabavi, M.; Spalla, O.; Cabane, B. J. Colloid Interface Sci. 1993, 160, 459. (22) Spalla, O.; Kekicheff, P. J. Colloid Interface Sci. 1997, 192, 43. (23) Crank, J. The Mathematics of Diffusion; Clarendon Press: Oxford, 1975. (24) Paunov, V. N.; Kralchevsky, P. A.; Denkov, N. D.; Ivanov, I. B.; Nagayama, K. Colloids Surf. 1992, 67, 119. (25) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B. Langmuir 1992, 8, 3183. (26) Velikov, K. P.; Durst, F.; Velev, O. D. J. Colloid Interface Sci. 1998, 14, 1148.

Nanolatex Particles Adsorbed to Mineral Surfaces and neutron scattering rather than that measured in the SPM images. This avoided overestimation of the surface coverage due to particle-probe convolutions which tend to exaggerate the particle size. Desorption Studies. The degree of desorption of the adsorbed nanolatex layer was checked by immersing latex-coated substrates into particle-free solutions at various pH and electrolyte conditions for various periods immediately after adsorption. For this series of tests the nanolatex particles were first adsorbed to the mineral substrates in the absence of salt at pH ) 4. Immediately after rinsing any nonadsorbed particles away, the substrates were placed vertically in particle-free solutions at either pH ) 4 or pH ) 7 for periods varying from 1 to 90 h. The substrates were then dried and scanned in the SPM to determine the degree of surface coverage. Lateral Migration. To determine whether the adsorbed particles can migrate laterally along the mineral surface, nanolatex initially was adsorbed to the mineral substrates at pH ) 7 and pH ) 8 for the sapphire substrates and CeO2 substrates, respectively, using the procedure described above. These substrates were rinsed in an appropriate particle-free solution (three times) and then re-immersed into particle-free solutions at specific pH and salt concentrations. The substrates were removed after 3 h of soaking, dried with compressed nitrogen and in air, and finally imaged using SPM TappingMode in air. Direct Force Measurements. The measurement of the interaction between opposing monolayers of adsorbed nanolatex particles was performed using the AFM following the same methodology as in ref 13. A “colloid probe” was made by gluing a spherical SiO2 particle (Polysciences Inc.) to a commercial silicon nitride imaging probe at its apex using a small quantity thermosetting resin (Epikote 1004). The colloid probes were cleaned by brief exposure to a H2O plasma (30 s) and immersed in a 20 g/L dispersion of CeO2 nanoparticles along with a freshly cleaved mica disks. A uniform monolayer of CeO2 particles was therefore adsorbed to both the silica sphere and the flat mica substrate. SPM imaging showed that CeO2 nanoparticles adsorb to SiO2 in a dense monolayer similar to that given on mica. The CeO2-coated colloid probe and mica substrate were rinsed, soaked overnight in acidified Milli-Q water, blown dry with pure nitrogen, and finally installed in the AFM. Milli-Q water at pH ) 2 was first injected into the chamber of the AFM, and the interaction between the two opposing CeO2 layers was measured. At pH ) 2, CeO2 was strongly positively charged and gave a repulsive interaction that was later used to calibrate the spring constant of each silicon nitride cantilever using the previous results of ref 22 on the same system. The AFM chamber was rinsed with Milli-Q water at pH ) 4 after which a 1% nanolatex dispersion at pH ) 4 was gently passed through to coat the probe and flat substrate with nanolatex particles. Any nonadsorbed particles were rinsed away by re-injecting particle-free Milli-Q water at pH ) 4. The result of this procedure was a nanolatex-coated sphere opposing a nanolatex-coated flat substrate. The nanolatex layers were never allowed to dry and hence should have presented their native surface chemical characteristics at each interface. A similar protocol was previously used14 to produce adsorbed layers of native silica nanoparticles for force experiments using an Israelachvili-type surface forces apparatus.27 The force-distance profiles for these opposing nanolatex layers were determined as a function of pH, usually in the presence of 0.001 M NaNO3. In some solution conditions the adsorbed layers of nanolatex were fragile and only the first force-distance profile measured on approach of the surfaces was considered reliable. The diameter of the spheres used to make the colloid probes was measured by scanning electron microscopy after the experiments and was typically in the range 5-10 µm. The adsorbed layer of nanolatex could not be resolved on our instrument. The flat substrates were always dried and then imaged using SPM, as described above, after the force experiments to check the quality of the adsorbed nanolatex layer. Reagents. Ethanol and other organic solvents were of analytical grade obtained from Prolabo. Analytical grade NaNO3 (27) Israelachvili, J.; Adams, G. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975.

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Figure 2. SPM images showing the negatively charged nanolatex particles adsorbed at different pH values onto the R-Al2O3 (sapphire) substrate. No added salt was present, and the samples were imaged in air using TappingMode scanning over an area of 2 × 2 µm. from Fluka was dried at 120 °C before use. NaOH and HNO3 were obtained from Merk and used without further purification. Milli-Q water was used throughout the experiments.

3. Results 3.1 Adsorption and Desorption of Nanolatex Particles. 3.1.1. Influence of pH and Monovalent Salt on Nanolatex Adsorption. Each image in Figure 2 shows a typical 2 × 2 µm surface scan of the surface of the sapphire substrates where adsorption was carried out in the absence of added salt over the range 4 < pH < 10. The number of particles adsorbed at pH ) 4 was highest, and decreased as the pH increased. Very little adsorption was noted higher than pH ) 8 and virtually no adsorbed particles are observed on the substrates at pH ) 10. The particles are distributed quite randomly but in some cases appear to be slightly aggregated. The surface coverage was calculated according to eq 3 after counting the particles observed in each image. The results are shown in Figure 3 and represent the average from no less than five different images taken on different positions on the same substrate surface. A similar series of images was recorded when a background electrolyte of 10-3 M NaNO3 was present in the nanolatex dispersions. The images are not shown here but the calculated surface coverage has been given in Figure 3. At pH ) 4 the surface coverage was very similar to that observed in the absence of added salt. At intermediate pH (5-7) the surface coverage was significantly higher with salt present until finally no adsorbed particles were seen beyond pH ) 8. The adsorption of the nanolatex particles onto the CeO2coated mica substrates showed some similar trends as well as some important differences compared with the adsorption on the sapphire substrates. Figure 4 shows a

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Figure 3. The number of nanolatex particles adsorbed to the R-Al2O3 (sapphire) substrate (with and without added NaNO3) determined by counting the particles present on no less than five 4-µm2 scans at each pH value studied. The fraction surface coverage as defined in eq 3 is also shown on the right-hand axis. Note that adsorption occurs even above the PZC of the substrate.

Figure 4. SPM images showing the negatively charged nanolatex particles adsorbed at different pH values onto the CeO2-coated mica substrate. No added salt was present, and the samples were imaged in air using TappingMode scanning over an area of 2 × 2 µm.

series of scans of the CeO2 substrate covering a range of pH values in the absence of added salt. The highest number of adsorbed particles was once again seen at the lowest pH and virtually no particles were adsorbed at pH ) 10. At each pH value the number of particles is higher than the corresponding pH on the sapphire substrate. Furthermore, the particles are distributed randomly and appear less aggregated with respect to the sapphire substrate. The surface coverage according to eq 3 is presented in Figure 5 for this series of images and also for the adsorption density observed in the presence of 10-3 M NaNO3. When the background electrolyte was present, the number of particles adsorbed increased over the whole range of pH. At pH ) 10, however, virtually no particles

Antelmi and Spalla

Figure 5. The number of nanolatex particles adsorbed to the CeO2-coated mica substrate determined by counting the particles present on no less than five 4-µm2 scans at each pH studied. The fraction surface coverage as defined in eq 3 is also shown on the right-hand axis. Adsorbing the nanolatex particles in the presence of a background electrolyte increased the overall adsorption. Displacing the PZC of the substrate from 10 to 8.6 (the washed CeO2 substrate) gave an overall reduction of the surface coverage. Virtually no particles adsorbed above the PZC in any of the three cases shown.

were adsorbed. At the other extreme (pH ) 4) some multilayer patches of particles were seen across the surface which did not allow counting of the total number of particles. 3.1.2. Influence of Substrate PZC. A striking difference between the adsorption of the nanolatex on the two different substrates was that in the case of CeO2, no particles adsorbed above the PZC (Figure 5). By contrast, significant adsorption occurred at and above the PZC of the sapphire substrate (Figure 3). The influence of the PZC was examined using the CeO2-coated mica substrates that had been soaked in a solution at pH ) 12 for 3 h. As mentioned above these substrates had a PZC of 8.6 as opposed to 10 for the untreated CeO2 substrates.21 The surface coverage was calculated from eq 3 and plotted in Figure 5. The overall adsorption follows a trend similar to that observed on the CeO2 substrate with a PZC ) 10. However, the overall surface coverage is reduced. No adsorption was seen for pH > 7. 3.1.3. Desorption?. No evidence of desorption was observed for either substrate even after soaking the coated substrates in particle-free solution for up to 90 h. A range of particle-free soak solutions were used at pH ) 4 and 7 and at varying ionic strengths. 3.2 Properties of the Adsorbed Nanolatex Layers. 3.2.1. Lateral Migration. The nanolatex particles adsorbed to the sapphire (R-Al2O3) substrates, in some cases, were seen to exist in an aggregated state (Figure 2). This could be a phenomenon related to the capillary attractions between the particles where the particles are pulled together as the water film evaporates from the substrate. Nevertheless, the particles on the CeO2 substrates were usually well dispersed and appeared as randomly adsorbed single particles (Figure 4). The effect of the soaking conditions (pH and salt concentration) on the clustering of the preadsorbed layers was checked systematically. The series of images shown in Figure 6 were taken after 3 h of soaking the sapphire substrates in various particle-free solutions of specific pH and ionic strength. The nanolatex particles appear to be in various states of aggregation, more strongly aggregated in the presence of added salt. The particles adsorbed on the sapphire did aggregate over time at pH ) 7 with 1 M NaNO3 and at pH ) 2.5 with or without salt. This


Figure 6. Series of SPM images taken after soaking R-Al2O3 (sapphire) substrates, supporting preadsorbed nanolatex layers, in particle-free solutions at different conditions of pH and electrolyte concentration. Large aggregates can form especially at low pH or high electrolyte concentration. The samples were imaged in air using TappingMode scanning over an area of 2 × 2 µm.

clustering could have two different origins. First, it could be due to the drying process or second, it could be due to lateral migration and aggregation of the particles while still immersed in the solution. Capillary forces cannot entirely explain the observations because virtually no aggregation was observed at pH ) 7 without added salt. Aggregation is expected in the presence of 1 M electrolyte, however, and is consistent with the rapid aggregation of the bulk nanolatex dispersion in such conditions. Similarly, a bulk dispersion of the nanolatex is not stable at pH ) 2.5 where the particles are less negatively charged. Hence, the 2D aggregation is most likely a result of migration of the particles along the surface. Nevertheless, the role of the capillary forces cannot be ruled out definitely and may still provide a contribution especially if the particles migrate closer together while still immersed in the solution. Unfortunately, our attempts to image the particles using liquid TappingMode, and so avoid the drying stage, failed because the SPM tip swept the particles from the scan region. By contrast, the nanolatex particles adsorbed to the CeO2-coated mica substrates appear far less aggregated for all the solution conditions studied (Figure 7). The case of 1 M salt at pH ) 2.5 is the most interesting because a bulk dispersion of nanolatex in such ionic conditions aggregates totally. Hence, the absence of clustering of the adsorbed layer on the CeO2-coated mica indicates that the aggregation has been prevented and the particles are locked into their adsorption sites. This could be due to the granular nature of the CeO2 layer or to a high energy of adsorption (discussed later). 3.2.2. Interaction Between Adsorbed Nanolatex Layers. The monolayers of nanolatex particles adsorbed onto the

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Figure 7. Series of SPM images taken after soaking CeO2coated mica substrates, supporting preadsorbed nanolatex layers, in particle-free solutions at different conditions of pH and electrolyte concentration. In contrast to the R-Al2O3 (sapphire) substrates, few aggregates are observed. The samples were imaged in air using TappingMode scanning over an area of 2 × 2 µm.

flat mineral substrates were used further to investigate the interactions between nanolatex layers by direct force experiments. This also provided a means to measure the interaction between native latex particles in a variety of solution environments. The insert of Figure 8 shows the configuration of the modified commercial AFM probe (to give a “colloid probe”) by which such interactions were measured using the AFM. The adsorption of the nanolatex to the CeO2-coated sphere and flat substrate was always effectuated at pH ) 4. This lead to surface coverages of about 25% which was always checked after the experiments by imaging the flat substrate. Figure 8a shows the force between the nanolatex-coated colloid probe and the nanolatex-coated CeO2/mica substrate at pH ) 9.3 and 6.2 with a background NaNO3 concentration of 10-3 M. The overall force is repulsive in both cases and does not show an attractive van der Waals component at small distances. It must be kept in mind, however, that the roughness of such adsorbed layers is of the order of nanometers and contact between asperities on the surfaces probably occurs before any short-range attraction measurable in the experiment begins to act. The electrostatic repulsion is therefore seen until the two surfaces are in contact with each other. The solid lines in Figure 8 are theoretical fits of the data using the nonlinear solution to the Poisson-Boltzmann equation under conditions of constant charge (upper solid line) or constant surface potential (lower solid line).28 The experimental data are well described by such an electrostatic model and fall within the limits of these two boundary conditions. The fitted surface potentials also agree reasonably well with the measured zeta potential (28) Chan, D. Y. C.; Pashley, R. M.; White, L. R. J. Colloid Interface Sci. 1980, 77, 283.

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Figure 9. Interaction between a colloid probe encapsulated with nanolatex and a flat substrate coated with a monolayer of nanolatex at pH ) 2 (see insert, Figure 8a). The insert proposes an explanation of the observed oscillations where the nanolatex layers rupture under the compressive force. Separation of the surfaces also gives oscillations in the force-distance profile caused by various particle-particle and particlesubstrate adhesions.

Figure 8. Interaction between a colloid probe encapsulated with nanolatex and a flat substrate coated with a monolayer of nanolatex for (a) pH ) 9.3 and 6.2, and (b) pH ) 5.2 and 4. The experimental configuration gives the nanolatex/nanolatex interaction as shown schematically by the insert. Only the force measured on approach of the surfaces is given. The shaded areas give the nonlinear Poisson-Boltzmann fit with constant charge (upper solid lines) and constant potential (lower solid lines) boundary conditions. The parameters used to make the theoretical fits were: Ψ ) 60 mV, K -1 ) 14 nm at pH ) 9.3; Ψ ) 35 mV, K-1 ) 9 nm at pH ) 6.2; and Ψ ) 30 mV, K-1 ) 42 nm at pH ) 5.2. No theoretical fit for the curve at pH ) 4 was attempted.

measurements. For both curves shown in Figure 8a, only the data measured on approach of the surfaces is shown. The data measured upon separation of the surfaces showed no adhesion and superimposed on the curves measured on approach. These findings are consistent with the bulk behavior of the nanolatex dispersion which is stable across this pH range. Figure 8b shows similar experiments, but this time at pH ) 5.2 and 4.1 with no added background electrolyte. The smaller repulsive force is consistent with the lower surface charge on the latex particles at these pH values. No fit was performed for the data measured at pH ) 4.1, but the data measured at pH ) 5.2 show good agreement with the Poisson-Boltzmann model. The data measured upon separation of the surfaces in these cases has also been presented. A small adhesive force seen at both pH values is also consistent with the smaller electrostatic repulsive component operating at these pH values. The bulk nanolatex dispersions are essentially stable across this pH range. The small adhesion upon separation of the surfaces indicates that some particle collisions in a bulk dispersion would lead to flocculation, especially at pH )

4 where there is no significant repulsive potential between the particles. In practice, the nanolatex dispersion is stable in this pH range, but some aggregates can be seen after months of storage. The measured force-distance profiles are once again consistent with these bulk observations. Figure 9 shows a force distance profile for the symmetric nanolatex configuration measured at pH ) 2. Large oscillations in the force are seen both upon approach of the surfaces and upon separation. Given that the nanolatex particles are essentially uncharged at this pH, no background electrostatic force was detected. The oscillations, however, indicate that the layer of adsorbed nanoparticles becomes ruptured under the compressive force of the spherical probe on the flat substrate. A proposed mechanism is shown schematically in the insert of Figure 9. Because the absolute surface separation is not measured directly in the AFM experiment, one cannot say that both layers are completely squeezed out from between the two surfaces. Indeed the distance scale in Figure 9 shows that the two jumps that occur upon approach of the surface are each less than a particle diameter. It is important to note that the F/R values at the jump positions are almost the same, which demonstrates that the expulsion events are approximately equivalent. Therefore, it seems that one adsorbed nanolatex layer ruptures to release the strain and then the other ruptures equivalently once the strain rebuilds. (By contrast, expulsion of successive surfactant bilayers from confined geometries is not always equivalent.) The rupture of each layer at an equivalent applied strain should be expected, because the system is symmetric and both layers of latex are adsorbed to underlying CeO2 layers. The data measured upon separation of the surfaces confirms, however, that the contact region has been severely damaged as indicated by the many small discontinuities in the force-distance profile. Such oscillations suggest that many adhesive contacts between the adsorbed nanolatex particles or CeO2 layers were established and broken during the separation of the surfaces. Note that although the oscillatory force-distance profile was always observed at pH ) 2, the position and distance between oscillations varied from experiment to experiment. The rupture of the adsorbed nanolatex layers was not seen at higher pH, which shows that the adhesion between


the particles and the underlying CeO2 layer is weakened when the charge on the latex particles is almost canceled. 4. Discussion The SPM study presented above has defined some conditions under which nanolatex can be adsorbed to the two mineral substrates to create a protective barrier against flocculation. For both substrates the strongest adsorption was seen at the lowest pH values (about pH ) 4). Both mineral substrates bear a positive surface charge at this pH, whereas the nanolatex is charged negatively. The driving force for the adsorption of the nanolatex particles onto the mineral substrates would therefore appear to be predominantly electrostatic. That no adsorption of nanolatex onto the CeO2-coated mica substrate occurs above its PZC is also consistent with a predominantly electrostatic mechanism. However, significant adsorption was observed above the PZC of the sapphire substrate. This may indicate that this substrate is heterogeneous and a significant number of positive sites are present above the PZC, or that a more specific interaction provides the adsorption-driving mechanism. We will first discuss adsorption to the CeO2 substrate and concentrate on the parameters responsible for limiting the surface coverage in terms of the experimental conditions used. In a second stage, the encapsulation efficiency will be discussed. 4.1. Model for Adsorption. 4.1.1. Basic Outline. It was verified experimentally that the adsorbed nanolatex particles do not desorb even when the substrates are soaked in a solution free of particles. This demonstrates that the adsorbed layer is not in equilibrium with the dispersion, at least over the time scale of the experiments. The formation of the layer, and in particular the existence of a limit in the surface coverage, therefore appears to be determined by a kinetic process rather than a thermodynamic equilibrium. Such an adsorption process can be understood by considering the interactions driving the adsorption and how these are modified as more and more particles become adsorbed. The CeO2-coated mica is positively charged across the whole range of pH studied, providing an attractive potential to the adsorption of the negatively charged nanolatex particles. At the beginning of the adsorption process the first particles diffusing to the surface will be drawn onto the surface and adsorb unhindered, under the influence of this electrostatic attraction, Uatt(h). When the density of adsorbed particles F increases, the preadsorbed particles hinder the adsorption of the approaching particles because (i) they occupy some of the available adsorption sites, and (ii) they repel the approaching particles electrostatically. The first effect is taken into account by the RSA model, whereas the second effect has been examined in different ways by several authors.3,6 Adsorption of particles to the substrate creates an energetic barrier U to the adsorption of additional particles. The characteristics of the barrier depend on the position, b r, at which an approaching particle arrives, and on the distance of the approaching particle, h. When a particle approaches a particular adsorption site, the maximum U* of U(r b,h) versus h is determined. Hence, in the Monte Carlo procedure used to simulate the process of adsorption, a successful particle adsorption occurs according to the probability e-βU*(rb,h*). We have used a simpler protocol which is efficient when the surface coverage (at saturation) is low. It is clear in that case, that the long-range electrostatic repulsions play a predominant role in limiting the surface coverage. Indeed, when a particle approaches an empty site (which

Langmuir, Vol. 15, No. 22, 1999 7485

remains the first requirement for adsorption), even the closest particles stay far from the approaching particle (for instance, see Figure 4, pH 8) and numerous particles contribute to the repulsive potential. Accordingly the summation of the repulsive contributions will not depend too much on the positions of the adsorbed particles around the empty site. Therefore, we assume that U(r b,h) does not depend on the position b r but only on the distance of approach h. This assumption gets weaker when the repulsion decreases and the surface coverage increases. The next step is to calculate the repulsive term. To do this analytically, we assume that the existing adsorbed particles are distributed homogeneously with a surface density F around the target adsorption site of the approaching particle. One could choose to distribute the particles on a lattice around the target site or even use the pair correlation function deduced from renormalized RSA. This would slightly change the numerical results but not the basic principle of an homogeneous barrier to overcome. At fixed pH and ionic strength, the maximum of U(h), U*, depends on F. As more particles adsorb, the height of the energy barrier increases to the point where fewer and fewer collisions have the energy to penetrate the barrier to give a successful adhesive contact. Beyond this point adsorption is so slow that it essentially appears to be stopped (within the experimental time frame of 10 min). The model above is realized using the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) description of colloidal interactions incorporating kinetic considerations which set a criterion that limits the adsorption density. First, the attractive energy between the CeO2coated mica and the nanolatex particles Uatt(h) is calculated from the known charge characteristics of the interfaces. The amplitude of repulsive barrier provided by the adsorbed particles against the adsorption of approaching particles is then calculated. The sum of these two contributions gives rise to a interaction profile with a long-range repulsion and a strong attraction at short range. Thus a repulsive barrier exists at intermediate range which increases as the adsorption density increases. We first calculate both the attractive and repulsive interaction as a function of the surface potential of the substrate Φ0, the effective charge Zeff of interaction of the latexes, and the density of adsorption F. 4.1.2. Attractive Component. The attractive free energy between the nanolatex particles and the substrate surface arises from their surface charge of opposite sign. The magnitude can be calculated most conveniently in the framework of the weak overlap approximation. This approximation is strictly only valid if the particle is located at a distance of several Debye lengths from the surface. Nevertheless, it will be demonstrated that the pertinent part of the interaction occurs at such distances validating this assumption. To begin, the interaction energy between two spheres of different diameters (with no conditions imposed on the value of κa1,2) is given by:29

βUatt(r) )

e-κ(r - a1-a2) r (1 + κa1)(1 + κa2) Zeff,1Zeff,2LB

(4)

where r is the center-to-center distance between the two spheres of radius a1 and a2. The effective charge of interaction Zeff is assumed to be homogeneously distributed over the surface of the two spheres. When the radius of one sphere tends toward infinity, the geometry is then a (29) Bell, G. M.; Levine, S.; McCartney, L. N. J. Colloid Interface Sci. 1970, 33, 335.

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Figure 11. Interaction energy, U(h), of a nanolatex particle approaching a partially covered flat substrate. The number of adsorbed nanolatex particles is 404 per µm2, the ionic strength is 0.25 mM, the charge on the nanolatex is 77.5 units, and the potential on the substrate is 60 mV.

Here, U1,2(r) is the DLVO30 potential between two particles in a bulk solution given by: Figure 10. Definition of geometric variables for eqs 8-11 describing the repulsive force encountered by a particle approaching a partially covered substrate.

e-κ(r - 2a1) βU1,2(r) ) Z2effLB r(1 + κa1)2

sphere approaching a plane as in our experimental geometry. In this case eq 4 reduces to:

The total energy of repulsion is simply:

att

βU (h) )

Zeff,2 Zeff,1LBe

-κh

κa22 (1 + κa1)

(5)

Zeff,1LBe-κh

∑2 κ(1 + κa1)

-κr

∫2a∞ xe r 1

dx (10)

The lower boundary of integration (2a1) comes from the requirement of an empty site. The integral on the righthand side of eq 10 can be calculated using rdr ) xdx:

or

βUatt(h) ) 4π

e2κa1 βUrepF(h) ) 2πFZ2effLB (1 + κa1)2

(9)

(6)

where h is the face-to-face distance and ∑2 is the surface charge of the planar surface which is related to the effective surface potential of the plane by ∑2 ) -(eκΦ0/4πLBkT). Substituting this into eq 6 gives:

e2κa1 e-xh + 4a1 βUrepF(h) ) 2πFZ2effLB κ (1 + κa1)2 2

2

(11)

where Φ0 is the “effective” surface potential of the plane which is generally comparable with the zeta potential of the surface. One can further notice that the electrostatic attraction is directly proportional to the effective charge of the nanolatex particles Zeff. 4.1.3. Repulsive Component. As the adsorption progresses, free particles approaching the surface will feel an additional repulsive force because of their interaction with particles that are already adsorbed. This repulsive component can be estimated considering an empty adsorption site surrounded by adsorbed particles distributed homogeneously. The number of particles in an annulus of thickness ∆x and radius x is then 2πFx ∆x, as shown in Figure 10. When a free particle approaches the adsorption site and arrives at distance h (Figure 10), it experiences a repulsion caused by the particles in the annulus of radius x and thickness ∆x, which can be estimated by:

Equation 11 shows that the repulsion depends linearly on the product FZ2eff. When the attractive component (eq 7) and the repulsive component (eq 11) of the interaction are summed, the resulting energy profile exhibits a longrange repulsion and a short-range attraction as shown in Figure 11. The repulsive energy experienced by an approaching particle is maximal when the particle starts to penetrate into the preadsorbed layer. It is important to note that the energy maximum is located at a particle/ substrate separation of around 250 Å, which is more than two times the Debye length of the system (for an ionic strength of 10-3 M). The use of the weak overlap approximation in the calculation of the particle substrate electrostatic component in eq 4 is therefore justified to some extent. 4.1.4. The Limiting Surface Coverage. To use eqs 7 and 11 numerous electrostatic parameters need to be evaluated. First of all, the Debye length, defined by the ionic strength, was unambiguous when 10-3 M NaNO3 was present in the experiments. However, when no additional salt was added, such as the some of the data presented in Figures 2 and 4, the ionic strength was due to free counterions plus the acid and base added to adjust the pH of the dilute suspension of nanolatex. For each sample, we estimated the ionic strength to be I ≈ 2-2.5‚10-4 M giving K-1 ≈ 19 nm.

δβUx(h) ) 2πxF∆xβU1,2(h)

(30) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.

βUatt(h) )

eΦ0 Zeff e-κh kT (1 + κa1)

(7)

(8)


Figure 12. Number of nanolatex particles adsorbed per µm2 versus pH for the CeO2-coated mica substrate. The full circles and empty circles are the experimentally observed number of adsorbed nanolatex particles with 10-3 M NaNO3 and without added salt, respectively (same data as in Figure 4). The lines are the number of adsorbed nanolatex particles required to give an energy barrier equal to 10 kT (dashed line), 15 kT (full line), and 22 kT (dash-dot line). Bold lines correspond to an ionic strength of 1 mM (i.e., 10-3 M added NaNO3) while the plain lines correspond to an ionic strength of 0.25 mM (i.e., no added salt case). The two lower lines are the renormalized RSA predictions following eqs 13 and 14 (solid line for I ) 1 mM and dotted line for I ) 0.25 mM). Table 1. Electrostatic Surface Potential of the CeO2 Substrate (Φ0) and the Electrostatic Charge of the Nanolatex Particles (Zstructural and Zeff) Used to Calculated the Lines Shown in Figure 12 Zstructural Zeff Zstructural Zeff (e/particle) (e/particle) (e/particle) (e/particle) Φ0 pH (mV) K-1 ) 192 Å K-1 ) 192 Å K-1 ) 96 Å K-1 ) 96 Å 4 5 6 7 8 9

70 60 45 45 40 25

80 90 130 200 290 480

71 78 99 120 134 147

80 130 180 280 400 590

72.4 104 125 150 165 177

The substrate surface potential Φ0 used to calculate the total interaction was determined by acoustophoresis measurements on CeO2 particles (see Figure 10 in ref 22). Thus, the only unknown parameter is the effective charge of the nanolatex Zeff. However, the structural charge and its dependence on pH was measured (Figure 1). As mentioned before, a fixed charge of 80 units per particle is already present at pH ) 4. Starting at this value an increment was added for dispersions at pH > 4 determined from the titratable charge shown in Figure 1. Several different methods31 are available to calculate an effective charge. We chose to solve the PB-Cell (Belloni, program facilities) with Φ ) 1% by putting a structural charge on the particles and equalizing the potential at the border of the cell given by the nonlinearized PB solution to the equivalent Debye-Hu¨ckel solution.32 The linearized solution defines an effective charge of the particle which is summarized in Table 1 together with all other electrostatic parameters. From the parameter summarized in Table 1 we calculate the density of adsorption required to produce an energy barrier of 10, 15, and 22 kT. The results are plotted in Figure 12 for each pH studied together with the experimental results for the CeO2-coated mica substrate. With (31) Belloni, L. Colloids Surf. A 1998, 140, 227. (32) Alexander, S.; Chaikin, P. M.; Grant, P.; Morales, G. P.; Pincus, P.; Hone, D. J. Chem. Phys. 1984, 80, 5776.

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no added salt, the surface coverage does not exceed 25% and the agreement with the experimental results is the best for an energy barrier between 15 kT and 22 kT. Nevertheless, it is clear from Figure 12 that the agreement becomes poor at low pH when salt is present. As already mentioned, our first assumption of the independence of U*(r b,h) on b r is wrong when the repulsion is not long range enough, and a full approach as done in refs 3 or 6 has to be used. The surface coverage varies by a factor of 5 from pH ) 9 to pH ) 4 and it is interesting to calculate the value of the attractive and repulsive components at the barrier distance h* at each pH. When no salt was added Uatt(h*) ) -33 kT and -36 kT at pH ) 4 and 9, respectively, whereas Urep(h*) ) 48 kT and 51 kT at pH ) 4 and 9, respectively. Clearly, the respective components of the interaction do not vary greatly with pH. This can be understood for the attractive component from eq 7, which shows that the attractive energy is proportional to Φ0Zeff whereas Table 1 shows the decrease in CeO2 surface potential is compensated by an increase of the effective charge of the nanolatex. On the other hand, the repulsive component varies, such as FZ2eff implying that F should vary as Zeff-2 with the pH to keep the energy constant. In practical terms, the pseudo-constant nature of the attractive term originates from the large difference in the PZC of the two components (pH ) 2 for nanolatex and pH ) 10 for CeO2). This large difference is necessary in the system, however, to generate a driving force for adsorption over a wide range of pH. Such behavior should be quite general rather than just that observed in the systems studied here. When the experimentally observed adsorption limit is reached, room still exists on the surface for further adsorption. The repulsive barrier, which cannot be overcome by the approaching particles in the limited time of the experiment, prevents further adsorption. Nevertheless, further adsorption will go on albeit at a very slow rate. Several authors have studied this under the surface reaction approximation model. In particular, Prieve and Ruckenstein33 gave an approximate expression for the rate of deposition J (g/m2/s) of brownian particles from a suspension of concentration c (g/m3) onto a surface:

γ f( )e x2πkT h

J ) Kc with K ) D∞

a1

-βU*

(12)

Here, D∞ is the diffusion coefficient of the particles far from the surface, U* is the height of the energy barrier, f(a1/h) is a function of the order of one (far from the surface), and γ is the second derivative of the energy at the barrier distance. The absence of adsorption yields an upper limit of the rate of deposition K. Suppose that one waits an extra 10 min and considers that the rate of adsorption is such that only one additional particle will adsorb (changing the relative value of θ by 1%), then this criterion yields a rate of deposition: K < 1.4‚10-12 m/s. If at any time during the deposition (which could even be as low as milliseconds after being exposed to the colloidal dispersion), the rate K falls below this value, the residual time of adsorption will have no influence on the experimental result. The value of K can then be used to give a value of the energy barrier, U*, if the second derivative γ can be estimated. From Figure 11 the second derivative is of the order 10-1 kT/nm2 giving an energy barrier of 20 kT. Hence, no further adsorption of particles (33) Ruckenstein, E.; Prieve, D. C. J. Chem. Soc., Faraday Trans. II 1973, 69, 1522.

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should occur (over the time scale of our experiment) when the height of the barrier grows beyond 20 kT. This criterion is in agreement with what has been deduced from the fitting procedure. 4.1.5. Comparison with the RSA Model. The predictions of the RSA model with a renormalized radius were calculated as in refs 6 and 11 using the relation:

N)

θmaxSc πa21

)

0.547Sc 2 πa1,eff

(13)

where a1,eff is the renormalized radius of the nanolatex. Ref 34 provides accurate analytical formulas for the determination of a1,eff:

a1,eff )

ln(A/ln A) e2κa1 with A ) 2.8*Z2effκLB 2κ (1 + κa1)2 (14)

The renormalized jamming limits were calculated and are shown in Figure 12 for the two salinities. We observe, as did Prieve and Ruckenstein, that calculated values are well below the experimental results. Nevertheless, it is clear from eq 13 that a change in the effective radius of interaction can improve the agreement. The renormalized radius of interaction is given for particle interaction in bulk, whereas one has to consider here two particles’ interaction in the vicinity of an oppositely charged surface. 4.2. Interaction Between Nanolatex Layers and the Encapsulation Efficiency. The data shown in Figures 8 and 9 represent the force-distance profiles between two opposing layers of nanolatex particles adsorbed onto CeO2 at a surface coverage of about 25% (the highest possible). There were several important observations about the solution conditions studied. First, the longrange part of the interaction demonstrates an electrostatic interaction from which a surface potential was extracted. This surface potential decreased from 60 mV at pH ) 9.3 to about 0 mV at pH ) 2. The dependence of the surface potential on pH is similar to that measured by electrophoresis; however, it must be remembered that the force measurements effectively average over an interaction area of a few tens of square micrometers. The measured surface potential cannot be directly related to the surface potential of the nanolatex particles because of the granular and incomplete nature of the nanolatex layer on the positively charged CeO2-coated mica substrate. As the two nanolatex layers were brought into contact, three types of behavior were observed. Above pH ) 5 (Figure 8) the layers remained intact, and a steep repulsive barrier was experienced. When the pH was lowered toward 4, a small adhesion was observed (Figure 9), but once again no expulsion of the nanolatex layers was observed. The weak adhesion would be due to direct contact between the nanolatex particles in the opposing layers and of van der Waals origin. The situation changed drastically at pH ) 2 (Figure 9) where layers of nanolatex could be expelled successively under the applied pressure. These results give a measure of the encapsulation efficiency; and in particular, they define under which conditions is it possible to mechanically expel an adsorbed layer from the gap between the two substrates. Several different mechanisms could be proposed for this process with two limiting situations. First, the stress builds to a point where the layer ruptures (analogous to a yield stress (34) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989.

phenomenon). Such a process would be accompanied by a discontinuity in the force-distance profile. Second, the particles may simply slide out from the confined region under the applied pressure. This mechanism may be applicable for particles that are strongly adsorbed to the substrate but able to migrate laterally (nanolatex on sapphire is a possible example). The force-distance profile in this latter situation, however, should be more continuous in nature and not show discrete jumps in the forcedistance profile. Given the results of Figure 9, the discontinuous jumps would imply that the first mechanism is in operation. The ejection of an adsorbed nanolatex layer should occur when the applied energy F/2πR (related to the applied force F/R through the Derjaguin approximation) is larger than the surface energy of the layer:

()

N F N > E - Ps 2πR Sc Ads Sc

(15)

Here, the surface energy is shown as the sum of two terms assuming, first of all, that the energy of adsorption EAds is independent of the surface coverage N/Sc. The second term Ps(N/Sc) is the two-dimensional pressure of the adsorbed layer approximated as the pressure of a layer of hard disks:

Ps )

N kT*ZHD Sc

(16)

where ZHD is the osmotic coefficient of hard disk given in ref 35: as:

ZHD )

1 + θ2/8 (1 - θ)2

(17)

The first term on the right-hand side of eq 15 can be calculated from the adsorption isotherm (Figure 5) and eq 7. At pH ) 2, using Zeff ) 25 charges/particle and Φ0 ) 70 mV, one obtains an adsorption energy of 13 kT per particle. Putting N ) 400 particles/µm2, the first term of eq 15 comes to 0.021 mJ/m2, whereas eqs 16 and 17 give Ps ) 2.6 × 10-3 mJ/m2. The surface energy of the layer is thus 0.018 mJ/m2 which corresponds to a normalized force of F/R ) 0.11 mN/m. The calculated value, therefore, is in relative agreement with the experiment given that the measured force required to cause layer rupture, F/R ) 0.7 mJ/m2, was higher (Figure 9). Similar calculations at pH ) 4 lead to Eads ) 110 kT and an expulsion threshold value of F/2πR ) 0.175 mJ/m2 corresponding to a normalized force of F/R )1.10 mN/m necessary to cause layer rupture. Indeed, we did not observe an expulsion of the layers up to an applied normalized force of approximately 0.14 mN/m as shown in Figure 8b, which is lower than the calculated value. Stronger forces would have been applied to reach the expulsion. The results give some guidelines for the design of encapsulation layers that provide a mechanically stable steric barrier. First, the particles should be adsorbed preferably as monolayers and be fixed in their adsorption sites. If particles are laterally mobile only the surface pressure Ps, shown to be almost negligible by eq 16, will prevent them from being swept along the substrate surface during collision of the substrate particles. In that respect slightly rough surfaces will be more efficiently protected by the adsorption of small particles. For instance, the (35) Henderson, D. Mol. Phys. 1975, 30, 971.


adsorbed layer on the sapphire would not be expected to be as good as that on the CeO2 substrates given its lateral mobility (Section 3.2.1). A worthwhile extension to the force work would be to use the sapphire surfaces instead of the CeO2-coated substrates and determine the force required to rupture the adsorbed layers. Finally, the particles should be adsorbed in a range of pH where the energy of adsorption is the highest possible. 6. General Conclusions This report has described an investigation of the adsorption of nanolatex particles to mineral surfaces to better understand the parameters pertinent to the encapsulation of inorganic pigments with latex. Two model mineral substrates, namely sapphire (R-Al2O3) and CeO2, were chosen given the possibility of manufacturing substrates of well-defined geometry suitable for application of direct-imaging and force-measuring techniques. There are two general conclusions common to the different substrates. First, the adsorption density is strongly influenced by the surface charge of the two components and the ionic strength. This is particularly important for nanoparticles because they interact strongly even at low volume fractions, which must be taken into account when designing an encapsulation process. Second, the layers are irreversibly adsorbed, which indicates that the adsorption is controlled kinetically. Several important differences in the adsorption properties were distinguished between the two substrates. Adsorption of nanolatex to the CeO2 substrate was consistent with classical electrostatic mechanisms. The driving force for adsorption was due to the opposite charge carried by the nanolatex and substrate over the pH range studied. No adsorption of nanolatex occurred above the PZC of the CeO2 substrate. In contrast, significant adsorption was seen above the PZC of the sapphire substrate, where both the nanolatex and the sapphire were negatively charged. Such an observation may indicate a different driving mechanism for adsorption, such as a specific “chemical” interaction.

Langmuir, Vol. 15, No. 22, 1999 7489

Although both mineral substrates appeared to provide a different mechanism of particle adsorption, the same trend in the adsorption density was observed in both cases. That is, the surface coverage density was maximal at low pH and decreased as the pH increased. This demonstrates that the interparticle repulsion is extremely important in determining the limiting surface coverage. We have used a simple procedure, relevant for low surface coverage, to fit the experimental data. The model reproduces the experimental dependence of the adsorbed amount on the surface charge of the two components which can be controlled by adjusting the pH. The main result is that the attractive component plays a major role in setting the maximum of adsorption in this range of low surface coverage. In our case, it is almost constant and the adsorbed amount behaves like Zeff-2. The systematic study of the pH dependence presented here is, to our knowledge, the first of that type. Finally, the value of direct force measurements between nanolatex layers was demonstrated. A symmetric configuration of opposing adsorbed nanolatex layers allowed the interaction profile between nanolatex particles to be measured directly. This technique provided method of determining interaction profiles between colloidal particles which is complimentary to other bulk techniques such as osmotic pressure experiments.36 The direct measurement closely approximates the interaction between encapsulated particles and also yields information as to how they resist rupture under compression. Acknowledgment. D.A.A. gratefully acknowledges support for this work from Rhodia Recherches (Centre d’Aubervilliers, France). The authors thank Roland Reeb for synthesizing the nanolatex at Rhodia Recherches, and also thank Ce´cile Bonnet-Gonnet, Jean Christophe Castaing, Sabine Desset, and Luc Belloni for helpful discussions. LA9816858 (36) Bonnet-Gonnet, C.; Belloni, L.; Cabane, B. J. Colloid Interface Sci. 1994, 160, 4012.

Adsorption of Nanolatex Particles to Mineral Surfaces of Variable

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