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Adsorption of Poly(amido amine) (PAMAM) Dendrimers on Silica: Importance of Electrostatic Three-Body Attraction Brian P. Cahill,† Georg Papastavrou,† Ger J. M. Koper,‡ and Michal Borkovec*,† Department of Inorganic, Analytical, and Applied Chemistry, UniVersity of GeneVa, 30 Quai Ernest-Ansermet, 1211 GeneVa, Switzerland, and DelftChemTech, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands ReceiVed July 17, 2007. In Final Form: October 11, 2007 Adsorption of poly(amido amine) (PAMAM) dendrimers to silicon oxide surfaces was studied as a function of pH, ionic strength, and dendrimer generation. By combining optical reflectometry and atomic force microscopy (AFM), the adsorbed layers can be fully characterized and an unequivocal determination of the adsorbed mass becomes possible. For early stages, the adsorption process is transport limited and of first order with respect to the dendrimer solution concentration. For later stages, the surface saturates and the adsorbed dendrimers form loose but correlated liquidlike surface structures. This correlation is evidenced by a peak in the pair correlation function determined by AFM. The maximum adsorbed amount increases with increasing ionic strength and pH. The increase with the ionic strength is explained by the random sequential adsorption (RSA) model and electrostatic repulsion between the dendrimers. The adsorbing dendrimers interact by the repulsive screened Coulomb potential, whose range decreases with increasing ionic strength and thus leads to increasing adsorbed densities. The pH increase is interpreted as an effect of the substrate and is quantitatively explained by the extended three-body RSA model. This model stipulates the importance of a three-body interaction acting between two adsorbing dendrimers and the charged substrate. The presence of the charged substrate weakens the repulsion between the adsorbing dendrimers and thus leads to higher surface densities. This effect can be interpreted as an additional attractive three-body interaction, which acts in addition to the usual two-body repulsion and originates from the additional screening of the Coulomb repulsion by the counterions accumulating in the diffuse layer.
Introduction Dendrimers represent a novel class of highly uniform globular macromolecules with a characteristic treelike branched architecture. Various synthetic routes and structural modifications of dendrimers have been proposed, and several of their properties are now understood.1-4 Various applications are currently emerging, for example, as catalysts in the synthesis of metal nanoparticles or as nonviral gene vectors.1,2,5-7 While dendrimers interact strongly with interfaces, their adsorption properties and the resulting organization at interfaces have only received modest attention so far.8-14 Potential * To whom correspondence should be addressed. Telephone: ++41 22 379 6405. E-mail:
[email protected]. † University of Geneva. ‡ Delft University of Technology. (1) Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallos, G.; Martin, S.; Roeck, J.; Ryder, J.; Smith, P. Macromolecules 1986, 19, 2466-2468. (2) Bosman, A. W.; Janssen, H. M.; Meijer, E. W. Chem. ReV. 1999, 99, 1665-1688. (3) Ballauff, M.; Likos, C. N. Angew. Chem., Int. Ed. 2004, 43, 2998-3020. (4) Koper, G. J. M.; van Genderen, M. H. P.; Elissen-Roman, C.; Baars, M. W. P. L.; Meijer, E. W.; Borkovec, M. J. Am. Chem. Soc. 1997, 119, 6512-6521. (5) Hudde, T.; Rayner, S. A.; Comer, R. M.; Weber, M.; Isaacs, J. D.; Waldmann, H.; Larkin, D. P. F.; George, A. J. T. Gene Ther. 1999, 6, 939-943. (6) Lang, H.; Maldonado, S.; Stevenson, K. J.; Chandler, B. D. J. Am. Chem. Soc. 2004, 126, 12949-12956. (7) Yeung, L. K.; Crooks, R. M. Nano Lett. 2001, 1, 14-17. (8) Pericet-Camara, R.; Papastavrou, G.; Borkovec, M. Langmuir 2004, 20, 3264-3270. (9) Kleijn, J. M.; Barten, D.; Cohen Stuart, M. A. Langmuir 2004, 20, 97039713. (10) Tully, D. C.; Frechet, J. M. J. Chem. Commun. 2001, 1229-1239. (11) Su, A. H.; Tan, S. S.; Thapa, P.; Flanders, B. N.; Ford, W. T. J. Phys. Chem. C 2007, 111, 4695-4701. (12) Tokuhisa, H.; Zhao, M. Q.; Baker, L. A.; Phan, V. T.; Dermody, D. L.; Garcia, M. E.; Peez, R. F.; Crooks, R. M.; Mayer, T. M. J. Am. Chem. Soc. 1998, 120, 4492-4501. (13) SayedSweet, Y.; Hedstrand, D. M.; Spinder, R.; Tomalia, D. A. J. Mater. Chem. 1997, 7, 1199-1205.
applications of dendrimers at surfaces are just emerging, for example, in surface-based sensors or surface nanopatterning.15-17 Several authors have focused on their adsorption at the airliquid interface and the resulting properties of Langmuir-Blodgett films.11,13,14 The adsorption of poly(amino amine) (PAMAM) and poly(propylene imine) (PPI) dendrimers from aqueous solutions to solid substrates has been studied in some detail.8,9,15,18-22 Adsorption studies of these dendrimers on gold have suggested that electrostatic interactions play a negligible role and that PPI and PAMAM dendrimers behave similarly.9,19 With scanning angle reflectometry, it was shown that electrostatic interactions are important in the adsorption of PPI dendrimers on glass.21,22 While the adsorbed mass is comparable to those of other studies,8,9,15 an unusually small initial adsorption rate of PPI dendrimers to the glass surface has been reported.21 The latter observation was explained by the particular properties of the optical glass used. Adsorption of PAMAM dendrimers, particularly of higher generations, was further studied by atomic force microscopy (AFM).8,15,23-25 These studies revealed that (14) Saville, P. M.; Reynolds, P. A.; White, J. W.; Hawker, C. J.; Frechet, J. M. J.; Wooley, K. L.; Penfold, J.; Webster, J. R. P. J. Phys. Chem. 1995, 99, 8283-8289. (15) Pericet-Camara, R.; Cahill, B. P.; Papastavrou, G.; Borkovec, M. Chem. Commun. 2007, 266-268. (16) Arrington, D.; Curry, M.; Street, S. C. Langmuir 2002, 18, 7788-7791. (17) Crooks, R. M.; Ricco, A. J. Acc. Chem. Res. 1998, 31, 219-227. (18) Rahman, K. M. A.; Durning, C. J.; Turro, N. J.; Tomalia, D. A. Langmuir 2000, 16, 10154-10160. (19) Esumi, K.; Ichikawa, M.; Yoshimura, T. Colloids Surf., A 2004, 232, 249-252. (20) Manriquez, J.; Juaristi, E.; Munoz-Muniz, O.; Godinez, L. A. Langmuir 2003, 19, 7315-7323. (21) van Duijvenbode, R. C.; Rietveld, I. B.; Koper, G. J. M. Langmuir 2000, 16, 7720-7725. (22) van Duijvenbode, R. C.; Koper, G. J. M.; Bohmer, M. R. Langmuir 2000, 16, 7713-7719. (23) Li, J.; Piehler, L. T.; Qin, D.; Baker, J. R., Jr.; Tomalia, D. A.; Meier, D. J. Langmuir 2000, 16, 5613-5616.
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such dendrimers flatten substantially upon adsorption and that sometimes aggregates can be observed on the surface, particularly, at higher pH. It was further reported that PAMAM dendrimers adsorb on mica and silica in correlated liquidlike monolayers and that repulsive electrostatic interactions between the dendrimers lead to low adsorption densities. Consequently, the adsorbed amount increases strongly with the salt level, but a substantial dependence on pH was equally observed.8,15 This article presents a detailed study of the adsorption of PAMAM dendrimers to the water-silica interface. The combination of optical reflectivity with AFM imaging permits an unequivocal determination of the adsorbed mass. Electrostatics indeed plays a major role in the adsorption process. In particular, the pH and ionic strength dependence of the maximum adsorbed amount can be rationalized in terms of an extended random sequential adsorption (RSA) model, which involves electrostatic interactions not only between two dendrimers but also the substrate. In particular, the classical two-body screened Coulomb repulsion between two adsorbing dendrimers is weakened by an attractive three-body component. This three-body attraction is of the same origin as recently discussed for colloidal suspensions at low salt conditions.26-28 This additional interaction is due to the increased screening by the counterions accumulated in the diffuse layer near a charged interface. While the eventual importance of this effect was already suggested by Oberholzer et al.,29 the same authors dismissed its relevance for the larger colloidal particles investigated. For the small dendrimers considered here, however, this additional attraction is very important and explains increased adsorption with increasing pH. Some of the discussed results were presented in a preliminary note.15 Experimental Section Materials. PAMAM dendrimers of generations G8 and G10 were obtained as aqueous solutions from Dendritech (Midland, MI). Solutions were prepared with Milli-Q water whereby the pH was adjusted with HCl and KOH and the ionic strength was adjusted with KCl. The refractive index increment dn/dc of the dendrimers in pure water was measured with a differential refractometer (Chromatix KMX-16). The value of dn/dc ) 0.194 mL/g was found to be independent of the dendrimer generation. Whenever necessary, the density of the dendrimers was assumed to be 1.2 g/mL.24 Additional properties of dendrimers are summarized in Table 1. Polished silicon wafers (p-type, boron doped, Silchem GmbH) were thermally oxidized in a furnace at 1000 °C for 75 min. The oxidized wafers were then cut into squares of about 12 mm. The wafers were cleaned in a mixture of 24% NH3, 30% H2O2, and water mixed in a ratio of 1:1:5 by volume at 70-80 °C for 10 min.30 The wafers were subsequently stored in water. Prior to experiments, the wafers were rinsed profusely with Milli-Q water and dried in a stream of nitrogen. For each wafer, the thickness of the silicon oxide surface layer was determined by null ellipsometry in air (Multiskop, Optrel). Thereby, the refractive index used for the silicon base was 3.85 + 0.02i. The thermally grown silica layers had a typical thickness (24) Betley, T. A.; Hessler, J. A.; Mecke, A.; Banaszak Holl, M. M.; Orr, B. G.; Uppuluri, S.; Tomalia, D. A.; Baker, J. R., Jr. Langmuir 2002, 18, 31273133. (25) Muller, T.; Yablon, D. G.; Karchner, R.; Knapp, D.; Kleinman, M. H.; Fang, H.; Durning, C. J.; Tomalia, D. A.; Turro, N. J.; Flynn, G. W. Langmuir 2002, 18, 7452-7455. (26) Klein, R.; von Grunberg, H. H.; Bechinger, C.; Brunner, M.; Lobaskin, V. J. Phys.: Condens. Matter 2002, 14, 7631-7648. (27) Dobnikar, J.; Brunner, M.; von Grunberg, H. H.; Bechinger, C. Phys. ReV. E 2004, 69, Article No. 031402. (28) Russ, C.; Brunner, M.; Bechinger, C.; Von Grunberg, H. H. Europhys. Lett. 2005, 69, 468-474. (29) Oberholzer, M. R.; Stankovich, J. M.; Carnie, S. L.; Chan, D. Y. C.; Lenhoff, A. M. J. Colloid Interface Sci. 1997, 194, 138-153. (30) Kern, W.; Puotinen, D. A. RCA ReV. 1970, 31, 187.
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Figure 1. Schematic drawing of the optical reflectometer. A fourway valve allows switching between the background electrolyte and the solution containing dendrimers. A laser beam reflects from the oxidized silicon wafer at the stagnation point of the impinging jet. A polarizing beam splitter splits the reflected beam into its p and s polarizations, whose intensities are subsequently measured by two photodiodes. Table 1. Properties of the PAMAM Dendrimers Used in This Work groupsa
total number of amine number of primary amine groupsa maximum molecular mass (kDa)a radius in solution (nm)b lateral radius in adsorbed state (nm)c height in adsorbed state (nm)c
G8
G10
2046 1024 233 4.85 6.35 1.47
8190 4096 935 6.75 9.15 4.28
a From molecular structure. b From dynamic light scattering provided by Dendritech. These radii are in good agreement with those from smallangle X-ray scattering.57 c From AFM imaging in the dry state.8 The coefficient of variation of these values is about 10-20%.
of 90 nm and a refractive index of 1.46 as determined by scanning angle ellipsometry in air.31 Optical Reflectometry. The adsorption of PAMAM dendrimers was studied in situ by poor man’s reflectometry.31-33 The homebuilt setup used a He-Ne laser with a wavelength of 632.8 nm and an impinging jet cell (see Figure 1). An incident laser beam was reflected from the surface through a truncated prism. The fluid was injected perpendicularly to the horizontal surface through a vertical bore hole of radius F = 0.50 mm, and it escaped sideways through a parallel slit of width h = 0.85 mm between the prism and the wafer. All measurements were performed at a goniometer angle of 45.0°. Due to refraction within the prism, the actual angle of incidence was 53.7°. The cell was initially flushed with an inert salt solution of given pH, and then the input solution was switched to a dendrimer solution in the same electrolyte. All experiments were carried out at a temperature of 25 °C. The reflected light beam was separated into its parallel (p) and perpendicular (s) components with a polarizing beam splitter. The light intensities of each of these two polarizations, which are detected separately as a function of time t, are proportional to the reflectances R(p) and R(s). The experimental signal is proportional to the ratio of these two quantities, and one measures R ) CR(p)/R(s), where C is an unknown instrumental constant. This constant was eliminated by normalizing the signal to its initial value S(t) )
R(t) - R(0) R(0)
(1)
where t ) 0 defines the injection time. This normalized quantity can be directly converted to the time-dependent adsorbed mass Γ(t). We (31) Kleimann, J.; Lecoultre, G.; Papastavrou, G.; Jeanneret, S.; Galletto, P.; Koper, G. J. M.; Borkovec, M. J. Colloid Interface Sci. 2006, 303, 460-471. (32) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. AdV. Colloid Interface Sci. 1994, 50, 79-101. (33) Bohmer, M. R.; van der Zeeuw, E. A.; Koper, G. J. M. J. Colloid Interface Sci. 1998, 197, 242-250.
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use a standard homogeneous slab model and the island theory to describe the optical response of the dendrimer covered surface.31-33 Both models agree within 5% or better over the whole range considered. At low surface loading, the signal is directly proportional to the adsorbed mass Γ(t) )
S(t) A
(2)
whereby the sensitivity factor is A ) 12.5 ( 0.1 m2/g. At higher loading, the relationship is weakly nonlinear. We find experimentally that our setup reaches a detection limit of 10 mg/L cannot be measured in our system properly. Figure 6a shows the initial adsorption rate dΓ/dt|t)0 plotted as a function of the dendrimer concentration for pH 5 and an ionic strength of 1 mM. One observes direct proportionality between the initial adsorption rate and the dendrimer concentration over 2 orders of magnitude. This observation confirms that the adsorption rate is indeed of first order with respect to the dendrimer concentration in the bulk solution. Thus, an adsorption rate coefficient k as defined in eq 4 can be determined with confidence. In similar situations, some authors have reported a weaker dependence than direct proportionality relation at higher polymer concentrations.21,45,46 In particular, such a behavior was clearly demonstrated in the detailed study of PPI dendrimer adsorption (45) Popa, I.; Cahill, B. P.; Maroni, P.; Papastavrou, G.; Borkovec, M. J. Colloid Interface Sci. 2007, 309, 28-35. (46) Lok, B. L.; Cheng, Y.; Robertson, C. R. J. Colloid Interface Sci. 1983, 91, 104-116.
Adsorption of PAMAM Dendrimers on Silica
Figure 6. Doubly logarithmic plot of the initial adsorption rate dΓ/dt|t)0 as a function of the dendrimer concentration c at pH 5 and an ionic strength of 1 mM. The solid line corresponds to first-order kinetics with respect to the solution concentration and yields an adsorption rate coefficient of kads ) 4.13 µm/s.
Figure 7. Initial adsorption rate coefficient kads (right axis) and corresponding sticking coefficient β (left axis) of PAMAM dendrimers on silica as a function of pH for different ionic strengths adjusted with KCl. Generations (a) G8 and (b) G10.
on glass for dendrimer concentrations above 10 mg/L.21 Similar change in the concentration dependence was also observed for the adsorption of proteins and polyelectrolytes.45,46 One possible explanation of these deviations is the influence of the dead time of the cell as discussed here,45 while it was also suggested that the steady-state approximation inherent to eq 3 breaks down at higher flux.46 In the present case, we observe no deviations from the first-order rate law, provided the dead time of the cell is properly considered. The adsorption rate coefficient k and the corresponding sticking coefficient β are shown in Figure 7 as a function of pH at different ionic strengths. The sticking coefficient is the ratio between the measured rate coefficient and the theoretical one based on perfect sink conditions (cf. eqs 4 and 6 in the Theory section). The two dendrimer generations G8 and G10 give similar results. The
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sticking coefficient β always lies in the range of 0.3-0.8. Values in the same range were reported in systems with attractive interactions, namely, for dendrimers, polyelectrolytes, and colloidal particles.9,31,33,45 The sticking coefficient below unity could be caused by the fact that the area illuminated by the laser beam is comparable to the cross-sectional area of the bore hole, and therefore, the average flux to the surface is somewhat smaller than predicted by eq 4.33,47 Nevertheless, it is hardly conceivable that this effect alone could explain the values of the sticking coefficient observed. For this reason, we suspect that the main reason for the observed values of the sticking coefficients is that hydrodynamic interactions, which lead to a slow-down of the diffusion of the dendrimers toward the surface, are more important than attractive dispersion interactions. The sticking coefficient decreases with increasing pH, while it remains basically independent of the ionic strength (see Figure 7). We suspect that the pH dependence is primarily caused by the aggregation of dendrimers in solution. The fact that dendrimers aggregate above pH 8 has been demonstrated in the solution phase4,48 and in the adsorbed state.8,24 Aggregates have lower diffusion coefficients in comparison with individual dendrimers. While the adsorption process still remains transport limited, the presence of aggregates reduces the adsorption rate with respect to the one estimated on the basis of isolated dendrimers in solution. Dendrimer aggregation is probably driven by dispersion or hydrophobic attraction, which becomes dominant due to the absence of electrostatic repulsion at higher pH. Note that dendrimers are fully charged at pH < 4, while for pH > 8 their charge decreases substantially.49 While variations of the dendrimer charge with pH seem to modify the dendrimer-dendrimer interactions and induce their aggregation in solution, the analogous variations of the dendrimer charge and of the surface charge seem to play a negligible role on the initial adsorption process, where the dendrimer-substrate interactions are important. One would expect that dendrimers could shrink with increasing pH, even though experimental results on this point remain controversial.3,24,50,51 An eventual shrinkage should increase the diffusion coefficient and lead to an enhanced adsorption rate, which is in contrast to the observations. Furthermore, the decrease of their charge at higher pH would lead to weaker electrostatic attraction and thus to a smaller adsorption rate, but this effect could be partially compensated by the higher magnitude of the charge density of silica at higher pH. All these electrostatic effects seem to play a minor role, as further evidenced by the absence of any enhancement of the adsorption rate at low ionic strength. Such an enhancement is well-documented for the deposition of colloidal particles to oppositely charged surfaces52,53 and heteroaggregation of oppositely charged particles.54,55 Maximum Saturation Coverage. The adsorption experiments were carried out at different pHs and ionic strengths, and the final plateaus were determined from the adsorption transients as (47) Adamczyk, Z.; Siwek, B.; Warszynski, P.; Musial, E. J. Colloid Interface Sci. 2001, 242, 14-24. (48) Zheng, J.; Stevenson, M. S.; Hikida, R. S.; Van Patten, P. G. J. Phys. Chem. B 2002, 106, 1252-1255. (49) Cakara, D.; Kleimann, J.; Borkovec, M. Macromolecules 2003, 36, 42014207. (50) Lee, I.; Athey, B. D.; Wetzel, A. W.; Meixner, W.; Baker, J. R., Jr. Macromolecules 2002, 35, 4510-4520. (51) Nisato, G.; Ivkov, R.; Amis, E. J. Macromolecules 2000, 33, 4172-4176. (52) Elimelech, M. J. Colloid Interface Sci. 1991, 146, 337-352. (53) Kleimann, J.; Gehin-Delval, C.; Auweter, H.; Borkovec, M. Langmuir 2005, 21, 3688-3698. (54) Lin, W.; Kobayashi, M.; Skarba, M.; Mu, C.; Galletto, P.; Borkovec, M. Langmuir 2006, 22, 1038-1047. (55) Puertas, A. M.; Fernandez-Barbero, A.; de las Nieves, F. J. J. Colloid Interface Sci. 2003, 265, 36-43.
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Figure 8. Maximum adsorbed mass Γmax (right axis) and fractional coverage θmax (left axis) of PAMAM dendrimers on silica as a function of the screening parameter κa for different pH values. The screening parameter increases with increasing ionic strength. The experimental data (points) are compared with the extended three-body RSA model (full lines). For pH 4, the predictions of the three-body and twobody models are identical on the scale of the graph (dotted line). The model contains no adjustable parameters. Generations (a) G8 and (b) G10.
the one shown in Figure 2. The maximum adsorbed mass Γmax is represented in Figure 8 as a function of the dimensionless screening parameter κa where a is the lateral dendrimer radius in the adsorbed state and κ-1 is the Debye length. The maximum fractional surface coverage θmax is equally given in Figure 8, and this parameter is obtained from the adsorbed mass as8
θmax )
NAπa2 Γ M max
(19)
where NA is Avogadro’s constant and M is the dendrimer molecular mass (see Table 1). Since the screening parameter κa increases with increasing ionic strength, Figure 8 illustrates the strong increase of the adsorbed amount with increasing ionic strength. A notable increase of the adsorbed amount with increasing pH is equally observed. The lateral radius obtained from AFM was also used previously to analyze the adsorption of dendrimers,8 but this choice is not very critical. By using, for example, the solution radius, all data would be shifted somewhat, but all trends would remain the same. Figure 8 further compares the experimental results with the classical two-body RSA model and the extended three-body RSA model proposed here. Again, the dendrimer radius a in the adsorbed state is being used. This model is based on the modified screened Coulomb potential (eq 17). From this potential, the effective radius is obtained, and this radius is used to estimate the surface coverage (cf. eqs 7 and 10). The dendrimer radii in
the adsorbed state given in Table 1 and the surface charge density obtained from the basic Stern model (eq 18) are used in the calculations. Keeping in mind that the model contains no adjustable parameters, the agreement of the extended three-body RSA model with the experimental data must be considered to be most satisfactory. For the G10 dendrimers, the model predicts the dependence on pH as well as on ionic strength very well. For the G8 dendrimers, the agreement is poorer, but the trends are still reasonably well-reproduced. The classical two-body RSA model describes the data in a satisfactory fashion at the lowest pH only. The good agreement between experiment and the extended three-body RSA model provides strong support that the characteristic dependence of dendrimer adsorption on the ionic strength and pH is of electrostatic origin. The underlying mechanism can be understood qualitatively as follows. The ionic strength dependence has already been discussed within the classical two-body RSA model, which involves the screened Coulomb potential in bulk (eq 8). Note that this model is recovered from the three-body RSA model for pH e 4. The characteristic ionic strength dependence originates from the repulsion between the diffuse layers around the individual dendrimers. The range of the soft repulsive interactions determines the area excluded around a single dendrimer, and this range is approximately given by the Debye length. The latter parameter decreases with increasing ionic strength and consequently leads to an increase of the maximum coverage. However, the classical two-body RSA model applies quantitatively for weakly charged substrates only. For silica, these conditions are only met for pH e 4, where the magnitude of surface charge density is just a few millicoulombs per square meter. At higher pH, the surface charge density of the silica substrate increases due to dissociation of the silanol groups. For example, at pH 8, one finds magnitudes of charge densities of 50-150 mC/m2 depending on the ionic strength. These high charge densities are compensated by elevated concentrations of counterions in the diffuse layer. Close to the surface, these counterions provide additional screening of the electrostatic interactions between the dendrimers in the lateral direction. The interaction thus remains approximately of the screened Coulomb type, but the effective screening length is reduced through the additional counterions within the diffuse layer (cf. eq 15). This additional screening leads to a smaller interaction range and to a higher coverage. The effect becomes progressively important with increasing magnitude of the charge density. Since the latter increases strongly with increasing pH, the maximum coverage increases with pH as well. This reduction in the strength of the interaction between the dendrimers in the presence of the interface can be interpreted as an additional attractive three-body interaction between the two dendrimers and the charged surface. The attractive three-body interactions recently reported between charged colloidal particles are of the same origin.26-28 Several simplifications enter the present description, but we suspect that they are approximatively justified. First, the effective charge of the dendrimers was estimated from the saturation value of the charge condensation model (cf. eq 9). This approximation is likely to be valid up to pH 9, since under these conditions the effective charge of the dendrimers is small compared to their bare charge.49 However, the effective charge was assumed to remain unaltered in the presence of the charged surface, which might not really be the case. Second, the model assumes that the centers of the point charges are situated exactly at the surface, while in reality the adsorbed dendrimers have a finite thickness, thereby shifting the centers of these charges above the surface.
Adsorption of PAMAM Dendrimers on Silica
This effect is probably corrected for in the approximate expression for charged spheres of finite radius (cf. eq 17), where the factor of 2 involving point charges at the interface is omitted. Third, the model neglects image charge effects, which can be estimated from the integral expression (cf. eq 14). Preliminary calculations indicate that these effects are not very important, especially for a substrate of low dielectric constant and if the centers of the charge are located above the surface. Fourth, the accuracy of the used perturbation expansion around the PB solution of a flat plane can also be questioned, but since one is interested in interactions at large separations, the perturbation approach probably remains valid. Possibly, some of these effects are more important for G8 dendrimers than for G10 dendrimers, leading to better agreement with the model predictions for the latter. Finally, the effective hard sphere model to obtain the maximum RSA coverage remains an approximation. However, it was confirmed by computer simulations that this approximation works quite well.36,40 In several other systems, similar effects of charged substrates have been reported.8,15,31,45,56 We suspect that the same mechanism is operational in these systems. The adsorbed amount of PAMAM dendrimers was observed to be much higher on mica than on silica at low ionic strength and low pH.15 Under these conditions, mica bears a much higher surface charge density, thus pointing toward an enhanced three-body attraction. It was further reported that nanosized latex particles adsorb more strongly to silica than to cellulose at high pH.31 This phenomenon can be explained in the same fashion, as silica is more highly charged than the cellulose surface for the conditions studied. The same mechanism might be equally responsible for the increase in the adsorbed amount of cationic polyelectrolytes on silica with increasing pH.45,56 (56) Bauer, D.; Buchhammer, H.; Fuchs, A.; Jaeger, W.; Killmann, E.; Lunkwitz, K.; Rehmet, R.; Schwarz, S. Colloids Surf., A 1999, 156, 291-305. (57) Prosa, T. J.; Bauer, B. J.; Amis, E. J. Macromolecules 2001, 34, 48974906.
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Conclusion The adsorption of PAMAM dendrimers to silica substrates has been studied by optical reflectometry and AFM. The initial adsorption rate is found to be of first order with respect to the dendrimer concentration and is close to transport limited, as one expects for an adsorption process driven by attractive forces between the dendrimers and the substrate. Thus, the initial adsorption rate depends on the solution composition only weakly. On the other hand, the maximum adsorbed amount increases strongly with the ionic strength and pH. The classical two-body RSA model describes the data at the lowest pH only, where the silica substrate is basically uncharged. At higher pH, silica develops a strong negative charge, and a quantitative description is only possible with the extended three-body RSA model. The latter model uses a three-body potential involving two dendrimers and the charged surface, and for a highly charged substrate its range is reduced with respect to the classical two-body screened Coulomb potential. This reduction in the repulsion originates from the additional screening of the interaction between the adsorbing dendrimers by the counterions in the diffuse layer of the charged substrate. This novel mechanism can also be viewed as an additional attractive electrostatic three-body interaction, which weakens the classical two-body repulsion between charged particles, and is entirely analogous to the one reported for charged colloidal particles at low salt concentrations.26-28 Similar interactions were further suggested to be important in particle deposition.29,42 This additional three-body attraction seems to be equally relevant in the adsorption of colloidal particles or polyelectrolytes to highly charged substrates. Acknowledgment. This work was supported by the Swiss National Science Foundation and the University of Geneva. Partial support from COST D43 is acknowledged. LA7021352
