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Light Reflectivity Study on the Adsorption Kinetics of Poly(propylene imine) Dendrimers on Glass Rene´ C. van Duijvenbode* and Ivo B. Rietveld Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
Ger J. M. Koper Laboratory of Physical Chemistry, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Received March 24, 2000. In Final Form: June 23, 2000 The rate of adsorption of positively charged poly(propylene imine) dendrimers on glass, an oppositely charged surface, has been studied as a function of generation and charge (by systematic adjustment of pH and ionic strength) using scanning angle reflectometry and an impinging-jet cell. A comparison of the mass transport conditions for this geometry and the bulk long-time self-diffusion coefficient obtained from pulsed field gradient NMR experiments shows that a sticking probability of the order of 3% is needed to relate the diffusion toward the surface with the long-time self-diffusion in the bulk. The adsorption kinetics were mostly diffusion/convection controlled with a linear dependence on the bulk concentrations up to 10 mg/L at pH 7 and in 0.1 M NaCl. At higher bulk concentrations there is a drop in concentration dependence into a 1/3 power law dependence. This crossover concentration shifts to higher concentrations with decreasing pH (increasing dendrimer charge).
Introduction In our previous article1 we studied the adsorption properties of poly(propylene imine) dendrimers at saturation. As already stated there, the interest in the adsorption properties of these dendrimers is closely related to the high number of functional groups on very small size scales. Because the dendrimer under study is completely built up from tertiary amines (inner shells) and primary amines (outermost shell), it is possible to vary the charge on the dendrimer with pH and ionic strength in a systematic way and study the influence on its adsorption behavior. Here we investigate the role of these parameters on the adsorption kinetics, which play an important role in the understanding of the driving forces for adsorption. More insight into the rate at which adsorption takes place gives the possibility to control the surface layer composition. There are two processes that govern the adsorption kinetics of small molecules: (i) diffusion and/or convection toward the surface, and (ii) attachment. For polymers a third rate-limiting step can appear, namely rearrangement at the interface, due to the many degrees of freedom the flexible polymers exhibit. The conformations of an isolated polymer chain, as a function of the adsorption energy, are investigated thoroughly in the literature and lead to the widely accepted loop-train-tail model.2 Like polymers, dendrimers have a large number of functional groups, with which they can attach to the surface. However, because of the well-defined and constrained geometry, rearrangement in terms of a looptrain-tail model seems very unlikely.3,4 It would therefore * To whom correspondence should be addressed. (1) van Duijvenbode, R. C.; Koper, G. J. M.; Bo¨hmer, M. R. Langmuir 2000, 16, 7713. (2) Takahashi, A.; Kawaguchi, M. Adv. Polym. Sci. 1982, 46, 1-66 and references therein. (3) Tsukruk, V. V.; Rinderspacher, F.; Bliznyuk, V. N. Langmuir 1997, 13, 2171-2176.
be interesting to see what dominates the adsorption kinetics for this type of molecule, which has only a limited number of segments that can attach to the surface. Therefore, we present here a kinetic study of adsorption of the poly(propylene imine) dendrimers on a glass substrate, which is oppositely charged. A fully automated and computer-controlled scanning angle reflectometer is used to obtain these results. Reflectometry has the advantage over depletion methods or microscopy techniques that it is an in situ and nondestructive technique. This is almost a necessity, because an adsorbed polymer film is nothing but a very concentrated polymer solution. Not only the features of the dendrimers are affected, but also the properties of the solvent. In the present study we vary the solvent properties by changing the pH and ionic strength, and control the hydrodynamics near the surface using a stagnation point flow setup with well-defined dimensions. We can thus investigate the influence of the different parameters on the adsorption kinetics of the poly(propylene imine) dendrimers in a quantitative way. Experimental Section a. Materials. The materials used are identical to those described in the previous paper, in which the properties of the adsorbed layer of poly(propylene imine) dendrimers on glass were studied.1 Here we will therefore give only the main characteristics of the materials. The dendrimers used in these adsorption studies are generations 2-5 of a poly(propylene imine) dendrimer, with a 1,4diaminobutane backbone (DSM, Geleen, The Netherlands). In the literature these compounds are often addressed with the abbreviation DAB-dendr-(NH2)x, with x the number of primary amines in the outermost shell (8, 16, 32, and 64) A twodimensional drawing of the fifth generation, DAB-dendr-(NH2)64, is shown in Figure 1. The protonation behavior of these amine groups is extensively studied in the literature as a function of (4) Mansfield, M. L. Polymer 1996, 37, 3835-3841.
10.1021/la0004552 CCC: $19.00 © 2000 American Chemical Society Published on Web 09/02/2000
Poly(propylene imine) Dendrimers on Glass
Figure 1. Two-dimensional presentation of the fifth-generation poly(propylene imine) dendrimer. The core is 1,4-diaminobutane, from which five additional shells of propylamine branches emanate. pH and ionic strength.5 For instance, at pH 7 two-thirds of the amine groups are protonated, among which the complete outermost shell of primary amines. The collector in these adsorption studies was the optically flat hypotenuse of a rectangular prism of Schott BK 7 glass with an overall negative surface charge at pH > 4.6 Experiments were performed on one prism, which was chemically etched with 0.1 M NaOH before and after each adsorption measurement.7,8 The surface roughness and surface charge density vary with pH and ionic strength, as shown in Figures 5 and 6 of ref 1, giving typical surface charge densities of the order of a few microcoulombs per square centimeter. Experiments performed after rigorously cleaning with piranha liquid gave varying numbers in adsorbed mass. However, trends as a function of generation, ionic strength, and pH were fully reproducible. The advantage of presenting the experiments here of one glass substrate is that throughout the paper the collector’s properties remain constant at constant ionic strength and pH. To study the influence of dendrimer charge on the adsorption behavior of the poly(propylene imine) dendrimers, the ionic strength and pH were systematically adjusted with NaCl, NaOH, and HCl (all Merck). b. Reflectometry. The adsorption behavior was studied in an impinging-jet cell with scanning angle reflectometry (see Figure 2). The reflection coefficient for p-waves (selected with two Glan Thompson polarizers (Melles Griot), before and after reflection) is measured as a function of the angle of incidence around the Brewster angle using a monochromatic laser beam (λ ) 632.8 nm, Melles Griot). The angle of incidence can be selected with an accuracy of 1/1000° with two fully automated and computer-controlled laser- and detector-supports. A peristaltic pump (LKB 12000 VarioPerpex) is used to control the flow rate toward the surface. The stagnation point is positioned such that it coincides with the reflection spot of the light source. A thorough explanation of the conversion of the measured intensities into the reflectivity Rp(θ) and the adsorbed amount is given in ref 1. It was proven there that there was no detectable change in Brewster angle during adsorption of these nanosized molecules. With only one degree of freedom (upward shift of reflectivity) it was possible to perform fixed near-Brewster (5) van Duijvenbode, R. C.; Koper, G. J. M.; Borkovec, M. Polymer 1998, 39, 2657-2664. (6) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (7) Fu, Z.; Santore, M. M. Colloids Surf., A 1998, 135, 63-75. (8) Vigil, G.; Zhenghe, X.; Steinberg, S.; Israelachvili, J. J. Colloid Interface Sci. 1994, 165, 367-385.
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Figure 2. Schematic diagram of the scanning angle reflectometer: (L) light source; (P and A) polarizers, aligned in the plane of incidence; (C) impinging-jet cell; (D) photodetector. A blown-up picture of the impinging-jet cell is shown underneath. It has a distance h ) 1 mm between the collector surface and the inlet tube, and the radius of the inlet tube R ) 0.6 mm. For the ratio h/R ) 1.7, extensive studies on the hydrodynamic conditions of particle deposition in stagnant flow are available.10 incident angle measurements in time. The change in reflectivity at the Brewster angle θB as a function of time was then proportional to the adsorbed amount for thin films7,9
(
Γ(t) ) Γ(∞)
)
xR(θB,t) - xR(θB,0) xR(θB, ∞) - xR(θB,0)
(1)
The stagnation point flow setup (see Figure 2) has a wellchosen geometry with a ratio h/R ∼ 1.7, where R is the radius of the inlet tube and h is the distance between the collector surface and the inlet tube. For these particular dimensions, hydrodynamics and deposition are extensively discussed by Dabros and van de Ven.10 The equations describing the diffusive/convective mass transport can be applied to study the initial adsorption kinetics of the dendrimers more quantitatively. For very small Pe´clet numbers the flux of particles toward the surface can be described in terms of the dendrimer concentration difference cb - cs between the bulk and at the surface11,12
∂Γ/∂t ) kβ(cb - cs)
(2)
where β is the sticking probability and k is a transport coefficient given for the given geometry and flow as
j Re)1/3R k ) 0.776(νD2R
(3)
where the diffusion coefficient D of the dendrimer and the kinematic viscosity ν of the fluid are dependent on the system under study. R j is a dimensionless flow intensity parameter, determined by the ratio h/R and the Reynolds number Re. This (9) Schaaf, P.; Dejardin, P.; Schmitt, A. Langmuir 1987, 3, 11311135. (10) Dabros, T.; van de Ven, T. G. M. Colloid Polym. Sci. 1983, 261, 694-707. (11) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1994, 27, 3207-3218. (12) Dijt, J. C.; Cohen Stuart, M. A.; Hofman, J. E.; Fleer, G. J. Colloids Surf. 1990, 51, 141-158.
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Figure 3. Example of adsorption kinetics for generations 2-5 on glass, at bulk concentrations of 100 mg/L, Re ) 13, pH 7, and ionic strength 0.1 M. parameter is taken from Figure 5 in ref 10, where R j is calculated numerically as a function of Re for h/R ) 1.7. In early adsorption stages the “perfect sink” boundary condition cs ) 0 is assumed to be valid. The transport equation does not include blocking effects induced by already adsorbed particles and is therefore, at higher coverage, no longer applicable. Furthermore, this equation is only valid for a steady-state situation in which the bulk concentration of the inflowing fluid is constant. c. Pulsed Field Gradient NMR. The self-diffusion measurements were performed with the pulsed field gradient NMR method.13 A Bruker AM200 has been used with a wide bore magnet of 4.7 T, connected to a Bruker Aspect 3000 spectrometer. A magnetic field gradient, G ) 4.3 T m-1, was generated at a maximum current of 12 A by an actively shielded gradient coil. A Techron 7570 amplifier, coupled to the spectrometer, delivered almost rectangular gradients of a duration of 20 ms. The sampling time of each experiment was 16.8 ms. Radio frequency (rf) pulses were chosen in such a way that the magnetization changed 90° from the z-axis in the xy plane (and back) in about 7 µs. After each gradient pulse there was a delay of 1.2 ms, to allow for the relaxation of possible eddy current, prior to the application of the rf-pulse or the signal accumulation. The amplitude of the Fourier transform of the acquired signal, AG, is given by14
(
(
AG ) A0 exp -γ2G2δ2D ∆ -
δ 3
))
(4)
with A0 the echo amplitude at zero magnetic field gradient, γ the gyromagnetic ratio of the nucleus, G the gradient amplitude, δ the length of the gradient pulse, ∆ the gradient pulse interval, and D the self-diffusion coefficient of the monitored nuclei. The pulsed field stimulated echo method15 has been used, because the longitudinal relaxation time of the dendrimers was larger than the transversal relaxation time. The diffusion coefficient is obtained from a fit of eq 4 through the data. A more extended description of the method will appear in ref 16.
Results a. Kinetics. An example of typically observed evolution in the adsorbed amount of dendrimers on glass is presented in Figure 3 for generations 2-5. These curves are linearly dependent on time for almost the complete adsorption process, an indication that the kinetics are mostly diffusion/convection controlled. The calculated maximum surface coverage is of the order of 10-15%, using dimen(13) Stejskal, E. O. J. Chem. Phys. 1965, 43, 3597-3603. (14) Stillbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (15) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523-2526. (16) Rietveld, I. B.; Bedeaux, D. Submitted to Macromolecules.
Figure 4. Initial kinetics (∂Γ/∂t)0 presented as a function of dendrimer concentration in the bulk cb for various generations at pH 7, 0.1 M NaCl, and Re ) 13. The linear dependence of the initial rate of adsorption on cb, as predicted by eq 2 for the case of diffusion/convection controlled rate of adsorption, is observed experimentally for cb < 10 mg/L, using a sticking probability β ) 3% and diffusion coefficient D ) 10-10 m2/s (solid line). At cb > 10 mg/L, there is a 1/3 power law dependence (dashed line).
sions provided in the literature for these poly(propylene imine) dendrimers.17,18 At these coverages it is not expected that blocking effects play an important role. Blocking of incoming particles by already adsorbed dendrimers is indeed not visible in the curves, which show the same rate of adsorption up to more than 90% of the maximally reached coverage. In Figure 4 the initial kinetics (∂Γ/∂ t)0 are plotted as a function of the bulk concentration of dendrimers cb. It shows the linear dependence on cb predicted by eq 2. Strangely enough, the dependence only holds up to bulk concentrations of the order of 10 mg/L and changes abruptly into a cb1/3 dependence at higher bulk concentrations. In the literature it is observed more often for polymers and proteins that the initial adsorption rate is much slower than expected at higher bulk concentrations. Even the concentrations reported in the literature at which this usually happens are comparable to the crossover concentration cb ∼ 10 mg/L in Figure 4.7,19,20,21 A satisfactory explanation for this phenomenon is however not available up to now. To get more insight into this problem, a more thorough investigation is needed on the parameters that control mass transport. Therefore, the flow dependence, the sticking probability, and the diffusion coefficient are studied in more detail below for this particular system. The influence of the flow intensity (Reynolds number and flow intensity parameter R j ) is studied for various dendrimer concentrations, including one in the higher concentration regime, where the initial adsorption rate was shown to have a cb1/3 dependence. The results are plotted in Figure 5, together with calculations of the initial adsorption with eqs 2 and 3, with for βD2/3 the values as (17) Scherrenberg, R.; Coussens, B.; van Vliet, P.; Edouard, G.; Brackman, J.; de Brabander, E.; Mortensen, K. Macromolecules 1998, 31, 456-461. (18) Rietveld, I. B.; Smit, J. A. M. Macromolecules 1999, 32, 46084614. (19) Walter, H.; Harrats, C.; Mu¨ller-Buschbaum, P.; Je´roˆme, R.; Stamm, M. Langmuir 1999, 15, 1260-1267. (20) Wertz, C. F.; Santore, M. M. Langmuir 1999, 15, 8884-8894. (21) Lok, B. L.; Cheng, Y.; Roberton, C. R. J. Colloid Interface Sci. 1983, 91, 104-116.
Poly(propylene imine) Dendrimers on Glass
Figure 5. Initial adsorption rate studied as a function of flow intensity for various concentrations at pH 7 and in 0.1 M NaCl. The lines are calculations with eqs 2 and 3 using D(cb) from Figure 4, where Re ) 13. R j (Re) is obtained from Figure 5 in ref 10.
obtained at Re ) 13 (the slopes in Figure 4). R j is roughly proportional to Re for these flow conditions (see Figure 5 in ref 10). According to eqs 2 and 3, mass transport as the limiting step will result in a 1/3 power law dependence of the initial flux of particles on the product (R j Re). A comparison with the data points shows that this is indeed the case for these experiments. The same dependence on the flow parameters is obtained at concentrations cb > 10 mg/L, from which we conclude that the drop in concentration dependence cannot be ascribed to a change in the flow intensity dependency. Lok et al.21 ascribe this effect to be caused by a breakdown of the validity of the steady-state transport equation (eq 2). At higher concentrations the surface is then assumed to be saturated at much faster time scales than the concentration can settle throughout the cell; that is, there is a transient period in which the bulk concentration is climbing toward the bulk value. The concentration near the surface is then lower than the bulk concentration, and rather than eq 2, a time-dependent mass transfer equation needs to be applied. The crossover concentration is called the “breakdown concentration”. However, the authors do not give a satisfactory explanation for why this breakdown leads to a 1/3 concentration dependence. Stamm et al., who also reported a change in concentration dependence of the adsorption kinetics, interpreted this effect in terms of a change in the diffusion coefficient.19 They compared the diffusion toward the surface with the slow mode diffusion coefficient obtained from dynamic light scattering experiments. This slow mode diffusion coefficient refers to the diffusion of interchain domains or, in other words, aggregation (see also refs 22-25). When the mass transport equation (eq 2) is applied to the experimental data in Figure 4, one can plot a combination of β and D (obtained from the slopes in Figure 4) as a function of the bulk concentration. Figure 6 shows the same power law dependence at cb > 10 mg/L as Stamm (22) Sedla´k, M.; Kona´k, C.; Sˇ tepa´nek, P.; Jakesˇ, J. Polymer 1987, 28, 873-880. (23) Sedla´k, M.; Amis, E. J. J. Chem. Phys. 1992, 1, 826-834. (24) Tanahatoe, J. J.; Kuil, M. E. J. Phys. Chem. B 1997, 101, 92339239. (25) Fo¨rster, S.; Schmidt, M.; Antonietti, M. Polymer 1990, 31, 781792.
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Figure 6. Long-time self-diffusion coefficient measured with pulsed field gradient NMR for the fifth-generation poly(propylene imine) dendrimer at pH 7 in 0.1 M NaCl (b). A comparison is made with the diffusion coefficient obtained from an interpretation of the adsorption rate in terms of mass transport (O) (eq 2). A sticking probability β of the order of 3% is needed to change the diffusion coefficient in the mass transport equation into the long-time self-diffusion coefficient. For bulk concentrations cb > 10 mg/L, D shows a cb-1 dependence.
et al. presented for their starlike ampholytic diblock copolymer. However, because of the considerable dendrimer charge densities,5 we see no reason to associate the adsorption rate with aggregation, and in addition to that, the adsorption statics did not show any peculiarity at these concentrations at pH 7.1 To investigate a possible concentration dependence of the diffusion toward the surface further, we measured the long-time self-diffusion coefficient under similar conditions (pH 7 and 0.1 M NaCl) for the fifth generation with pulsed field gradient NMR. The results are plotted together with the diffusion coefficient obtained from the adsorption experiments using the mass transport equation (eq 2) in Figure 6. At these extremely low concentrations, corresponding to volume fractions of 10-6 to 10-4, a concentration independent value of 10-10 m2/s is observed. With the Einstein-Stokes relation, a hydrodynamic radius of 2 nm is calculated out of this diffusion coefficient for the fifth generation, comparable to values in the literature.16,17 No change in this concentration regime was observed with concentration, which indicates that there is at least no direct link between the diffusion toward the surface and the bulk diffusion coefficient. The difference in the concentration domain cb < 10 mg/L between the two diffusion coefficients can be related to a sticking probability β in eq 2, which would then be of the order of 3%. For all generations the same transport coefficient k in eq 2 is obtained, which means that differences in the diffusion time toward the surface as a function of generation are not detectable within experimental error. As an aside, the adsorption kinetics are probably not only through the diffusion coefficient dependent on dendrimer size; the sticking probability can also vary with generation. The presented results do not allow us to distinguish between these two factors. Experiments performed with glass surfaces rigorously cleaned with piranha liquid gave varying numbers in adsorption rates, up to a factor 3 less or more of what is reported here. However, trends as a function of generation, ionic strength, and pH were fully reproducible, and even the crossover concentration where
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Figure 7. Ionic strength dependence of the initial adsorption rates on glass shown for the fifth generation at pH 7 and Re ) 13, for both cb ) 1 mg/L (O) and 30 mg/L (0). The line is a guide for the eye. There is no detectable effect of ionic strength on the initial kinetics, neither below nor above cb ) 10 mg/L.
the linear dependence on cb changes into a 1/3 power law remains at 10 mg/L for different glass substrates. b. Ionic Strength. In Figure 7 the influence of ionic strength on the kinetics of dendrimer adsorption is shown for the fifth generation at pH 7. Experiments were performed with cb ) 1 and 30 mg/L, both at Re ) 13. We observed no change in the initial adsorption rate as a function of the ionic strength. When the two attracting double layers of both the surface and the particle overlap, the particle is attached to the surface.26 The Debye screening length decreases with ionic strength and thus enhances adsorption rate. However, the effects of ionic strength are apparently no longer experimentally accessible at Reynolds numbers and ionic strengths as used in the present paper, as is shown both theoretically and experimentally by Adamczyk et al.27 c. pH. The rate of adsorption is also measured as a function of pH at constant ionic strength; the data are presented in Figure 8. With potentiometric titration results,5 the pH can be translated into the dendrimer charge. The more charge on the dendrimer (lower pH), the steeper the initial slope (∂Γ/∂t)0. An explanation in terms of mass transport would mean an increase in the combination of the sticking probability β and the diffusion coefficient D. The with pulsed field gradient NMR determined long-time self-diffusion coefficient did not show any dependence on pH going from pH 10 to pH 3. The pH dependence of the initial adsorption kinetics was tested on bulk concentration, with data sets for cb ) 1 and 100 mg/L. Figure 8 shows that the rate of adsorption increases much faster with dendrimer charge at very low bulk concentrations. This means that the crossover or breakdown concentration shifts to lower values with a decrease in pH or increase in dendrimer charge. The crossover concentration in Figure 4 is at cb ) 10 mg/L, obtained at pH 7. In the fully deprotonated state (pH 9-10), the crossover would be around 30 mg/L; in the fully protonated state (pH 3), it would shift to 3 mg/L. Discussion and Conclusion The adsorption kinetics of positively charged poly(propylene imine) dendrimers on glass were studied by means of light reflectivity as a function of generation, pH, and ionic strength. The data on adsorption kinetics as a function of concentration and flow intensity (Figures 4 and 5, (26) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. A. Particle Deposition & Aggregation; Butterworth-Heinemann, Woburn, MA, 1995. (27) Adamczyk, Z.; Siwek, N.; Zembala, M.; Warszynski, P. J. Colloid Interface Sci. 1989, 130, 578-587.
Figure 8. Effect of pH on the adsorption kinetics of generations 3 (0), 4 (4, 2) and 5 (O, b) of the unmodified poly(propylene imine) dendrimer in 0.1 M NaCl on a glass substrate. Measurements are performed for the two concentration regimes on both sides of the crossover concentration cb ) 10 mg/L (see also Figure 4). The lines through the points are guides for the eye and clearly show there is a different dependence on pH on either side of the crossover concentration, which shifts the crossover concentration as a function of pH.
respectively) clearly show that the rate of adsorption is mostly diffusion/convection controlled. The shape of the adsorption curves, such as those presented in Figure 3, shows similarities with the results of an analysis of adsorption kinetics by Adamczyk et al.28 in terms of a generalized random sequential adsorption (RSA) model, taking into account diffusion, particle/wall hydrodynamic interactions, and external forces. There is a buildup in chemical potential near the wall due to repulsive interactions between the already adsorbed particles and the incoming particles. This eventually prevents the system from further adsorption long before blocking effects can even play a role (see also ref 29). The adsorption rate is constant until it becomes suddenly very small and finally vanishes (Figure 3 in ref 28). The shape of the observed curves thus indicates that there is an energy barrier building up close to the surface. This leads to an abrupt stop in the layer evolution while the maximally reached surface coverage is still rather low. At these low coverages (saturation level at 10-15%), we see, however, no reason to believe that this barrier is the effect of repulsive interactions between incoming particles and already adsorbed dendrimers. We strongly sympathize with the idea that the adsorption is governed by the limited number of available glass surface sites for the dendrimers to attach to.30,31 It was already proposed in a previous paper that the adsorption on glass as a function of generation, pH, and ionic strength is strongly influenced by the glass conditions.1 The fact that the presented kinetic measurements show a dependence on the cleaning procedure of the glass as well enhances the idea that the dendrimers are searching along the surface to optimize their contact with the glass substrate. This results in the same effect on the kinetics as the energy barrier proposed by Adamczyk and co-workers, as this (28) Adamczyk, Z.; Senger, B.; Voegel, J.-C.; Schaaf, P. J. Chem. Phys. 1999, 110, 3118-3128. (29) Antelmi, D. A.; Spalla, O. Langmuir 1999, 15, 7478-7489. (30) Lu¨thi, Y.; Ricka, J.; Borkovec, M. J. Colloid Interface Sci. 1998, 206, 314-321. (31) Weiss, M.; Lu¨thi, Y.; Ricka, J.; Jo¨rg, T.; Bebie, H. J. Colloid Interface Sci. 1998, 206, 322-331.
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search is already something that shows up for the first few dendrimers that reach the surface. In the analysis in terms of mass transport, the change in the number of glass sites would return in a change in the sticking probability, because a higher number of glass sites eases the search for the dendrimers. It is important to realize that the dendrimers have relatively rigid structures, which only cover a minor part of the surface. This automatically means that there are only a few contacts with the substrate, in contrast to what is commonly observed for ordinary polyelectrolytes. A value of a few percent for the sticking probability is then no longer surprising. In terms of adsorption kinetics, there is thus a difference between the arrival of the dendrimers close to the surface and real attachment. Our idea is that these dendrimers form a diffusive layer close to the surface.28,32-34 This layer builds up rather rapidly in time compared to the real adsorption to the surface, and the concentration in the layer is linear with the bulk concentration up to a concentration where the particles in the layer will start to interact with each other. When parameters such as pH and ionic strength are chosen to be constant, the collector’s properties remain identical,1 and in the adsorption kinetics, the data can be analyzed in terms of a constant sticking probability. The concentration where the particles start to interact with each other then is around cb ∼ 10 mg/L. At sufficiently low concentrations, the kinetics show apparent mass transport behavior, but the cb dependence drops at higher concentrations. Of course further investigation is needed to support this hypothesis and to explain the apparent cb1/3 dependence. The initial kinetics show a drop in concentration dependence at cb ∼ 10 mg/L for adsorption measurements
performed at pH 7. Because, with a change of the ionic strength from 0.01 to 1.0 M, both the glass surface area and the surface charge density are not dramatically changed,1,35 it is not expected that the sticking probability changes much on the basis of the glass properties. The conditions are completely governed by the size and charge of the dendrimer, and it was already stated before that the presented ionic strengths and flow intensities are too high to show much influence on the adsorption rate.26,36 The adsorption kinetics do show an increase with a decrease in pH. Although the dendrimer charge increases at the same time, it is not expected that the increase in the rate of adsorption is due to changes in dendrimer charge. Even at high pH, the charge density in the outermost shell is higher than the overall glass surface charge density.5 At pH 9, for example, there are about 50 charged amine groups, leading to a surface charge density of 60 µC/cm2 when the dendrimer is adsorbed at the surface, 10-fold the glass surface charge density.1 The increase in the adsorption rate is therefore more likely to be caused by the increase in the available glass surface area, which changes dramatically with pH, as shown in Figure 5 of ref 1. The search along the surface is accelerated, and the sticking probability is enhanced. However, the pH dependence is different on either side of the crossover concentration in Figure 8. Therefore, this crossover concentration changes with pH. With higher dendrimer charge (lower pH), the crossover concentration shifts to lower concentrations. In the picture of a diffuse layer close to the surface, this would fit in perfectly: the point where the dendrimers start to interact in this layer shifts to lower concentrations when the dendrimer charge is increased. The drop in concentration dependence would then start at lower bulk concentrations, and that is exactly what is observed here experimentally.
(32) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1991; Vol. I. (33) Adamczyk, Z.; van de Ven, T. G. M. J. Colloid Interface Sci. 1984, 97, 68-90. (34) Adamczyk, Z.; van de Ven, T. G. M. J. Colloid Interface Sci. 1984, 97, 91-104.
LA0004552 (35) Bolt, G. H. J. Phys. Chem. 1957, 61, 1166-1169. (36) Adamczyk, Z.; Warszynski, P. Adv. Colloid Interface Sci. 1996, 63, 41-149.
