Adsorption and Electrokinetic Properties of Polyethylenimine on Silica

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Adsorption and Electrokinetic Properties of Polyethylenimine on Silica Surfaces Ro´bert Me´sza´ros,*,†,‡ Laurie Thompson,† Martin Bos,† and Peter de Groot† Unilever Research Port Sunlight Laboratory, Quarry Road East, Bebington, CH63 3JW, U.K., and Department of Colloid Chemistry, Lora´ nd Eo¨ tvo¨ s University, P. O. Box 32, Budapest 112, Hungary H-1518 Received December 7, 2001. In Final Form: February 15, 2002 The adsorption on silica wafers of a hyperbranched, high molecular weight polyethylenimine (PEI) was investigated using reflectometry. The pH and ionic strength dependence of PEI adsorption kinetics and that of the adsorbed amount were interpreted according to the complex balance of segment/segment and segment/surface site interactions. The observed adsorption properties show significant deviations from the recently studied features of polyvinylamine adsorption on cellulose coated silicas. The different behavior can be attributed to the pronounced difference in the nonelectrostatic affinity of polyamines toward the two different types of surfaces. The role of electrostatic interactions was also characterized by electrokinetic measurements. Due to the adsorption of PEI, significant charge reversal and shift in the isoelectric point of silica wafers occur. The ζ potential-pH curves show a maximum, which can be interpreted qualitatively by the adsorption characteristics of PEI. An attempt was also made to interrelate the adsorption and electrokinetic data via comparison of different estimates of the diffuse double layer charge of the PEI/silica system.

Introduction Polyethylenimine-based polyelectrolytes are widely used as adhesives, dispersion stabilizers, thickeners, and flocculating agents as well as in the paper industry as effective drainage and retention aids for paper fines, pigments, fillers, and dyes.1-3 In all of these applications the function of PEI is largely determined by its adsorption and electrokinetic properties. The adsorption of weak polyelectrolytes on oppositely charged surfaces depends on parameters including pH and ionic strength, which can significantly change the charge density of the polymer and the surface as well. However, the nonelectrostatic surface affinity and the solvent quality also play an important role.4 The actual balance of the interactions between the different constituents of the bulk solution and the surface layer (polymer segments, solvent molecules, surface groups, etc.) determines the equilibrium properties of the system. An additional feature of the adsorbed weak polyelectrolytes that their charge density is adjusted in the adsorbed layer due to the local electrostatic potential profile near the surface.5,6 As a consequence of this, a very complex diffuse double layer develops the structure that has been described using sophisticated theoretical simulations.5,7 In the case * Corresponding author. † Unilever Research Port Sunlight Laboratory. ‡ Lora ´ nd Eo¨tvo¨s University. (1) Lindquist, G. M.; Stratton, R. A. J. Colloid Interface Sci. 1976, 55, 45. (2) Horn, D.; Linhart, F. In Paper Chemistry; Roberts, J., Ed.; Blackie Academic & Professional: Glasgow and London, 1996; pp 64-82. (3) Alince, B.; Vanerek, A.; van de Ven, T. G. M. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 954. (4) Fleer, G. J.; Cohen Stuart, M. A.;., Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces, 1st ed.; Chapman and Hall: London, 1993; Chapter 7. (5) Evers, O. A.; Fleer, G. J.; Scheutjens, J. M. H. M.; Lyklema, J. J. Colloid Interface Sci. 1986, 111, 446. (6) Bo¨hmer, M. R.; Evers, O. A.; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. (7) Ennis, J.; Sjostrom, L.; Akesson, T.; Jonsson, B. J. Phys. Chem. 1998, 102, 2149.

of branched or starlike polyelectrolytes the problem is even more complicated since the adsorption of these structures is less understood than that of the linear ones.8 In addition to the obvious importance of equilibrium adsorption, the reversibility of polyelectrolyte adsorption is also an essential question.9-11 For example, there is strong evidence that the adsorption of some weak polyelectrolytes shows significant hysteresis in a pH cycle experiment.12 Therefore, the mechanism and kinetics of adsorption should also be carefully considered. The mechanism of polyelectrolyte adsorption can generally be viewed as a three-step process: transport from the bulk to the surface, attachment to surface, and rearrangement in the adsorbed layer. On the practical time scale of the adsorption experiments the kinetics are mainly determined by the balance of the first two steps, which can be readily monitored by the recently developed technique of the stagnation point flow cell.13 In this paper we present a comprehensive study of the ionic strength and pH-dependent dynamic and static adsorption properties of a hyperbranched polyethylenenimine on silica wafers. Our data will be compared with the recent results of Geffroy et al. for the adsorption of polyvinylamine (PVAm), which is a similar but linear polyamine, on cellulose-coated silica wafer,14 and an attempt will be made to explain the differences. Finally, electrokinetic measurements will be presented and the (8) Grest, G. S.; Fetters, L. J.; Huang, J. S.; Richter, D. In Advances in Chemical Physics; Prigogine, I., Stuart, A. R., Eds.; John Wiley & Sons: New York, 1996; Vol. XCIV, Chapter 2. (9) Schneider, H. M.; Frantz, P.; Granick, S. Langmuir 1996, 12, 994. (10) van Eijk, M. C. P.; Cohen Stuart, M. A. Langmuir 1997, 13, 5447. (11) Cohen Stuart, M. A.; Hoogendam, C. W.; de Keizer, A. J. Phys.: Condens. Matter 1997, 9, 7767. (12) Meadows, J.; Williams, P. A.; Garvey, M. J.; Harrop, R. A.; Phillips, G. O. Colloids Surf. 1988, 32, 275. (13) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Adv. Colloid Interface Sci. 1994, 50, 79. (14) Geffroy, C.; Labeau, M. P.; Wong, K.; Cabane, B.; Cohen Stuart, M. A. Colloids Surf. A 2000, 172, 47.

10.1021/la011776w CCC: $22.00 © 2002 American Chemical Society Published on Web 07/11/2002

Properties of PEI on Silica Surfaces

Langmuir, Vol. 18, No. 16, 2002 6165 oxidation of silicon wafer at 1000 °C for 1 h, resulting in a film thickness of 100 nm. The silica wafers were cleaned by putting them into concentrated persulfuric acid for 60 min. The purified samples were rinsed and then stored under Millipore water prior to the measurements. In Figure 1b the pH dependence of the electrokinetic potential of silica wafers, determined by streaming potential measurements, is shown in NaCl solutions. Due to the well-known characteristics of silica surfaces, their charge density varies with the pH in a way opposite that of the protonation degree of PEI. Reflectometry. The adsorption was measured by reflectometry on the basis of the standard method of Dijt et al.13,16 All the measurements were carried out at 295 K. In this method the flux of the polymer solution toward the solid substrate is controlled by a stagnation point flow cell. In a steadystate situation the flux can be described by the following equation:

Jo ) 0.776ν1/3R-1D2/3(R j Re)2/3c

(1)

where ν is the kinematic viscosity, R the radius of the tube, D the diffusion coefficient, R j the dimensionless flow intensity parameter, and Re the Reynolds number. During the experiments a laser source emits a polarized beam which is reflected off the wafer in the reflectometric cell. The reflected light is split into its parallel and perpendicular components, which are detected separately with photodiodes. The signal S is defined as

S)f

Rp Rs

(2)

where f is an equipment constant, Rp and Rs are the reflectivities of the parallel and perpendicular components. When the medium flows toward the surface, the initial signal So is constant, whereas with a flowing polymer solution when adsorption occurs the signal changes by ∆S. Under appropriate conditions14,17 the relative change of the signal is proportional to the adsorbed amount:

Γ) Figure 1. (a) Protonation degree of polyethylenimine as a function of pH at three different concentrations of NaCl solution. cPEI ) 200 ppm. (b) Electrokinetic potential of silica wafer against the pH at three ionic strengths.

double layer characteristics will be interpreted on the basis of the adsorption properties of PEI. Experimental Section Materials. Polyethylenimine (PEI) with a mean molecular weight of 750 000 g/mol was purchased from BASF in the form of a 33 wt % aqueous solution. This PEI sample is a hyperbranched polymer containing primary, secondary, and tertiary groups with 1:2:1 ratio, which results from the structure of monomer units with branch points at every 3-3.5 units.15 Because of the weak polyelectrolyte nature of the PEI, its charge density depends on the pH and ionic strength as well. In Figure 1a the overall protonation degree of the amino groups is plotted as a function of pH at three values of the ionic strength. As can be seen, the PEI is practically neutral at pH g 10.5 whereas it possesses considerable charge density in the neutral and acidic pH range. The determination of the charge density of PEI was based on the standard, potentiometric titration method.1 The pH of the solutions was adjusted with ACS reagents of HCl and (carbonate free) NaOH, and the supporting electrolyte was NaCl. All of these chemicals were purchased from SigmaAldrich. During the experiments ultraclean Millipore water was used for making solutions. As a surface substrate, strips of silicon wafers were used bearing thin layers of SiO2. The silica layers were made by thermal (15) Dick, C. R.; Ham, G. E. J. Macromol. Sci., Chem. 1970, A4, 1301.

1 ∆S As So

(3)

where As is the sensitivity factor which was calculated using the method of Hansen.17 This factor depends on the angle of incidence θi, the wavelength of the laser beam λ, and the refractive indices of the silicon, silica, adsorbed layer, and solution phase, as well as on the refractive index increments of the polymer solution (dn/dc). The values used here were nSi ) 3.8, nSiO2 ) 1.46, nPEI ) 1.36, nwater ) 1.333, dn/dc ) 0.21 cm3/g,18,19 θi ) 70°, and λ ) 632.8 nm. The refractive index data of the substrate layers and that of the adsorbed layer were determined by independent ellipsometry measurements. The operational,“equilibrium”, adsorbed amount was determined to extrapolate the adsorbed amount to t f ∞ from kinetic curves measured up to 20 min. In several cases the extrapolated adsorbed amount was compared at 10, 25, and 50 ppm concentrations of PEI. Significant differences were not detected, and the data at 50 ppm are presented here. Streaming Potential. The electrokinetic measurements were performed in the rectangular cell of an Electrokinetic Analyser (Anton Paar, KG, Graz, Austria) at 295 K. Due to the applied pressure (∆P) the medium was flowing through the capillary channel between the two tightly mounted silica wafers, in regularly alternating streams. As a consequence of this, a potential difference between the inlet and outlet part of the channel appeared which was measured by Ag/AgCl electrodes (∆U streaming potential). (16) Dijt, J. C.; Cohen Stuart, M. A.; Hofman, J. E.; Fleer, G. J. Colloids Surf. 1990, 51, 141. (17) Hansen, W. N. J. Opt. Soc. Am. 1968, 58, 380. (18) Park, I. H.; Choi, E. J. Polym. 1996, 37, 313. (19) Van den Berg, J. W. A.; Bloys Van Treslong, C. J.; Polderman, A. Recl. Trav. Chim. 1973, 92, 3.

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The zeta (ζ) potential was calculated from the following equation:

ζ)

η∆UKL or∆P

(4)

where KL is the specific conductivity of the streaming medium, η is the dynamic viscosity, r is the relative permittivity, and o is the permittivity of vacuum. In the case of 0.001 M NaCl solutions the effect of surface conductance was investigated by measuring the electric resistance of the same streaming cell containing 0.1 M KCl (RKCl) and the given solution (Rsol), respectively. The corrected electrokinetic potential was calculated according to the following equation:

ζ)

η∆UKKClRKCl or∆PRsol

(5)

where KKCl is the specific conductivity of the standard 0.1 M KCl solution. No significant deviation between eq 4 and eq 5 was found. The measurements were performed at the same wafer by changing the pH and NaCl concentration by means of an automatic titration unit (Anton Paar). During the experiments the ionic strength and the polymer concentration were kept constant, and prior to the measurements regular rinsing cycles were applied. Some text experiments were also performed in 0.01 M NaCl, where we made some measurements without titration. In this case 50 ppm PEI solutions with different pH values were applied on the separately cleaned silica wafers, with the same equilibration and rinsing procedure as previously. No deviations between the two series of measurements were detected. In the case of polyethylenimine solutions we investigated the effect of the adsorption time. The streaming potential data were compared after 15, 30, and 45 min in the presence of 50 ppm PEI. Since no differences were detected, the values after 15 min were used.

Results and Discussion Adsorption Kinetics. In Figure 2a the adsorbed amount of PEI is plotted as a function of time at various pH values and in the presence of 10-3 M NaCl. Each curve demonstrates that the mechanism of adsorption can be split into at least two distinct parts. At the onset of the adsorption the adsorbed amount linearly increases with time. Then the rate of adsorption tends to decrease suddenly: the lower the pH the greater the change in the slope of the curves and a plateau value of adsorption seems to be attained. The pronounced change in the kinetics is demonstrated in Figure 2b, where the adsorption rate is plotted as a function of the adsorbed amount. In Figure 3 the adsorption kinetic curves are shown at three ionic strengths and at pH ) 3. As can be seen, the curves start with an initial linear part and then the adsorption rate starts to decrease: the higher the ionic strength the more gradual the lowering of the adsorption rate and then later a plateau value of the adsorbed amount is attained. Figures 2 and 3 are similar in the sense that when the role of the electrostatic segment/segment repulsion becomes more pronounced, i.e., by increasing the degree of protonation of PEI and/or decreasing the ionic strength, the deviation from the initial adsorption rate becomes steeper, indicating the possible role of an electrostatic barrier in the kinetics. On the basis of the recent theory of polyelectrolyte adsorption kinetics (Cohen Stuart et al.11), the observed kinetics can be interpreted in the following way: At the beginning of the adsorption process the surface is almost empty and the net attraction between the surface and the PEI segments is dominant. At this stage the transport

Figure 2. (a) Adsorbed amount of PEI as a function of time. All the measurements were performed in the presence of 10-3 M NaCl and 50 ppm PEI. The different symbols belong to different pH values. (b) Adsorption rate, dΓ/dt, as a function of the adsorbed amount at 10-3 M NaCl.

from the bulk is the rate-determining step and the initial rate of adsorption (dΓ/dt)t)0 in Figures 2 and 3 is equal to the transport flux of eq 1. However, by increasing surface coverage a barrier against further adsorption develops; therefore, the attachment process slows down dramatically and eventually becomes the rate-determining step. It can be shown that the kinetic barrier against further polyelectrolyte adsorption is mainly electrostatic in nature at low ionic strength (except the high pH range (pH > 10.4) where the PEI is practically neutral).11,14 That also means that the higher the protonation degree of the PEI and lower the ionic strength, the higher the electrostatic barrier developed and the slower the adsorption process becomes, which agrees well with our observations. It should be noted that the observed plateau values of the adsorbed amounts in Figures 2 and 3 might be below the equilibrium adsorbed amount since the electrostatic resistance against further adsorption can shift the equilibration time far out of the practical laboratory time range (i.e., toward several years) especially at low ionic strength where the actual value of the electrostatic barrier can be estimated to be in the range of several kT units.11,14

Properties of PEI on Silica Surfaces

Figure 3. Adsorbed amount as a function of time. All the measurements belong to pH ) 3 and 50 ppm PEI. The different symbols denote different concentrations of NaCl.

Figure 4. Adsorbed amount against pH at three different ionic strengths and 50 ppm PEI. The various symbols belong to the different concentrations of NaCl.

The described mechanism of adsorption can also offer an approximation of characterizing the charged nature of the adsorbed layer. Namely, it can be presumed at low ionic strength (and at low and moderate pH) that when the adsorption rate starts to deviate from (dΓ/dt)t)0, i.e., at the values of the adsorbed amount at the break points in Figure 2b, then the surface charge becomes fully compensated.14 Therefore, the difference between the total adsorbed amount and the one at the break points of Figure 2b gives a rough estimate for the excess adsorbed amount of PEI (Γexc) which overcompensates the surface charge of the silica.14 Adsorbed Amount. In Figure 4 the adsorbed amount of PEI is shown as a function of pH at three ionic strengths. It can be clearly seen that the adsorption increases monotonically with increasing pH at fixed ionic strengths. This observation is different from the PVam adsorption results on cellulose substrate, where a maximum of adsorption in pH was found.14 A maximum adsorption as a function of polymer charge density was also observed for the adsorption of poly(acrylic acid) and quaternized polyvinylimidazoles onto oppositely charged surfaces.20,21

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In these latter cases,20,21 when the surface charge was fixed, the maximum can be generated on the basis of an extended version of the self-consistent field theory of polyelectrolyte adsorption.6,22 At high segment charge density the adsorption is low because of the strong segment/segment repulsion. By decreasing polymer charge density, the adsorption increases since the attractive surface/segment interactions gradually become dominant over the repulsive segment/segment interactions. However, a further decrease in the segment charge density can lower the adsorption again because of the strong competition between the small counterions and the polymer segments for the charged surface sites.22,23 In the case of polyamine adsorption onto silica or cellulose, the surface charge is not constant but varies conversely with the pH than the polyamine charge density. Therefore, on the basis of a similar argumentation as above, a maximum of adsorption as a function of pH can be predicted. The lack of a maximum in the observed pH range for the PEI adsorption on silica might be explained by the strong nonelectrostatic affinity of PEI toward this surface. This can in principle shift the predicted maximum to the very low polymer charge densities (extreme high pH range) since in this case, in addition to the surface charge compensation mechanism, there is a significant nonelectrostatic driving force toward the surface.6,23 The possible presence of a maximum at the extremely high pH range cannot be excluded and needs further investigation. Figure 4 also shows the effect of the ionic strength on PEI adsorption. The general trend is that the adsorption increases by increasing ionic strength. The influence of the added salt is more significant in the lower pH range where the PEI molecules are strongly charged. Upon increasing pH the effect of ionic strength gradually decreases, whereas at pH = 11 the adsorbed amount seems not to depend on the supporting electrolyte concentration. The effect of ionic strength on PEI adsorption indicates a significant nonelectrostatic affinity to the silica surface.23 At the lower pH range where the PEI molecules are highly charged and the surface bears only slight negative charge density, the repulsive segment/segment interactions are dominant; therefore, the adsorbed amount is small at low ionic strength. By screening the electrostatic interactions by increasing electrolyte concentration, the nonelectrostatic affinity of the PEI toward the silica surface starts to dominate and the adsorbed amount increases (screening enhanced adsorption23). Upon increasing pH the effect of ionic strength decreases since the role of the attractive segment/surface interactions becomes more and more pronounced. It should be noted that because of its weak polyelectrolyte nature the PEI charge density is adjusted in the adsorbed layer.6,22 That means that the amino units in contact with the negatively charged silica are more charged whereas the amino groups further from the silica are less charged than they are supposed to be according to their bulk protonation degree.6,22 This effect further increases the weight of the attractive segment/surface interactions at the expense of the repulsive segment/segment interactions by increasing pH. This also means that there must (20) Blaakmeer, J.; Bo¨hmer, M. R.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1990, 23, 2301. (21) Bo¨hmer, M. R.; Heeterbeek, W. H. A.; Deratani, A.; Renard, E. Colloids Surf. A 1995, 99, 53. (22) Evers, O. A.; Fleer, G. J.; Scheutjens, J. M. H. M.; Lyklema, J. J. Colloid Interface Sci. 1986, 111, 446. (23) Van de Steeg, H. G. M.; Cohen Stuart, M. A.; de Keizer, A.; Bisterbosch, B. H. Langmuir 1992, 8, 2538.

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be a pH where the adsorption does not depend on the supporting electrolyte concentration, and that was found to be at pH = 11. Figure 4 also suggests that above this pH the effect of ionic strength might reverse to the socalled screening reduced adsorption regime,23 where the polymer adsorption decreases with increasing ionic strength. These findings are in agreement with the model calculations of Van de Steeg et al.,23 who proved that there is a transition region between the screening enhanced and screening reduced polyelectrolyte adsorption depending on the segment and surface charge densities and on the nonelectrostatic affinity of the polymer as well. On the basis of their results the transition regime shifts toward the low segment charge by increasing the nonelectrostatic affinity and decreasing the surface charge density. The presence of this transition regime of PEI at high pH is another indication of the presence of strong non-Coulombic interactions between the PEI and the silica surface sites. The PVAm adsorption on cellulose-coated silica was found to decrease, eventually to zero with increasing ionic strength14 at pH ) 10, which means that in that case by screening the electrostatics the polymer could be perfectly displaced by the competing counterions.6,23 Another interesting difference is that the PVAm practically does not adsorb on the cellulose substrate below pH = 7, whereas we found measurable PEI adsorption on silica even at pH ) 3 at the same ionic strength. These results suggest a very low nonelectrostatic affinity of PVam toward the cellulose,4,6 although the slightly different charge densities of the PEI and PVam24 and that of the silica and cellulose surfaces25 may also play a role in the interpretation. It can be concluded that the observed adsorption behavior can be well explained on the basis of a strong, nonelectrostatic affinity of PEI toward the silica surfaces. The presence of strong specific interactions between the silica surface sites and polyamines in aqueous medium are also supported by potentiometric investigations of PEI/ SiO2 aerosol systems (Sidorova et al.26,27) and surface force measurements between glass plates in PVam solutions.28 The origin of these interactions might be explained by surface complexation and hydrogen bonding.14,26,27 The Charged Nature of the Adsorbed Layer. The electrokinetic data are closely related to the electrostatic potential profile in the surface layer, which depends on the surface and segment charge density and the distribution of the ions, solvent molecules, and segments in this layer.4,6 Therefore, the thickness and structure of the adsorbed layer as well as the decay length of the electrostatic interactions (the inverse Debye screening length) play an important role in the interpretation. It is known from atomic force microscopic investigations that the hyperbranched PEI adopts a bloblike adsorbed layer structure on mica and polystyrene surfaces29,30 and the adsorbed layer thickness was found to decrease by increasing substrate charge density. The exact structure (24) Bystryak, S. M.; Winnik, M. A.; Siddiqui, J. Langmuir 1999, 15, 3748. (25) Poptoshev, E.; Rutland, M. W.; Claesson, P. M. Langmuir 2000, 16, 1987. (26) Sidorova, M. P.; Golub, T. P.; Musabekov, K. Adv. Colloid Interface Sci. 1993, 43, 1. (27) Golub, T. P.; Skachova, A. L.; Sidorova, M. P. Colloid J. Russ. Acad. Sci. 1992, 54, 697. (28) Poptoshev, E.; Rutland, M. W.; Claesson, P. M. Langmuir 1999, 15, 7789. (29) Pfau, A.; Schrepp, W.; Horn, D. Langmuir 1999, 15, 3219. (30) Akari, S.; Schrepp, W.; Horn, D. Langmuir 1996, 12, 857.

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Figure 5. The ζ potential of silica in the presence of 50 ppm PEI against pH at three ionic strengths. The various symbols refer to the different concentrations of NaCl.

of the double layer is very complicated and out of the scope of this paper. In the following we will make an attempt to interrelate qualitatively the electrokinetic data with the discussed adsorption behavior. In Figure 5 the electrokinetic potential of silica with adsorbed PEI is plotted as a function of pH (at the same PEI concentration and ionic strengths as in the case of the adsorption measurements). One of the most interesting features of Figure 5 is the significant charge reversal and shift in the isoelectric point of the silica due to the adsorption of PEI. These results can be explained again by the presence of strong non-Coulombic interactions between the polymer and the surface. The observed isoelectric point at pH = 11 is in good agreement with the observation that the adsorption of PEI is not dependent on the ionic strength at this pH (Figure 4), suggesting a neutral adsorbed layer. By increasing ionic strength, the ζ potential decreases although the adsorbed amount of PEI increases. This effect is partly in connection with the shift in the shear plane position because of the changes in the adsorbed layer thickness. However, the main reason of this behavior is that the inverse Debye screening length (κ-1) decreases from κ-1 ≈ 10 nm in 0.001 M NaCl to κ-1 ≈ 1 nm in 0.1M NaCl; therefore, the excess surface charge is likely to be largely compensated within the adsorbed polymer layer at higher ionic strengths. Another interesting feature of Figure 5 is the maximum behavior of the electrokinetic potential in pH. Although the interpretation of this maximum is very complicated, one can give some reasonable explanation applying some simplifying assumptions and using the adsorption kinetic approximation of the excess adsorbed amount14 of PEI (Γexc) which overcompensates the surface charge (Figure 2b). Assuming a flat adsorbed layer and ignoring the double layer structure and the PEI charge density adjustment, the diffuse layer charge (σD) can be roughly approximated by the following expression:

σD ≈

RΓexc F M

(6)

where R is the bulk protonation degree of PEI (Figure 1), M is the relative molecular mass of the segments, and F is the Faraday constant. By increasing pH, the repulsive segment/segment interactions become less pronounced; therefore, it is likely to suppose that Γexc is a monotonically

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solution of the Poisson-Boltzmann equation for an infinite surface plane (and assuming ψD = ξ). As can be seen, both curves vary in a similar way, showing a maximum as a function of pH. In the case of eq 6 the diffuse layer charge is considerably overestimated, which is the obvious consequence of neglecting the counterion distribution and the double layer structure in the adsorbed PEI layer.

Figure 6. Different estimates of the diffuse layer charge density (σD) as a function of pH at 10-3 M NaCl. The filled circles denote the values of σD approximated according to the PoissonBoltzmann equation using the ζ potential values of Figure 5. The open circles denote the adsorption kinetic estimates of σD based on eq 6.

increasing function of the pH because of the nonelectrostatic affinity of PEI. On the other hand, R is a monotonically decreasing function of the pH; therefore, RΓexc ∼ ψD = ξ (ψD is the multilayer Stern potential6), a maximum behavior of the ξΓpH curves can be qualitatively predicted. In Figure 6 the diffuse layer charge density estimated from electrokinetic and adsorption data, respectively, are compared at 10-3 M NaCl. In the case of the electrokinetic measurements the σD values were estimated from the ζ potential values of Figure 5 according to the analytical

Conclusion The dynamic and static adsorption features of PEI on silica significantly depend on the subtle balance of the attractive segment/surface and repulsive segment/segment interactions. This balance determines the extent of the electrostatic barrier in the adsorption mechanism, the adsorbed amount, and their dependence on pH and ionic strength. The adsorption properties of polyvinylamine on cellulose14 show striking deviations from our observations. These differences can be interpreted in terms of a strong nonelectrostatic affinity of PEI toward the silica surfaces but a low non-Coulombic affinity of polyamines to cellulose substrates by contrast. The electrokinetic measurements also reflect the presence of non-Coulombic interactions between the PEI and the silica and can be well interpreted on the basis of the adsorption characteristics. The diffuse layer charge density approximated from the electrokinetic potential seems to be in reasonable agreement with the one estimated from adsorption kinetics data. Acknowledgment. The authors thank Dr. Andrea Ferrante for his valuable advice and help during this investigation. LA011776W