Electrokinetic Characterization of Poly(Acrylic Acid) and Poly(Ethylene

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Electrokinetic Characterization of Poly(Acrylic Acid) and Poly(Ethylene Oxide) Brushes in Aqueous Electrolyte Solutions Ralf Zimmermann,*,† Willem Norde,‡,§ Martien A. Cohen Stuart,‡ and Carsten Werner†,£ Department Biocompatible Materials, Leibniz Institute of Polymer Research Dresden and The Max Bergmann Center of Biomaterials Dresden, Hohe Strasse 6, 01069 Dresden, Germany, Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703HB Wageningen, The Netherlands, Department of Biomedical Engineering, University of Groningen, A. Deusinglaan 1, 6713AV, Groningen, The Netherlands, and Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada, M5S 3G8 Received January 24, 2005. In Final Form: March 23, 2005 Surfaces carrying hydrophilic polymer brushes were prepared from poly(styrene)-poly(acrylic acid) and poly(styrene)-poly(ethylene oxide) diblock copolymers, respectively, using a Langmuir-Blodgett technique and employing poly(styrene)-coated planar glass as substrates. The electrical properties of these surfaces in aqueous electrolyte were analyzed as a function of pH and KCl concentration using streaming potential/ streaming current measurements. From these data, both the zeta potential and the surface conductivity could be obtained. The poly(acrylic acid) brushes are charged due to the dissociation of carboxylic acid groups and give theoretical surface potentials of -160 mV at full dissociation in 10-3 M solutions. The surface conductivity of these brushes is enormous under these conditions, accounting for more than 93% of the total measured surface conductivity. However, the mobility of the ions within the brush was estimated from the density of the carboxylic acid groups and the surface conductivity data to be only about 14% of that of free ions. The poly(ethylene oxide) (PEO) brushes effectively screen the charge of the underlying substrate, giving a very low zeta potential except when the ionic strength is very low. From the data, a hydrodynamic layer thickness of the PEO brushes could be estimated which is in good agreement with independent experiments (neutron reflectivity) and theoretical estimates. The surface conductivity in this system was slightly lower than that of the polystyren substrate. This also indicates that no significant amount of preferentially, i.e., nonelectrostatically attracted, ions taken up in the brush.

Introduction In many applications,1-5 polymer films on a substrate are in contact with aqueous solutions. In these cases, the formation of an interfacial electric charge often determines the characteristics of the polymer/solution interface. Interfacial charge was found to be relevant for a number of fundamental phenomena such as wetting, adsorption, and adhesion.6-8 Furthermore, the kinetics of conjugation between ligands (proteins, nucleic acids) and biosensor * Author to whom correspondence should be addressed. Leibniz Institute of Polymer Research Dresden, Hohe Strasse 6, 01069 Dresden, Germany. Tel: +49-351-4658-258. Fax: +49-351-4658533. E-mail: [email protected]. † Leibniz Institute of Polymer Research Dresden and The Max Bergmann Center of Biomaterials Dresden. ‡ Wageningen University. § University of Groningen. £ University of Toronto. (1) Riepl, M.; Mirsky, V. M.; Novotny, I.; Tvarozek, V.; Rehacek, V.; Wolfbeis, O. S. Anal. Chim. Acta 1999, 392, 77. (2) Fodor, S. P. A.; Rava, R. P.; Huang, X. C.; Pease, A. C.; Holmes, C. P.; Adams, C. L. Nature 1993, 364, 555. (3) Braun, H.-G.; Meyer, E.; Kratzmu¨ller, T. In Micro Total Analysis Systems ’98, Proceedings of the µTAS ’98 Workshop; Harrison, D. J.; van den Berg, A., Eds.; Kluwer Academic Publishers: Dordrecht, 1998. (4) Jeon, S. I.; Andrade, J. D. J. Colloid Interface Sci. 1991, 142, 159. (5) Uyama, Y.; Kato, K.; Ikada, Y. Adv. Polym. Sci. 1998, 137, 1. (6) Grundke, K.; Jacobasch, H.-J.; Simon, F.; Schneider, S. J. Adhes. Sci. Technol. 1995, 9, 9327. (7) Bismarck, A.; Kumru, M. E.; Springer, J. J Colloid Interface Sci. 1999, 217, 377. (8) Schmitt, F.-J. Habilitation Thesis, Dresden University of Technology, 2002.

surfaces,9,10 as well as transport and separation processes in microscale bioanalytic devices,11,12 depend on the charge at the interface and on the electrokinetic and electrodynamic phenomena associated with this charge. The study of electrokinetic phenomena like electrophoresis, electroosmosis, streaming current, and streaming potential has quite a history in science and has been particularly intensively studied in the context of colloid and interface science.13 A central concept in theoretical treatments is the electrokinetic potential or zeta potential. This quantity is usually defined more or less operationally as the potential ‘at the plane of shear’, the idea being that one can effectively describe the dynamics of ions and solvent near the surface in terms of a plane separating the solution adjacent to a smooth and charged interface into two zones: an inner region where no fluid motion occurs and an outer region where the tangential velocity takes nonzero values. The zeta potential is then the potential at this separating plane, called plane of shear. This leaves its precise physical meaning and its relation to the charge (distribution) and the structure of the interfacial zone somewhat obscure, however. Recent (9) Liu, X.; Farmerie, W.; Schuster, S.; Tan, W. Anal. Biochem. 2000, 283, 56. (10) Baerga-Ortiz, A.; Rezaie, A. R.; Komives, E. A. J. Mol. Biol. 2000, 296, 651. (11) Erickson, D.; Li, D. Langmuir 2002, 18, 8949. (12) Stroock; A. D.; Weck, M.; Chiu, D. T.; Huck, W. T. S.; Kenis, P. J. A.; Ismagilov, R. F.; Whitesides, G. M. Phys. Rev. Lett. 2000, 84, 3314. (13) Lyklema, J. Fundamentals of Colloid and Interface Science; Academic Press: London, 1991; Vol. II.

10.1021/la050191p CCC: $30.25 © 2005 American Chemical Society Published on Web 04/23/2005

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investigations involving molecular simulations are beginning to shed light on the matter.14 A related problem is that of charge transport along (charged) surfaces. For those situations in which an external electrical field exists along the surface (electrophoresis, electroosmosis, streaming potential), a correct evaluation of the zeta potential requires proper assessment of the conductivity of the system. Since the solution near the interface has an ionic composition different from that of the bulk solution, not only the bulk conductivity (denoted KB) needs to be taken into account but also an excess surface conductivity (denoted Kσ). The relative importance of surface conduction is measured by the Dukhin number,13 which is the ratio of these conductivities corrected by a characteristic length, R, representing a volume-to-surface ratio:

hydrodynamic thickness. Experiments seem to agree with this,20 and the method has been used to follow desorption of polymers.21 In the experiments mentioned so far, surface conduction could be neglected because they were carried out at a small Dukhin number. In narrow pores and capillaries, however, this simplification would not be justified and the contribution of surface conduction would have to be accounted for. An even more complicated case is that of a penetrable layer with internal charges. Some experimental data on hydrogels of poly(acrylamide) co-polymerized with sodium acrylate were recently reported.22 Surface conduction data were used to assess not only the salt concentration within the gel and, hence, the Donnan potential but also to get the zeta potential from the measured streaming potential. Key assumptions here were that the fluid velocity inside the gel was nonzero throughout the gel layer and that the ion mobility was proportional to the solvent volume fraction within the gel, which was always very close to unity. A more detailed analysis allowing for finite fluid velocity within the gel has been worked out by Duval.23 An interesting class of penetrable surface layers which received great attention during the past decade are polymer brushes. A polymer brush is a dense array of end-attached polymer chains on a surface. Applications of these materials comprise affinity biosensors,1 microanalytical devices,2 chemical microreactors,3 protein resistant surfaces,4,5 thin-film waveguides,24 optical data storage,25 and liquid displays.26 Theories describing the static structure of brushes, both for neutral and for charged polymers, are well developed, and most predictions have been experimentally verified in quite some detail.27 The influence of chain length, grafting density, and solvency on, e.g., the thickness (height) and the segment density distribution profile normal to the substrate are now relatively well understood. Much less is known, however, on the mobility of solvent and small solute species inside brushes. To probe such dynamic properties, electrokinetic experiments are attractive since they are both simple and informative. We therefore decided to measure the streaming potential and streaming current of some brush-covered surfaces with the aim to investigate not only zeta potentials but also surface conductivity. This latter property is particularly suited to give some insight into the mobility of small solutes inside a brush. Two kinds of brushes were studied, a neutral one (poly(ethylene oxide), PEO) and an anionic one (poly(acrylic acid), PAA). The neutral brush is expected to qualitatively have the same effect as a neutral adsorbed layer: all electrokinetic quantities are reduced because the fluid velocity near the substrate, where most of the mobile charge resides, is lowered. Conduction may still occur in such layers, but it is not known to what extent. The polyelectrolyte brush is a quite different case because, although there is a

Du )

Kσ RKB

(1)

For experiments carried out at very small Du, surface conduction may be safely neglected, but at high Du, surface conduction may be very important. In principle, a good predictive model should be able to connect the surface charge density to a measured electrokinetic quantity in an unambiguous manner. This requires not only a good model for the double layer itself but also for the mobility of solvent and ions along the surface due to both electrical and hydrodynamic forces. Recent models for smooth interfaces between dense, impenetrable substrates and electrolyte solutions come rather close to fulfilling this requirement.15,16 The situation is much less clear for partly draining interfaces where an interfacial zone exists in which solvent and ions can penetrate and which may sometimes itself be the carrier of charge. One can think of, e.g., surfaces covered with either neutral or charged adsorbed polymer layers (as often used to stabilize colloidal particles), but also of the outer coating (glycocalyx) of biological cells. For such surfaces, more elaborate models are needed to establish an adequate relation between the measured electrokinetic quantities and the properties of the interface. For example, the streaming potential of a charged surface is lowered when it is covered with a layer of an uncharged water-soluble polymer because the polymer layer, even when it is dilute, is capable of suppressing shear to a large extent.17 The effect of the layer can be described in terms of an outward shift of the plane of shear, an idea already used three decades ago to determine thicknesses of adsorbed layers.18 For nonionized layers of a given thickness, the resulting effect varies with the ionic strength. This has been discussed by Cohen Stuart et al.19 For surfaces covered with an adsorbed homopolymer, using theoretically calculated polymer density profiles, one can rather generally argue that, in the limit of low electrolyte concentration, the Debye length would be the adequate yardstick to measure the thickness of the neutral adsorbed layers via its effect of the measured streaming potential. The thickness thus measured could be identified as the (14) Lyklema, J.; Rovillard, S.; de Coninck, J. Langmuir 1998, 14, 243. (15) Lo¨bbus, M.; Sonnefeld, J.; van Leeuwen, H. P.; Vogelsberger, W.; Lyklema, J. J. Colloid Interface Sci. 2000, 229, 174. (16) Lyklema, J. J. Phys. Condens. Matter 2001, 13, 5027. (17) Cohen Stuart, M. A.; Waaijen, F. H. W. H.; Cosgrove, T.; Vincent, B.; Crowley, T. L. Macromolecules 1984, 17, 1825. (18) Koopal, L. K.; Lyklema, J. Faraday Discuss. Chem. Soc. 1975, 59, 230. (19) Cohen Stuart, M. A.; Waaijen, F. H. W. H.; Dukhin, S. S. Colloid Polym. Sci. 1984, 262, 423.

(20) Cohen Stuart, M. A.; Mulder, J. W. Colloids Surf. 1985, 15, 49. (21) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1992, 25, 5416. (22) Yezek, L. P.; van Leeuwen, H. P. J. Colloid Interface Sci. 2004, 278, 243. (23) Duval, J.; van Leeuwen, H. P. Langmuir 2004, 20, 10324. (24) Mathy, A.; Mathauer, K.; Wegner, G.; Bubeck, C. Thin Solid Films 1992, 215, 98. (25) Sawodny, M.; Schmidt, A.; Urban, C.; Ringsdorf, H.; Knoll, W. Makromol. Chem., Makromol. Symp. 1991, 46, 217. (26) Machida, S.; Urano, T. I.; Sano, K.; Kawata, Y.; Sunohara, K.; Sasaki, H.; Yoshiki, M.; Mori, Y. Langmuir 1995, 11, 4838. Ulman, A. An Introduction to Ultrathin Organic Films Organic Films: From Langmuir-Blogett to Self-assembly; Academic Press: Boston, 1998. (27) Currie, E. P. K.; Norde, W.; Cohen Stuart, M. A. Adv. Colloid Interface Sci. 2003, 100-102, 205.

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significant charge at the periphery of the brush where the fluid velocity becomes appreciable (so that the streaming current is large), there is an even larger amount of mobile counterions inside the brush, so that one expects very high surface conduction, unless the counterions are severely restricted in mobility. One is therefore inclined to expect moderate streaming potentials also in this case but for a different reason, namely a substantial back current caused by the high surface conduction. PEO and PAA brushes were extensively studied by Currie et al.28,29 These authors developed a method to prepare brushes under full control of both chain length and grafting density by (i) using preformed polymers, (ii) employing a Langmuir-Blodgett technique to deposit the copolymer layer, and (iii) applying a heat treatment to permanently anchor the polymers. They reported results on brush thickness, bimodal brushes, density profiles, and charge-induced swelling. Hence, we can use their results as a starting point. The technique of choice to analyze the electrokinetic surface properties is the narrow slit method introduced by Werner et al.30,31 Since this method allows measuring both streaming potentials and streaming currents on parallel plates by using a very narrow and variable gap width (i.e., a high and variable Du), the surface conductivity and the zeta potential can be very accurately determined. Experimental Section Materials. Substrates. The grafted polymer layers for the electrokinetic measurements were prepared on polished glass carriers (20 × 10 × 3 mm3), which were purchased from Berliner Glas KGaA Herbert Kubatz GmbH and Co., Berlin, Germany. These glass carriers were cleaned by UV-ozone treatment (30 min) and subsequently covered with a solution (1 g/L) of vinyl-(PS)200 (PS ) poly(styrene)) in chloroform. The chloroform was evaporated in a stream of nitrogen after which the carriers were placed overnight in an oven under vacuum and at 150 °C. By this treatment, the (PS)200 is chemically attached to the glass surface.32 Excess polymer was removed by thoroughly washing with chloroform, whereafter the surfaces were dried in a stream of nitrogen. This modification resulted in a stable PS coating on the surface having a thickness of 2-3 nm as measured by ellipsometry. Poly(Acrylic Acid)- and Poly(Ethylene Oxide) Brushes. Brushes were prepared by means of a Langmuir-Blodgett method described by Currie et al., as described in refs 28 and 29. Monolayers of (PS)34-(PAA)368 and (PS)38-(PEO)700 block copolymers at an air/water interface were prepared in a Langmuir trough, and pressure-area isotherms were determined. At an interfacial area of 10 nm2 per polymer molecule the PS-coated glass carriers were dipped (air f water) and retracted (water f air) through the (PS)34-(PAA)368 or (PS)38-(PEO)700 monolayers, respectively, at a speed of 1 mm2/s, while keeping the interfacial pressure and, hence, the area per polymer molecule in the monolayer constant. Thus, a single layer of (PS)34-(PAA)368 or (PS)38-(PEO)700 was transferred from the monolayer at the air/ water interface onto the PS-coated carriers. Usually, a transfer ratio of unity was achieved, resulting in a polymer grafting density at the carrier that is the same as the one selected at the air/water interface, i.e., 10 nm2 per polymer chain. The samples were dried (28) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Macromolecules 1999, 32, 9041. Currie, E. P. K.; van der Gucht, J.; Borisov, O. V.; Cohen Stuart, M. A. Pure Appl. Chem. 1999, 71, 1227. (29) Currie, E. P. K.; Sieval, A. B.; Fleer, G. J.; Cohen Stuart, M. A. Langmuir 2000, 16, 8324. Currie, E. P. K.; Sieval, A. B.; Avena, M.; Zuilhof, H.; Sudho¨lter, E. J. R.; Cohen Stuart, M. A. Langmuir 1999, 15, 7116. (30) Ko¨rber, H.; Werner, C.; Jacobasch, H.-J. Patent DE 197 49 429.3, December 11, 1997. (31) Werner, C.; Ko¨rber, H.; Zimmermann, R.; Dukhin, S.; Jacobasch, H.-J. J. Colloid Interface Sci. 1998, 208, 329. (32) Maas, J. H.; Cohen Stuart, M. A.; Sieval, A. B.; Zuilhof, H.; Sudholter, E. J. R. Thin Solid Films 2003, 426, 135.

Zimmermann et al. and heated for 5 min at 95 °C (which is just beyond the glass temperature of PS); this treatment ensures that the PS block of the copolymer fuses with the PS coating and is essentially irreversibly attached after cooling to room temperature. Continuous washing with water did not remove any (PS)34-(PAA)368 and (PS)38-(PEO)700 from the surface, as probed by optical reflectometry under flowing water. Thus, the PS indeed firmly ‘anchors’ the (PAA)368 and (PEO)700 chains (like ‘buoys’) on the surface. It has been ascertained that at the chosen grafted chain density of 0.1 nm-2 the (PAA)368 and (PEO)700 layers adopt a brush conformation.33 Aqueous Solutions. The solutions for the electrokinetic and optical measurements were prepared from vacuum-degassed Milli-Q water by addition of 0.1 M potassium chloride, potassium hydroxide, and hydrochloric acid solutions (Bernd Kraft GmbH, Duisburg-Neumu¨hl, Germany). Methods. Electrokinetic Measurements. Electrokinetic measurements were carried out with the recently developed microslit electrokinetic setup30,31 at 22 °C. If one accepts the notion of an effective plane of shear, the zeta potential, ζ, can be evaluated from the streaming current data by use of the classical Smoluchowski equation:

ζ(IS) )

ηL dIS 0rbh dp

(2)

where IS is the streaming current, p is the pressure drop across the streaming channel, η is the dynamic viscosity of the fluid, 0 is the permittivity of vacuum, and r is the (relative) dielectric constant of the fluid. L and b are the length and width of the channel walls, respectively, and h is the wall/wall separation distance. To determine the surface conductivity of the brush-carrying substrates, streaming potential, US, and streaming current, IS, were measured at different separation distances of the parallel sample carriers. The surface conductivity was derived from the ratio of streaming current and streaming potential (evaluated at equal pressure) by a linear regression using eq 3:31

dIS/dp L KB ) h + Kσ dUS/dp 2b 2

(3)

Results and Discussion Two variants of well-defined polymer brush layers basing on a common design principle, i.e., on the formation, transfer, and annealing of Langmuir-Blodgett films of structurally related amphiphilic diblock copolymers, were for the first time analyzed in aqueous solutions by electrokinetic experiments. The copolymers, PS-PAA and PS-PEO and the resulting layers are similar in containing a highly polar block but different with respect to ionization in aqueous environments: While PAA is a polyelectrolyte, PEO will not undergo dissociation and hardly interacts with dissolved ions in general. Accordingly, the interfacial charging of the brush layers may be considered as two extreme cases, as schematically shown in Figure 1. The purpose of this study was to derive quantitative information on the interfacial ionization and ion mobility with the help of electrokinetic experiments. The distinct differences in the localization and mechanism of charging (Figure 1) had to be considered in the choice of the evaluation strategies employed. Poly(Acrylic Acid) Layers. The pH-dependent charging of the PAA layers was studied by streaming current experiments in 10-3 M KCl solutions. Since the swollen polymer chains themselves dissociate and create an ionized meshwork in part penetrated by the flowing solution, the determination of a discrete shear plane potential is certainly questionable and we restrict here reporting on (33) Currie, E. P. K.; Leermakers, F. A. M.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1999, 32, 487.

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Figure 1. Similarities and differences of the analyzed polymer layers: Two variants of highly polar brushlike polymer chains are assembled using a similar anchoring mechanism. PS-PAA layers contain a high frequency of intrinsic ionizable (carboxylic acid) moieties in the PAA block exposed to the environment (left). PS-PEO does not contain any dissociable functions and can only be charged through preferential electrolyte ion (hydroxide) adsorption from solution (right). The latter process is assumed to occur at PS surface segments underneath the PEO brushes.

Figure 2. pH dependence of the streaming current vs pressure gradient (dIS/dp) for the PAA layer in a 10-3 M KCl solution.

and evaluating streaming current and surface conductivity data. The dIS/dp vs pH plot and the position of the isoelectric point at pH ) 2.1 (Figure 2) indicate that the surface charge originates from the dissociation of the carboxylic acid groups of the PAA chains. Above the isoelectric point (pH > 2.1), the magnitude of the negative streaming current increases with the degree of deprotonation of the carboxylic acid groups at increasing pH values until a plateau is reached in the basic region corresponding to full dissociation of the carboxylic acid. To quantify the accumulation and distribution of mobile charge carriers at the interface, the surface conductivity was determined in a 10-3 M KCl solution at pH ) 9.0. From (dIS/dp)/(dUS/dp) as a function of h (eq 3), a value of 66.7 nS was obtained. As expected, the experimentally determined surface conductivity of the PAA brushes is very high at complete dissociation and must be due to the numerous counterions that are accumulated inside (Kσ,i) and outside (Kσ,d) of the brush:

Kσ ) Kσ,i + Kσ,d

(4)

The ion and potential distribution in the brush can be further analyzed by a model developed by Ohshima34 and specified by Dukhin et al.35 According to this model, a polyelectrolyte layer is characterized by the Donnan potential, ΨD, the potential value in the inner volume of (34) Ohshima, H. Colloids Surf., A 1995, 103, 249. (35) Dukhin, S. S.; Zimmermann, R.; Werner, C. J. Colloid Interface Sci. 2004, 274, 309.

Figure 3. Ion Distribution (a) and potential distribution (b) near a surface covered with a negatively charged polyelectrolyte layer.34

the polyelectrolyte brush, and by the surface potential, Ψ0, attributed to the outermost edge of the polymer chains, respectively (Figure 3). For the case of complete dissociation, ΨD can be calculated from the fixed charge density in the layer and the electrolyte concentration of the adjacent solution:

ΨD )

(

)

zbsN RT asinh zF 2zcdNA

(5)

where R is the gas constant, T the absolute temperature, z the valence of the ions, F the Faraday constant, zb the valence of the fixed charged groups, s the number of grafted chains per meter squared, N the number of charged groups per polymer chain, c the solution concentration, d the layer thickness, and NA the Avogadro number. Subsequently, the surface potential, Ψ0, can be obtained using the following equation:

Ψ 0 ) ΨD -

( )

zFΨD RT tanh zF 2RT

(6)

With N ) 368 and d ) 40 nm29, a Donnan potential of

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Zimmermann et al.

-186 mV and a surface potential of -161 mV were calculated for the brush in the case of complete dissociation. The contribution of the diffuse layer charge “outside” the brush layerscharacterized by the potential Ψ0sto the experimentally determined surface conductivity can be evaluated according to the Bikerman equation:36

Kσ,d )

[

(

)

3m+ 2z2F2c D+(e-zFΨ0/2RT - 1) 1 + 2 + RTκ z 3mzFΨ0/2RT D-(e - 1) 1 + 2 z

(

)]

Kσ,i esN - Kσ,d m /u0

u ) FS(f) u0

(

(7)

(8)

where e is the elementary charge and Kσ,d m is the contribution of the diffuse layer to Kσ,d caused by the movement of the ions with respect to the liquid.35 Assuming that for the case pH ) 9 all 368 acrylic acid units in a chain are deprotonated, we find u ) 1.1 × 10-8 m2 V-1 s-1. This may be compared with the mobility of potassium ions in dilute electrolyte solution for which one has (from the tabulated equivalent conductance λ of about 74 S cm2 mol-1) u0 ) λ/F ) 7.7 × 10-8 m2 V-1 s-1. Hence, the brush is very conductive, but the mobility of individual ions within the layer is no more than about 14% of their value in bulk electrolyte solution. The drag exerted by the polymers on the ions moving in the polymer layer can be modeled in various ways.41-49 One possibility we consider to be adequate was suggested by Brady46 who introduced the idea that the mobility in a polymer network can be written as the product of factors F and S, where F accounts for hydrodynamic effects and (36) Bikerman, J. J. Kolloid Z. 1935, 72, 100. (37) Zimmermann, R.; Dukhin, S. S.; Werner, C. J. Phys. Chem. B 2001, 105, 8544. (38) Werner, C.; Ko¨nig, U.; Augsburg, A.; Arnhold, C.; Ko¨rber, H.; Zimmermann, R.; Jacobasch, H.-J. Colloids Surf., A 1999, 159, 519. (39) Chan, Y. H. M.; Schweiss, R.; Werner, C.; Grunze, M. Langmuir 2003, 19, 7380. (40) Dicke, C.; Ha¨hner, G. J. Phys. Chem. B 2002, 106, 4450. (41) Langdon, A. G.; Thomas, H. C. J. Phys. Chem. 1971, 75, 1821. (42) Ba´ra´ny, S.; Dukhin, S. Colloids Surf., A 2002, 192, 307. (43) Minor, M.; van Leeuwen, H. P.; Lyklema, H. Langmuir 1999, 15, 6677. (44) Solomentsev, Y. E.; Anderson, J. L. Phys. Fluids 1996, 8, 1119. (45) Tong, J.; Anderson, J. L. Biophys. J. 1996, 70, 1505. (46) Brady, J. F. Hindered diffusion. In Extended Abstracts, American Institute of Chemical Engineers, Annual Meeting; American Institute of Chemical Engineers: San Francisco, 1994; p 320. (47) Phillips, R. J. Biophys. J. 2000, 79, 3350. (48) Brinkman, H. C. Appl. Sci. Res. 1947, A1, 27. (49) Johnson, E. M.; Berk, D. A.; Jain, R. K.; Deen, W. M. Biophys. J. 1996, 70, 1017.

(9)

In eq 9, f depends on the polymer volume fraction, φ, the radii of the ions, aI, and the polymer chains, aP:

f) 1+

where m( ) (RT/F)2(20r/3ηD() describes the relative contribution of the electro-osmosis to Kσ,d, κ-1 is the Debye length, and D( are the diffusivities of the ions. Using eq 7 and Ψ0 ) -161 mV, we obtain Κσ,d ) 4.6 nS. In comparison with the experimentally determined surface conductivity of 66.7 nS, this is about 7%, i.e., the vast majority of counterions is located within the brush. If we apply the classical Smoluchowski eq 2 for the evaluation of the streaming current data (Figure 2), a zeta potential of about -60 mV is obtained for pH ) 9.0. This corresponds to less than 1% of the countercharge. How mobile are the ions inside the PAA brush? If the ions outside the brush can move in an electrical field with the mobility u0, the mobility, u, of ions in the brush can be simply estimated from the charge distribution as follows

u)

S for steric or tortuosity effects:47

)

aI 2 φ aP

(10)

The factor F can be calculated using the Brinkman equation:48

F)

1 1 + aI/xkD + (1/9)a2I /kD

(11)

where kD is the Darcy permeability. To include the obstacle (tortuosity) effect of the polymer network on diffusing solutes, Johnson at al. proposed for the steric factor S(f):49

S(f) ) e-084f

1.09

(12)

For the PAA brushes we are considering here, the volume fraction of polymer, φ, is given by φ ) Nsνmon/d, where νmon is the volume of a monomer unit, about 0.26 nm3. With N ) 368, s ) 0.1 nm-2 and d ) 40 nm29 we find that φ is about 0.24 at pH ) 9.0. With u/u0 ) 0.14, aI ) 0.13 nm (potassium ion radius), and aP ≈ xNνmon/(πd) ) 0.9 nm we obtain for the Darcy permeability kD ) 1.5 × 10-3 nm2. Note that the model used for the estimation of kD does not account for several factors as electrostatic ion brush interactions or Brownian motion. Consequently, the value estimated for kD has to be considered as the lower limit of this parameter. Poly(Ethylene Oxide) Layers. In contrast to the grafted PAA, the grafted PEO (of 700 monomer units) showssindependent of the solution pHsvery small negative streaming potentials and streaming currents in 10-3 M KCl solutions. Since the polymer chains have no chemically bound charges, the small negative charge detected by the electrokinetic measurements is either caused by ions physisorbed to the PEO chains or by ions adhering to the underlying PS substrate. To further unravel the formation and compensation of the charge located at the interface, elektrokinetic measurements at pH 6 and as a function of the KCl solution concentration were performed on the bare PS substrate, as well as on PEO brushes. The corresponding results, in terms of zeta potential, are given in Figure 4. First, we notice that bare PS, although it has no chemically bound charges, has a significant negative zeta potential, which decreases with increasing ionic strength. Many other apolar polymer films behave likewise. It is quite generally accepted that the negative surface charge in these cases is caused by unsymmetrical ion adsorption, i.e., by the preferential adsorption of one ion type.37-40 In a recent study of the authors,37 the variation of the solution concentration of HCl, KOH, and KCl, respectively, revealed the impact of the different dissolved ions: The strongest preferential adsorption was observed for the hydroxide ions which predominate over the adsorption of the hydronium ions. No effect of preferential adsorption was found for the potassium and chloride ions. The density of the preferentially adsorbed ions, NI, can be estimated from surface conductivity data according to ref 37. Using this approach NI ) 2.5 × 1016 m-2 was obtained for PS in

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Figure 4. Zeta potential vs KCl solution concentration for the substrate (PS) both with (circles) and without (diamonds) grafted PEO, pH ) 6.0.

Figure 5. Position of the shear plane, δe, versus lg(κ-1/nm) for the PEO layer.

10-5 M KCl solution (Kσ ) 1.17 nS). The decrease of the absolute zeta potential values with increasing (KCl) solution concentration is a well-known feature to be attributed to the “compression” of the double layer, i.e., at higher ionic strength of the solution a higher fraction of surface charge is compensated within the hydrodynamic immobile layer ‘behind’ the slipping plane. The zeta potential of the grafted PEO is also negative, but in comparison to the bare substrate (PS), the absolute zeta potential values of the grafted PEO are significantly lower. Since (i) data on the swelling of PEO in aqueous solution, at these low ionic strengths, give no indication whatsoever of ion binding on the polymer, (ii) the area occupied by an anchor of the PEO chains is only about 0.01 nm2, and (iii) the total ion density at the PS substrate is in the same magnitude as the packing density of the PEO brushes, it seems most likely that the charge detected by the streaming current measurements is still caused by the excess adsorption of hydroxyl ions at the substrate. Because the penetration of the hydrodynamic (shear) field into the brush is strongly impeded, one expects that a small fraction of the counterions, which decreases with increasing ionic strength, can contribute to the zeta potential. This would imply that the zeta potential of the PEO layer strongly decreases when the KCl solution concentration is raised and that it eventually becomes very small when the brush thickness substantially exceeds the Debye length. This is qualitatively corroborated by the data. Furthermore, a surface conductivity of 0.86 nS in a 10-5 M KCl solution was found for the brush, which is slightly lower than for the PS substrate. Since there is only a small difference between both conductivities and ζ drops to about half the bare value when we have a brush on the surface, the hypothesis about the ion adsorption at the PS is also supported by the Kσ data. If we apply the simplified picture of a shear plane located at δe, separating zones of completely immobilized counterions (distances below δe), and of unhindered flow (beyond δe), the value of δe must satisfy the following equation suggested by Cohen Stuart and Mulder:20

( )

tanh

( )

zeζ0 -κδe zeζ ) tanh e 4kT 4kT

(13)

Here, δe is the shift in position of the slipping plane (originally at δ0), ζ and ζ0 are the zeta potentials measured in the presence (slipping plane at δ0 + δe) and in the absence (slipping plane at δ0) of the polymer, k is the Boltzmann

constant, and κ-1 is the Debye length. For partly draining polymer layers, as considered in this paper, there is of course no sharp slipping plane, but one can interpret eq 13 as a defintion of the effective position of that plane. On the basis of a simple hydrodynamic model, Cohen Stuart et al.20 showed that δe, as defined by eq 13, strongly depends on the ionic strength, whereas, at low ionic strength, δe tends to a limiting value which may be identified with the ‘hydrodynamic thickness’, δh, that would be obtained by considering the solvent velocity profile rather than the ionic velocity profile. Results obtained for δe derived from the data in Figure 4 are given in Figure 5. An increase of δe with increasing Debye length was found for the grafted PEO layers, qualitatively similar to the shift observed by Cohen Stuart et al.20 for simple adsorbed layers. At κ-1 ≈ 30 nm (cKCl ) 10-4 mol/l), δe levels off; the hydrodynamic thickness of the PEO layer can be estimated from this part of the curve to be about 40 nm. This value compares well with that derived from neutron reflectivity measurements on a similar PEO brush50 and with the theoretical value for the equilibrium thickness of a neutral brush assuming a parabolic density distribution in the PEO layer.33 Conclusions Surfaces carrying PAA or PEO brushes immersed in aqueous KCl solutions were characterized by means of microslit electrokinetic experiments. The obtained streaming potential, streaming current, and surface conductivity data were further evaluated according to different strategies to describe the interfacial electrical charging by means of Donnan potential, surface potential, and zeta potential, respectively, and to discuss the localization and mobility of electrolyte ions within the brush layers. Charge formation at the PAA brushes was confirmed to be caused by the dissociation of carboxylic acid groups. The surface conductivity of the PAA brush is enormous in the case of complete dissociation. However, under the same conditions, the diffuse layer charge “outside” the polymer brushes reflected by the magnitude of the surface potential contributed only to about 7% to the surface conductivity which indicates that the hydrodynamically immobile layer contains many ions capable of contributing to conduction. The mobility of the ions in the PAA layer was estimated from the grafting density and the surface conductivity data to be as low as 14% of the bulk value. (50) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Physica B 2000, 283, 17.

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The electrokinetic measurements performed at the PEO layers showed very low zeta potentials whenever the thickness of the double layer was smaller than the thickness of the brush. Clearly, the charge of the underlying substrate is effectively screened by the polymer chains and no nonelectrostatically attracted ions are taken up in the brush. This is quantitatively corroborated by surface conductivity data obtained for both the PEO brush and the PS substrate. The thickness of the hydrodynamic

Zimmermann et al.

immobile layer in the presence of the PEO was estimated from zeta potential data obtained for the substrate and for the polymer film. The electrokinetically determined value compares well with that derived from neutron reflectivity measurements on a similar PEO brush28 and with the theoretical value for the equilibrium thickness assuming a parabolic density distribution in the PEO layer.29 LA050191P