pubs.acs.org/Langmuir © 2009 American Chemical Society
Electrokinetics of Diffuse Soft Interfaces. IV. Analysis of Streaming Current Measurements at Thermoresponsive Thin Films Jer^ome F. L. Duval,*,† Ralf Zimmermann,*,‡ Ana L. Cordeiro,‡ Nelly Rein,‡ and Carsten Werner‡,§ †
Laboratoire Environnement et Min eralurgie, Nancy-Universit e, CNRS UMR 7569, 15 avenue du Charmois, B.P. 40, 54501 Vandoeuvre-l es-Nancy, cedex France, ‡Leibniz Institute of Polymer Research Dresden, Max Bergmann Center of Biomaterials Dresden, Hohe Strasse 6, 01069 Dresden, Germany, and §Institute of Biomaterials and Biomedical Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada, M5S 3G8 Received April 4, 2009. Revised Manuscript Received May 10, 2009
Streaming current measurements were performed on poly(N-isopropylacrylamide)-co-N-(1-phenylethyl) acrylamide [P(NIPAAm-co-PEAAm)] thermoresponsive thin films above and below the transition temperature of the polymer (i.e., at 22 and 4 C, respectively). Electrokinetic measurements (ionic strength 0.01-10 mM KCl, pH 2.5-9.5 in 1 mM KCl) revealed that the charging of the polymer/aqueous solution interface is determined by unsymmetrical adsorption of hydroxide and hydronium ions onto the Teflon AF substrate that supports the hydrogel film. The magnitude of the streaming current significantly decreased with decreasing temperature, that is, when the hydrogel was swelling. The pHand ionic strength-dependent data for unswollen and swollen films were interpreted on the basis of the here-reported general theory for the electrokinetics of diffuse soft gel layers. The formalism based on the Debye-Brinkman equation for hydrodynamics and the nonlinear Poisson-Boltzmann equation for electrostatics extends previous theoretical studies by considering the most general situation of a charged gel layer supported by a charged rigid surface. Full analytical expression is provided for the streaming current in the limit of homogeneous distribution of segments under low potential conditions. Numerical analysis of the governing transport and electrostatic equations allows for the computation of streaming current for cases where analytical developments are not possible. The theory successfully reproduces the electrokinetic data for the P(NIPAAm-co-PEAAm) copolymer film at 22 and 4 C over the whole range of pH and ionic strength examined. It is found that the 3-fold increase of the hydrogel film thickness with decreasing temperature from 22 to 4 C (i.e., from 23 to 70 nm as measured by ellipsometry), is in line with homogeneous swelling and an increase of the hydrodynamic penetration length (1/λo) by a factor of ∼1.6. Additionally, the hydrodynamic thicknesses (δH) of the swollen and unswollen hydrogels are evaluated in terms of their respective hydrodynamic penetration length and electrosurface characteristics of the supporting Teflon AF surface.
1. Introduction Hard and soft polymer coatings are used in widespread applications such as biosensors,1 protein-resistant surfaces,2 tissue engineering scaffolds,3 antifouling coatings,4 microfluidic systems,5 liquid displays,6 and drug delivery.7 Within the field of polymer surface engineering, stimuli-responsive polymers are of high interest as the properties of the polymer can be changed by an external trigger.7,8 The most studied stimuli-responsive polymer is poly(N-isopropylacrylamide) (PNIPAAm).9 PNIPAAm undergoes a sharp temperature-induced coil-to-globule transition at 32 C in water. The transition temperature of PNIPAAm can *Corresponding author. E-mail:
[email protected]; tel: 00 33 3 83 59 62 63; fax: 00 33 3 83 59 62 55 (J.F.L.D.). E-mail: zimmermn@ ipfdd.de; tel: 00 49 351 4658 258; fax: 00 49 351 4658 533 (R.Z.). Both authors equally contributed to this work. (1) Ding, Z.; Fong, R. B.; Long, C. J.; Stayton, P. S.; Hoffman, A. S. Nature 2001, 411, 59–62. (2) Uyama, Y.; Kato, K.; Ikada, Y. Adv. Polym. Sci. 1998, 137, 1–39. (3) Pompe, T.; Markowski, M.; Werner, C. Tissue Eng. 2004, 10, 841–848. (4) Krishnan, S.; Weinman, C.; Ober, C. J. Mater. Chem. 2008, 18, 3405–3413. (5) Zhang, Y.; Kato, S.; Anazawa, T. Sens. Actuators, B 2008, 129, 481–486. (6) Machida, S.; Urano, T. I.; Sano, K.; Kawata, Y.; Sunohara, K.; Sasaki, H.; Yoshiki, M.; Mori, Y. Langmuir 1995, 11, 4838–4843. (7) Schmaljohann, D. Adv. Drug Delivery Rev. 2006, 58, 1655–1670. (8) de las Heras Alarcon, C.; Pennadam, S.; Alexander, C. Chem. Soc. Rev. 2005, 34, 276–285. (9) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163–249. (10) Taylor, L. D.; Cerankowski, L. D. J. Polym. Sci., Polym. Chem. Ed. 1975, 13, 2551–2570.
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be tuned by various means via, e.g., copolymerization with hydrophilic or hydrophobic comonomers.10-12 The structural transition induced by variation of temperature above and below the lower critical solution temperature (LCST) can be explained through the critical balance between hydrogen bonding and hydrophobic dehydration.9 In many of the aforementioned applications, polymer films supported by a rigid substrate are in contact with aqueous solutions.1-7 The formation of an interfacial electric charge and the occurrence of ion specific phenomena then often determine the electrostatic properties of the polymer/solution interface. Interfacial charge was found to be relevant for a number of fundamental phenomena such as wetting,13 adsorption,14 and adhesion,15 as well as ion binding and ion condensation.16,17 It is now widely recognized that electrokinetic measurements are useful for investigating charge formation processes at interfaces between polymers and aqueous (11) Bae, Y. H.; Okano, T.; Kim, S. W. J. Polym. Sci., Part B: Polym. Phys. 1990, 28, 923–936. (12) Feil, H.; Bae, Y. H.; Feijen, J.; Kim, S. W. Macromolecules 1993, 26, 2496– 2500. (13) Grundke, K.; Jacobasch, H.-J.; Simon, F.; Schneider, S. J. Adhes. Sci. Technol. 1995, 9, 327–350. (14) Zimmermann, R.; Osaki, T.; Gauglitz, G.; Werner, C. Biointerphases 2007, 2, 159–164. (15) Schmitt, F.-J. Habilitation Thesis, Dresden University of Technology, 2002. (16) Lyklema, J. Colloids Surf., A 2006, 291, 3–12. (17) Dukhin, S. S.; Zimmermann, R.; Werner, C. J. Phys. Chem. B 2007, 111, 979–981.
Published on Web 06/11/2009
DOI: 10.1021/la9011907
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solutions.18,19 The measurements are usually interpreted in terms of electric double layer (EDL) models. In principle, an appropriate EDL model should be able to connect the electrostatic properties of the investigated system to a measured electrokinetic quantity in an unambiguous manner. This requires not only a relevant representation for the EDL itself, but also for the hydrodynamic flow and ion mobility along the surface. Formalisms for the interpretation of electrokinetic measurements at hard (impermeable) surfaces were established many years ago,18,20 while the community has showed interest in the electrokinetics of soft (permeable) surfaces during the past decades.21-40 Surprisingly, the number of formalisms pertaining to electrokinetic effects at macroscopic soft surfaces is very limited as compared to that found for, e.g., the electrophoresis of soft colloidal particles.28-37 In their pioneering work on the electrokinetics of planar polymer-coated surfaces,21 Dukhin et al. investigated the effect on electrokinetic phenomena of an adsorbed neutral polymer phase where segments are evenly distributed. Donath and Voigth developed a model for the streaming potential/streaming current of hard surfaces covered with a charged, ion-permeable polymer layer.23 Their work mainly stressed the importance of enhanced conductivity within the charged polymer layers on the resulting electrokinetic response. In reference 24, Ohshima and Kondo reported a model for the streaming potential/streaming current and electroosmotic flow between two parallel plates covered with ion-permeable polymer layers. Their calculation is strictly valid within the Debye-H€ uckel approximation and introduces two relevant parameters: the fixed volume charge density of the layer and the penetration length of solvent flow within the layer. Starov and Solomentsev further reported an analysis of the impact of specific interactions between ions and hydrogels on electrokinetic phenomena.25,26 A different approach was suggested by Dukhin et al. for the characterization of soft polymer layers.27 The proposed methodology is essentially based on surface conductivity measurements and enables the evaluation of the charge
V.; Gonzalez-Caballero, F.; Hunter, R. J.; Koopal, L. K.; (18) Delgado, A. Lyklema, J. J. Colloid Interface Sci. 2007, 309, 194–224. (19) Zimmermann, R.; Osaki, T.; Schweiss, R.; Werner, C. Microfluid Nanofluid 2006, 2, 367–379. (20) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: London, 1981. (21) Dukhin, S. S.; Semenikkin, N. M.; Bychko, W. A. 1979. Surface forces in thin layers, USSR, Acad. Science, Nauka, Moskow, 85-93. (22) Cohen Stuart, M. A.; Waajen, F. H. W. H.; Dukhin, S. S. Colloid Polym. Sci. 1984, 262, 423–426. (23) Donath, E.; Voigth, A. J. Colloid Interface Sci. 1986, 109, 122–139. (24) Ohshima, H.; Kondo, T. J. Colloid Interface Sci. 1990, 135, 443–448. (25) Starov, V. M.; Solomentsev, Y. E. J. Colloid Interface Sci. 1993, 158, 159– 165. (26) Starov, V. M.; Solomentsev, Y. E. J. Colloid Interface Sci. 1990, 158, 166– 170. (27) Dukhin, S. S.; Zimmermann, R.; Werner, C. J. Colloid Interface Sci. 2004, 274, 309–318. (28) Jones, S. I. J. Colloid Interface Sci. 1979, 68, 451–461. (29) Wunderlich, R. W. J. Colloid Interface Sci. 1982, 88, 385–397. (30) Ohshima, H. Colloids Surf., A 1995, 103, 249–255. (31) Ohshima, H. Adv. Colloid Interface Sci. 1995, 62, 189–235. (32) Ohshima, H. J. Colloid Interface Sci. 2001, 233, 142–152. (33) Garcia-Salinas, M. J.; Romero-Cani, M. S.; de las Nieves, F. J. J. Colloid Interface Sci. 2001, 241, 280–285. (34) Cohen, J. A.; Khorosheva, V. A. Colloids Surf., A 2001, 195, 113–127. (35) Hill, J. R.; Saville, D. A.; Russel, W. B. J. Colloid Interface Sci. 2003, 258, 56–74. (36) Ogawa, K.; Nakayama, A; Kokufuta, E. J. Phys. Chem. B. 2003, 107, 8223– 8227. (37) Duval, J. F. L.; Ohshima, H. Langmuir 2006, 22, 3533–3546. (38) Duval, J. F. L.; van Leeuwen, H. P. Langmuir 2004, 20, 10324–10336. (39) Duval, J. F. L. Langmuir 2005, 21, 3247–3258. (40) Yezek, L. P.; Duval, J. F. L.; van Leeuwen, H. P. Langmuir 2005, 21, 6220– 6227.
10692 DOI: 10.1021/la9011907
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carried by the layer at any degree of ionization for the functional groups distributed within the polymer layer. The models listed above were essentially developed for charged hydrogel layers with homogeneous distribution of polymer segments. This basically implies that the transition between the charged layer and the outer electrolyte solution is sharp and stepfunction like, and that the gel layer is defined by a constant density of polymer segments. In the first two articles of this series,38,39 Duval and co-workers relaxed this sometimes restricting representation of the gel interface. They proposed a formalism for the electrokinetics of charged diffuse soft hydrogels in which the polymer segment density distribution gradually decays from the bulk value in the gel to zero in the bulk electrolyte solution. The formalism was developed in the thin EDL limit where Donnan partitioning across the gel holds, and was further applied to charged gel layers supported by uncharged rigid surfaces. In the third article of this series,40 the theoretical approach was supported by experimental data collected for macroscopic crosslinked polyacrylamide-co-sodium acrylate layers, which experienced interfacial swelling upon lowering ionic strength. An extension of the above electrokinetic model is reported here by tackling the most general situation where a diffuse charged gel layer is supported by a charged rigid surface. The theory does not suffer from any restrictions on the magnitude of (i) the volume charge density of the gel, (ii) the electrokinetic potential of the supporting rigid surface, and (iii) the thickness of the gel layer (nanometer to micrometer range). It further allows one to introduce any diffuse distribution of the polymer segment density from the charged supporting surface to the outer electrolyte medium. The analytical expression for the streaming current is given within the Debye-H€uckel approximation in the practical limit where the thickness of the gel is well below the transversal dimension of the cell, and for a homogeneous distribution of polymer segments within the gel. In addition, explicit analytical expressions for the electrokinetic and hydrodynamic thickness of the gel are provided for the first time as a function of the relevant electrostatic and hydrodynamic parameters. In order to evaluate the fundaments of this formalism, streaming current measurements were performed at a charged Teflon AF surface coated with a poly(N-isopropylacrylamide)-co-N-(1-phenylethyl) acrylamide [P(NIPAAm-co-PEAAm)] thermoresponsive hydrogel film. Measurements were carried out over a large range of ionic strength and pH values (ionic strength 0.0110 mM KCl, pH 2.5-9.5 in 1 mM KCl) at temperatures above and below the LCST of the polymer, i.e., when the gel layer was collapsed and swollen, respectively. The paper is organized as follows: In a first part, the theory is developed, and the numerical treatment of the governing electrohydrodynamic equations is given and further supported by an analytical expression for the streaming current under conditions of homogeneous distribution of polymer segments within the Debye-H€uckel approximation. The typical electrokinetic properties of diffuse gel layers supported by charged rigid substrates are then discussed on the basis of a set of illustrative simulations. In the second part, streaming current data for P(NIPAAm-co-PEAAm) are quantitatively analyzed using the formalism discussed in the first section.
2. Theory We consider the electrokinetic properties of a soft (permeable) charged hydrogel layer supported by a rigid hard surface of given electrokinetic potential, ζ, mounted in a conventional parallelepipedic cell of experimental arrangement and dimensions (width l, length Lo, and height H) given in Figure 1. The thickness of the Langmuir 2009, 25(18), 10691–10703
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In the following, we represent the diffuse distribution of the polymer segment density, ns(x), by ns ðxÞ=ns,o ¼ f ðxÞ
Figure 1. Schematic representation of the electrokinetic cell with spatial arrangement of the polymer-coated surfaces. Our nomenclature is indicated as well as the typical dimensions of the cell.
gel layer is denoted as d. The Cartesian coordinate system chosen is also represented. A pressure gradient, ΔP/Lo, is applied along the thin-layer chamber in the cell (y-axis) and pulls a symmetrical z:z electrolyte of bulk concentration c¥ from one extremity of the cell to the other. Two electrodes placed at the extremities of the chamber allow measuring the current produced by the flow (streaming current). The height to width aspect ratio (H/l ) allows one to neglect edge effects on the hydrodynamic flow velocity within the cell.41 Consequently, the direction of the bulk flow stream is parallel to the surface and the steady-state velocity profile in the channel is represented by ν(x), where x is the direction perpendicular to the surface. The velocity distribution, ν(x), and the electrostatic potential, ψ(x), are determined under the following conditions of practical interest: (i) hydrodynamic interactions are neglected, which is justified for laminar flow regime (Reynolds number
