pubs.acs.org/Langmuir © 2010 American Chemical Society
Electrokinetics of a Poly(N-isopropylacrylamid-co-carboxyacrylamid) Soft Thin Film: Evidence of Diffuse Segment Distribution in the Swollen State )
Ralf Zimmermann,*,† Dirk Kuckling,‡ Martin Kaufmann,† Carsten Werner,†,§ and Jer^ome F. L. Duval*,
)
† Leibniz Institute of Polymer Research Dresden, Max Bergmann Center of Biomaterials Dresden, Hohe Strasse 6, 01069 Dresden, Germany, ‡University of Paderborn, Department of Chemistry, Warburger Strasse 100, 33098 Paderborn, Germany, §University of Toronto, Institute of Biomaterials and Biomedical Engineering, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8, and 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
Received September 3, 2010. Revised Manuscript Received October 12, 2010 Streaming current measurements were performed on poly(N-isopropylacrylamid-co-carboxyacrylamid) (PNiPAAMco-carboxyAAM) soft thin films over a broad range of pH and salt concentration (pH 2.5-10, 0.1-10 mM KCl) at a constant temperature of 22 C. The films are negatively charged because of the ionization of the carboxylic acid groups in the repeat unit of the copolymer. For a given salt concentration, the absolute value of the streaming current exhibits an unconventional, nonmonotonous dependence on pH with the presence of a maximum at pH ∼6.4. This maximum is most pronounced at low electrolyte concentration and gradually disappears with increasing salinity. Complementary ellipsometry data further reveal that the average film thickness increases by a factor of ∼2.2 with increasing pH over the whole range of salt concentration examined. The larger the solution salt concentration, the lower the pH value where expansion of the hydrogel layer starts to take place. The dependence of film thickness on pH and electrolyte concentration remarkably follows that obtained for surface conductivity. The streaming current and surface conductivity results could be consistently interpreted on a quantitative basis using the theory we previously derived for the electrokinetics of charged diffuse (heterogeneous) soft thin films complemented here by the derivation of a general expression for the surface conductivity of such systems. In particular, the maximum in streaming current versus pH is unambiguously attributed to the presence of an interphasial gradient in polymer segment density following the heterogeneous expansion of the chains within the film upon swelling with increasing pH. A quantitative inspection of the data further suggests that pK values of ionogenic groups in the film as derived from the streaming current and surface conductivity data differ by ∼0.9 pH unit. Such a difference is attributed to the impact of position-dependent hydrophobicity across the film on the degree of ionization of carboxylic sites.
1. Introduction Stimuli-responsive materials, as engineered from thermo-, light-, or pH-sensitive polymers, have gained widespread interest in numerous scientific areas and industrial applications (e.g., biosensing,1 bioadhesion,2 drug delivery,3 tissue engineering,4,5 or microfluidics).6 A mandatory prerequisite for optimizing the performance of these smart materials is a complete analysis of the interfacial properties of their constitutive polymer films in terms *Both authors contributed equally to this work. Corresponding authors. (R.Z.)
[email protected]. Tel: 00 49 351 4658 258. Fax: 00 49 351 4658 533. (J.F.L.D.)
[email protected]. Tel: 00 33 3 83 59 62 63. Fax: 00 33 3 83 59 62 55. (1) Ding, Z.; Fong, R. B.; Long, C. J.; Stayton, P. S.; Hoffman, A. S. Nature 2001, 411, 59–62. (2) Cordeiro, A. L.; Pettitt, M. E.; Callow, M. E.; Callow, J. A.; Werner, C. Biotechnol. Lett. 2010, 32, 489–495. (3) Okano, T.; Bae, Y. H.; Jacobs, H.; Kim, S. W. J. Controlled Release 1990, 11, 255–265. (4) Schmaljohann, D.; Oswald, J.; Jorgensen, B.; Nitschke, M.; Beyerlein, D.; Werner, C. Biomacromolecules 2003, 4, 1733–1739. (5) Yamada, N.; Okano, T.; Sakai, H.; Karikusa, F.; Sawasaki, Y.; Sakurai, Y. Makromol. Chem., Rapid Commun. 1990, 11, 571–576. (6) Zhang, Y.; Kato, S.; Anazawa, T. Sens. Actuators, B 2008, 129, 481–486. (7) Dukhin, S. S.; Zimmermann, R.; Werner, C. J. Colloid Interface Sci. 2004, 274, 309–318. (8) Zimmermann, R.; Norde, W.; Cohen-Stuart, M. A.; Werner, C. Langmuir 2005, 21, 5108–5114. (9) Dukhin, S. S.; Zimmermann, R.; Werner, C. J. Colloid Interface Sci. 2008, 328, 186–195.
Langmuir 2010, 26(23), 18169–18181
of electric double layer formation and charge screening by mobile ions in an aqueous environment.7-13 In addition, such an analysis should necessarily address how these properties are affected by variations in polymer structure following, for example, swelling or shrinking processes as a result of changes in pH, temperature, or light exposure. To achieve such a degree of understanding, streaming potential or streaming current methods are well-established electrokinetic techniques that allow for the capture of basic electrohydrodynamic features of soft (permeable) polymeric materials.8-15 It is now increasingly accepted by the community that an appropriate interpretation of the electrokinetics of such systems necessarily requires abandoning the classical concept of zeta potential that is strictly applicable to hard (impermeable) surfaces. Instead, more rigorous theories are available, and most of them adequately account for the fundamental peculiarities of soft interfaces with regard to electrostatic and hydrodynamic field distributions (10) Duval, J. F. L.; Zimmermann, R.; Cordeiro, A. L.; Rein, N.; Werner, C. Langmuir 2009, 25, 10691–10703. (11) Duval, J. F. L.; van Leeuwen, H. P. Langmuir 2004, 20, 10324–10336. (12) Duval, J. F. L. Langmuir 2005, 21, 3247–3258. (13) Yezek, L. P.; Duval, J. F. L.; van Leeuwen, H. P. Langmuir 2005, 21, 6220– 6227. (14) Werner, C.; K€orber, H.; Zimmermann, R.; Dukhin, S. S.; Jacobasch, H.-J. J. Colloid Interface Sci. 1998, 208, 329–346. (15) Delgado, A. V.; Gonzalez-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. J. Colloid Interface Sci. 2007, 309, 194–224.
Published on Web 11/02/2010
DOI: 10.1021/la103526b
18169
Article
under lateral flow conditions.7-12,16-21 The theories for soft surface electrokinetics (SSE) generally differ according to their degree of validity and sophistication. Some of them are applicable to poorly charged films (i.e., within the framework of the Debye-H€uckel approximation).11 Others are based on the Donnan picture for ion partitioning across the polymer phase, which is correct provided that the film thickness well exceeds the Debye length (in the case of micrometric gels).11-13 More recently, numerical solutions of the governing electrostatic and hydrodynamic equations were provided by Duval et al. for the evaluation of the streaming current of soft polymer films regardless of the magnitude of the volume charge density that they carry and the thickness.10 The proposed electrokinetic formalism further includes the possibility of a gradual decay for the segment density from the bulk value in the film to zero in the bulk electrolyte solution. Such a representation of diffuse interphases is particularly relevant for investigating hydrogel swelling via electrokinetics.10 This model by Duval and co-workers for the electrokinetics of diffuse soft interphases also applies to composite hard/ soft systems, thus making possible the analysis of electrohydrodynamic properties of nanometric soft thin films supported by a charged hard surface.10 A concrete application was published in ref 10, where streaming current data of uncharged thermoresponsive thin films carried by charged Teflon AF surfaces were shown to agree with theory over a broad range of pH and salt concentration for temperatures above and below the lower critical solution temperature (LCST). In particular, the confrontation between theory and experiment allowed for addressing (i) the homogeneous character of the film in both swollen and collapsed states and (ii) the applicability of the Brinkman equation with the stress continuous boundary condition in SSE.22 According to the theory by Duval et al.,10 the streaming current strongly decreases in absolute value with increasing diffuseness of the film. This is the result of an increase in friction exerted on fluid flow by the polymer tails pointing toward the outer solution. The effect, which is related to the presence of a diffuse interface, is analogous to that predicted within the context of electrophoresis of diffuse soft particles.23 Whereas numerous electrophoretic data on bacteria and microgel particles support the existence of the aforementioned hydrodynamic effect at low ionic strengths (see the recent review in ref 24), no evidence for heterogeneous segment density distribution within the planar soft interphase has been reported from streaming current/streaming potential analysis. The only exception is perhaps the work by Yezek et al.,13 albeit restricted to the electrokinetics of micrometer-thick hydrogels where the Donnan condition applies. Their analysis of the interfacial gel swelling, as based on the interpretation of the streaming potential as a function of ionic strength, was further strongly impaired by (i) large ionic back-conduction within the gel phase and (ii) the impossibility of measuring the gel expansion accurately at the very interphase formed with the outer solution, which is mostly probed by electrokinetics. (16) Dukhin, S. S.; Semenikkin, N. M.; Bychko, W. A. In Surface Forces in Thin Layers; Derjaguin, B. V., Ed.; Acad. Science USSR, Nauka: Moskow, 1979; pp 85-93 (in Russian). (17) Donath, E.; Voigth, A. J. Colloid Interface Sci. 1986, 109, 122–139. (18) Ohshima, H.; Kondo, T. J. Colloid Interface Sci. 1990, 135, 443–448. (19) Starov, V. M.; Solomentsev, Y. E. J. Colloid Interface Sci. 1993, 158, 159– 165. (20) Starov, V. M.; Solomentsev, Y. E. J. Colloid Interface Sci. 1993, 158, 166– 170. (21) Donath, E.; Pastuschenko, V. Bioelectrochem. Bioenerg. 1980, 7, 31–40. (22) Dukhin, S. S.; Zimmermann, R.; Duval, J. F. L.; Werner, C. J. Colloid Interface Sci. 2010, 350, 1–4. (23) Duval, J. F. L.; Ohshima, H. Langmuir 2006, 22, 3533–3546. (24) Duval, J. F. L.; Gaboriaud, F. Curr. Opin. Colloid Interface Sci. 2010, 15, 184–195.
18170 DOI: 10.1021/la103526b
Zimmermann et al.
In this article, we present a detailed investigation of the electrokinetic properties (streaming current) and nanometric swelling of thermoresponsive poly(N-isopropylacrylamid-co-carboxyacrylamid) (PNiPAAM-co-carboxyAAM) soft thin films. Measurements were performed at room temperature (22 C). The swelling state of the films, as monitored by ellipsometry, was modulated by changing the pH and salt concentration of the electrolyte. The study was complemented with measurements of the surface conductivity. It is shown here how the whole set of these interfacial properties validates the fundamentals of the generalized theory reported in ref 10 for the electrokinetics of diffuse soft films. In particular, the remarkable nonmonotonous variation of the streaming current with pH and salt concentration is intrinsically connected to changes in the polymer segment density distribution following the heterogeneous swelling of chains from the bulk film to the outer periphery. Additionally, it is demonstrated that a consistent analysis of surface conductivity and streaming current allows for the retrieval of precious information on the different ionization states of carboxylic groups located within the bulk of the film and those positioned at the very interface formed with the electrolyte solution.
2. Experimental Section 2.1. Materials. Poly(glycidyl methacrylate) (PGMA, Mw = 30 000 g mol-1) was purchased from Polymer Source (Dorval, Canada). The PNIPAAm copolymer (Mw = 123 000 g/mol, see Figure 1 for the chemical structure) was synthesized as thoroughly described in ref 25. Polished glass carriers mounted in the microslit cell were purchased from Berliner Glass (Berlin, Germany). Polymer films for ellipsometry measurements were prepared on thermally oxidized (30 nm) silicon wafers. The electrolyte solutions used in this study (0.1-10 mM KCl, pH 2.5-10) were prepared from vacuum-degassed deionized water (Milli-Q gradient A10, Millipore Co.) by the addition and/or appropriate dilution of 0.1 M KCl, HCl, and KOH stock solutions (VWR International GmbH, Darmstadt, Germany). 2.2. Polymer Films. Thin films of the PNIPAAm copolymer were covalently attached to glass and silicon carriers according to the following protocol.26 The substrates were precleaned by sonication in deionized water and ethanol for 30 min. Subsequently, the substrates were freshly oxidized in a mixture of ammonium hydroxide (29 wt %, Acros Organics, Geel, Belgium), hydrogen peroxide (35 wt %, not stabilized, Merck, Darmstadt, Germany), and deionized water (NH4OH/H2O2/H2O = 1:1:5) at 70 C for 10 min and rinsed intensively in deionized water. After the substrates were dried, a thin PGMA film was spin coated from a 0.35% (w/w) solution in chloroform (Fluka, Deisenhofen, Germany). The PGMA was covalently attached to the substrate by tempering at 110 C (10 min under vacuum) using the high reactivity of its epoxy groups with surface hydroxyl groups.26 The PNIPAAm copolymer was then dissolved to a concentration of 1.5% (w/w) in isopropanol (Argos Organics, Geel, Belgium) and spin coated onto the precoated carriers. The copolymer films were tempered at 170 C overnight in vacuum to allow for the reaction of COOH groups of the copolymer with epoxy groups of the PGMA. Then, surfaces were rinsed so as to remove unbound PNIPAAm copolymer and were finally dried in a stream of nitrogen. A dry film thickness of about 15 nm was measured by ellipsometry (M-44, J. A. Woolam Co. Inc.). The samples were stored under an argon atmosphere and were used for experiments within four weeks. 2.3. Ellipsometry. An M-44 ellipsometer (Woolam Co., Inc.) with a rotating analyzer and a detector array of 44 wavelengths (25) Kuckling, D.; Adler, H.-J. P.; Arndt, K.-F.; Ling, L.; Habicher, W. D. Macromol. Chem. Phys. 2000, 201, 273–280. (26) Kaufmann, M.; Jia, Y.; Renner, L.; Gupta, S.; Kuckling, D.; Werner, C.; Pompe, T. Soft Matter 2010, 6, 937–944. (27) Iyer, K. S.; Zdyrko, B.; Malz, H.; Pionteck, J.; Luzinov, I. Macromolecules 2003, 36, 6519–6526.
Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
Article
Figure 1. Schematic representation of the microslit setup and chemical structure for the poly(N-isopropylacrylamid-co-carboxyacrylamid) soft thin film. In the formula, n denotes the length of the alkyl spacer (n = 10) and y denotes the content of comonomer (y = 10 mol %).
between 428 and 763 nm was used. The layer thickness and refractive index of the hydrogel were determined on the basis of an optical model that involves four different layers (Si/SiO2/hydrogel/aqueous solution). The optical constants of the various components of the interphasial system analyzed were taken from the literature.28 The thickness and refractive index of the hydrogel film were determined by assuming a homogeneous segment distribution (box model). In doing so, the film thickness obtained by ellipsometry must be considered to be an average across the film in the x direction.29 2.4. Electrokinetic Methods. Streaming current (Istr) measurements were performed at rectangular streaming channels (20 mm 10 mm 24 μm, Figure 1) formed by two sample surfaces using the microslit electrokinetic setup (MES).14 The electrokinetic measurements were started at alkaline pH. Each pH value and electrolyte concentration was equilibrated for about 40 min prior to measurement. For each pH and salt concentration examined in this study, the respective concentrations of all ions present in the medium were back-computed by appropriately taking into account the dilution factor and contributions stemming from the addition of aliquots of 0.1 M HCl and KOH solutions used to fix the solution pH. To determine the surface conductivity of the soft thin film supported by the glass/PGMA carriers, streaming potentials (Ustr) were measured. The surface conductivity (Kσ) of a single surface was then derived from the ratio Istr/Ustr according to14 Kσ ¼
Lo Istr =ΔP H - KB 2l Ustr =ΔP 2
ð1Þ
where ΔP is the applied pressure gradient, L0 and l are the length and width of the cell, respectively, H is the separation distance between the samples, and KB is the bulk solution conductivity. Please note that the MES is currently not equipped for measurements above room temperature. As a consequence, this study is restricted to measurements at various pH and salt concentrations at constant temperature (22 C).
3. Theory The basics for the general theory of electrokinetics of charged, diffuse (heterogeneous) soft thin films supported by a hard(28) Werner, C.; Eichhorn, K.-J.; Grundke, K.; Simon, F.; Gr€ahlert, W.; Jacobasch, H.-J. Colloids Surf., A 1999, 156, 3–17. (29) De Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1758– 1772.
Langmuir 2010, 26(23), 18169–18181
charged surface in a symmetrical z:z electrolyte were recently reported by Duval et al.10 The main lines of the theory together with the assumptions underlying its validity are briefly recalled here. Results are extended to the more general situation where charges within the soft thin film are partially dissociated and the electrolyte is composed of N ions of valence zi and bulk concentrations c¥ i with i = 1,...,N. A general expression for the experimentally accessible surface conductivity pertaining to the interphase hard surface/soft thin film/electrolyte solution is also provided. We adopt the nomenclature introduced in ref 10 and consider a composite hard/soft interphase mounted in a microslit setup of experimental arrangement and dimensions (width l , length Lo and height H) given in Figure 1. Under the action of an applied pressure gradient ΔP/L0, a streaming current Istr arises from the displacement of a net number of mobile charges located in the electric double layer that extends within and outside the diffuse soft surface layer. In line with experimental conditions of interest here, the theory is valid for the laminar flow regime and for steady-state hydrodynamic and electrostatic fields under the assumption that there is no overlap of the soft surface layers within the cell and edge effects are negligible. Besides, we strictly tackle situations where the water content in the thin film is large enough to consider only the first-order term in the hydrodynamic volume fraction of polymer segments in the expression of the friction exerted by segments on the flow. The reader is referred to ref 10 for further details. 3.1. Hydrodynamics. Under the conditions given above, the liquid flow is parallel to the surface (y dimension) and the velocity field v(x) depends on the dimension x perpendicular to the interface according to the Brinkman equation written in the form10 d2 VðXÞ - ðλo HÞ2 f ðXÞ VðXÞ ¼ - 1 dX 2
ð2Þ
where X = x/H, V(X) = v(X)/v0 with v0 = ΔPH2/(ηL0), and η is the dynamic viscosity of water. In eq 2, f is a normalized function reflecting the diffuse (position-dependent) distribution of polymer segment density within the thin soft surface layer. In the limit where f is a step function of width d, the soft thin film reduces to a homogeneous layer of thickness d. The factor DOI: 10.1021/la103526b
18171
Article
Zimmermann et al.
(λ0H)2 f(X) in eq 2 basically defines the position-dependent friction exerted by the polymer segments on the fluid flow. The function f necessarily satisfies f(x . d) f 0, which expresses the vanishing of the soft surface layer sufficiently far away from the rigid supporting surface. The quantity λ0 is the so-called hydrodynamic softness of the film, and 1/λ0 is the Brinkman length that reflects the flow penetration within the thin film when it is homogeneously distributed. We adopt for the profile f the expression10,23 ! ω x-d 1 - tanh ð3Þ f ðxÞ ¼ 2 R This choice is strongly motivated by neutron reflectivity results on pH-responsive polybase brushes,30 by ellipsometry analysis of surface-attached dimethylacrylamide films,31 and by the characterization of N-isopropylacrylamide-based thermoresponsive films with surface plasmon resonance/optical waveguide mode spectroscopy.32 Parameter R is the characteristic decay length for the segment distribution with the limit of the homogeneous layer retrieved by setting R f 0. For R ¼ 6 0, the distribution of the segment density is gradual from the supporting surface to the outer electrolyte and the thickness of the gel layer may then be taken as d þ 2.3R.23 The scalar quantity ω in eq 3 further ensures that the total number of polymer segments within the gel layer remains constant irrespective of the segment distribution. For the situation of interest here where the hydrogel undergoes swelling with increasing pH, the polymer segment distribution may be considered to be homogeneous in the collapsed state (i.e., at very low pH values). Denoting as d0 the corresponding film thickness, we then obtain for ω ω ¼
R H=2 0
2d0 ! x-d dx 1 - tanh R
dVðXÞ dX
¼ 0
ð5aÞ
ð5bÞ
X ¼ 1=2
which reflect the no-slip condition at the rigid supporting surface and the symmetry of the velocity field with respect to X = 1/2, respectively. 3.2. Electrostatics. In line with the chemical composition of the soft thin film of interest here, we consider that the charge in the (30) Sanjuan, S.; Perrin, P.; Pantoustier, N.; Tran, Y. Langmuir 2007, 23, 5769– 5778. (31) Toomey, R.; Freidank, D.; R€uhe, J. Macromolecules 2004, 37, 882–887. (32) Junk, M. J. N.; Anac, I.; Menges, B.; Jonas, U. Langmuir 2010, 26, 12253– 12259.
18172 DOI: 10.1021/la103526b
- COOH a - COO - þ Hþ
ð6Þ
with the acidity constant written as K = 10-pK. Assuming a uniform distribution of ionogenic sites along a given polymer chain, the local electrostatic potential ψ(x) is then governed by the nonlinear Poisson-Boltzmann equation that may be arranged in the form of ( N d2 yðXÞ ðKHÞ2 X ¼ - N zi ci expð - zi yðXÞÞ 2 P dX i ¼ 1 2 ci zi i¼1
Fo =F f ðXÞ þ pK - pH expð - yðXÞÞ 1 þ 10
) ð7Þ
where the dimensionless potential y is defined by y = Fψ/RT and N the reciprocal Debye thickness is defined by κ = [Σi=1 F2cizi2/ εoεrRT)]1/2, with F being the Faraday constant, c being the salt concentration, R being the gas constant, T being the temperature, ε0 being the dielectric permittivity of vacuum, and εr being the relative dielectric permittivity of the aqueous medium. In eq 7, Fo/ F corresponds to the overall concentration of carboxylic groups (except for the sign) in the collapsed film (R f 0, ω = 1). The second term in brackets on the rhs of eq 7 refers to the positionand pH-dependent densities of fixed charges across the film. In the absence of electric double layer overlap within the electrokinetic cell, the potential verifies the boundaries
ð4Þ
where H .2d. In the limit where homogeneous swelling takes place (R/d f 0), ω reduces to ω = d0/d = f(x). Substitution into eq 2 leads to d2V(x)/dx2 - (λo[d0/d]1/2)2V(x) = -H2. Assimilating in this latter equation the factor preceding V(x) to the square of the hydrodynamic softness λ for the homogeneous swollen gel of thickness d, we obtain the relationship λ/λ0 = (d0/d)1/2, which is in agreement with that derived in ref 10. In the collapsed state where d = d0, we have λ = λ0, thus justifying the physical definition given above for the quantity λ0. The boundary conditions associated with eq 2 are VðX ¼ 0Þ ¼ 0
film originates only from the deprotonation of carboxylic acid groups (-COOH) following the acid-base equilibrium
yðX ¼ 0Þ ¼ ~ζ
ð8aÞ
1 ¼ 0 y Xf 2
ð8bÞ
Equation 8a states that the surface potential of the supporting rigid substrate is assimilated to the electrokinetic (zeta) potential ζ~ = Fζ/RT. Equation 8b expresses the bulk electroneutrality condition, taking the value 0 as a reference for the potential far from the interface between the thin film and the electrolyte solution. In situations where the charge density in the hydrogel film significantly exceeds the charge of the supporting surface, the contribution of the latter to the potential distribution across the interface becomes negligible.10 y(X = 0) is then mainly determined by the charge density of the gel near the hard surface, and eq 8a may be replaced by the condition dy/dX|X=0 = 0. 3.3. Electrokinetics. The streaming current Istr represents the charge transport due to pressure-driven flow. The expression of Istr normalized with respect to the applied pressure ΔP reads after some rerrangement10 Istr 2l FH 3 ¼ ΔP ηLo
Z
1=2
VðXÞ 0
N X
zi ci expð - zi yðXÞÞ dX
ð9Þ
i¼1
where the velocity and potential profiles, V(X) and y(X), are solutions of eqs 2-5 and 7-8, respectively. 3.4. Surface Conductivity. The surface conductivity, Kσ, of the interphasial system analyzed here consists of two contributions:7,11 (i) a conduction contribution, Kσm, stemming from the migration of mobile ions in the tangential field Ustr/L0 σ along the interphase and (ii) a convective component, Keo , produced by the electroosmotic flow originating from the action Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
Article
of the field Ustr/L0 on mobile charges located within and outside the soft thin film σ K σ ¼ Kmσ þ Keo
ð10Þ
Using the notations and dimensionless space variable as previously specified, we obtain for Kσm the expression Kmσ ¼
HF 2 RT
Z
N 1=2 X 0
jzi jDi ci βi ðXÞ½expð - zi yðXÞÞ - 1 dX
i¼1
ð11Þ where Di is the diffusion coefficient of ion i in the bulk electrolyte solution and βi(X) stands for the ratio between the mobility of ion i at position X and that in the bulk electrolyte solution. For highwater-content hydrogels, we may legitimately consider βi(X) to be ∼1.13 The convective contribution Kσeo is obtained via an appropriate evaluation of the electroosmotic current defined by the transport of mobile charges by the field-induced flow and can be written as (Supporting Information) σ ¼ Keo
Hεo εr RTðKHÞ2 η
Z
1=2
Veo ðXÞ
0
N X
zi ci expð - zi yðXÞÞ dX
i¼1
ð12Þ where Veo(X) is the normalized electroosmotic flow velocity at N cizi2/(ηLo)). position X according to Veo(X) = veo/(UstrFH2Σi=1 The quantity Veo(X) is governed by the Brinkman equation with the charge source term d2 Veo ðXÞ - ðλo HÞ2 f ðXÞ Veo ðXÞ dX 2 N P
¼ -
i¼1
zi ci expð - zi yðXÞÞ N P i¼1
ð13Þ ci zi 2
The boundaries verified by Veo(X) are similar to those written for the pressure-driven flow in eqs 5a and 5b. 3.5. Numerical Solution. The spatial distributions for the pressure-driven flow velocity V(X), the electrostatic potential distribution y(X), and the electroosmotic flow velocity Veo(X) were obtained by a numerical evaluation of differential eqs 2, 7, and 13 (with appropriate boundaries as specified in sections 3.1 and 3.2), respectively, according to a methodology identical to that described in ref 10. The numerical algorithm was successfully tested upon comparison with analytical solutions provided in ref 10 for the flow velocity V(X) under conditions of homogeneous polymer segment distribution (R f 0). Additionally, it was verified that for cases of complete dissociation (pH . pK) and symmetrical electrolytes (N = 2,|zi|=z), results for the electrostatic potential distribution coincide with those derived in ref 10.
4. Results and Discussion 4.1. Experimental Results. 4.1.1. Swelling Properties of a (PNiPAAM-co-carboxyAAM) Soft Thin Film. The dependence of the average film thickness d on solution pH is displayed in Figure 2 for 0.1, 1, and 10 mM KCl solutions. As expected for a surface layer containing weakly acidic groups, an overall increase in d is observed with increasing pH from 2 to 11. This indicates a significant electrostatically driven expansion of the polymer chains within the film upon gradual dissociation of Langmuir 2010, 26(23), 18169–18181
Figure 2. Average film thickness d determined by ellipsometry as a function of pH for 0.1, 1, and 10 mM KCl solutions, as indicated. Experimental data are represented by symbols. Solid lines represent the best fit of the data to eq 15 with parameters d0, d1, pHd, and ΔpHd specified in Table 1.
the therein distributed carboxylic groups. The thickness of the film at equilibrium is determined by the condition of zero overall osmotic pressure, denoted as Π and defined by33 Π ¼ Πion þ Πmix þ Πel
ð14Þ
where Πion, Πmix, and Πel are the electrostatic, polymer-solvent mixing (chain entropy), and chain elastic components of the overall osmotic pressure. An inspection of the pH dependence of d allows us to discriminate among three distinct pH regimes. In regime 1, corresponding to low pH values where carboxylic groups are not or are poorly dissociated (pH 6 to 7. The expansion of the polymer chains that were originally in a collapsed state (regime 1) is attributed to strong repulsions between adjacent carboxylic groups that are increasingly dissociated. The corresponding increase in film charge and Πion results in an entropy loss for the counterions confined within the film. As a result of the increased osmotic pressure, chains expand in space to counterbalance that entropy loss until the equilibrium situation as determined by the condition Π = 0 is reached. In addition, the larger the salt concentration, the lower the pH value at which film expansion starts to occur. Qualitatively, this is so because the extent of site dissociation at fixed pH increases with increasing ionic strength in solution.34 Finally, for significantly large pH, the film thickness reaches a maximum value that is nearly independent of salt concentration, d = d1 ≈ 88 nm. This is the regime where site dissociation is complete and Πion and film expansion are maximized (regime 3). Above pH 11, any further increase of pH will lead to a significant increase in ionic strength (especially in 0.1 mM KCl solution). Therefore, a decrease in film thickness is expected beyond the maximum pH considered in this study. (33) Flory, P. J. Principles of Polymer Chemistry; Cornel University Press: Ithaca, NY, 1953. (34) Lyklema, J. Fundamentals of Colloid and Interface Science; Academic Press: London, 1991; Vol. 2.
DOI: 10.1021/la103526b
18173
Article
Zimmermann et al.
A quantitative interpretation of the electrokinetic and surface conductivity properties of the film, as detailed in section 4.2, requires a mathematical expression for the dependence of the average film thickness d on the pH and salt concentration. For that purpose, the data in Figure 2 could all be accurately fitted within the studied pH range (solid lines in Figure 2) using "
# d1 - d0 pHd - pH 1 - tanh dðpHÞ ¼ d0 1 þ ΔpHd 2d0
ð15Þ
where d0 and d1 are the film thickness at low and high pH values, respectively. The parameter pHd corresponds to the pH value where there is an inflection point in the pH dependence of d. The quantity ΔpHd reflects the pH range where the transition between regime 1 and regime 3 occurs. Table 1 collects the values of d0, d1, pHd, and ΔpHd for 0.1, 1, and 10 mM KCl solutions. In line with the discussion given above, d0 and d1 are nearly independent of the salt concentration within the experimental error, and the same holds for ΔpHd. However, the pH value of the transition between d0 and d1, pHd, increases with decreasing salt concentration, in agreement with the underlying retardation of site dissociation at lower ionic strength. 4.1.2. Surface Conductivity. Figure 3A shows the surface conductivity, Kσ, as a function of solution pH for the PNiPAAMco-carboxyAAM soft thin film at KCl salt concentrations of 0.1 and 1 mM. Any reliable estimation of Kσ at a concentration of 10 mM was impossible because of the high conductivity KB of the bulk electrolyte solution. Qualitatively, the dependence of Kσ on pH and salt concentration is remarkably similar to that commented Table 1. Parameters d0, d1, pHd, and ΔpHd defining the pH Dependence and Salt Concentration Dependence of the Average Film Thickness d (Equation 15) Determined by Ellipsometry (Figure 2)
0.1 mM 1 mM 10 mM
d0 (nm)
d1 (nm)
pHd
ΔpHd
39.6 41.4 39.8
88.0 87.3 86.9
9.00 8.23 7.50
0.76 0.76 0.76
on in section 4.1.1 for the average film thickness d. Namely, Kσ is very low (6.4 is most significant at low salt concentration. In addition, for a given pH value lower than ∼7.5, |Istr/ΔP| decreases with increasing salt
Figure 3. (A) Surface conductivity Kσ (eq 1) of one thin film mounted in the electrokinetic cell as a function of pH for 0.1 and 1 mM KCl (as indicated). Experimental data are represented by symbols. Solid lines represent the reconstruction of the data by means of the theory detailed in section 3.4 with fitting parameters collected in Table 2. (The pH- and concentration-dependent average film thickness values are defined by the parameters listed in Table 1). (B) Plots of the normalized film thickness d = (d - d0)/(d1 - d0) (open symbols) and normalized surface conductivity K σ = (Kσ - Kσ,0)/(Kσ,1 - Kσ,0) (filled symbols) vs pH for 0.1 mM (blue, open and solid circles) and 1 mM (red, open and solid squares) KCl solutions. All symbols are issued from experimental data (Figures 2 and represent the theory for the evaluation of R 3A). Solid lines pK-pH the normalized site dissociation degree across the heterogeneous film Ω = (H/ωd) ¥ exp(-y(X))] dX (blue, 0.1 mM KCl 0 [f(X)/(1 þ 10 solution; red, 1 mM KCl solution). Model parameters are listed in Table 2. 18174 DOI: 10.1021/la103526b
Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
Figure 4. Ratio of the streaming current over applied pressure, Istr/ΔP, as a function of pH for 0.1, 1, and 10 mM KCl solutions, as indicated. Experimental data are represented by symbols. Solid lines represent the reconstruction of the data by means of the theory detailed in section 3.3 with fitting parameters collected in Table 2. The pH- and concentration-dependent average film thickness values are defined by the parameters listed in Table 1. The inset shows the dependence of R on pH and salt concentration necessary for reproducing the experimental electrokinetic data in the pH range of 2.5-10.
concentration. This is in agreement with the expected screening of charges within the film by mobile ions present within and outside the hydrogel. However, with increasing pH from ∼8 to 10, the respective positioning of the Istr/ΔP versus pH curves for the three salt concentrations of concern gradually becomes opposite to that expected on the basis of a simple charge-screening effect. Obviously, this feature is incompatible with the standard electric double layer representation and must be related to the swelling of the thin film. A closer inspection of the data in Figure 4 further reveals that the pH range of 2.5-6.4 where |Istr/ΔP| increases does not match the pH window of 6-10 where there is a significant increase in the surface conductivity Kσ. The effect of pH on both Kσ and film thickness d is expected to result from the dissociation of carboxylic groups within the film, and the apparent mismatch between electrokinetic and surface conductivity data asks for a consistent quantitative interpretation that should further account for the “anomalous” presence of a maximum in |Istr/ΔP| with varying pH. This interpretation is given out in the next section where the data are analyzed on the basis of the theoretical formalism outlined in section 3. 4.2. Quantitative Interpretation and Comparison of Experiments and Theory. 4.2.1. Electrosurface Properties of the Supporting Material in the Absence of the Soft Thin Film. To interpret the surface conductivity and electrokinetic data displayed in Figures 3 and 4, the first requirement is the a priori evaluation of the impact of the electrosurface properties of the substrate supporting the PNiPAAM-co-carboxyAAM soft thin film on the surface conductivity and electrokinetic data measured in the presence of the film. To do so, streaming current measurements were carried out as a function of pH at 0.1, 1, and 10 mM KCl on glass (SiO2) surfaces covered with PGMA only. Results are shown in the Supporting Information and underpin classical pH dependences for Istr/ΔP: the isoelectric point is located at ∼2.5 and |Istr/ΔP| monotonously increases with increasing pH and reaches a plateau at pH >6. Furthermore, for a given pH, |Istr/ΔP| decreases with increasing salt concentration. Langmuir 2010, 26(23), 18169–18181
Article
Streaming current data were then converted into zeta potentials (ζ) using the Smoluchowski relation Istr/ΔP = ε0εrHl ζ/(ηL0), and the boundary given by eq 8a could be then fully expressed. Adopting this boundary, we determined the charge density carried by the hydrogel (details in section 4.2.3) for appropriately recovering the magnitude of the surface conductivity increase in the pH range of 6 to 10. We verified a posteriori that the charge density of the hydrogel is so large that the theoretical Kσ value actually remains independent of ζ. This means that the surface conductivity is determined by the coupled electrohydrodynamic and swelling features of the hydrogel only. Another argument in favor of disregarding the surface charge of the material supporting the hydrogel is that the large increase in Kσ for pH >6 to 7 is not compatible with the quasi-constant surface potentials obtained in this pH range for the SiO2/PGMA interfacial system. The streaming current measured in the presence of the hydrogel solely reflects, similarly to surface conductivity, the searched coupled electrohydrodynamic and swelling properties of the hydrogel. This is so because the hydrodynamic softness of the hydrogel, as determined below, makes it impossible for the tangential flow to probe electric double layer features in the vicinity of the supporting material. In view of these elements, theoretical results given in the following text were obtained by adopting the boundary dy/dX|X=0 = 0 to determine the electrostatic potential distribution. This boundary further circumvents the impossibility of experimentally determining the electrostatic features of the supporting material in the presence of the hydrogel coating. It is indeed expected that PNiPAAM-co-carboxyAAM chains penetrate into the PGMA during the immobilization process, thereby increasing the charge in the vicinity of the SiO2/PGMA region as compared to the situation of reference where the hydrogel is absent. 4.2.2. Dependence of Segment Distribution on pH. To address the possible influence of segment distribution across the film on Kσ and Istr/ΔP in the pH range of 2.5 to 10, we assume a priori that the characteristic decay length R involved in the profile f(x) (eq 3) varies with pH according to the expression RðpHÞ ¼
R1 pHR - pH 1 - tanh ΔpHR 2
ð16Þ
where R1 is the value adopted by R at large pH where film swelling is important, pHR is the pH value of the inflection point in the pH dependence of R, and ΔpHR reflects the pH range where the transition between a homogeneous film distribution (collapsed state, R f 0 at pH , pHR) and a diffuse (heterogeneous) segment density profile (full expansion of the film, R f R1 at pH . pHR) occurs. The choice of eq 16 is motivated by the form of eq 15, which accounts for the dependence of the average film thickness d on pH as independently determined by ellipsometry. This choice is validated a posteriori in the sense that eq 16 reproduces the peculiar dependence of Istr/ΔP on pH and salt concentration for pH >6.4 (section 4.2.3). Given eqs 15 and 16, the analysis then consists of consistently reconstructing the dependence of Kσ (eqs 3-5, 7, 8, 10-13) and Istr/ΔP (eqs 2, 7-9) on both pH and salt concentration. For that purpose, six parameters remain unknown and act as adjustable variables, namely, F0, λ0, pK, R1, pHR, and ΔpHR. It should be realized that the fit of the electrokinetic and surface conductivity data is extremely constrained by the coupled nature of the electrostatic, hydrodynamic, and swelling properties of the film. In particular, the variation of R1 leads to different degrees of diffuseness for the segment distribution in the film with increasing pH, which in turn affects the potential distribution y(X) in the film DOI: 10.1021/la103526b
18175
Article
Zimmermann et al.
(eq 7) and thus possibly modulates both Kσ (eqs 10-13) and Istr/ ΔP (eq 9). Also, varying R1 affects the pH dependence of the local friction exerted by the segments on the fluid flow (eqs 2 and 13), which a priori impacts the convective contribution Kσeo (eqs 12 and 13) to the overall surface conductivity Kσ and the pressure-driven flow distribution (eq 2) or equivalently the streaming current (eq 9). 4.2.3. Discussion. 4.2.3.1. Comparison with Experiment and Theory. We found that Kσ and Istr/ΔP data could be consistently recovered by the theory over the whole range of pH and Table 2. Set of Parameters Used for Consistently Reconstructing the Surface Conductivity Kσ and Electrokinetic Data Istr/ΔP Displayed in Figures 3 and 4, Respectively -Fo/F (mM)
pK
1/λo (nm)
R1 (nm)
pH
ΔpH
6.65a 0.50 210.0 9.75 1.65 5.75b 1 mM 240 6.65a 0.55 53.0 8.60 1.75 5.75b 10 mM 240 4.95b 0.55 6.8 6.00 3.00 a For the pK values, the values derived from surface conductivity analysis. See the text for details. b For the pK values, the values derived from an analysis of streaming current data. See the text for details.
0.1 mM
270
salt concentration examined (solid lines in Figures 3 and 4). The values of Fo, λo, pK, R1, pHR, and ΔpHR required for the best fit of all data are collected in Table 2. Before discussing these results in relation to the swelling properties of the film (section 4.2.3.2), it is necessary to ascertain the unicity of the solution. For that purpose, a systematic analysis of the impact of these variables on Kσ and Istr/ΔP was carried out (Figures 5-7). This analysis is presented below and reveals key elements of the peculiar way that the above variables affect Kσ and Istr/ΔP. i. The surface conductivity Kσ (Figure 5A,B) is mainly determined by the total density Fo of ionogenic groups together with the acidity constant K = 10-pK associated with reaction 6. As expected, the former governs the magnitude of the increase in Kσ with increasing pH and the latter fixes the pH range where site dissociation within the hydrogel becomes significant and Kσ increases. In addition, the Kσeo contribution represents about 10% of the total conductivity Kσ (value reached at large pH), in agreement with the semiquantitative expectation drawn by Dukhin et al.7 This implies that the hydrodynamic softness λo governs Kσ to a small extent only. It is also found that Kσ is nearly independent of the segment distribution within the film as controlled by parameters R1, pHR, and ΔpHR. This is in agreement
Figure 5. (A, B) Dependence of Kσ on the pH-dependent diffuseness for the film/solution interphase as mediated by the quantity R1 (indicated) at (A) 0.1 mM and (B) 1 mM KCl. Experimental data are represented by symbols. Solid and dashed lines (referring to heterogeneous and homogeneous film swelling, respectively) are obtained from theory (with other model parameters given in Table 2). The pH- and concentration-dependent average film thickness values are defined by the parameters listed in Table 1. (C) Profiles f(x) for the density of segments across the thin film at three pH values (indicated) and 1 mM KCl. Dashed lines are determined from theory with R1 f 0. Solid lines are determined from theory with R(pH) governed by the parameters specified in Table 2 (with film thickness defined by the parameters given in Table 1 with pK = 6.65). (D) Potential distribution across the film under the conditions of panel C. The meaning of the curves is identical to that for panel C.
18176 DOI: 10.1021/la103526b
Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
Article
Figure 6. Dependence of Istr/ΔP on the pH-dependent diffuseness for the film/solution interphase as mediated by the quantity R1 (indicated) at (A) 0.1, (B) 1, and (C) 10 mM KCl. Experimental data are represented by symbols. Solid and dashed lines (referring to heterogeneous and homogeneous film swelling, respectively) are determined from theory (with other model parameters given in Table 2). The pH- and concentration-dependent average film thickness values are defined by the parameters listed in Table 1.
Figure 7. Dependence (for 1 mM KCl) of Istr/ΔP on (A) pK for the dissociation of carboxylic groups, (B) ΔpHR, (C) pHR, and (D) 1/λo. Experimental data are represented by symbols. Solid lines are determined from theory. (Model parameters other than those specified in the Figures are given in Table 2.) The pH- and concentration-dependent average film thickness values are defined by the parameters listed in Table 1.
with the weak influence of the diffuse segment distribution on the surface conductivity as qualitatively predicted in ref 9. It can be explained by the dependence of the potential distribution across the thin film on the quantity R1, as illustrated in Figure 5C,D. Langmuir 2010, 26(23), 18169–18181
For increasing values of R at a fixed average film thickness d (i.e., for increasing R1), the local concentration of ionogenic groups and therefore the magnitude of the local potential y decrease for x e d and increase for x g d. As a result, the value DOI: 10.1021/la103526b
18177
Article
of the integrals defined by eqs 11 and 12 remain nearly constant upon varying R1 and so does Kσ. Figure 5A,B suggests that the lower the electrolyte concentration, the more the (still-restricted) impact of R1 on Kσ becomes appreciable. This is explained by the loss of antisymmetry for the potential distribution with respect to the point (x = d, y(x = d)) when departing from the Debye-H€uckel regime (i.e., with decreasing ionic strength).11,12 To support the fact that the surface conductivity and film layer thickness both reflect the same dissociation properties of the carboxylic groups, the average normalized degree of dissociation R pK-pH exp(-y(X))] dX across the Ω = (H/ωd) ¥ 0 [f(X)/(1 þ 10 heterogeneous film is plotted in Figure 3B at 0.1 and 1 mM KCl solution. (The model parameters are those in Table 2). ii. Figure 6 clearly demonstrates that the maximum found for |Istr/ΔP| with varying pH is due to the heterogeneous extension of the soft thin film. The prediction obtained with R1 f 0 (homogeneous swelling, ω = d0/d = f(x), λ/λo = (d0/d)1/2) indeed leads to a monotonous increase in |Istr/ΔP| with increasing pH and to a more or less pronounced decrease at large pH that is not sufficient to reproduce the experimental data. This slight decrease at large pH values solely results from a decrease in the volume charge density (ω = d0/d < 1, see dashed lines in Figure 5C) that gradually counteracts the increase in film permeability with increasing pH (λ/λo = (d0/d)1/2). To recover the maximum in |Istr/ΔP|, it is necessary to increase R1, i.e., to increase at a given pH and average film thickness d, the diffuseness or heterogeneity of the interphase between the thin film and the electrolyte solution (as subsumed in the quantity R, see eqs 3 and 4). This leads to an increase in friction exerted by the outer tails of the polymer segments on the fluid flow and thus to an important reduction of |Istr/ΔP| (the hydrodynamic effect). Simulations reported in Figure 7B,C further clarify that the parameters ΔpHR and pHR determine the shape of the maximum in |Istr/ΔP|. In detail, the lower the ΔpHR, the more abrupt the increase in R with increasing pH (eq 16) and the sharper and more pronounced the maximum in |Istr/ΔP| (Figure 7B). Additionally, the lower the pHR, the earlier the decrease in |Istr/ΔP| with increasing pH, and for sufficiently low pHR, the maximum becomes more shallow or even vanishes (Figure 7C), in agreement with the corresponding dependence of R on pH. Figure 7A highlights that the pK value for the carboxylic groups controls the slope of the increase in |Istr/ΔP| at low pH (collapsed state for the film) and further determines the pH value where this increase takes place with increasing pH as a result of the dissociation of carboxylic groups. Finally, it is strongly emphasized that the plateau value adopted by |Istr/ΔP| at a large pH where site dissociation and film swelling are complete is controlled by the magnitudes of R1 (Figure 6) and 1/λo (Figure 7D) but remains independent of ΔpHR (Figure 7B) and pHR (Figure 7C). The question then arises as to whether the couple (R1,1/λo) adopted for appropriately reconstructing the behavior of |Istr/ΔP| at large pH is unique. The positive answer to that question is provided by the analysis of the dependence of |Istr/ΔP| on R at fixed 1/λo (Figure 8). For a given 1/λo, |Istr/ΔP| decreases as a result of the impact of the polymer segment density gradient on the hydrodynamic flow field distribution at the film/solution interphase. The rate of decrease for |Istr/ΔP| is very steep at small R and gradually vanishes upon further increases in R. At sufficiently large R, |Istr/ΔP| asymptotically reaches a plateau. The physical reason for the decrease in ∂|Istr/ΔP|/∂R with increasing R is the corresponding increase (in magnitude) of the local potentials y(x) in the outer film region, which is electrokinetically active. The thickness of that region is determined by the film permeability or equivalently by the (position-dependent) quantity 1/λ.10 As a result, the impact of R 18178 DOI: 10.1021/la103526b
Zimmermann et al.
Figure 8. Dependence (at 1 mM KCl) of Istr/ΔP on R for various values of 1/λo (indicated). Model parameters other than 1/λo and other than those defining the diffuseness of the interphase are listed in Table 2. The vertical and horizontal red dashed lines indicate the value of R1 and corresponding Istr/ΔP relevant for the hydrogel layer at 1 mM KCl solution. The pH- and concentration-dependent average film thickness is defined by the parameters listed in Table 1.
on the electrostatic potential distribution (that would lead to an increase in |Istr/ΔP| if solely considered) gradually counterbalances the hydrodynamic effect invoked above. The regime where |Istr/ΔP| reaches a plateau corresponds to that observed at large pH values (Figures 7D and 8). The magnitude of this plateau increases with 1/λo because of the corresponding increase in the number of electrokinetically active ions. This plateau further sets in at lower values of R (or equivalently at lower pH, see the arrow in Figure 8) for decreasing 1/λo. For extreme values of R, |Istr/ΔP| decreases to zero. This is essentially due to the corresponding decrease in ω that expresses a significant local reduction in the film charge density (in absolute value) following film swelling. Altogether, Figure 8 underlines that there is a unique set of (R1, 1/λo) for appropriately reproducing the behavior of |Istr/ΔP| at large pH, in particular, the magnitude of that plateau and the pH range where it is observed. As a last comment, we mention that 1/λo partially controls, together with the pK, the magnitude of Istr/ΔP at low pH (Figure 7D). 4.2.3.2. On the Coupled Electrohydrodynamic and Swelling Properties of the PNiPAAM-co-carboxyAAM Soft Thin Film. As a proof of the value that should be given to the modeling, all electrokinetic and surface conductivity data collected over two orders magnitude in salt concentration and 8 pH units are consistent with a single volume concentration of carboxylic groups, |Fo| = 255 ( 15 mM, and a single value of the hydrodynamic penetration length, 1/λo = 0.525 ( 0.025 nm. These quantities refer to the hydrogel film in the collapsed state where d = d0 ≈ 40 nm (independent of salt concentration). The pH dependence and position dependence for the charge density and flow penetration length (or equivalently hydrodynamic friction) within the film are governed by the segment density distribution and the way that the latter evolves with increasing pH. (See eqs 3, 4, 15, and 16 and comments below eqs 2 and 7.) The theory allows for the reproduction of the impact of salt concentration on the dissociation features of carboxylic groups (Figure 3). Finally, it unambiguously identifies the heterogeneous swelling of the film with increasing pH as the process that gives rise to the unconventional presence of a maximum in |Istr/ΔP| (section 4.2.3.1). At low pH, the increase in |Istr/ΔP| with pH originates from the gradual Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
Article
Figure 9. Theoretical profiles for the segment density distribution across the film at various pH values (indicated) and in (A) 0.1, (B) 1, and (C) 10 mM KCl solutions. Theoretical profiles for the electrostatic potential distribution at various pH values (indicated) and for (D) 0.1, (E) 1, and (F) 10 mM KCl solutions. Model parameters in panels A-F are specified in Table 2 (with pK values determined from electrokinetics). The pH- and concentration-dependent average film thickness values are defined by parameters listed in Table 1.
dissociation of the carboxylic groups, and in this pH range, |Istr/ΔP| decreases at a fixed pH with salt concentration as a result of charge screening. In more detail, it is found from the analysis of the electrokinetic data that the larger the salt concentration, the earlier the heterogeneous swelling of the film occurs with increasing pH. (See values of pHR and ΔpHR in Table 2.) This is in line with the effect of ionic strength on the (local) dissociation properties of carboxylic groups across the thin film. In addition, values obtained for pHR compare satisfactorily to those estimated for pHd from the average film thickness. However, whereas the quantity ΔpHd is independent of salt concentration, ΔpHR is found to increase significantly from 0.1 to 10 mM. This reflects the slow decrease in |Istr/ΔP| at 10 mM and pH >6.4 as compared to that observed in the same pH range at 0.1 and 1 mM KCl. Also, for 0.1 and 1 mM KCl, we systematically obtain ΔpHR > ΔpHd. This is attributed to the smeared-out character of the ellipsometry analysis, whereas the electrokinetics is very sensitive to the refined local electrostatic and hydrodynamic properties of the film, with both being related to the segment density distribution. More importantly, the decay length for the segment distribution R1 (pertaining to high pH) increases significantly with decreasing salt concentration (R1 = 210, 53, and 6.8 nm for 0.1, 1, and 10 mM, respectively). At large pH values, where site dissociation is complete, the magnitude of the local electrostatic potentials within the film increases with decreasing salt concentration as a result of a reduction in charge screening. As a result, the local repulsive force experienced by the Langmuir 2010, 26(23), 18169–18181
chains supporting the charged groups increases. This ultimately leads to a larger expansion of the thin film, as captured by the increase in R1 with decreasing salt concentration. The segment density profiles, as governed by the quantities R1, pHR, and ΔpHR, are given in Figure 9A-C for different pH values of 0.1, 1, and 10 mM KCl solutions together with the corresponding potential distributions across the thin film (Figure 9D-F). For a given pH value, the distribution of segment density within the film becomes increasingly diffuse with decreasing salt concentration, in line with the increase in R1. This is accompanied by an increase in the local electrostatic field within the film or, as stated otherwise, by a deviation of the potentials within the film from the value dictated by the Donnan condition. For a diffuse polymeric interphase, the local stretching of the chain in the film should be viewed as the local balance among Πion, Πmix, and Πel (see definitions for these entities in section 4.1) with the position-dependent Πion provided by Πion(x) = RT Σi ci¥[exp(-ziy(x)) - 1]. For homogeneous films satisfying the condition κd . 1, this expression for Πion reduces to the conventional Πion = RT Σi ci¥[exp(-ziyD) - 1] (yD is the reduced Donnan potential) as commonly adopted within Flory theory for the evaluation of the equilibrium film thickness.13,33,35 At a fixed salt concentration, it is worth mentioning that two processes concomitantly govern the magnitude of the local potentials: the dissociation of the carboxylic groups and the swelling of the film (increasing R). The former contributes to the (35) Okay, O.; Sariisik, S. B.; Zor, S. D. J. Appl. Polym. Sci. 1998, 70, 567–575.
DOI: 10.1021/la103526b
18179
Article
Zimmermann et al.
increase in y(x) (and thus |Istr/ΔP|) with increasing pH, and the latter leads to a dilution of the fixed carboxylic charges at sufficiently large pH and therefore to a decrease in y(x). This is clearly seen in Figure 9D-F where y(x) first increases (in magnitude) within the region adjacent to the supporting surface and decreases at sufficiently large pH values (i.e., for significant film swelling). For the sake of completeness, the flow-field profiles across the soft thin film (Supporting Information, Figure S2) reveal that for a given position x from the rigid surface the swelling of the film is accompanied by a gradual suppression of the flow velocity, which renders the therein distributed “mobile” ions less active from an electrokinetic point of view. Finally, we comment on the pK values obtained from the analysis of the electrokinetic data (Table 2, pK = 5.75) and surface conductivity (pK = 6.65) in 0.1 and 1 mM KCl solutions. The discrepancy between these values indicates that the streaming current and surface conductivity effectively probe fixed charges in the film that differ according to their dissociation properties. We argue that Kσ is indeed a quantity that reflects the average electrostatic features of the whole thin film (integral eq 11) whereas the streaming current mostly probes features pertaining to ionogenic groups located within the electrokinetically active part of the film (outer region of the film). The pK data summarized in Table 2 then basically suggest that the degree of dissociation of the groups is a function of the position across the film. When embedded within the film, carboxylic groups undergo a retarded dissociation as compared to those facing the electrolyte side of the interphase between the film and solution. This is likely due to an increase in the hydrophobicity of the molecular environments of the ionogenic groups distributed deeper within the film. Such an impact of hydrophobicity on the stabilization of charged groups has been clearly documented in the literature, in particular, via AFM force spectroscopy analysis.36 When the salt concentration increases from the 1 to 10 mM KCl solution, the pK value determined from the analysis of electrokinetics decreases appreciably (pK = 5.75 and 4.95, respectively). Following the argument given above on the discrepancy between pK values obtained from electrokinetics and surface conductivity data, this difference suggests that at large salt concentrations, electrokinetics probes the carboxylic groups that are located in the direct vicinity of the electrolyte side whereas at lower concentrations, fixed charges embedded within the film significantly contribute to the electrokinetic response. This trend is in agreement with the theoretical results reported in ref 10 (Figure 3 therein), which illustrate the effect of ionic strength (or κd) on the hydrodynamic screening of charges located deep inside the hydrogel layer (with the latter being fully accessible in the limit of 1/λo f ¥).
5. Conclusions In this article, we report on the intertwined electrostatic, hydrodynamic, and swelling properties of pH- and ionic strength-responsive soft poly(N-isopropylacrylamid-co-carboxyacrylamid) thin films. The analysis is based on the consistent quantitative interpretation of streaming current and surface conductivity data collected over 2 orders of magnitude in salt concentration and 8 pH units. It further integrates the pH dependence and salt concentration dependence of the average film thickness as independently determined by ellipsometry. Beyond the evaluation of the volume charge density and dissociation properties of carboxylic groups across the film, the analysis unambiguously addresses the (36) Song, J.; Duval, J. F. L.; Cohen Stuart, M. A.; Hillborg, H.; Gunst, U.; Arlinghaus, H. F.; Vancso, G. J. Langmuir 2007, 23, 5430–5438.
18180 DOI: 10.1021/la103526b
heterogeneous character of the film swelling with increasing pH. This is reflected by an atypical maximum for the streaming current upon changing pH that is most pronounced at low salt concentration. From the combined interpretations of surface conductivity and electrokinetic data, we evaluate the changes in the segment density distribution with pH and electrolyte concentration and thereby access the spatial profile for the density of fixed charges carried by the film together with the distribution of local friction exerted by polymer segments on the tangential fluid flow. Because of the versatile application of stimuli-responsive hydrogel films, e.g., in micro- and nanofluidic systems, as support for lipid bilayer membranes or for the coating of cell culture carriers, the results will contribute to a better understanding of interactions and transport processes at those surfaces. The introduced methodology of combined electrokinetic and swelling experiments in combination with an adequate numerical solution of the governing electrohydrodynamic equations allows a comprehensive and consistent characterization of polymer surfaces in contact with aqueous solution and thus provides a basis for further progress in polymer surface engineering. Acknowledgment. We thank Nelly Rein and Karina Schreiber (Leibniz Institute of Polymer Research Dresden, Dresden, Germany) for performing sample preparation, electrokinetic measurements, and ellipsometry. J.F.L.D. acknowledges the French program ANR-07-JCJC-0024-01 PHYSCHEMBACT and the ERC framework 7 integrated project BIOMONAR for financial support.
List of Symbols Di = diffusion coefficient of ion i (m2 s-1) F = Faraday constant (C mol-1) H = height of the streaming channel (m) I = ionic strength (mol m-3) Istr = streaming current (A) Lo = length of the streaming channel (m) N = number of different ions in the electrolyte R = gas constant (J mol-1 K-1) T = temperature (K) Ustr = streaming potential (V) V = normalized pressure-driven flow velocity Veo = normalized electroosmotic flow velocity X = normalized coordinate perpendicular to the surface c = concentration (mol m-3) ci = concentration of ion species i (mol m-3) d = layer thickness (m) d = normalized layer thickness d0 = layer thickness in the collapsed state (m) d1 = layer thickness in the expanded state (m) f = segment distribution function l = width of the streaming channel (m) n = alkyl spacer length pHd = inflection point in the pH dependence of d pHR = inflection point in the pH dependence of R v = pressure-driven flow velocity (m s-1) vo = pressure-driven flow velocity at the center of the channel (m s-1) veo = electroosmotic flow velocity (m s-1) x = coordinate perpendicular to the surface (m) y = coordinate parallel to the surface, corresponding to the flow direction (m) y = content of comomomer (mol %) y = dimensionless electrical potential zi = valence of ion i Langmuir 2010, 26(23), 18169–18181
Zimmermann et al.
z = coordinate parallel to the surface (i.e., perpendicular to the flow direction) (m) ΔP = pressure difference (N m-2) ΔpHR = pH range of the transition from homogeneous to diffuse (inhomogeneous) segment distribution ΔpHd = pH range of the transition from the collapsed state to the swollen state KB = bulk solution conductivity (S m-1) Kσ = surface conductivity (S) K σ = normalized surface conductivity Kσ,0 = surface conductivity at pH 4 (S) Kσ,1 = surface conductivity at pH 10 (S) Kσm = migration component of the surface conductivity (S) Kσeo = electroosmotic component of the surface conductivity (S) Π = overall osmotic pressure (N m-2) Πel = elastic component of the osmotic pressure (N m-2) Πion = electrostatic component of the osmotic pressure (N m-2) Πmix = polymer-solvent mixing (chain entropy) component of the osmotic pressure (N m-2) Ω = normalized degree of dissociation of ionogenic groups R = decay length of the segment distribution (m) R1 = maximum decay length of the segment distribution (m)
Langmuir 2010, 26(23), 18169–18181
Article
βi = ratio between mobilities of ion i in a hydrogel film and in a bulk electrolyte εo = dielectric permittivity of vacuum (C V-1 m-1) εr = relative dielectric permittivity of the aqueous medium ψ = electrical potential (V) κ = reciprocal Debye length (m-1) η = dynamic viscosity (N s m-2) λ = hydrodynamic softness (m-1) λo = hydrodynamic softness in the case of a homogeneous segment distribution (m-1) Fo = volume density of fixed charges in the thin film (C m-3) ω = parameter that ensures a constant number of segments for any segment distribution ζ = zeta potential (V) Supporting Information Available: Streaming current versus pressure gradient data for a poly(glycidyl methacrylate) thin film on a glass (SiO2) substrate as a function of pH and ionic strength. Flow-field profiles for the soft thin film at various pH values and 0.1, 1, and 10 mM KCl electrolyte concentrations. Details on the derivation of eq 12. This material is available free of charge via the Internet at http:// pubs.acs.org.
DOI: 10.1021/la103526b
18181
