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Control of Persistent Nonequilibrium Adsorbed Polymer Layer Structure by Transient Exposure to Surfactants Alan D. Braem,† Simon Biggs,‡ Dennis C. Prieve,† and Robert D. Tilton*,† Department of Chemical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and Department of Chemistry, University of Newcastle, Callaghan, New South Wales 2308, Australia Received September 4, 2002. In Final Form: December 20, 2002 By adsorbing polymers in the form of polymer/surfactant complexes, it is possible to control the nonequilibrium structure of adsorbed polymer layers. At moderate NaCl concentrations, the extent of poly(ethylene oxide)-b-(propylene oxide)-b-(ethylene oxide) triblock copolymer adsorption to silica surfaces is increased by a sequential sodium dodecyl sulfate (SDS) complex coadsorption procedure, when compared to the extent of adsorption in the absence of surfactant. The complex adsorption procedure entails polymer/ surfactant complex formation and coadsorption at high SDS concentrations, followed by SDS dilution and eventually complete SDS removal, while maintaining a constant polymer concentration in solution. The amount of polymer that remains adsorbed after the complex adsorption procedure is nearly 40% greater than the amount that ordinarily adsorbs for the same polymer concentration in the absence of surfactant. We use independent atomic force microscopy and streaming current techniques to measure the polymer layer thicknesses. Both techniques indicate that polymer layers that were produced by the complex adsorption procedure followed by thorough rinsing in surfactant-free polymer solutions are significantly denser than the ordinary layers produced by adsorption in the absence of surfactant. Layers produced by complex adsorption contain more mass per unit area but are only approximately 70% as thick as the ordinary layers. The differences between the two adsorption procedures persist even during continued bathing of the layers in identical surfactant-free polymer solutions for 6 h. Polymer/surfactant complex adsorption thereby provides a tool for guiding adsorbed polymer layers into persistent nonequilibrium structures that might not be accessible by ordinary adsorption procedures.
Introduction Experiments often indicate that kinetic barriers prevent equilibration of polymer layers adsorbed to solid/liquid interfaces, at least on practical time scales.1-3 Physisorbed polymer layers are often hysteretic; that is, their properties depend on their processing history, and therefore it is doubtful that measurements made on such layers reflect the properties of a globally equilibrated system. Hysteresis effects may be magnified when polymers coadsorb with surfactants.4-7 In fact, the tendency of polymers to adsorb irreversibly imposes hysteretic effects on the surfactants with which they coadsorb, even in cases when pure surfactant adsorption is readily reversible. Consequently, the amounts of reversibly adsorbed surfactant and irreversibly adsorbed polymer may each depend on the order in which the polymer and surfactant are exposed to the surface. A case in point is the coadsorption of Pluronic poly(ethylene oxide)-b-(propylene oxide)-b-(ethylene oxide) * To whom correspondence should be addressed. E-mail: tilton@ andrew.cmu.edu. † Carnegie Mellon University. ‡ University of Newcastle. Current address: School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom. (1) Schneider, H. M.; Frantz, P.; Granick, S. Langmuir 1996, 12, 994. (2) Pagac, E. S.; Prieve, D. C.; Solomentsev, Y.; Tilton, R. D. Langmuir 1997, 13, 2993. (3) Sukhishvili, S. A.; Dhinojwala, A.; Granick, S. Langmuir 1999, 15, 8474. (4) Furst, E. M.; Pagac, E. S.; Tilton, R. D. Ind. Eng. Chem. Res. 1996, 35, 1566. (5) Pagac, E. S.; Prieve, D. C.; Tilton, R. D. Langmuir 1998, 14, 2333. (6) Dedinaite, A.; Claesson, P. M.; Bergstro¨m, M. Langmuir 2000, 16, 5257. (7) Velegol, S. B.; Tilton, R. D. Langmuir 2001, 17, 219.
triblock copolymers (PEO-PPO-PEO) with sodium dodecyl sulfate (SDS) surfactants at the silica/water interface.8 We previously used optical reflectometry to measure the surface excess concentration of PEO-PPO-PEO adsorbed on silica via two different adsorption pathways. We compared the following: (1) a complex adsorption pathway wherein the polymer was initially coadsorbed with surfactant, and the surfactant concentration was decreased stepwise at a constant bulk solution polymer concentration until the solution ultimately contained no surfactan; and (2) an “ordinary” pathway wherein polymer adsorbed from a solution that contained the same bulk polymer concentration as above but contained no surfactant. In the end, we compared the final states produced by the two pathways under identical conditions of equal polymer and salt bulk concentrations and no surfactant. The comparison between these two polymer adsorption pathways depended on the NaCl concentration. At low (0.1 mM) NaCl concentrations, the polymer surface excess concentration produced by the complex coadsorption pathway was less than that produced by the ordinary pathway, but at a higher (150 mM) NaCl concentration, the complex adsorption pathway produced a 37% higher polymer surface excess concentration than the ordinary adsorption pathway. The surface excess concentrations during the sequential coadsorption of Pluronic F108 and SDS at high NaCl concentration are shown in Figure 1.8 The leftmost point in both plots indicates the surface excess concentration of Pluronic F108 after SDS has been completely removed (complex adsorption pathway). For comparison, the surface excess concentration of directly (8) Braem, A. D.; Prieve, D. C.; Tilton, R. D. Langmuir 2001, 17, 883.
10.1021/la0265070 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/12/2003
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third thinner than the ordinary layers. Thus, the polymer layers have been made denser by the complex adsorption procedure. Experimental Section
Figure 1. Total surface excess concentration, Γ, of SDS and F108 in 150 mM NaCl, 1000 ppm F108 solutions. Complex coadsorption proceeded sequentially, beginning with the highest SDS concentration and decreasing the SDS concentration stepwise to zero. The horizontal line indicates the surface excess concentration achieved by ordinary adsorption from surfactantfree, 1000 ppm F108 solutions. The SDS concentration scaling on the left plot indicates the extent of polymer saturation by bound surfactant. Cooperative complexation between SDS and F108 commences at the cac and saturates at Csat, corresponding to a scaled concentration range of zero to unity. The left-most data point corresponds to [SDS] ) 0 mM. In 150 mM NaCl and 1000 ppm F108 solutions, cac ) 0.052 mM and Csat ) 17.1 mM. Data reproduced from Braem et al.8
adsorbed F108 (ordinary adsorption pathway) is shown with the horizontal line. The discrepancy in polymer surface excess concentration attained via the two adsorption pathways persisted long after removal of surfactant from the system, even though both layers were bathed in identical 1000 ppm (0.1 wt %) F108 solutions after removal of surfactant. The surface excess concentration remained stable for at least 1 h of direct observation after rinsing of surfactant from the system. (This time should be compared to the several second time scales that were characteristic of all other observed changes in an adsorbed amount in response to changing solution compositions.) One or both sets of adsorbed layers must have been trapped in a persistent nonequilibrium state. Now, focusing exclusively on the 150 mM NaCl condition, we consider how the structures of the two types of persistent nonequilibrium PEO-PPOPEO layers differ when they are produced by the two different adsorption pathways. Originally, we hypothesized that the surfactantenhanced polymer adsorption was due to a stretching of the polymer chains during complex coadsorption, induced by electrostatic repulsions between neighboring polymerbound SDS aggregates and between those aggregates and the negatively charged silica surface. Since the thickness and refractive index of an adsorbed polymer layer may not be decoupled reliably in the optical reflectometry data analysis, we were motivated to use two independent techniques to test the chain-stretching hypothesis. Using atomic force microscopy (AFM) to measure the steric repulsion between two opposing layers on silica surfaces, we extract information about the relative thicknesses of “ordinary” polymer layers as opposed to “surfactantprocessed” layers produced by the complex adsorption pathway. We also use a streaming current technique to measure the shift in ζ-potential caused by these two polymer adsorption pathways, from which we extract the hydrodynamic thicknesses of the two types of polymer layers on silica, in the absence of surfactant. For consistency, the adsorption pathways used in the current work are the same as those in Braem et al.8 Results from the two independent experimental techniques are mutually consistent. Both indicate that instead of leaving the polymer in the hypothesized stretched conformation, the surfactant-processed layers that contain more mass per unit area are in fact approximately one-
Materials. Pluronic F108 was obtained in prill form as a gift from BASF Corporation, lot WP10-549B. Pluronic F108 is the highest molecular weight Pluronic. On the basis of manufacturer literature, the average composition of Pluronic F108 is EO133PO50-EO133, and the total molecular weight is 14600 g/mol. Critical micelle concentrations (cmc) reported at 25 °C for Pluronic F108 are highly variable, ranging from 321 to 7140 ppm.9-12 The polymer concentration was 1000 ppm (0.1 wt %) in all experiments reported here. Previous pyrene solubilization studies indicate that our 1000 ppm solutions are not micellar.8 SDS was purchased from Fluka (Micro-Select grade, >99% pure) and used as received. Comparison of as-received SDS to SDS purified by the acetone-washing procedure13,14 showed that any impurities in the as-received SDS sample did not affect coadsorption results in this system. Fresh SDS solutions were prepared the day of each experiment. The critical aggregation concentration (cac) for SDS binding to Pluronic F108 in solution is approximately 3-5% of the cmc.8 In Pluronic F108 solutions containing 150 mM NaCl, the SDS cac is 0.05 mM. RBS 35 detergent solution, ACS-grade NaCl, Chromerge, and ACS-grade hydrochloric acid were purchased from Fisher Scientific, and sodium hydroxide pellets were purchased from EM Science. All were used as received. All water was purified by reverse osmosis followed by treatment with the Milli-Q Plus system of ion exchange and organic adsorption cartridges from Millipore Corp. The pH of all solutions was unmodified from the air-equilibrated water pH of 5.5-6.0. All experiments were conducted at room temperature, approximately 21-22 °C for AFM and 23-25 °C for streaming current experiments. Adsorption Substrates. Fused silica microscope slides for AFM experiments were obtained from ESCO Products, Inc., and cut into 1 × 1 cm pieces before cleaning according to the protocol below. Surfaces for streaming current experiments were sodalime glass microscope slides from Fisher Scientific (Fisher Finest). All slides were precleaned by sonication in RBS detergent solution for 10 min in a Branson Ultrasonic Bath. Then, the substrates were soaked in Chromerge for 30 min, followed by a 30-min soak in 6 N hydrochloric acid. A subsequent 30-min soak in 10 mM sodium hydroxide solution yielded negatively charged surfaces that were completely water-wettable. Extensive water rinses followed each soaking step. Cleaned slides were stored in water. Immediately before the start of each experiment, the slides were thoroughly rinsed with freshwater and dried under a purified nitrogen (Valley National Gases, Inc.) jet that produced a uniform retreat of a water film from the surface. Ultrasharp silicon AFM cantilevers with nominal 10-nm radius of curvature tips were purchased from K-Tek International, Inc. These tips display native oxide layers on their surfaces. Depending on the particular cantilever chosen for each experiment, the spring constant varied from 0.01 to 0.08 N/m. All cantilevers were cleaned by exposure to an ozone-generating UV lamp for 45 min (Jelight Model 42). After the slide and cantilever were assembled in the AFM fluid cell, they were soaked for 30 min in 10 mM NaOH solution and finally were rinsed profusely with water. Electrodes. Ag/AgCl electrodes for the streaming current measurements were prepared by cutting lengths of 99.99% pure, 16-gage silver wire (Aldrich), then processing, and coating according to the method of Westermann-Clark.15 The electrodes (9) Alexandridis, P.; Holzwart, J. F.; Hatton, T. A. Macromolecules 1994, 27, 2414. (10) Meilleur, L.; Hardy, A.; Quirion, F. Langmuir 1996, 12, 4697. (11) Lopes, J. R.; Loh, W. Langmuir 1998, 14, 750. (12) Batrakova, E. V.; Lee, S.; Venne, A.; Alakhov, V. Y.; Kabanov, A. V. Pharm. Res. 1999, 16, 1375. (13) Kim, J.-H.; Domach, M. M.; Tilton, R. D. J. Phys. Chem. B 1999, 103, 10582. (14) Kim, J.-H.; Domach, M. M.; Tilton, R. D. Langmuir 2000, 16, 10037. (15) Westermann-Clark, J. M.S. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1979.
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were tested by measuring the bias potential when both electrodes were immersed together in a beaker of 1 mM NaCl solution. Electrodes with bias potentials that exceeded 1 mV or that fluctuated by more than 10% were rejected. Sets of electrodes were tested routinely before use. Determining Polymer Layer Thickness by Atomic Force Microscopy. A Nanoscope III AFM from Digital Instruments was used to measure in situ forces between adsorbed layers on opposing silica surfaces. The liquid cell volume was approximately 0.1 mL. To change the solution composition in the liquid cell, at least 10 mL of the solution of interest was flushed through the cell without disassembling it. Force measurements were made by maintaining the tip above one location on the surface and vertically translating the surface (via the calibrated piezoelectric driver) with 1-Hz oscillatory motion. The amplitude of the piezooscillation was chosen so that there was both a significant distance over which the tip had no interaction with the surface (no cantilever deflection) and a significant distance over which the tip moved in constant compliance with the piezoelectric driver. Forces were calculated from the measured cantilever deflection by applying Hooke’s Law with a predetermined cantilever spring constant. In the work presented here, the nominal spring constant and tip radius values that were provided by the manufacturer were used. Although this introduced uncertainty in the force magnitude, we used the shape of the force curve, not the magnitude, to determine the polymer layer thickness. Changes in the separation distance, ∆D, were determined directly from the calibrated piezoelectric driver displacement and the measured cantilever deflection. There was some ambiguity in the absolute separation distance D because of the uncertain definition of the point of zero separation. As is customary, we took the onset of the constant compliance regime of the force curve (where the tip deflection exactly corresponds to the piezoelectric translation) to represent the zero separation distance between the opposing surfaces. This would not necessarily correspond to direct contact between tip and surface because constant compliance would occur whenever the force gradient exceeded the cantilever spring constant. It is possible that some polymer would be trapped in the gap. Given the uncertainty in the absolute separation distance, it is preferable to calculate the polymer layer thickness from the decay length of the steric repulsive force,16 rather than estimate the apparent separation distance that marks the onset of the steric repulsion. The Alexander-de Gennes scaling model17,18 provides the force per unit area, f, between two flat plates with grafted polymers at relatively high surface coverage,
[( ) ( ) ]
f ≈ kTΓ3/2
2L0 D
9/4
-
D 2L0
3/4
(1)
where Γ is the polymer surface excess concentration, L0 is the polymer layer thickness (the distance from the surface at which the local polymer concentration equals the bulk concentration), and D is the separation distance between the two underlying surfaces. This equation is valid for D/(2L0) < 1. For 0.2 < D/(2L0) < 0.9 the above expression can be approximated by19,20
f ≈ 50kTΓ3/2e-πD/L0
(2)
Applying Derjaguin’s approximation, the force divided by radius for a sphere interacting with a flat plate becomes
F 100L0 ) kTΓ3/2e-πD/L0 R π
(3)
Thus, steric force curves may be fit to an exponential decay in a certain regime, and the resulting decay lengths may be (16) Butt, H.-J.; Kappl, M.; Mueller, H.; Raiteri, R.; Meyer, W.; Ruehe, J. Langmuir 1999, 15, 2559. (17) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (18) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189. (19) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press Inc.: San Diego, 1992. (20) O’Shea, S. J.; Welland, M. E.; Rayment, T. Langmuir 1993, 9, 1826.
interpreted as being proportional to the steric thickness. Uncertainty in the exponential prefactor does not affect the layer thickness calculation. Although the Alexander-de Gennes model was developed for high-molecular-weight grafted polymers, Luckham has shown that the model successfully predicts force data for both lowmolecular-weight grafted polymers and for freely adsorbed homopolymers.21 Meaningful comparisons of decay lengths are possible when the force curve is exponential in shape. Each experiment was conducted with fresh surfaces and tips. The NaCl concentration of all solutions used in all AFM experiments was 150 mM. This was the concentration where increased adsorption was observed previously, and the range of the electrostatic double-layer repulsion would be sufficiently compressed as to reliably distinguish steric forces from doublelayer forces. Before adsorbing polymer layers, we routinely measured the force between opposing bare silica surfaces in 150 mM NaCl solutions. To proceed with the experiment, we required that the baseline portion of this force curve be flat and that the exponential decay length of the measured force agree (within 10%) with the theoretically predicted Debye length for electrostatic doublelayer repulsion. For clean silica surfaces, there should also be no adhesion or hysteresis upon retraction of the surfaces. If the bare surface criteria were met, we proceeded with the adsorption from F108 or F108/SDS solutions by displacing the polymer-free NaCl solution with at least 100 cell volumes of the solution of interest. In all cases, force curves were measured in the presence of 1000 ppm Pluronic F108 and 150 mM NaCl. In the first type of experiment (probing “ordinary” F108 layers that were never exposed to surfactant) there was no difference between the force curves acquired after 5 min or after 1 h of adsorption. For the second type of experiment (probing “SDS-processed” F108 layers) we flushed the liquid cell with solutions containing 1000 ppm F108, 150 mM NaCl, and 50 mM SDS. We then sequentially proceeded through a series of surfactant concentrations, diluting from 50 mM SDS to 10, 5, 2.5, 1, and finally 0 mM, always in the presence of 1000 ppm F108 and 150 mM NaCl. We allowed a 5-min pause between each solution change. We began acquiring force curves 5 min after completion of the final 0 mM SDS flush (still in the presence of 1000 ppm F108 and 150 mM NaCl). As was the case with “ordinary” F108 layers, the force curves no longer changed 5 min or more after this final step. Determining Polymer Layer Thickness by Streaming Current. The ζ-potential is the electrostatic potential that exists at the hydrodynamic plane of shear adjacent to a charged surface. Adsorbed polymers shift the shear plane away from the underlying surface. The extent of this shift defines the hydrodynamic thickness of the polymer layer. Because of this shift in the shear plane, the ζ-potential will be smaller in magnitude after adsorption of uncharged polymers than before, as the electrostatic double-layer potential decreases in magnitude with increasing distance from the surface. Assuming the polymer does not significantly displace adsorbed ions or otherwise disturb the charge density of the underlying surface, this change in ζ-potential may be analyzed to determine the thickness of an adsorbed layer of nonionic polymers.2 The adsorption substrate for streaming current measurements was soda-lime glass. The primary chemical structure in this glass is the SiO2 tetrahedron.22 This glass surface acquires charge in water through dissociation of surface silanol groups (isoelectric point ) 2-3).22 Another source of charge is the specific adsorption of co-ions.23-25 For the purpose of this discussion, it suffices to note that the degree of co-ion adsorption will depend on the ionic strength of the solution and that different co-ions may have different affinities for the surface. (21) Luckham, P. F. Adv. Colloid Interface Sci. 1991, 34, 191. (22) Shelby, J. E. Introduction to Glass Science and Technology; Royal Society of Chemistry: Cambridge, 1997. (23) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981. (24) Hunter, R. J. Foundations of Colloid Science; Clarendon: Oxford, 1989; Vol. 2. (25) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: San Diego, 1995; Vol. 2.
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We use the classical Gouy-Chapman-Stern model for the structure of the charged layers near a flat surface,23 and we take the ζ-potential to represent the potential ψd at the outer Helmholtz plane (OHP), that is, the origin of the diffuse part of the double layer. In a solution of symmetric electrolytes, GouyChapman theory predicts that the potential decays as a function of distance y from the OHP according to
(
tanh
)
( )
zeψd zeψ(y) ) tanh exp(-κy) 4kT 4kT
(4)
where e is the charge of an electron, z is the valency of the electrolyte, k is Boltzmann’s constant, and T is the absolute temperature. κ is the Debye parameter
κ)
x
2e2cz2 0rkT
(5)
where c is the electrolyte concentration, 0 is the permittivity of free space, and r is the dielectric constant of the solvent. The density of charges in the diffuse layer, F(y), is given by Poisson’s equation:
∇2ψ(y) ) -
F(y) r0
(6)
Finally, the surface charge density is given as a function of surface potential by
( )
20κkT zeψd sinh ze 2kT
σ0 )
∑[|z |∫ [c (y) - c (∞)] u (y) dy] ∞
i
i
0
i
i
∫
Is ) 2w
i
(8)
where F is the Faraday constant, zi is the valence of ions of type i, ci(y) is the molar concentration of ionic species i as a function of distance y from the surface, ci(∞) is the corresponding bulk concentration, and ui is the distance-dependent mobility of ionic species i.27 Unfortunately, the current understanding of the (26) Lyklema, J.; Minor, M. Colloids Surf., A 1998, 140, 33. (27) Werner, C.; Ko¨rber, H.; Zimmerman, R.; Dukhin, S.; Jacobasch, H. J. Colloid Interface Sci. 1998, 208, 329.
h/2
0
vz(y) F(y) dy
(9)
where vz(y) is the velocity profile, w is the gap width, and h is the gap height. Ions below the shear plane, where there is no convection, experience no flux. For large w/h, the velocity profile is described by the Poiseuille equation for fully developed, laminar flow, linearized near the wall for the typical case that the diffuse layer is very thin relative to the gap height (y , h/2),
vz )
(7)
The following discussion is presented in some detail to establish the operational difference between streaming current and streaming potential measurements. A streaming potential or streaming current arises when liquid is driven past a charged surface by the application of a pressure gradient. Consider a charged conduit connected to liquid reservoirs on both ends. Each reservoir has an identical reversible electrode placed inside, and the electrodes are connected to an external circuit. When a pressure gradient is applied to the reservoirs, fluid flows through the conduit, and the diffuse layer ions are convected to one of the electrodes. This ion flux is the streaming current. If the external circuit has a very low resistance, then the ion flux is converted to electron flux through the external circuit and the streaming current is measurable. If the external circuit has a very high resistance, charge builds up on the electrodes and a streaming potential arises instead. This potential difference causes a conductive current in the opposite direction of the fluid flow that counterbalances the streaming current. We previously used streaming potential measurements to characterize adsorbed polymer layer thicknesses,2 but that method suffers from the uncertain influence of surface conductivity on the ζ-potential measurement. Surface conduction refers to the migration of charge groups in the double layer in response to an electric field. Significant debate persists in the literature as to the mechanisms of surface conductivity. The description by Lyklema and Minor,26 summarized below, is the most frequently invoked explanation of the phenomenon. The surface conductivity, λs, is a surface excess property that can be described by
λs ) F
properties of ions in fixed layers is limited, and the ionic mobility function ui(y) is not known.25-28 Within this framework, two important issues arise when using an electrokinetic technique to determine a polymer hydrodynamic layer thickness. First, the surface conductivity of the fixed ion layer will be directly related to the concentration of ions adsorbed to the surface, which may be altered by adsorption of the polymer. Second, the presence of uncharged adsorbed species at the surface (e.g., neutral polymer) may alter the surface conductivity by altering the mobility of both the fixed layer and diffuse layer ions. It is therefore preferable to measure the ζ-potential by a method that is not influenced by surface conductivity. As will be shown below, this is the advantage of the streaming current method over the streaming potential method. The equations that describe the streaming current or streaming potential caused by pressure-driven laminar flow between parallel flat plates may be derived from the Gouy-Chapman theory. Following the derivation by Hunter,23 first one defines the streaming current Is as the total flux of diffuse layer ions due to convection of fluid in the z direction,
∆Ph y 2µL
(10)
where ∆P is the pressure drop over the length L of the flow channel and µ is the fluid viscosity. Substituting this expression for velocity and the Poisson equation, eq 6 for the charge distribution into eq 9 yields
Is )
-0∆Pwh µL
∞ 2
∫ ddyψ y dy 0
2
(11)
Integrating by parts, taking the product y dψ/dy ) 0 both at the surface (y ) 0) and outside the diffuse layer (y ) ∞), and then simplifying yields
Is ) -
0ζ∆Pwh µL
(12)
This is the streaming current one would measure if a lowresistance ammeter were connected to electrodes at both ends of the fluid cell. Note that the streaming current is not a function of the surface conductivity since there is no electric field along the direction of flow parallel to the surface when the resistance of the external circuit is negligible. If instead one connected a large resistance voltmeter to the electrodes, then charge buildup on the electrodes would create a potential difference along the fluid cell. This streaming potential, Es, in turn would generate a conduction current, Ic, in the direction opposite to the fluid flow direction:
Ic )
whEsλb 2wEsλs + L L
(13)
Here, λb is the bulk electrical conductivity of the solution and λs is the specific surface conductivity. The conduction occurs within the fixed and diffuse parts of the double layer as well as the bulk; λs as defined above contains both fixed and diffuse parts of the double layer, and λb only refers to the conductivity outside the double layer. A steady-state streaming potential is achieved in the cell when the two currents balance each other, so Is + Ic ) 0. Substituting the expressions for Is and Ic and (28) Lyklema, J. Colloids Surf., A 1994, 92, 41.
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solving for the streaming potential yields
Es )
∆P0ζ 2λs µ λb + h
[
]
(14)
A typical approach in the literature is to assume that all conductance occurs in the bulk fluid, setting λs equal to zero in eq 14.25 Unfortunately, the assumption that there is no surface conductivity is frequently unacceptable.25-30 In cases where surface conductivity may be significant, it is clearly necessary to either use streaming current to determine the ζ-potential or to combine streaming potential measurements with some independent measurement of the surface conductivity. The device used in the current work has the capability of measuring both streaming current and streaming potential. Electrokinetic techniques have been used to measure the adsorption of surfactants,32-34 particles,33,34 proteins,27,35 and polymers.2,29,36-39 To interpret an adsorption-induced change of ζ-potential in terms of the adsorbed layer thickness, the layer should not alter the surface charge density. For the adsorption of uncharged polymers, such as the Pluronic F108 triblock copolymers, the underlying surface charge could in principle be altered by competitive displacement of adsorbed co-ions by polymer segments or by a change in the degree of dissociation of ionizable surface groups. Churaev et al.37 found that this is not a significant factor for PEO homopolymer adsorption to glass capillaries. The change in ζ-potential is then dominated by the shift in the hydrodynamic shear plane. Given measurements of the ζ-potential before adsorption, ζbare, and after adsorption, ζads, the polymer layer thickness, δ, is found by equating ζbare ) ψd, that is, ψ(y ) 0), and ζads ) ψ(δ) in eq 4 and rearranging as
( ) ( ) ( )
zeζbare 4kT δ ) κ-1 ln zeζads tanh 4kT tanh
(15)
One should perform a consistency check on the thickness measurements by determining δ at several different Debye lengths (i.e., several ionic strengths). Assuming the adsorbed polymer layer structure to be insensitive to ionic strength variations, δ should not vary. Streaming Current Apparatus. A primary concern with this type of apparatus is the avoidance of fluid leaks while forcing fluid flow at large pressures through extremely narrow gaps. Use of common chemical sealants such as silicone grease should be strictly avoided as a potential source of contamination. Our apparatus is illustrated schematically in Figure 2. The fluid only comes into contact with inert fluorinated polymers, electrodes, and the test glass surfaces. There is also no possibility of fluid paths between the fluid reservoirs (where the electrodes are located) other than the well-defined rectangular flow channel, eliminating the possibility of extraneous conduction paths. The gap height may be fixed at a known value between 0.05 and 0.25 mm so that significant pressure drops may be achieved to produce readily measurable streaming currents or potentials. The width and height of the flow channel are determined by a pair of (29) Minor, M.; van Leeuwen, H. P.; Lyklema, J. Langmuir 1999, 15, 6677. (30) Gu, Y.; Li, D. J. Colloid Interface Sci. 2000, 226, 328. (31) Johnson, S. B.; Drummond, C. J.; Scales, P. J.; Nishimura, S. Langmuir 1995, 11, 2367. (32) Nishimura, S.; Scales, P. J.; Biggs, S.; Healy, T. W. Langmuir 2000, 16, 690. (33) Hayes, R. A. Colloids Surf., A 1999, 146, 89. (34) Zembala, M.; Adamczyk, Z. Langmuir 2000, 16, 1593. (35) Elgersma, A. V.; Zsom, R. L. J.; Lyklema, J.; Norde, W. Colloids Surf. 1992, 65, 17. (36) Churaev, N. V.; Sergeeva, I. P.; Zorin, Z. M.; Gasanov, E. K. Colloids Surf., A 1993, 76, 23. (37) Churaev, N. V.; Sergeeva, I. P.; Sobolev, V. D. J. Colloid Interface Sci. 1995, 169, 300. (38) Eremenko, B. V.; Malysheva, M. L.; Rusina, O. D.; Kutsevol, N. V.; Zeltonozskaya, T. B. Colloids Surf., A 1995, 98, 19. (39) Gittings, M. R.; Saville, D. A. Langmuir 2000, 16, 6416.
Figure 2. Schematic of the flat plate streaming current apparatus. The parallel slit flow channel of width w, thickness h, and length L is assembled by placing two Teflon strips (crosshatched in figure) between the top and bottom glass microscope slides (standard 1 in. × 3 in. × 1 mm slides, shown stippled in end view). Two additional Teflon strips below the lower slide and two above the top slide cushion them against cracking when the device is tightly closed by screwing an aluminum clamping piece to the top of the base piece. Two Teflon fluid reservoirs that serve the inlet and outlet of the flow channel are sealed against the ends of the slides by two rectangular Viton (fluorinated elastomer) gaskets, each newly prepared for each experiment by cutting a slit in a Viton sheet. This slit, outlined by dotted lines in the end view, is larger than the gap between the slides but smaller than the outer dimensions of the slide sandwich, to prevent leakage while not impeding flow into or out of the channel. The reservoir pieces are held in place by aluminum pieces (shaded gray in top view) that both guide the reservoirs into alignment with the flow channel and rigidly secure them in place. Each reservoir has four ports: one for flow in or out, one for electrode insertion, one for connecting to a pressure transducer, and one extra (plugged in current experiments). Ag/AgCl electrodes are connected to an electrometer/picoammeter. incompressible Teflon spacer strips placed between the two glass slides. The reservoirs are fitted with pressure transducers to directly measure the pressure drop across the flow channel, rather than inferring it from volumetric flow rate measurements. The Teflon fluoropolymer reservoir pieces have no sharp corners where bubbles might be trapped. Furthermore, the reservoir chambers end in a gradual taper to the width of the Viton fluoropolymer gasket slit where they meet the flow channel, thus reducing hydrodynamic entrance and exit effects. No internal dimension of the reservoir is small enough to contribute significantly to the total pressure drop in the system. Electrodes are inserted through a leak-proof Viton fluoropolymer septum in each reservoir and firmly held in place with a threaded nut. The total volume of the combined reservoirs and flow channel is 10 mL. The instrument comprises the flow cell described above, a syringe pump (Orion Sage model M362), a differential pressure transducer (Validyne Corp., Model DP1-15-38 with reader model CD23-A-1-A-1-B), two Ag/AgCl electrodes, and an electrometer (Keithley Model 6514) that can function either as a high impedance voltmeter (to measure streaming potential) or as a picoammeter (to measure streaming current). Streaming Current Protocol. We filled the apparatus carefully to eliminate air bubbles anywhere in the system. To change the solution composition (SDS or NaCl concentration), we displaced the first solution by pumping 600 mL of the new solution (60 flow system volumes) through the system while measuring the conductivity of the bulk effluent (Omega conductivity meter, Model PHH-10-KIT). Thus, we deemed the solution changeover to be complete when we verified that the effluent conductivity was identical to the source solution conductivity. Before we began the pressure-driven flow, we recorded the bias current (current with no pressure-driven flow)
Control of Nonequilibrium Polymer Layer Structure and then proceeded to increase the pressure stepwise. Five to ten seconds was required for the streaming current to stabilize after each step change in pressure drop. After sampling the desired range of pressure drops, we then repeated one of the lower pressure drops to check for hysteresis (routinely nonexistent) and finally re-checked the bias current. The standard deviation of the individual streaming current measurements was typically
