A Combined Streaming-Potential Optical Reflectometer for Studying

Langmuir 2005, 21, 10127-10139

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A Combined Streaming-Potential Optical Reflectometer for Studying Adsorption at the Water/Solid Surface† O. Theodoly,‡,§ L. Casca˜o-Pereira,‡,| V. Bergeron,⊥ and C. J. Radke*,⊥ Chemical Engineering Department, University of California, Berkeley, California 94720-1462, and Ecole Normale Superieure de Lyon, Laboratoire de Physique, 69007 Lyon, France Received March 14, 2005. In Final Form: May 13, 2005 A novel in-situ streaming-potential optical reflectometry apparatus (SPOR) was constructed and utilized to probe the molecular architecture of aqueous adsorbates on a negatively charged silica surface. By combining optical reflectometry and electrokinetic streaming potentials, we measure simultaneously the adsorption density, Γ, and zeta potential, ζ, in a rectangular flow cell constructed with one transparent wall. Both dynamic and equilibrium measurements are possible, allowing the study of sorption kinetics and reversibility. Using SPOR, we investigate the adsorption of a classic nonionic surfactant (pentaethylene glycol monododecyl ether, C12E5), a simple cationic surfactant (hexadecyl trimethylammonium bromide, CTAB) of opposite charge to that of the substrate surface, and two cationic polyelectrolytes (poly(2(dimethylamino)ethyl methacrylate), PDAEMA; (poly(propyl methacrylate) trimethylammonium chloride, MAPTAC). For the polyethylene oxide nonionic surfactant, bilayer adsorption is established above the critical micelle concentration (cmc) both from the adsorption amounts and from the interpretation of the observed ζ potentials. Near adsorption saturation, CTAB also forms bilayer structures on silica. Here, however, we observe a strong charge reversal of the surface. The SPOR data, along with Gouy-Chapman theory, permit assessment of the net ionization fraction of the CTAB bilayer at 10% so that most of the adsorbed CTAB molecules are counterion complexed. The adsorption of both C12E5 and CTAB is reversible. The adsorption of the cationic polymers, however, is completely irreversible to a solvent wash. As with CTAB, both PDAEMA and MAPTAC demonstrate strong charge reversal. For the polyelectrolyte molecules, however, the adsorbed layer is thin and flat. Here also, a Gouy-Chapman analysis shows that less than 20% of the adsorbed layer is ionized. Furthermore, the amount of charge reversal is inversely proportional to the Debye length in agreement with available theory. SPOR provides a new tool for elucidating aqueous adsorbate molecular structure at solid surfaces.

Introduction The adsorption of aqueous surface-active solutes, such as surfactants, polymers, polyelectrolytes, and proteins, onto solid surfaces has important applications in a wide variety of technologies and undergirds colloid science. Hence, the adsorption process has been studied extensively1-4 using an impressive array of experimental tools, including among others ellipsometry, small-angle neutron scattering, optical and total internal reflection, vibrational sum frequency spectroscopy, atomic force microscopy (AFM), the quartz crystal microbalance, optical waveguide spectroscopy, fluorescence quenching, surface plasmon resonance, and the surface forces apparatus. Most solid surfaces immersed in water, especially oxides, are charged depending on the solution pH and ionic strength. The surface charge strongly influences and in many cases controls the equilibrium adsorption amount and the sorption kinetics by determining the molecular configu†

Part of the Bob Rowell Festschrift special issue. * To whom correspondence should be addressed. E-mail: radke@ berkeley.edu. Phone: 510-642-5204. Fax: 510-642-4778. ‡ University of California. § Currently at Complex Fluid Laboratory, Rhodia, Inc., Cranbury, New Jersey 08512-7500. | Currently at Genencor International, Palo Alto, California 94304-1013. ⊥ Ecole Normale Superieure de Lyon. (1) Atkin, R.; Craig, V. S. J.; Wanless, E. J.; Biggs, S. Adv. Colloid Interface Sci. 2003, 103, 219. (2) Tiberg, F.; Brinck, J.; Grant, L. Curr. Opin. Colloid Interface Sci. 2000, 4, 411. (3) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent B. Polymers at Interfaces; Chapman & Hall: New York, 1993. (4) Malmstead, M. Biopolymers at Interfaces; Surfactant Science Series; Marcel Dekker: New York, 2003; Vol 110.

ration that the adsorbate exhibits at the solid surface. Hence, knowledge of the surface charge density, in addition to adsorbed amounts, is highly desirable for elucidating adsorption mechanisms. Almost always, surface charge (e.g., typically garnered from electrokinetic measurements) is assessed separately from the measurement of adsorption coverage. Accordingly, there can be concern as to whether the exact same surface and solution conditions are present in each distinct experiment. Further, a determination of the transient surface charge during the adsorption or desorption process is not currently possible. The goal of this work is to assess both the dynamic surface charge and adsorbate density simultaneously on the same solid surface for either adsorption (loading) or desorption (washout). Optical reflection from a flat, solid surface that constitutes one wall of a narrow flow channel along with electrokinetic streaming appeared to be a promising instrument design. On the basis of this reasoning, we constructed a novel SPOR apparatus that couples in-situ measurement of both streaming potential and opticalreflection intensity. The new instrument determines simultaneously the zeta (ζ) potential of the solid/water surface and the adsorption density, Γ, of the adsorbing species. In addition, both ζ and Γ are followed in time, permitting the study of sorption kinetics. This information permits an assessment of not only surface equilibrium mass and charge densities but also the kinetics of adsorption and desorption. Below we describe the design and construction of the combined SPOR and its operation. This is followed by illustrations of its usefulness by studying the adsorption of simple aqueous nonionic and ionic surfactants and aqueous polyelectrolytes on silica.

10.1021/la050685m CCC: $30.25 © 2005 American Chemical Society Published on Web 08/16/2005

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Figure 1. Overall schematic of the streaming-potential optical reflectometer (SPOR) including the optical train. A chopper and lock-in amplifiers are employed to increase the signal-to-noise ratio.

where , η, and κe are, respectively, the dielectric permittivity, the Newtonian viscosity, and the conductivity of the bulk solution. To garner precise values of ζ from eq 1, the pressure drop across the channel must be large enough to create a measurable voltage difference. This criterion demands sufficiently narrow channels such that reasonable flow rates can generate voltage differences on the order of 1 V yet still remain in the laminar regime. We employ channel depths of around 100 µm. As discussed later, such small channel depths cause difficulty in the reflection optics, obviating the simple linear relation between IP/IS and Γ. By utilizing a noncoherent light source as the excitation beam, we overcome this limitation and successfully determine both Γ and ζ simultaneously as functions of time.

Optical Flow Cell. Figure 2 illustrates that the flow channel is a sandwich of a silicon wafer coated with 100 nm of SiO2, a slotted film of Teflon (McMaster-Carr), and a fused silica plate. The use of a silica-coated silicon wafer is requisite for the reflectometry measurement of adsorption, as described below. The transparent silica plate serves both as an optical window allowing the light beam to enter and reflect off the wafer SiO2/water interface and as a matching silica surface for the deposited SiO2 film. Thus, the channel consists of two opposing silica surfaces. Dimensions of the channel are controlled by cutting the desired shape into the Teflon spacer. The channel depth is controlled by the thickness of the Teflon film with different values available from 25 µm and larger. We mostly use a 60 × 15 × 0.125 mm3 channel. As shown in Figure 3a, the flow channel fits into a Teflon fixture and is held in place by two stainless steel retaining plates. Two cavities in the Teflon body at the flow channel inlet and outlet provide space for pressure and electrode taps. These taps are drilled into the opposing sides of the Teflon fixture, as illustrated in Figure 3b. Flow enters into the lower front face of the fixture and leaves through the top front face. A 20-mm 45° fused silica prism (Optosigma 0550197), pictured in both Figures 2 and 3a, is placed at the front face of the silica channel plate. It allows entrance of the light beam into the channel at an angle that is smaller than the angle of total reflection at the silica/air interface. Good optical contact is ensured between the plate and the prism by a specific indexmatching oil (Cargille Labs 50350). Reflectometer. Our optical reflectometer is based on an instrument developed by Heuvelstand and Oldenzeel6 that allows continuous measurement of the adsorbed amount. A linearly polarized laser beam is reflected off the adsorbing solid surface. The reflected beam is split via a broadband polarizing beam splitter (Optosigma

(5) Hunter, H. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981.

(6) Heuvelstand, W. J. M.; Oldenzeel, M. Chem. Weekbl. 1989, 85, 307.

Apparatus Design Rationale. Figure 1 provides an overall schematic of the apparatus. Basically, the aqueous solution under study flows through a rectangular channel whose walls are flat to permit reflectometry via an optical prism. The reflected beam from the back wall of the flow channel is split into normal and parallel component intensities, IS and IP, respectively, where under the particular cell design chosen the ratio IP/IS is linearly related to the solute adsorption amount Γ. While the optical intensity ratio is monitored, the axial pressure and voltage differences along the flow channel are also measured dynamically, as depicted in Figure 1. The ζ potential of the solid/water interface or the electrostatic potential at the plane of noslip is determined by the Smoluchowski relation for laminar flow in a closed channel5

∆V ) ζ ∆P ηκe

(1)

Adsorption at the Water/Solid Surface

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Figure 2. Perspective schematic of the flow channel. The transparent silica plate serves as a channel wall and permits light reflection from the SiO2 coating on the silicon wafer.

Figure 3. Schematic of the flow channel incorporated into the optical cell. (a) View from the top displaying the optical prism and light path. (b) View from the front highlighting the pressure and electrode taps.

0672240, wavelength range 460-680 nm) into its normal (IS) and parallel (IP) intensity components (with respect to the plane of incidence). IP and IS are directly measured using photodiodes. The relevant physical parameter in this experiment is the ratio between the parallel and the perpendicular reflection coefficients, RP and RS, respectively,

IP RP )f RS IS

(2)

where f is an instrument parameter that accounts for the different losses through the prism and the beam splitter as well as for the difference in sensitivity of the two

photodiodes. f is determined experimentally using a known substrate for which the theoretical ratio RP/RS can be calculated. Here f is determined before each adsorption experiment using the bare substrate as a reference, as outlined in Appendix A. A very important aspect of the reflection technique is the nature of the solid adsorbent. It is necessary to use a silicon wafer overlaid with about a 100-nm layer of grown silica (UC Berkeley MicroFabrication Laboratory) as the adsorbent because the optical properties of this specific system immersed in aqueous solution permit a linear relation between RP/RS and the adsorption density Γ that is independent of the refractive index profile of the adsorbate:6,7

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RP ) aΓ + b RS

Theodoly et al. Table 1. Optical Parameters

(3) nSi

In this expression, a and b are instrument constants that depend on the beam wavelength λ, the angle of incidence θi, the refractive index of the substrate, the thickness and refractive index of the SiO2 overlayer, and the refractive index increment, dn/dc, characteristic of the adsorbate in the solvent, as determined here from laser differential refractometry (Chromatix KMX-16). Pertinent refractive index increments are listed in Table 1 of Appendix A. Given this information, a and b are calculated on the basis of Fresnel reflection from a multilayer-slab optical model. Details of the calculation are given in Appendix A. Because IP and IS are measured dynamically, eqs 2 and 3 permit the measurement of the adsorption kinetics through Γ(t). The working angle of incidence, θi ) 72.5°, is chosen to be close to the Brewster angle to maximize the sensitivity of the instrument. Streaming Potential. A small centrifugal pump (Metering Pump, Inc., model QRP 2-CKC) provides flow through the channel. The pump head is made of Teflon and ceramic and needs no lubricant, which is crucial to avoid contamination. Likewise, all tubing (3.15 and 6.35 mm) as well as the cell body are made of Teflon, which allows ease of cleaning. Pressure pulses induced by the pump are dampened using two in-line corrugated Teflon bellows placed directly upstream and downstream from the pump. The pressure drop between the inlet and the outlet of the channel is measured via two silicon detectors (Druck PMP 1240). The difference in the electrostatic potential is detected with two Ag/AgCl reference electrodes (Futura Reference, AgCl, quartz fiber, 12 × 130 mm2, Beckman) and a high-entry impedance electrometer (Keithley model 602, entry impedance 1014 Ω). The Ag/AgCl electrodes are reversible to solution chloride ions, making them stable during operation with little offset potential. Also, the commercial reference Ag/AgCl electrodes isolate the active surfaces of the electrode from the different adsorbates in the flow channel. Thus, electrode performance does not degrade or drift over time. All experiments were conducted at ambient temperature, 22 °C, and at a typical flow rate of 110 mL/min. The resulting pressure drop across the rectangular flow channel (60 × 15 × 0.125 mm3) was about 40 kPa, giving a Reynolds number of 180 that is well within the laminar regime. We experimentally verified that both the pressure drop versus flow rate and the streaming-potential difference (offset corrected) versus pressure drop relations were linear according to the Poiseuille and Smoluchowski laws, respectively. To follow the dynamic ζ potential, we use eq 1 with the ∆V and ∆P signals monitored versus time and corrected by any offset values measured in the absence of flow. Transient ζ potentials were in excellent agreement with calibrating measurements made via a step sequence of increasing or decreasing flow rates. Multiple Reflections. As noted above, the use of a narrow 100-µm-thick channel is necessary to ascertain the ζ potential, but the small channel depth introduced a serious complication in the reflectometry measurement when using a He/Ne laser light source. Figure 4 illustrates this complication. Here, the reflectivity ratio, IP/IS, and the cell pressure drop, ∆P, are graphed as functions of time upon initiation of flow with an aqueous KCl solution, denoted by the vertical arrow. As the pressure drop rises, (7) Dijt, D. C.; Cohen Stuart, M. A.; Hofman, J. E.; Fleer, G. J. Colloids Surf. 1990, 51, 141.

nSiO2

dSiO2 nm

dn/dc (mL/g) nw

3.88-j*0.002 1.46 107 1.33

MAPTAC PDAEMA C12E5 CTAB 0.18

0.18

0.13

0.14

the reflectivity ratio oscillates over very large values before reaching the steady state. Subsequent slight increases or decreases in the flow rate yielded the same behavior pattern of large reflectivity-ratio oscillations. Similar large variations in IP/IS were observed with small changes in the beam incidence angle. Note that changes in the reflectivity ratio are at least 2 orders of magnitude larger than those necessary to detect adsorbed amounts at the solid/water interface, thereby obviating the method. Noise and drift in the signal were also prohibitive. We established that the large reflectivity variations seen in Figure 4 are due to multiple reflections across the shallow flow channel. As discussed in Appendix A, the highly coherent laser light source allowed multiple reflections and interference over the 100-µm depth of the flow channel. The resultant reflected beam is then the superposition of the beam reflected on the coated silicon wafer and of all the beams that experience multiple reflection in the channel (Figure A2). All multiple reflected beams not only superimpose but also interfere together. Consequently, the collected intensities, and as a result IP/IS, depend on the thickness of the flow channel and on the angle of incidence with an enormous sensitivity, as illustrated in Figure 4. We demonstrate in Appendix A that the reflectivity oscillations seen in Figure 4 arise from a slight swelling of the channel depth due to the increased pressure imposed upon initiation of flow. To overcome the reflectivity oscillations, we replaced the laser with a noncoherent Hg/Xe arc lamp (Oriel, model 6291, 200 W). Noncoherent light does not interfere across a 100-µm-thick channel. Replacement of the light source eliminated the problem of the signal oscillations and the extreme sensitivity to the channel depth and incident beam angle. However, we now must account for the superimposition of the intensities from the multiple reflected beams. Appendix A presents the calculations. Once RP/RS is extracted, the adsorbed amount is again obtained from eq 3. The use of an arc lamp requires that the light source be collimated and shaped into a monochromatic and parallel beam. For this purpose, a pinhole is inserted into the beam line and coupled to a collimating lens (f-stop ) 50 mm) to generate a parallel beam. A narrow band-pass filter (λ ) 546.1 ( 2 nm) is inserted to make the light beam monochromatic. Unfortunately, with the arc-lamp source, the signal to the photodectors is extremely low compared to that using a laser-light source. We therefore

Figure 4. Transient intensity ratio and pressure drop in the SPOR upon initiation of flow (vertical arrow) when illuminated with a He/Ne light source. Note the large oscillations in IP/IS as the pressure drop increases. Such large oscillations obviate the SPOR instrument for solute adsorption studies.


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Figure 5. Chemical structures for the homopolyelectrolytes PDAEMA and MAPTAC.

amplified the signal using a chopping/lock-in amplification system. As diagrammed in Figure 1, a chopper wheel (Boston Electronics Corporation, 3OEM) is inserted before the pinhole. The signal is collected using two shunted silicon photodiode detectors (Melles Griot, 13DSI009) and amplified using a lock-in amplifier (Scitech Instruments, Inc.; EG&G Brookdeal) for each photodiode. A personal computer records the final signal using a Digital Instrument interface. The signal-to-noise ratio is slightly poorer than that obtained with a laser source and a stagnationpoint flow cell.8 Nevertheless, we have been able to use the SPOR for coupled measurements of adsorbed amounts and ζ potentials. Experiment Materials. All aqueous solutions were prepared with distilled water that was further purified with a four-stage Milli-Q reagentgrade water system (Millipore, resistivity greater than 18.2 mΩ‚ cm). When exposed to air, the pH of the distilled/deionized (DI) water was close to 5.5 because of CO2 absorption. Other desired pH values were obtained by minute additions of concentrated NaOH (Fisher Scientific, Pittsburgh, PA, certified ACS) or HCl (Fisher Scientific, Pittsburgh, PA, certified ACS plus). Before use, the KCl salt (Fisher Scientific, Pittsburgh, PA, certified ACS) was roasted at 400 °C for 24 h to drive off organic contaminants. Nonionic surfactant (pentaethylene glycol monododecyl ether, C12E5) and cationic surfactant (hexadecyl trimethylammonium bromide, CTAB) were purchased from Fluka (greater than 99% purity) and used without further purification. Confirmation of their purity was established by surface tension measurements that demonstrated a sharp break at the critical micelle concentration (cmc) in DI water of 5 × 10-5 for C12E59 and 9 × 10-4 for CTAB,1,10 respectively. Poly(2-(dimethylamino)ethyl methacrylate) (PDAEMA), whose structure is shown in Figure 5, was synthesized by Rhodia, Inc., Mississoga, Canada. It was purified by several sequential precipitations in acetone. Our samples were supplied in the citrate salt form. The molecular weight is about 200 kDa with a polydispersity index of around 3. This polymer is a weak base with a pKa of around 8. The poly(propyl methacrylate) trimethylammonium chloride (MAPTAC) polyelectrolyte, also pictured in Figure 5, was likewise synthesized by Rhodia Inc., Mississoga, Canada. It was purified by dialysis against DI water. The molecular weight is about 220 kDa again with a polydispersity index of about 3. MAPTAC is a quaternary polyamine; therefore, its ionization is independent of pH. Silicon wafers with a thermally grown SiO2 layer of 100 nm were prepared in the micromachining laboratory at UC Berkeley. The SiO2 thickness was precisely measured for each sample by ellipsometry. Before each experiment, the surfaces of the silicon wafer and the fused silica plate were cleaned in a piranha solution (8) Dijt, D. C.; Cohen Stuart, M. A.; Fleer, G. J. Adv. Colloid Interface Sci. 1994, 50, 79. (9) Meguro, K.; Ueno, M.; Esumi, K. In Nonionic Surfactants: Physical Chemistry; Schick, M. J., Ed.; Surfactant Science Series; Marcel Dekker: New York, 1987; Vol. 23, pp 125-127. (10) van Oss, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic, and Nonionic Surfactants; Elsevier: New York, 1993; pp 114-115.

Figure 6. ζ potential of the silica surface as a function of pH from the SPOR (filled circles) and from the literature11 (open circles). (i.e., a 2:1 v/v mixture of concentrated H2SO4 (J. T. Baker, Phillipsburg, NJ) and H2O2 (J. T. Baker, Phillipsburg, NJ)) for 10 min, copiously rinsed with DI water, dried in air, and assembled into the optical flow cell. Drying of the surfaces makes it easier to avoid contamination during the mounting of the cell. The Teflon tubing, the channel Teflon spacer, and the Teflon cell body were all washed with a 1 wt % detergent solution (Liquinox, Alconox Inc.) and thoroughly rinsed with warm water (50 °C) and then DI water. Measurement of the nascent silica ζ potential at the beginning of the experiment provides a sensitive check of the cleaning procedures. Figure 6 reports the bare-silica ζ potentials versus solution pH (filled circles) and compares them to those of Wiese et al.11 (open circles). Agreement with the literature data is excellent, establishing both the accuracy of our ζ-potential measurements and the adequacy of our cleaning procedures. Procedures. We initially flush the optical cell with aqueous KCl because a minimal background electrolyte concentration is necessary to control the ionic strength of the solution and to ensure a finite amount of chloride ion in solution for reliable potential measurement with the Ag/AgCl electrodes. The solution pH, if not specifically adjusted, is around 5.5 (because of equilibrium with atmospheric CO2). The flow rate during an experiment is kept constant, usually at 110 mL/min. Once both signals of reflectometry and streaming potential are steady during the flow of the KCl solution, the adsorbate solution is injected for at least three cell-plus-tubing dead volumes. Then, the same loading solution is recirculated through the cell to minimize the amount of adsorbate consumed. Once steady state is obtained in the loading direction, we perform a washout utilizing the initial aqueous KCl solvent. Many variants of this standard operating procedure can be adopted, such as challenging the cell with aqueous solutions of different pH and ionic strength values.

Results and Discussion Nonionic Surfactant (C12E5). Figure 7 displays the dynamic adsorption and ζ potential during the loading and subsequent washout of 0.24 mM C12E5 on silica. In the 1 mM KCl, pH 5.5 aqueous solvent, this corresponds to 5 times the cmc. Initially, solvent alone flows through the cell. Thus, the -75 mV ζ potential in Figure 7 corresponds to the bare silica surface, and the corresponding adsorbed amount is zero. At time t ) 2 min the C12E5 solution is circulated through the cell. The adsorbed amount increases, and simultaneously, the ζ potential increases (i.e., becomes less negative) until both attain plateau values in less than 1 min. At 4.5 min, solvent is injected, washing surfactant out of the cell. Both signals (11) Wiese, G. N.; James, R. O.; Healy, T. W. Discuss. Faraday Soc. 1971, 52, 302.

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Figure 7. Adsorption and ζ-potential dynamics on silica of a 0.24 mM aqueous C12E5 solution at pH 5.5 in 10-3 M KCl as measured by SPOR.

again simultaneously return to their initial values before surfactant loading. This is consistent with the fact that C12E5 adsorbs reversibly on silica.12,13 Both adsorption and desorption of C12E5 at the silica/ water interface are known to be fast.13,14 Figure 7 demonstrates that the rate of C12E5 desorption is very close to that for adsorption. Accordingly, the spread in the load/washout dynamic data in Figure 7 mostly likely diagnoses the amount of mass transfer and dispersive mixing in the optical flow cell. Hence, we conclude that for this simple nonionic adsorbate the delay in adsorption and desorption is due to mixing in our optical flow cell. Plateau adsorption in Figure 7 is about 2.2 mg/m2, in agreement with others.12,13 This value can be compared to the adsorbed amount of a dense, vertically oriented monolayer of C12E5, which with an area per molecule of 60 Å2 corresponds to an adsorption density of about 1.1 mg/m2. Our measurement of 2.2 mg/m2 is thus consistent with the formation of a bilayer on the silica surface. Optical reflectometry gives only spatially averaged information for an assumed featureless flat surface. However, it is known from AFM that simple nonionic ethylene oxide surfactants on the silica surface form bilayers and/or micellar globules near and above the cmc.2,14 Our measured adsorption densities are consistent with that picture. Because C12E5 is nonionic, any change in the ζ potential during adsorption or desorption likely arises from a shift in the location of the plane of no-slip relative to that of the bare surface. As the surfactant adsorbs, the shear plane moves farther away from the silica surface, and the ζ potential falls. Figure 8 diagrams this picture along with the electrostatic potential, ψ, as a function of distance from the interface, z. In this diagram, ψd represents the outer Helmholtz plane (OHP) electrostatic potential before adsorption occurs at a molecular distance dOHP away from the surface (not shown). For the bare silica surface, the no-slip shear plane potential, or ζo, is well-approximated by ψd (i.e., the value at the outer Helmholtz plane or at the commencement of the diffuse double layer5). It is also well accepted that the no-slip plane resides almost exactly at the outer surface of the adsorbed surfactant layer.5 Thus, in Figure 8 when the surfactant bilayer builds, the ζ potential falls as the no-slip plane shifts from the distance dOHP outward into the solution to the thickness of the bilayer, d. (12) Tiberg, F. J. Chem. Soc., Faraday Trans. 1996, 92, 531. (13) Tiberg, F.; Jo¨nsson, B.; Lindman, B. Langmuir 1994, 10, 1994. (14) Grant, L. M.; Tiberg, F.; Ducker, W. A. J. Phys. Chem. B 1998, 102, 4288.

Figure 8. Schematic of the electrostatic potential decay and the ζ potential in the case of silica covered with a bilayer of C12E5. ψd () ζo) is the outer Helmholtz plane potential or the ζ potential of the bare silica.

Figure 9. ζ potential and adsorbed amount of C12E5 on silica versus the background electrolyte KCl concentration. The dark solid line is a best fit to eq 4, yielding a thickness of 6 nm for the adsorbed layer.

One way to confirm the premise underlying Figure 8 is to study C12E5 adsorption from a solution with the same concentration of surfactant but with different ionic strengths. Using KCl concentrations between 10-4 and 10-2 M, we find in Figure 9 that the adsorbed amount remains unchanged (light filled squares), whereas the ζ potential decreases strongly (dark filled circles). To understand this effect, we approximate the electrostatic profile, ψ(z), as that of the diffuse double layer with the only change being that surfactant adsorption shifts the no-slip plane to the average thickness of the bilayer. Following Mathai and Ottewill,15 we adopt the smallpotential Debye-Hu¨ckel equation to describe the ζ potential after adsorption

ζ ) ζo exp[-κ(d - dOHP)]

(4)

where κ-1 () λD) is the Debye length and ζo () ψd) is the ζ potential of the bare silica surface. Because dOHP is about 0.1 nm, it is neglected in eq 4. The fit solid line in Figure 9 shows that a value of d ) 60 Å in eq 4 well describes (15) Mathai, K. G.; Ottewill, R. H. Trans. Faraday Soc. 1966, 62, 759.


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Figure 10. Adsorption and ζ-potential dynamics on silica of a 1.37 mM aqueous CTAB solution at pH 5.5 in 10-3 M KCl as measured by SPOR.

the measured ζ potentials as a function of ionic strength. Given that the length of a C12E5 molecule is about 35 Å,16 this result shows that the adsorbed layer thickness corresponds roughly to 2 times the length of a C12E5 molecule. This result is quite consistent with the reflectometry adsorption density measurement indicating a bilayer structure. Our analysis is rudimentary in that we neglect the details of the surfactant bilayer structure and the large electrostatic potential drop across that bilayer. Nevertheless, from the excellent agreement between the reflectometry and streaming-potential results, the main feature of bilayer adsorption is confirmed. Finally, these results for a small, reversibly adsorbed surfactant establish that the combined SPOR is a useful apparatus for revealing adsorbate molecular structure, even when the surfactant is nonionic. Adsorbed amounts and ζ potentials are in good agreement with literature data, and dispersive mixing in the optical flow cells appears to be minimal. Cationic Surfactant (CTAB). Figure 10 shows the kinetics of the adsorbed amount and ζ potential during the adsorption and desorption of CTAB on silica. The solvent is DI water in equilibrium with the atmospheric CO2 (pH 5.5) with 1 mM added KCl. As before, the flow rate during the experiment is kept constant at 110 mL/ min. At the beginning of the experiment, aqueous electrolyte is flushed through the cell. A solution containing CTAB at a concentration of 1.37 mM (1.5 cmc in 1 mM KCl1) is injected at t ) 4 min and recirculated for 8 min. The cationic surfactant is then eluted with the 1 mM KCl aqueous solvent. Clearly, the reflectometry signal returns to zero after washout. Thus, CTAB adsorption on the oppositely charged silica surface is also reversible. The kinetics of CTAB desorption is, however, sensibly slower than that of C12E5. The adsorbed amount of 1.6 mg/m2 observed at the plateau is in very good agreement with that reported by Velegol et al.17 This agreement is verification of the calibration method for our narrowchannel reflectometer (Appendix A), as are the results for C12E5 above. A plateau adsorption of 1.6 mg/m2 indicates the formation of a bilayer of CTAB on silica.17 AFM of CTAB on silica reveals admicelles1,17,18 consistent with our measured adsorption density near the cmc. Measured ζ potentials reported in Figure 10 establish that CTAB adsorption on silica at pH 5.5 induces a major potential reversal from -75 mV (bare silica) to +120 mV. Hence, the positively charged CTAB molecules adsorb (16) Thomas, R. K. Prog. Colloid Polym. Sci. 1997, 103, 216. (17) Velegol, S. B.; Fleming, B. D.; Biggs, S.; Wanless, E. J.; Tilton, R. D. Langmuir 2000, 16, 2548. (18) Subramanian, V.; Ducker, W. A. Langmuir 2000, 16, 4447.

Figure 11. Schematic of the electrostatic potential profile for an adsorbed bilayer of CTAB on silica. The CTAB molecules in the bilayer may not be completely ionized.

strongly enough to reverse the negative charge of the bare silica surface. Once again, the measured ζ-potential values are in good agreement with literature data.19 The washout experiment reveals a long tail characteristic of slow desorption kinetics. The fact that the washout streaming potential is relatively more stretched indicates that ζ is more sensitive to small amounts of adsorbed CTAB than is optical reflectometry. To gain further understanding of the charge state of the adsorbed CTAB on the silica surface, Figure 11 sketches the adsorbed bilayer along with the expected shape of the electrostatic potential profile. The silica surface potential is negative. However, the positively charged adsorbed CTAB molecules overcompensate for the negative surface charge so that the potential at the outer plane of the bilayer is positive. This positive potential at the bilayer then decays monotonically through the diffuse double layer. Figure 11 portrays the CTAB molecules in the adsorbed bilayer as completely ionized, whereas complete dissociation may not be the case. We show that it is possible to take advantage of the combination of measurements of the ζ potential and the adsorbed amount to establish the degree of ionization of CTAB in the adsorbed bilayer. Electroneutrality of the silica/water interface demands that

σo + σa + σd ) 0

(5)

where σo is the charge density of the silica substrate, σa is the positive surface charge density from the adsorbed surfactant molecules, and σd is the surface charge density in the diffuse double layer. Not all of the adsorbed CTAB molecules are fully ionized so that

σa ) ReΓ

(6)

(19) Zorin, Z. M.; Churaev, N. V.; Esipova, N. E.; Sergeeva, I. P.; Sobolev, V. D.; Gasanov, E. K. J. Colloid Interface Sci. 1992, 152, 1.

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where Γ in eq 6 is in molecular units and R is the average degree of ionization of the adsorbed cationic surfactant. Γ is measured directly, whereas σo and σd are inferred from our SPOR experiments, as detailed below. The degree of adsorbed surfactant ionization then follows from eqs 5 and 6. Implicit in eq 6 is the assumption that our measured adsorbed amounts correspond to the CTA+ ion, whereas the index-of-refraction increment adopted in the optical theory is based on dn/dc values determined for bulk CTAB solutions. We justify this approximation below and find it valid over a large range of surfactant concentration. The diffuse-layer charge in eq 5 is accurately estimated from the ζ-potential measurements. The plane of zero slip resides at the outer periphery of the adsorbed layer and locates the commencement of the diffuse double layer. Gouy-Chapman theory5 then specifies the correspondence between the ζ potential and the diffuse-double-layer charge density σd

σd ) -

2kTκ eζ sinh e 2kT

( )

(7)

where is the dielectric permittivity of the aqueous medium, e is the charge of the electron, k is the Boltzmann constant, and T is the temperature. Finally, σo in eq 5 is subject to some uncertainty. Although silica is an extensively studied substrate, its surface potential and charge characteristics are not yet completely understood. On the basis of the number of silanol groups available at the silica surface, Armistead et al.20 found a value of 4.6 groups/nm2 corresponding to a maximum (negative) surface charge density of 80 µC/ cm2 if all groups are ionized. However, σo measured by titration of the actual surface charges of silica in water is always much smaller than 80 µC/cm2. Indeed, the surface charge of silica depends on the preparation procedure.1 Typical literature values range from -1.8 µC/ cm2 from Healy and White21 to -18 µC/cm2 from Minor et al.22 Furthermore, measured surface-charge densities and ζ potentials of bare silica are not consistent with eqs 5 and 7 in that measured ζ potentials are always low compared to those predicted. Two disparate models have been proposed to explain this discrepancy. One of them23,24 argues that there is a gel layer at the surface of silica. Instead of being located on a single plane, surface charges are spread throughout this porous region. The second or site-binding model of the silica surface considers that the acid-base ionization of surface silanol groups involves local ion-complexation with solution counterions.21,25 The titration of the surface assesses the total number of silanol groups that are both deprotonated and ion-complexed, whereas the ζ potential is most sensitive to the deprotonated SiO- surface groups. To circumvent the ambiguity in the value of σo, we experimentally estimate the effective surface charge on our silica substrate. From Figure 12, the ζ potential reverses sign at a particular concentration of CTAB that we denote as the point of ζ reversal (pzr). At the pzr, the ζ potential is zero, and hence the charge in the diffuse double layer is also zero. Accordingly, surface electro(20) Armistead, C. G.; Tyler, A. J.; Hambleton, F. H.; Mitchell, S. A.; Hockey, J. A. J. Phys. Chem. 1969, 73, 3947. (21) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci. 1978, 9, 303. (22) Lyklema, J. Croat. Chem. Acta 1971, 43, 165. (23) Lyklema, J. Faraday Discuss. Chem. Soc. 1978, 65, 47. (24) Vigil, G.; Xu, Z.; Steinberg, S.; Israelachvili, J. J. Colloid Interface Sci. 2000, 165, 367. (25) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480.

Figure 12. CTAB equilibrium adsorption and ζ potentials on silica at pH 5.5 in 10-3 M KCl as a function of surfactant concentration, as measured by SPOR.

Figure 13. Calculated values of the average ionization of CTAB in the adsorbed layer versus the bulk surfactant concentration.

neutrality simplifies to

σo + ReΓ ) 0

(8)

For 1 mM added indifferent electrolyte, Figure 12 reveals that that pzr corresponds to extremely low CTAB concentrations (∼10-5 M). The corresponding adsorbed amount is also very low and close to the limit of accuracy of our reflectometer. A maximum value of 0.1 mg/m2 is the best approximation that can be inferred from our experiment. Given these extremely low values and the fact that the very first stage of adsorption is mainly driven by electrostatic interactions,1 one can reasonably assume that the CTA+ ions adsorb without their Br- counterions. In other words, the first stage of adsorption corresponds to an ion-exchange process at the interface; therefore, R ≈ 1. Using these approximations, eq 8 leads to a silica charge density of σo ) -2.6 µC/cm2. This value is in good agreement with that measured by Healy and White21 and is adopted here. Given the adsorbed amounts and ζ potentials in Figure 12 and the above estimates of σo and σd, eqs 5 and 6 provide an estimate of the fractional ionization of the adsorbed layers. The dependence of R on the CTAB bulk concentration is reported in Figure 13. At the lowest concentration where an adsorbed amount is measurable, R ) 1, a restriction imposed in the estimate of σo above. Near the pzr, CTAB+ ions adsorb onto the silica surface without their counterions in order to match the negative surface


Langmuir, Vol. 21, No. 22, 2005 10135

Figure 14. Adsorption and ζ-potential dynamics on silica of a 0.01 wt % aqueous PDAEMA solution at pH 5.5 in 10-3 M KCl as measured by SPOR.

charge. As the concentration of CTAB increases, the fractional ionization of the adsorbed layer decreases quite rapidly and reaches a value of 10% for a concentration higher than 2 × 10-4 M. This value of R is consistent with that of 12% found by Zorin et al.19 above the cmc. One can notice that the degree of ionization of CTAB on a silica surface is significantly lower than that of CTAB micelles.26 One possible reason is the curvature effect that is less favorable for ionization in the case of a flat surface in comparison to a curved one.27 Except at concentrations below the pzr, we confirm here that most of the CTAB molecules adsorb along with their neutralizing counterion. This finding validates the approximation used in the reflectometry optical equations that employs the refractive index increment of CTAB in the bulk solution to calculate adsorbed amounts. Finally, we again note the usefulness of SPOR to garner molecular information about the adsorbed layer of simple surfactants. Cationic Homopolymers (PDAEMA and MAPTAC). Figure 14 shows the adsorption/desorption kinetics of an aqueous solution of a cationic homopolymer: poly(2-(dimethylamino)ethyl methacrylate (PDAEMA). The concentration of 0.01 wt % is low enough that the solution conductivity and pH are not affected by the presence of the polymer. At pH 5.5, PDAEMA is highly charged because its pKa value is 8. As with the CTAB cationic surfactant, here too we observe a strong ζ-potential reversal from -75 to +45 mV at a correspondingly moderate adsorption density of about 0.6 mg/m2. This value is in good agreement with those measured by Shin et al.28,29 for a lower-molecular-weight PDAEMA. Both the ζ potential and the adsorbed amount level off in less than 2 min. From the washout experiment, it is clear that the adsorbed amount is unchanged, as expected for a highmolecular-weight polyelectrolyte on an oppositely charged surface. However, the SPOR experiment reveals an interesting phenomenon. Whereas the adsorbed amount remains constant upon rinsing, the ζ potential increases noticeably and eventually stabilizes. This effect is attributed to ion exchange of the citric counterions from the adsorbed polyelectrolyte layer by chloride ions upon washout with the aqueous KCl solution. Indeed, the same experiment reproduced with the MAPTAC polymer that has chloride as the counterion shows stable signals in (26) Aswal, V. K.; Goyal, P. S.; Amenitsch, H.; Bernstoff, S. Pramana 2004, 63, 333. (27) Stephen, B. J.; Drummond, C. J.; Scales, P. J. Colloids Surf., A 1995, 103, 195. (28) Shin, Y.; Roberts, J. E.; Santore, M. M. J. Colloid Interface Sci. 2001, 244, 190. (29) Shin, Y.; Roberts, J. E.; Santore, M. M. J. Colloid Interface Sci. 2002, 247, 220.

Figure 15. Equilibrium ζ potentials of 0.01 wt % aqueous MAPTAC at pH 5.5 as a function of KCl concentration as measured by SPOR (filled squares). Also shown are calculated values of the surface-charge overcompensation, ∆σ (filled circles).

Figure 16. Equilibrium adsorption of 0.01 wt % aqueous MAPTAC at pH 5.5 as a function of KCl concentration (dark filled circles) as measured by SPOR. Also shown are calculated values of the effective ionization of MAPTAC in the adsorbed layer (light filled circles).

both reflectometry and streaming potential. After the load/ washout experiment, the silica-coated wafer was dried, and a thickness of approximately 0.7-1.0 nm was measured by ellipsometry. In summary, we verify here that the adsorption of aqueous homopolyelectrolytes on an oppositely charged solid surface is moderate and irreversible. To avoid ion exchange with the citrate counterions of PDAEMA, we focus in what follows on the adsorption of MAPTAC. Load/washout experiments were performed for a polymer concentration of 0.01 wt % and for different KCl background concentrations varying from zero to 10 mM. We report as filled squares in Figure 15 the ζ potential after MAPTAC adsorption versus the background KCl concentration at pH 5.5. It is remarkable that ζ is independent of ionic strength over several orders of magnitude of KCl concentration. However, as illustrated by the dark filled circles in Figure 16, the adsorbed amount from reflectometry does vary; adsorption increases as the ionic strength increases. At low ionic strength, the adsorbed amount and corresponding layer thickness are small. This is consistent with the fact that highly charged polyelectrolytes are known to form thin, flat monolayers on oppositely charged

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Theodoly et al.

compensation of the surface charge, ∆σ ) σa + σo, varies as

( )

∆σ ≈ κδ 1 +

Figure 17. Schematic of the polyelectrolyte chain (a) in bulk solution and (b) adsorbed on an oppositely charged solid surface. ξe is the electrostatic blob size. Note the flattening of the adsorbed polyelectrolyte chain relative to ξe.

surfaces at low ionic strength.30,31 The chains spread on the surface to form a “monolayer”. To enhance the electrostatic attractive interactions, the cationic polymer tends to adsorb flat on the surface so that the negative charge of the substrate is neutralized with a minimum amount of polymer.30,31 This scenario is consistent with the existence of very thin adsorbed layers. However, it implies that the surface bears little effective charge after adsorption, which is obviously not the case in Figure 15. Indeed, our experiments in Figures 14 and 15 show a dramatic charge reversal. Polyelectrolytes of opposite charge to that of the surface have been observed to reverse the surface charge in many systems.32-34 To understand this phenomenon, the change in the entropy upon adsorption must be considered. The adsorbed polymer resists complete flattening on the surface, preferring to maintain some favorable chain entropic freedom (which is responsible for the small but nonnegligible thickness of the adsorbed layer). The gain of entropic freedom of the chains partially balances the repulsive monomer-monomer electrostatic energy due to the excess of chain positive charge, as illustrated pictorially in Figure 17. In addition, upon adsorption, the small counterions are released from the polyelectrolyte, providing a positive entropy contribution to the overall adsorption free energy. Considerable theoretical effort has been devoted to this problem.35-38 In particular, Joanny et al.36,37 determined the equilibrium polyelectrolyte adsorbed configuration by applying self-consistent mean-field theory to describe the statistics of the polymer chain coupled with the linearized Poisson-Boltzmann equation to describe the relevant electrostatics. In the low-salt regime (i.e., when the thickness of the adsorbed layer, δ, is much smaller than the Debye length), Joanny at al.36,37 find that the over(30) Barnett, K. G.; Cosgrove, T.; Crowley, T. L.; Tadros, T. F.; Vincent, B. Faraday Symp. Chem. Soc. 1981, 16, 101. (31) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: New York, 1993; Chapter 7. (32) Decher, G.; Hong, J. D.; Schmitt, J. Thin Solid Films 1992, 210, 831. (33) Decher, G.; Lehr, B.; Lowack, K.; Lov, Y.; Schmitt, J. Biosens. Bioelectron. 1994, 9, 677. (34) Ladam, G.; Schaad, P.; Decher, G.; Cuisinier, F. Langmuir 2000, 16, 1249. (35) Netz, R. R.; Joanny, J. F. Macromolecules 1999, 32, 9013. (36) Joanny, J. F. Eur. Phys. J. B 1999, 9, 117. (37) Andelman, D.; Joanny, J. F. C. R. Acad. Sci. Paris 2000, 4, 1153. (38) Dobrynin, A. V.; Deshkovski, A.; Rubinstein, M. Macromolecules 2001, 34, 3421.

δ2 ξe2

(9)

where ξe () a(akT/e2)1/3) is the so-called electrostatic blob size of the bulk polyelectrolyte, pictured in Figure 17a, and a is the monomer size. In our experiments, we altered the ionic strength by more than 2 orders of magnitude (from CKCl < 10-4 M up to 10-2 M). This corresponds to a change in the Debye length from λD > 30 nm to λD ) 3.0 nm. In this range, the condition δ , λD required for eq 9 is valid. Because the chains form a rather flat monolayer in the low-salt regime, we expect δ to depend weakly on ionic strength.36,37 Consequently, changes in δ are small in comparison to the changes in λD, which is varied experimentally by 1 order of magnitude. Under these conditions, eq 9 implies that the overcompensation charge ∆σ is inversely proportional to the Debye length (i.e., is directly proportional to the square root of the KCl concentration). To establish whether this argument is correct, we note from eq 5 that -σd is equal to the overcompensating charge ∆σ. Then, from our ζ-potential measurements and eq 7, we can assess the charge in the diffuse double layer. These results are shown in Figure 9 as filled squares. Because the measured ζ potentials are independent of ionic strength in Figure 15, eq 7 demands a linear dependence of ∆σ() -σd) on κ, in excellent agreement with the theory of Joanny et al.36,37 Physically, at low ionic strength, the attractive electrostatic energy between the negatively charged surface and the positively charge polyelectrolyte dominates the interaction energy of the chains at the interface. The equilibrium state of the system corresponds to low entropy for the chains due to a strong electrostatic confining attraction with the substrate. The overall charge of the substrate and polymer is low, there is a minimal double layer, and small polyelectrolyte counterions have a maximum in entropy. The observed increase in overcompensation charge ∆σ with ionicity implies a concomitant increase in the adsorbed amount of positive charge at the interface and, hence, of polymer. This trend is indeed confirmed experimentally in Figure 16. To investigate in more detail the consistency of the changes in the charge and adsorbed amount, we apply eqs 5-7 in the same way as for the CTAB system above. σo is estimated using the pzr obtained from CTAB; the polyelectrolyte adsorbed amounts Γ and ζ potentials are measured by SPOR. Corresponding calculated values of the effective ionization fraction, R, in the polyelectrolyte adsorbed layer are reported in Figure 16 as light filled circles. R is reasonably constant over the whole range of ionic strength. The observed value of 20% fractional ionization at the surface is consistent with that expected for a highly charged polyelectrolyte in dilute solution. Indeed, the Manning condensation model39 predicts an effective ionization fraction of 30%. Fractional dissociation in the concentrated environment of the adsorbed layer is expected to be lower than in the bulk. Our SPOR measurements are in very good agreement with theoretical predictions for aqueous polyelectrolyte adsorption on an oppositely charged solid surface. Furthermore, it is possible to obtain accurate estimates of the ionization state of the adsorbed polyelectrolyte layer, again demonstrating the usefulness of the instrument. Never(39) Manning, G. J. Chem. Phys. 1969, 51, 924.


theless, we assumed purely electrostatic attraction between the surface and the polyelectrolyte with no other surface/polyelectrolyte energetic interactions. As reported in Figure 14, however, PDAEMA adsorption is irreversible (as is MAPTAC adsorption) even upon rinsing with a lowpH solution where this polymer is uncharged. Clearly, for this low-pH adsorption to occur, nonelectrostatic attractive forces must be present. Because MAPTAC has a similar molecular structure to PDAEMA, it also likely interacts with the silica surface by nonelectrostatic attractive interactions. Agreement with the theory of Joanny et al.36,37 in eq 9 apparently means that electrostatic attraction dominates other driving forces when the polymer is highly charged and opposite to that of the adsorbing surface. Conclusions We have constructed a unique apparatus coupling insitu measurement of reflectometry and streaming potential. The new streaming-potential optical reflectometer (SPOR) permits the simultaneous measurement of adsorption amounts and ζ potentials in the transient mode. Accordingly, both kinetic and equilibrium studies are possible. Here we focused on loading and washout sequences to establish sorption reversibility, although many other transient sequences are possible. Because of multiple interference in the narrow flow channel, our SPOR utilizes a noncoherent light source and requires reinterpretation of the reflectometry signals. The SPOR apparatus is most appropriate to study the adsorption/ desorption of charged species on solid/liquid interfaces, but it also proves quite useful for pursuing nonionic adsorbates because the ζ potential gauges the surface charge at the plane of no-slip reflective of the adsorbedlayer thickness. SPOR allows a quantitative measurement of adsorbed amounts and therefore of the amount of charge brought to the interface by adsorption. Because both Γ and ζ are followed dynamically, sorption kinetics and reversibility may be followed. A balance of the charges of the substrate, the adsorbed layer, and the diffuse double layer allows the determination of the fractional ionization of charged species in the adsorbed layer. We have used this approach to determine the fractional dissociation of a simple cationic surfactant (CTAB) at the negative silica surface. Because of its amphiphilicity, CTAB reverses the charge of silica by forming bilayers. Fascinatingly, the ionization fraction at adsorption saturation is only 10%. We have also investigated charge reversal induced by the adsorption of cationic homopolylectrolytes (PDAEMA and MAPTAC) on silica. In this case, the polyelectrolyte adsorbs in a thin, flat configuration; charge reversal is due to the entropic gain of the released counterions originally neutralizing the polymeric chain. Our experiments are compatible with theoretical predictions proposing a chargereversal amount that is inversely proportional to the Debye length of the bulk solution. For MAPTAC, we likewise establish an average ionization inside the adsorbed layer of 20%, independent of the solution ionic strength. This value is compatible with the ionization fraction expected along a polyelectrolyte chain in the bulk. The new SPOR instrument is a useful tool for elucidating the molecular behavior of aqueous adsorbates on solid surfaces. Acknowledgment. This work was partially funded by the Assistant Secretary for Fossil Energy, Office of Oil, Gas, and Shale Technologies of the U.S. Department of Energy under contract DE-AC03-76SF00098 awarded to the Lawrence Berkeley National Laboratory of the Uni-

Langmuir, Vol. 21, No. 22, 2005 10137

versity of California. O.T. acknowledges a postdoctoral fellowship sponsored by Rhodia, Inc. H. Hervet provided helpful technical advice. Appendix A: Reflectometry in a Narrow Channel Single Reflection. Classical reflectometry to measure adsorption at solid surfaces is typically practiced with a single reflection.6,7 As noted in the text, the relevant parameter in an optical reflectometer is the ratio RP/RS, where RP and RS are the reflection coefficients of the surface. Following eq 3, this ratio varies linearly with the adsorbed amount on the particular substrate that we are using (silicon with 100 nm of silica overgrowth). Constants a and b in eq 3 can be calculated from the refractive indices of the substrate (nSi) and the solvent (nw), the thickness and refractive index of the oxide layer (dSiO2, nSiO2), the angle of incidence (θi), the wavelength of light (λ), and the measured refractive index increment of the adsorbate solution (dn/dc), where n is the refractive index of the bulk solution and c is the bulk concentration of adsorbate. Table 1 lists the requisite optical constants for this work. The calculation of a and b is based on multiple Fresnel reflection in the multilayered surface illustrated in Figure A1a by the Abeles method.7,40,41 For a standard optical reflectometer, the beam exiting the cell is the result of the reflection on the single surface being probed. The intensity IP (IS) of the polarization P (S) is then proportional to the coefficient RP (RS)

Ij ) fjRjI0

for j ) P, S

(A1)

where I0 is the intensity of the incident beam and fP and fS are instrument parameters that account for the different losses of intensity in the cell as well as for the difference in sensitivity of the two photodiodes. The ratio IP/IS is then proportional to RP/RS as noted in eq 2 of the text. In eq 2, f ) fP/fS is independent of I0 and depends only on the cell design. To determine f, we make use of the known optical parameters for the bare substrate (i.e., nSi, nw, dSiO2, and nSiO2 from Table 1) to calculate (RP/RP)0. Thus, the calibration factor f can be determined from the measurement of the nascent surface reflection intensity ratio (IP/IS)0 at the beginning of the experiment (before adsorption):

f)

(IP/IS)0 (RP/RS)0

(A2)

Because a and b are known from calculation, Γ can finally be determined from eqs 2, 3, and A2:

Γ)

[

() ]

1 (RP/RS)0 IP -b a (IP/IS)0 IS

(A3)

Multiple Reflections. Although eq A3 is well known,7,40,41 it is valid only for a single reflection in the optical path. As drawn in Figure A2, our optical cell is narrow (to permit ζ-potential measurements) and is therefore vulnerable to multiple reflections and interference when illuminated with a coherent light source. To establish that multiple reflections and interference are the cause of the large variations in the intensity ratio signal seen in Figure 4, we have calculated the effect of interference on the signal IP/IS. To perform this calculation, (40) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1977. (41) Born, W.; Wolf, E. Principles of Optics; Pergamon Press: New York, 1970.

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Figure A1. Schematic of the optical-layer model used for the calculation of the adsorbed amounts in reflectometry (a) for the case of a deep channel with no multiple reflections and (b) for the case of a narrow channel accounting for a water layer.

Figure A3. Comparison of the calculated (light solid line) and experimental (dark filled circles) reflectometry signal vs the angle of incidence in a 100-µm narrow channel. A dashed line indicates the corresponding calculated signal for single reflection in a deep channel.

Figure A2. Schematic of the multiple reflections in the narrow flow channel optical cell.

we note that multiple reflection and interference in the micrometer-scale channel also occur in the nanoscale layers of SiO2 and adsorbed polymer. Accordingly, multiple reflections in the water channel can be accounted for simply by adding one layer of water to the optical model, as illustrated in Figure A1b. The thickness of the water layer corresponds to the thickness of the flow channel. The upper medium is now the silica coating of the upper plate. With this extended optical model, we confirm the oscillations of IP/IS observed in Figure 4 simply by varying the thickness of the channel by a few micrometers in the optical calculations. Swelling or shrinking of the flow channel is expected during changes in flow rate because of the corresponding changes in cell pressure. Unfortunately, we have no direct measure of the flow-channel thickness to confirm this hypothesis. Fortunately, an absolute experimental comparison can be made with the multiple-reflection optical model by varying the angle of incidence. (θi can be precisely controlled via the rotation stages.) Such a comparison is presented in Figure A3 between the measured and calculated RP/RS values as a function of θi for a rather narrow range of incident angles between 57.5 and 58.5°. The horizontal dashed line in Figure A3 corresponds to the RP/RS ratio calculated for a thick flow cell with no interference artifacts. There is almost no variation in RP/ RS over this narrow range of incident angles. The light solid line in Figure A3 corresponds to the same calculation taking into account the effect of a 100-µm-deep channel. Here, RP/RS clearly demonstrates oscillations with a very large amplitude and a very short wavelength. The experimental variation of RP/RS corresponds to the filled circles in Figure A3. We clearly observe experimental oscillations in RP/RS versus the angle of incidence; the amplitude and wavelength of the oscillations are in perfect agreement with the optical calculations. We are therefore confident that multiple interference is responsible for the

Figure A4. Schematic of the different reflection and transmission coefficients necessary to quantify optical reflectometry with multiple reflections.

drastic changes in the intensity ratio IP/IS (between 0.2 and 2), whereas the changes observed typically for adsorption are from 1 to 1.1.7 The IP/IS signal is very sensitive to the thickness of the channel and to the light angle of incidence. Because it is not possible to control either the angle of incidence or the thickness of the channel with sufficient accuracy, the use of a coherent laser beam in the SPOR is catastrophic. To overcome multiple interference, we incorporated a noncoherent arc-lamp light source. The coherence length for natural light (a few micrometers) is much smaller than the optical path in the channel (>100 µm). As a result, the intensities of the different reflected beams are still additive, but they do not interfere with each other. With no multiple interference, the resultant reflected intensity depends smoothly on the angle of incidence and, more importantly, is completely insensitive to micrometer changes in the channel thickness. The use of a noncoherent light source makes reflectometry possible in our narrowchannel SPOR. Multiple Reflection Optical Calculations. Here we discuss the analysis of the noncoherent optics that allows us to extract adsorbed amounts. We must account for the sum of different reflected beams instead of only one single reflection. Upon adopting the nomenclature of Figure A4


Langmuir, Vol. 21, No. 22, 2005 10139

for the reflection coefficients, R, and the transmission coefficients, T, at the different interfaces involved, IP/IS can be written as

IP G G′ ) fp(R G P + T P RPT P ) I0

(A5)

IS G G′ ) fS(R G S + T S RST S ) I0

(A6)

() IP IS

and

∞

∑ n)0

G G′ RG P + T P RPT P

)f RG S

+

n (R G′ P RP)

∞ n G′ TG R T (R G′ S S S S RS) n)0

(A4)

∑

where RP and RS are the coefficients of reflection from the silicon wafer and the other coefficients have a superscript G for the transition from glass to water and a superscript G′ for the transition from water to glass (Figure A4). Equation A4 reveals that the dependence of IP/IS on RP/RS is no longer linear as in eq A3. Hence, the extraction of RP/RS from IP/IS requires additional effort. Two approximations to eq A4 allow the determination of RP/RS. First, the coefficients of reflection and transmission at the glass/water interface are not sensitive to solute adsorption at the incident angles that we employ. They can thus be considered to be constants and can be estimated by calculation. Second, the contribution of terms for n > 0 in eq A4 are negligible (to within 5%). IP and IS then follow the approximate expressions

where IP, IS, and I0 can be measured experimentally. The unknowns are fP, fS, RP, and RS. All other coefficients can be calculated. The experimental coefficients fP and fS are determined separately by experiment in the same way that the coefficient f was determined above. That is, we use the bare substrate as a reference. RP0 and RS0 are calculated for the bare substrate, giving fP and fS as the only unknowns in eqs A5 and A6 when they are applied to the bare substrate. Given fP and fS, the actual values of RP and RS are extracted at any time during a SPOR experiment. Finally, Γ is determined from eq A3. Thus, quantitative reflectometry measurements are possible in a narrow flow channel provided that a noncoherent light source is employed, I0 is monitored in addition to IP and IS, and additional calculations are performed as described above. That eqs A5 and A6 permit a quantitative assessment of solute adsorption is established in the main text by comparing our measured adsorption amounts to those reported in the literature obtained from reflectometry. LA050685M

A Combined Streaming-Potential Optical Reflectometer for Studying

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