Letter pubs.acs.org/Langmuir
Direct Observation of Confinement-Induced Charge Inversion at a Metal Surface Ran Tivony, Dan Ben Yaakov, Gilad Silbert,† and Jacob Klein* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel S Supporting Information *
ABSTRACT: Surface interactions across water are central to areas from nanomedicine to colloidal stability. They are predominantly a combination of attractive but short-ranged dispersive (van der Waals) forces, and long-ranged electrostatic forces between the charged surfaces. Here we show, using a surface force balance, that electrostatic forces between two surfaces across water, one at constant charge while the other (a molecularly smooth metal surface) is at constant potential of the same sign, may revert smoothly from repulsion to attraction on progressive confinement of the aqueous intersurface gap. This remarkable effect, long predicted theoretically in the classic Gouy−Chapman (Poisson−Boltzmann) model but never previously experimentally observed, unambiguously demonstrates surface charge reversal at the metal-water surface. This experimental confirmation emphasizes the implications for interactions of dielectrics with metal surfaces in aqueous media.
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INTRODUCTION Understanding surface interactions across water is central to areas ranging from nanomedicine1 to electrochemical processes.2 Such interactions are predominantly a combination of attractive but short-ranged dispersive (van der Waals, vdW) forces, and electrostatic forces between the charged surfaces.3,4 The Poisson−Boltzmann (PB) equation for the electrostatic potential ψ(x) a distance x from a charged surface (inherent in the Gouy−Chapman model) enables calculation of surface forces due to electrostatic double-layers at the surfaces,5,6 which, when suitably augmented by van der Waals forces and possibly other short-ranged effects,4 yield the overall interaction between the surfaces. The 1-D form, relevant for interactions between planar surfaces, is ∇2ψ(x) = (2c0e/εε0)·sinh[eψ(x)/ kT], where c0 is the concentration of ions in the bulk solution, ε0 is the permittivity of free space, ε is the dielectric constant, kB is the Boltzmann constant, T is the absolute temperature, and e is the electronic charge. Interacting, uniformly charged surfaces of the same potential (or charge) sign are of particular interest as their long-ranged repulsion underlies colloidal stabilization by preventing approach of the surfaces to adhesive vdW contact. At the same time, the PB equation predicts that, when the potential of at least one of the surfaces is constant, such electrostatic repulsion may peak and revert to attraction5−10 as the gap between the surfaces is progressively confined, due to charge inversion on the constant−potential surface. However, all experiments to date that directly measured forces between like-potential surfaces7−9,11−21 have shown that the repulsion between them increases continuously (i.e., it does not peak) as they approach each other across water, from large separations © 2015 American Chemical Society
down to the range of the vdW attraction. The presence of such a peak, as discussed further below, is a clear indication that charge reversal has occurred. Here we report that two likepotential surfaces, one a dielectric at constant (negative) charge and the other a metal at constant but lower (negative) potential, indeed repel across water at large separations, but as they approach the repulsion peaks at separations well beyond the range of significant vdW forces, decreases and may become an attraction. This demonstrates experimentally that the constant-potential surface has undergone charge inversion, resulting in a long-ranged electrostatic attraction.
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EXPERIMENTAL SECTION
We use a surface forces balance (SFB), described in detail previously22,23 to directly measure the normal forces Fn(D) between two molecularly smooth curved surfaces (mean curvature radius R ≈ 1 cm) at closest separation D (measured to ±0.3 nm) across purified water both with no added salt and also with low added salt. We note that the no-added-salt water, which is used to increase the range at which charge inversion occurs, nonetheless has a low concentration of electrolyte (see Figure 2, later), due to ions leached from glassware and to dissolved CO2 from ambient atmosphere.23 The surfaces used are a single-crystal sheet of mica, facing a template-stripped molecularly smooth gold surface,24 whose characteristics and mounting in the standard three-electrode configuration7,23 are shown in Figure 1. In addition to the smoothness of the gold (Figure 1A) and its [111] orientation,23 a cyclic voltammogram (Figure 1C) reveals the range −0.4 V − 0.3 V, at which the gold electrode is ideally polarized, and within which no faradaic current flows, nor chemical modification Received: September 3, 2015 Revised: November 4, 2015 Published: November 12, 2015 12845
DOI: 10.1021/acs.langmuir.5b03326 Langmuir 2015, 31, 12845−12849
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Langmuir
Figure 1. (A) AFM micrograph23 of gold electrode, 1 μm × 1 μm scan, showing RMS roughness of 0.116 nm. (B) The three-electrode configuration of the SFB, described in detail in ref 23. (C) Top: CV of gold electrode (in 1 mM KClO4) in range −0.4 to 0.3 V confirming the absence of faradaic current. Bottom: CV in range −0.4 to 1 V, showing oxidation and reduction peaks of the gold [111], consistent with earlier reports23 (scan rate 0.02 V/s for both CVs). More details in ref 23.
Figure 2. Interaction profiles Fn(D)/R between gold and bare mica surfaces across water with no added salt (pH ∼ 5.8), at a given contact point, under different applied potentials ΨApplied, color-coded as in the legend. The gray data is taken from a different contact point26 with ψApplied = −200 mV. ψGold values in legend are extracted from respective fits (black curves) to the PB equation with constant charge (mica) versus constant potential (gold) boundary conditions, augmented by vdW attraction Fn(D)/R = −AH/6D2 (also drawn separately for comparison as the dashed red line). Inset: Representative Fn(D)/R profiles in 3.5 × 10−4 M KClO4. Parameters used for all curves: σmica = 2.9 mC/m2; mica-water-gold Hamaker constant AH = 9 × 10−20 J;4 Debye length κ−1 = 34 nm for main figure fits (corresponding to 8 × 10−5 M 1:1 electrolyte) and 16 nm for inset fits (corresponding to 3.5 × 10−4 M KClO4).
match Ψapplied values in the legend in Figure 2. Also shown as a broken red line for reference is the purely dispersive (vdW) force expected between the mica and the gold across water. The potentials Ψapplied applied to the gold surface (relative to the reference electrode R) differ from the absolute surface potential ΨGold of the gold (which is relative to the potential of a free electron in vacuum and thus influenced by the potential of the surrounding solution23,25). We extract ΨGold by fitting the Fn(D, Ψapplied) profiles to the solution of the nonlinear PB equation with boundary conditions of constant charge (at the mica surface) versus constant potential (at the gold surface), shown in Figure 2 as solid lines, each corresponding to the respective
occurs, when an external potential is applied.23 This is the range in which we work. Fn(D) measurements between two bare mica surfaces across water, determine the negative charge on the bare mica, which is known to lose K+ ions from its surface.23
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RESULTS AND DISCUSSION The gold surface facing the bare mica across water is connected to a potential source (Figure 1B). Typical Fn(D) profiles are shown in Figure 2 for the gold surface held at different applied potentials Ψapplied relative to the platinum reference electrode R (Figure 1B), within the range −0.4 V to 0.3 V at which it is ideally polarized (Figure 1C);2 data symbols are colored to 12846
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Langmuir ΨGold values shown in the legend in Figure 2.26 Working in water with no-added-salt (main figure), where the screening length is larger, emphasizes the range at which the repulsion peaks and of electrostatic attraction, which is a signature of surface-charge reversal, well beyond the range of any significant van der Waals forces. Additional experiments at low added salt (3.5 × 10−4 M KClO4, inset to Figure 2, green data) are also fully consistent with the no-added salt case, revealing that in both cases the longer range electrostatic repulsion peaks and reverts to attraction. When ΨGold is positive (Figure 2, orange, purple, and cyan lower curves), there is a long-ranged electrostatic attraction between the gold and the negative-potential mica surface, as qualitatively expected between two oppositely charged surfaces. Likewise, when |ΨGold| is much larger than |Ψmica|, both being negative (black upper curve), there is a monotonic electrostatic repulsion, from large separations all the way to the range of vdW attraction (D < ca. 5 nm). The red-data curve has similar potential to the mica, but its peak is near the range of strong vdW attraction, obscuring the electrostatic interaction. However, where the gold surface with a small negative potential ΨGold faces the large negative Ψmica (markedly, the green and gray data), the profiles show an initial long-ranged electrostatic repulsion, which peaks at separations substantially larger than the relevant vdW range (red broken curve). For the case of the gray data, the profiles become clearly attractive (F/R < 0) at longer range than the vdW forces, while for the blue data, where |ΨGold| is negative but rather small (−15 mV), no clear peak is observed above the scatter, but a strong attraction between the two surfaces, much longer ranged than vdW, is clearly seen. This nonmonotonic behavior, especially the peak in repulsion (gray and green data), as well as the long-ranged attraction (blue data), between surfaces that are at the samesign potential can only arise as a result of charge inversion at the constant potential surface (gold), from a negative charge when the surfaces are far apart, to a positive charge as the surfaces approach (the potential of the gold remaining constant and negative throughout). This behavior is also replicated, at a shorter range reflecting the higher salt concentration, by the green profile in the inset to Figure 2 (and emphasizing its electrostatic nature). This is considered further below. In principle, solutions of the PB equation with the appropriate boundary conditions (suitably augmented with van der Waals attraction) predict both the full force vs separation profiles F(D) as well as the surface charge inversion, as has been done in several theoretical studies.5,6,10,27 Chan and co-workers10 in particular comprehensively analyzed interactions under several different boundary conditions, including the constant charge versus constant potential of the present study. A heuristic illustration of the onset of the charge inversion is given in Figure 3A. As the mica and gold surfaces (at same-sign potentials) approach from a large separation D0, (Figure 3A), with |Ψmica| > |ΨGold|, the overall potential ψ(x) in the gap between them is given (to leading order) by their sum (black solid curve).5 For a surface charge density σgold on the gold, the resultant electric field Ex(x) at the surface (x = 0) is, by Gauss’s law, given by Ex(0) = σgold/εε0.28 Since the field Ex = −(dψ/ dx), we have at the surface σgold = −εε0(dψ/dx)x=0. As the surfaces approach (D0 > D1 > D2 > D3), the slope |(dψ/dx)x=0|, indicated as a broken black line tangential to the potential at the gold surface, gradually decreases, and reaches zero, corresponding to zero charge, when the minimum in the potential ψ(x) disappears (D2). Further approach leads to
Figure 3. (A) Schematic of the potentials between mica (constant charge) and gold (constant potential) at different separations, illustrating the charge inversion at the gold surface (both Ψmica and ΨAu are negative in this schematic). The red and the blue dotted lines at D = D0 are the individual potentials due separately to the charges on the mica and gold, respectively, when far apart, and the black solid line in D1−D3, showing the potential ψ(x) between the surfaces, is approximately the sum of the two.5,10 The black dashed line is the slope (dΨ/dx) = −σgold/εε0 at the surface of the gold, which changes sign on going from separation D1 to D3, implying the gold surface charge inverts. See also discussion in text. (B) Solution of the PB equation for force profiles between a constant charge surface (i.e., mica) and a constant potential (i.e., gold) surface at the experimentally derived surface potentials of the latter from Figure 2 (using the same Hamaker constant and Debye length values), in the absence of vdW interaction (shown separately as the broken red curve). The curves are color matched to the data in Figure 2 and to the gold surface potential values ψGold shown in the legend. (The potential indicated for mica (−0.09 V) is its value at infinite separation from the gold, and varies as the surfaces approach.) The inset shows a magnified view of the calculated blue curve, corresponding to ψGold = −15 mV, though the experimental blue data (Figure 2) is too scattered to show any clear peak.
change of sign in (dψ/dx)x=0, as indicated at D = D3 in Figure 3A, corresponding to inversion of the surface charge on the gold, from negative to positive. We may also identify the points on the F(D) profiles of Figure 2 where charge inversion occurs, as well as the processes leading to it, by integrating the PB equation to obtain the wellknown expression5 for the electrostatic pressure Π between flat parallel surfaces: Π = A{cosh(eψ /kBT ) − 1} − B(dψ /dx)2
(1)
where A = 2c0kBT and B = εε0/2. We also recall that in the Derjaguin approximation,4 (F(D)/R) = 2πE(D) = 2π∫ ∞D Π(D′) dD′, where E(D) is the interaction energy per unit area between flat parallel plates obeying the same force− 12847
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Langmuir distance law, so that Π(D) = (1/2πR)(∂F/∂D). In equilibrium, Π is invariant across the gap; in particular, it applies at the gold surface where ψ = ψGold. Thus, the first term in eq 1 is fixed, and Π is a maximum when (dψ/dx) = 0 at the gold surface; that is, at the point where the charge on the gold is zero and inverts on further approach (as in Figure 3A, D2 to D3). Since the maximal value of |(∂F/∂D)|, and thus the point of charge inversion, is the point of inflection on the F(D)/R profile, this shows that a peak in the F(D)/R profile, as clearly seen in the green and gray curves of Figure 2, is indeed a clear signature that such charge inversion has occurred. One way of looking at the physics is that it is simply the interplay between the entropy penalty associated with progressively confining counterions between the surfaces, and the penalty of moving negative charges from the gold surface into the bulk (a change that clearly entails an electrostatic energy penalty). As the surfaces approach, the counterion confinement grows (thus the charge inversion is indeed a confinement-induced effect), and equilibrium is maintained by progressively reducing the negative surface charge on the gold surface, thus enabling release of counterions to the bulk. At the point of inflection on the F(D) profile, or alternatively of the maximum in Π as we have seen, the charge on the gold becomes zero and reverses on additional approach, i.e., the metal surface (at negative potential) becomes positively charged as electrons at the surface are further depleted by being “pushed back” into the metal. On further approach, the positive counterions of the mica surface are gradually all released from the gap into the bulk, and as the two surfaces come into contactas calculated explicitly in ref 10the mica potential becomes equal to that of the gold. Figure 3B reproduces the purely electrostatic part of the measured interactions for the profiles shown in Figure 2, based on the nonlinear PB equation with constant-charge versus constant-potential boundary conditions (Figure 3B lines color coded to match the Figure 2 data). The green and gray curves in Figure 3Bcorresponding to the electrostatic part of the fit to the green and gray data in Figure 2clearly show how the purely electrostatic repulsions are predicted to peak, with the charge inversion commencing at the point of inflection. For the case of the red curve in Figure 3B (corresponding to the red data in Figure 2), this inflection point is within the range of strong vdW attraction, so that it is obscured in the measured red data of Figure 2. For the case of the blue data (where the potential is negative but small), the inflection as well as the peak in the measured F(D) (Figure 2) are obscured as they are within the experimental scatter, but the strong attraction in this case, seen well beyond the range of vdW forces, clearly reveals the charge inversion.
from repulsion to attractioninto account, for interactions between dielectrics and metal surfaces in aqueous media in similar circumstances. These include phenomena such as colloidal interactions, adsorption of proteins, cells, or nanoparticles on metal surfaces, imaging of metal surfaces by ceramic AFM tips, and tribology of dielectric−metal interfaces in aqueous surroundings.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b03326. Details of (1) the surface force balance (SFB) measurements, (2) mica surface properties and nature of the noadded-salt water, (3) the gold surface preparation and properties, and (4) the three-electrode configuration used in this study (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address †
Adama Makhteshim Ltd., Beer Sheva, 84100, Israel
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the European Research Council (Advanced Grant HydrationLube), the Israel Science Foundation, the Minerva Foundation, and the Petroleum Research Fund (PRF # 55089ND10) for support of this grant. We thank Alexander Vaskevitch, Sam Safran, and Philip Pincus for useful discussions. This research has been made possible in part due to the historic generosity of the Harold Perlman family.
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REFERENCES
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OUTLOOK To summarize, our measurements show that when two surfaces with the same potential sign (and initially same charge sign) approach across water, if one of them is at constant charge while the other is a metal at a constant potential, the electrostatic repulsion between them may be nonmonotonic and attain a maximum, becoming attractive on closer approach. This effect, long-predicted theoretically6,10 but not previously observed, arises as progressive confinement of the trapped counterions forces charge rearrangement at the metal surface, resulting in charge inversion on the metal surface. Its experimental demonstration emphasizes the importance of taking such charge reversaland the accompanying crossover 12848
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Langmuir (10) McCormack, D.; Carnie, S. L.; Chan, D. Y. C. Calculations of electric double-layer force and interaction free energy between dissimilar surfaces. J. Colloid Interface Sci. 1995, 169, 177−196. (11) Barten, D.; Kleijn, J.; Duval, J.; Leeuwen, H. P. v.; Lyklema, J.; Cohen Stuart, M. Double layer of a gold electrode probed by AFM force measurements. Langmuir 2003, 19 (4), 1133−1139. (12) Biggs, S.; Mulvaney, P. Measurement of the forces between gold surfaces in water by atomic force microscopy. J. Chem. Phys. 1994, 100 (11), 8501−8505. (13) Biggs, S.; Mulvaney, P.; Zukoski, C.; Grieser, F. Study of anion adsorption at the gold-aqueous solution interface by atomic force microscopy. J. Am. Chem. Soc. 1994, 116 (20), 9150−9157. (14) Chai, L.; Klein, J. Interactions between molecularly-smooth gold and mica surfaces across aqueous solutions. Langmuir 2009, 25, 11533−11540. (15) Giesbers, M.; Kleijn, J. M.; Cohen Stuart, M. A. The electrical double layer on gold probed by electrokinetic and surface force measurements. J. Colloid Interface Sci. 2002, 248 (1), 88−95. (16) Wang, J.; Bard, A. J. Direct atomic force microscopic determination of surface charge at the gold/electrolyte interface the inadequacy of classical gcs theory in describing the double-layer charge distribution. J. Phys. Chem. B 2001, 105 (22), 5217−5222. (17) Frechette, J. l.; Vanderlick, T. K. Electrocapillary at contact: Potential-dependent adhesion between a gold electrode and a mica surface. Langmuir 2005, 21 (3), 985−991. (18) Valtiner, M.; Kristiansen, K.; Greene, G. W.; Israelachvili, J. N. Effect of Surface Roughness and Electrostatic Surface Potentials on Forces Between Dissimilar Surfaces in Aqueous Solution. Adv. Mater. 2011, 23, 2294−2299. (19) Larson, I.; Drummond, C. J.; Chan, D. Y. C.; Grieser, F. Direct force measurements between dissimilar metal oxides. J. Phys. Chem. 1995, 99, 2114−2118. (20) Larson, I.; Drummond, C. J.; Chan, D. Y. C.; Grieser, F. Direct Force Measurements between Silica and Alumina. Langmuir 1997, 13, 2109−2112. (21) Veeramasuneni, S.; Yalamanchili, M. R.; Miller, J. D. Measurement of Interaction Forces between Silica and α-Alumina by Atomic Force Microscopy. J. Colloid Interface Sci. 1996, 184, 594−600. (22) Klein, J.; Kumacheva, E. Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid to solid phase transitions. J. Chem. Phys. 1998, 108 (16), 6996−7009. (23) See Supporting Information, which contains further details on the SFB, the mica surface, the gold surface preparation and properties; and the three-electrode configuration, first described in L. Chai, PhD thesis, Weizmann Institute 2007. (24) Chai, L.; Klein, J. Large (cm2), molecularly smooth (0.2 nm r.m.s.) gold films for surface forces and other studies. Langmuir 2007, 23, 7777−7783. (25) Trasatti, S. Structure of the metal/electrolyte solution interface: new data for theory. Electrochim. Acta 1991, 36, 1659−1667. (26) For a given contact point, ΨGold values vary reproducibly and reversibly with ΨApplied, though at different contact points a given applied potential, ΨApplied, may lead to a different ΨGold value, as explained in the SI.23 (27) In principle, image charge interactions can alter the electric double-layer structure and consequently modify the forces between the surfaces, e.g., Wang and Wang, J. Chem. Phys. 2013, 139, 124702. However, as explicitly shown in this study, these effects are significant only at small surface separations, D ≲ 2nm, within the range of strong vdW interactions, and well below the separations at which surface charge inversion occurs in our study. For these reasons, we do not relate to them here. (28) Bleaney, B. I.; Bleaney, B. Electricity and Magnetism, 3rd ed.; Oxford University Press: London, 1971.
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