Measuring Electrostatic Double-Layer Forces at High Surface

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J. Phys. Chem. 1996, 100, 16700-16705

Measuring Electrostatic Double-Layer Forces at High Surface Potentials with the Atomic Force Microscope Roberto Raiteri,†,‡ Massimo Grattarola,† and Hans-Ju1 rgen Butt*,‡ DIBE, UniVersity of GenoVa, Via Opera Pia 11A, 16145 GenoVa, Italy, and Max-Planck-Institut fu¨ r Biophysik, Kennedyallee 70, 60596 Frankfurt, Germany ReceiVed: May 29, 1996; In Final Form: July 30, 1996X

The aim of this study was to measure interaction forces between surfaces with high electric potentials in aqueous electrolyte solutions. Therefore, the force between a platinum or gold sample, which served as the working electrode, and a silicon nitride tip of an atomic force microscope was measured. Various potentials were applied between the sample and a reference electrode. Experimental results were compared to forces calculated with the Poisson-Boltzmann equation. As predicted by theory, the electrostatic double-layer force changed only in a narrow potential range of about 300 mV and saturated below and above this range. Within this range the repulsion grew with more negative sample potentials. This was expected, since the tip was negatively charged at the high pH chosen. At strong negative sample potentials this saturation was not complete and the force continued to rise slightly when lowering the potential. Another surprising and yet unexplained observation was a weak long-range attraction at positive sample potentials. This attraction decayed with a decay length of typically 50 nm. In parallel, the structure of Au(111) was imaged. We confirmed a (x3 × p, p > 10) reconstruction at potentials below about -0.3 VSHE and the normal (1 × 1) hexagonal packing above this potential. Above about +0.8 VSHE the (1 × 1) structure disappeared and no crystalline packing was observed anymore.

Introduction Electrostatic double-layer forces in an aqueous electrolyte play an important role in physical chemistry, biology, engineering, and many industrial processes.1,2 Double-layer forces stabilize colloids or emulsions. They are one of the reasons for the swelling of clays, and they influence the conformation and function of biomolecules. In addition, the double-layer force contains valuable information about the behavior of the doublelayer itself. For this reason many direct measurements of double-layer forces have been carried out including measurements across soap films,3 between rubber and glass,4 between atomically flat mica surfaces,5 between surfactant and lipid bilayers,6 between silica,7 and between metal surfaces.8 This paper deals with surface forces at high surface potentials. To our knowledge up to now, all systematic measurements were done on surfaces with potentials below approximately 100 mV. One reason for the lack of high potential results is the difficulty of making smooth and clean surfaces with high potentials. Probably the only way to produce surface potentials significantly higher than 100 mV is to take a metal and apply an external potential. However, metal surfaces cannot be made with the necessary subnanometer roughness over several square micrometers. A roughness in the nanometer range would be necessary because the roughness limits the distance resolution. Since surface forces typically act in the nanometer range, the roughness needs to be smaller. This requirement needs to be fulfilled over the areas interacting in a surface force experiment. In a typical experiment the force between two crossed cylinders or between two spherical surfaces is measured. The radii of curvature of the cylinders or spheres are roughly 1 cm, which leads to interacting areas in the 100 µm2 range.9 With the invention of the atomic force microscope10 (AFM) and its application to measurement of surface forces in aqueous †

University of Genova. Max-Planck-Institut fu¨r Biophysik. * To whom correspondence should be sent. X Abstract published in AdVance ACS Abstracts, September 15, 1996. ‡

S0022-3654(96)01549-3 CCC: $12.00

medium11 (for review see ref 12), the interacting areas could be greatly reduced. For this reason surface forces between several materials have been measured, including gold.13,14 In AFM the force between a probe at the end of a microfabricated cantilever and a flat surface is measured. As probes, usually integrated tips are used. These have radii of curvature at the end of 5-50 nm, which leads to interacting areas of 10-4 to 10-3 µm2. Alternatively, many researchers measured the force between a small sphere (diameter of 2-10 µm) glued to the end of an AFM cantilever and a flat surface. In this case the interacting areas are roughly 0.1 µm2. For this paper we studied the electrostatic double-layer force between a microfabricated silicon nitride tip and a gold or platinum sample. A potential was applied between the sample and a platinum counter electrode. This potential was sweeped between typically (1 V in 20 s. During the potential sweep, the force vs distance curves were continuously recorded at a frequency of 5 Hz. We chose to measure the force between silicon nitride and a noble metal rather than between two metallic surfaces for several reasons. First, with silicon nitride tips the surface structure can be imaged at the same time with high resolution.15 Second, making a gold probe involves severe technical problems.16 Gold probes could be made by depositing gold onto microfabricated tips. This layer of gold, however, can easily be removed, and imaging is only possible at low resolution. Alternatively, one could glue a gold sphere onto the cantilever. In this case the interacting areas are significantly larger than with integrated tips and imaging is impossible. Materials and Methods All measurements were done with a commercial AFM (Nanoscope 2, Digital Instruments, California) using its standard electrochemical glass cell together with a homemade bottom part made of silicon, which contained the counter electrode and samples of different size (Figure 1). An electric potential was applied between the sample (which was the working electrode) © 1996 American Chemical Society

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Figure 1. Schematic of the experimental setup with the gold or platinum sample acting as the working electrode (WE), the counter electrode (CE), and a Ag/AgCl reference electrode (RE).

and a platinized platinum counter electrode. Both electrodes plus a commercial Ag/AgCl reference electrode with a salt bridge (DryRef, Precision Instruments) were connected to a homemade potentiostat. Standard V-shaped silicon nitride cantilevers of different stiffness and tip sharpness were used (Olympus sharpened tips with 100 µm length, 0.4 µm thickness, and a calculated spring constant of 0.09 N/m and Digital Instruments, Nanoprobes, with 100 µm length, 0.6 µm thickness, and a calculated spring constant of 0.2 N/m). The scanner was calibrated as described in ref 17. Gold, prepared by evaporating gold onto clean glass substrates, and platinum foils were used as samples. Platinum was cleaned before use by “Pirahan˜a Solution” (30% oxygen peroxide, 70% concentrated sulfuric acid). The cell, all connecting tubes and flasks, were excessively rinsed with hot water before use. Then tips, samples, and the whole cell were rinsed with ethanol and pure water (Millipore) and kept under UV light for 20 min in a laminar flow hood before each experiment. Immediately afterward, the cell was filled with water and mounted on the AFM. All measurements were done at pH 9-10 in order to have a high negative surface potential (about -80 mV) on the silicon nitride tip.18 Deionized Millipore water with a conductivity of 0.055 µS/cm was used. We chose a monovalent salt (KCl if not mentioned otherwise) at a concentration of 1 mM to get a suitable Debye length of 9.5 nm. The pH was adjusted by adding KOH. Argon was always bubbled into the solution for at least 30 min before starting an experiment. Then the solution was rinsed through the cell to a waste reservoir for several minutes. Finally, the flow was stopped and after several minutes the actual experiment started. During continuous force measurements with a frequency of 5 Hz (0.2 s for a whole force curve), the potential between the working and counter electrode was scanned. The potential waveform was triangular. Potential scan rates were varied between 1 and 0.02 V/s. Faster voltage sweeps were impossible, since not enough force curves could then be taken; force curves could not be taken with a higher frequency owing to hydrodynamic effects that led to a hysteresis.19 When choosing potential scan rates slower than 0.02 V/s, we had problems getting reproducible force measurements. Typically, we chose a sweep rate of 0.5 V/s. Cantilever deflection, current between working and counter electrode, and the voltage applied to the scanner of the AFM (which is proportional to the height of the scanner) were simultaneously recorded with an analog-to-digital converter of a personal computer. A typical record contained two complete potential sweeps and in the order of 100 force vs scanner position signals. Force vs scanner position curves were converted to force vs distance curves as described in refs 11 and 12.

Figure 2. Typical force curves obtained on a platinum sample in 1 mM KCl at pH 10. The potential of the platinum was at -0.44, +0.75, and +1.5 VSHE.

Results and Discussion Force Measurements on Platinum. Figure 2 shows typical force vs distance curves (from now on called force curves) measured on platinum at potentials of -0.44, +0.75, and +1.5 VSHE. At -0.44 and +0.75 VSHE the tip encountered a repulsive force that decayed exponentially with a decay length similar to the Debye length. We attribute this component to the electrostatic double-layer force, since it showed the expected distance dependency. At small distances the tip jumps onto the sample owing to an attractive force. This attractive component contains the van der Waals (vdW) force. Afterward, the tip is in contact with the sample surface. In the retracting part of the force curve the tip adhered to the sample at positive potentials; it had to be pulled off the sample with a certain force, the adhesion force. At +1.5 VSHE a long-range attractive force was observed. This force also decayed exponentially with increasing distance. The decay length of roughly 50 nm was much larger than the Debye length. At a distance of ∼12 nm the tip jumped onto the sample surface. In the retracting part of the force a strong adhesion of ∼5 nN can be seen. For each force curve the approaching part was fitted with a single exponential. Only distances larger than 7 nm or the jumpin distance was considered. A value of 7 nm is somewhat arbitrary. It is large enough so that the vdW attraction is negligible, although the major part of the double-layer component is still considered. In any case, the results did not depend critically on this value. Force amplitude, i.e., the fitted force extrapolated to zero distance, and decay length were noted. Second, from the retracting part of the force curve the adhesion force was determined. A plot of these parameters vs the potential at which they were measured is shown in Figure 3. In the behavior of the force amplitude three regions could be distinguished: 1. At low (negative) potentials a strong electrostatic repulsion was observed. The decay length agreed with the Debye length

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Figure 3. Fitted force amplitudes (positive forces are repulsive, negative forces are attractive), fitted decay lengths, and adhesion force for a typical experiment with a silicon nitride tip on platinum. The aqueous solution contained 1 mM KCl and was titrated with KOH to pH 10. A full voltage cycle took 10 s, which corresponds to a sweep speed of 0.45 V/s. The bottom figure shows the current between the platinum WE and the CE. It can probably be interpreted as follows.34 The voltammogram started at a negative potential of about -0.6 VSHE with the hydrogen peak. At the pH of 10 it was probably due to the reaction 2H2O + 2e- f H2 + 2OH-. Then followed the two hydrogen desorption peaks, which appeared as one broad maximum around -0.2 VSHE. After a narrow double-layer region the adsorption and oxidation of hydroxyl (Pt + OH- f PtOH + e- and 2PtOH f PtO + Pt + H2O) started at +0.4 VSHE. The voltage range was limited at +1.6 VSHE owing to oxygen formation. In the cathodic sweep the hydroxyl layer is desorbed again around -0.2 VSHE. It should be kept in mind that owing to the low ion concentration diffusion overpotentials might have occurred.

of 9.5 nm. Such a repulsion was expected because the tip carried a negative surface charge and should be repelled by the negatively charged platinum sample. The force amplitude was relatively constant with only a slight tendency to decrease linearly with increasing potential. Typically, it decreased by 5-10% per volt. This agrees with earlier results.20 2. The region of relative constant force amplitude was followed by a steep decline of the force amplitude between +0.6 and +0.9 VSHE. Within ∼300 mV the amplitude changed by 80%, falling from strong repulsion to zero or even attraction. A hysteresis of 100-200 mV was in some cases observed between the cathodic and the anodic potential sweep. 3. At high positive potentials the jump-in distance increased up to 10-15 nm, while at negative potentials it was significantly smaller. In addition, a weak attractive force with a constant amplitude of ∼0.5 nN was observed. This component could also be fitted with an exponential function with typical decay lengths of 50 nm. In Figure 3 the decay length increased discretely in one jump. In other experiments we observed a gradual increase.

Raiteri et al. We have yet no explanation or interpretation for this longrange attraction. Only the long-range hydrophobic force is of significant magnitude at such large separations.21 In our case, however, the silicon nitride tip and the platinum sample are hydrophilic and no hydrophobic force should be present. We would like to mention that measuring small attractive forces at such large distances with the AFM can lead to uncertainties in interpretation and one can easily measure artifacts. Constant drift of the cantilever deflection could, for instance, cause long-range effects. Such a drift would show attraction in the approaching part and repulsion in the retracting part of the force curve or vice versa. Since we observed attraction in both parts, we can exclude this effect. Interference of the laser beam, which is used to detect cantilever deflection, can cause an oscillating zero-force line.17 If one only measures to distances of half the wavelength (335 nm), this might be mistaken for a long-range attractive force. Especially on highly reflecting surfaces such as gold, interference effects are often a severe problem. In our experiments, however, we ensured that oscillations were negligible. In adhesion we observed a corresponding behavior: relatively low adhesion at negative potentials (region 1), relatively high adhesion at high positive potentials (region 3), and changing adhesion in region 2. At high positive potentials the adhesion increased probably because the electrostatic repulsion was absent. In addition, a distinct peak occurred in the cathodic sweep at +0.1 VSHE. We could not observe a correlation between this peak and any region in the voltammogram. The location of the peak was surprising, since adhesion is related to surface properties like the the surface energy.2 Electrochemical reactions, which change these properties, usually appear in the voltammogram. It is possible that the adhesion peak displays a certain structural or chemical state of the sample surface that is hidden in the voltammogram, i.e., the reactions leading to the peak are not correlated with a significant electric current. An alternative explanation is that the tip modifies the local electric field on the sample. In this case electrochemical reactions occurring directly underneath the tip might differ from reactions on the rest of the sample surface. The latter reactions are displayed in the voltammogram, since the area underneath the tip is small compared to the rest of the sample surface. Force Measurements on Gold. Results of force measurements on gold (Figures 4 and 5) showed a region of relatively constant force amplitude with, in some cases (as in Figure 5), a slight tendency to decrease with increasing potential at potentials below +0.7 VSHE (region 1). Then a steep decline of the repulsive force (region 2) at roughly +0.9 VSHE followed. A value of 80% of the amplitude change occurred within ∼300 mV. Hence, compared to platinum, the whole pattern was shifted to higher potentials. Such a shift is plausible because it is known that anions bind strongly to gold.21,23 Hence, to obtain a certain surface potential, the applied potential needs to be more positive to compensate for the negative charges. As a consequence of this shift, region 3 was absent in the force curves. In experiments with different anions the same behavior as with Cl- was observed with NO3- and SO4-. With the strongly adsorbing anions I- and Br-,22-24 however, no steep decline of the repulsive force occurred and region 1 dominated the whole voltage range (Figure 5). With KI the potential range was limited to potentials below +0.8 VSHE owing to a sharp current increase. This increase is probably due to the reactions 2I- f I2 + 2e- or I- + Au f AuI + e-.23 For all anions except I- the adhesion showed a peak in the anodic sweep around +0.6 VSHE and in both sweeps without

Electrostatic Forces

Figure 4. Fitted force amplitudes, fitted decay-lengths, and adhesion force for a typical experiment with a silicon nitride tip on gold (1 mM KCl, pH 9.5, 20 s cycle time). At the bottom the voltammogram is plotted. On gold the voltage sweep covered three regions, i.e., hydrogen evolution at potentials below -0.8 VSHE, the double-layer region, and oxide formation above +0.7 VSHE.23 Removal of the oxide layer is seen as a peak in the cathodic sweep around +0.5 VSHE.

hysteresis at +0.2 VSHE. In 1 mM KI these peaks were absent. Hence, they are probably related to oxidation and reduction of gold (see caption of Figure 4). This correlation, however, is not clear. We would have expected a correlation between the oxidized or reduced state of gold and adhesion. Peaks in the voltammogram indicate a change from the reduced to the oxidized state or vice versa. To the right from the oxidation peak in the anodic sweep, gold is oxidized; to the left from the peak in the cathodic sweep, it is reduced. However, adhesion did not correlate with these states of the gold surface. It did not even correlate precisely with the reduction or oxidation reaction: The adhesion peak is ∼0.2 V more negative than the oxidation peak in the anodic sweep of the voltammogram. In the cathodic sweep again the adhesion peak is ∼0.2 V more negative than the reduction peak of the voltammogram. We would like to mention that for platinum and gold the static deflection of the cantilever, i.e., the zero-force position of the cantilever, changed. At high positive sample potentials the cantilever was bent away from the sample by typically a few tens of nanometers. We have no explanation for this behavior. An electrophoretic effect is not likely, since the cantilever is negatively charged and one should expect a bending toward the positive sample. Ishino et al.25 coated AFM tips with gold and used the tip as a working electrode in force experiments on glass coated with stearic acid. Their experiments were done at pH ≈ 10 in 0.1 mM KOH at potentials of 0, +0.2, and +0.7 VSHE. They observed a strong decrease in repulsion between a potential of

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Figure 5. Fitted force amplitudes, fitted decay-lengths, adhesion force, and voltammogram for a typical experiment with a silicon nitride tip on gold in 1 mM Kl at pH 9.5 (20 s cycle time).

0 and +0.7 VSHE. This qualitatively agrees with our results assuming that their voltage range included region 2. In our case, however, region 2 was around +0.9 VSHE and it was significantly narrower. Comparison with Poisson-Boltzmann Theory. To interpret the results, we calculated the electrostatic force per unit area with a simple continuum theory.1,2 First, the distance dependent potential was numerically calculated with the onedimensional Poisson-Boltzmann equation for a monovalent salt:

d2y 1 y ) (e - e-y) du2 2 Here, y ) eψ/kT is the reduced potential and u ) x/λD with

λD )

x

0kT 2e2m

the reduced position coordinate. The other symbols are ψ, the potential that depends on the position x, e, the unit charge,  and 0, the permittivities of water and of free space, respectively, k, the Boltzmann constant, T, the temperature, n, the number of salt molecules in the bulk in particles per m3, and λD, the Debye length. In addition to the Poisson-Boltzmann equation, boundary conditions need to be fulfilled. For the metal surface we assumed a constant potential. Hence, y(x ) 0) ) y1. For the tip we calculated y(x) for constant potential, y(x ) D) ) y2, and constant charge,

σ dy dψ )S )| | dx x)D 0 du x)D

σ

x20kTn

conditions. D is the distance between the two surfaces. Once ψ(x) was known, the force per unit area could be

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Figure 6. Force per unit area vs distance calculated for different potentials of the sample. For the tip surface a constant charge density of -0.004 35 C m-2, which leads to a surface potential of -50 mV for an infinite distance between tip and sample, was assumed. The sample potential was -200, -150, -100, -50, 0, +50, +100, +150, and +200 mV from top to bottom. Positive forces are repulsive, negative forces attractive.

Figure 7. Force amplitude per unit area obtained by extrapolating the calculated force vs distance curve at large distances (D > 3λD) to zero distance. For the tip surface either a constant charge density of -0.004 35 C m-2 (thick continuous line), which leads to a surface potential of -50 mV for an infinite distance between tip and sample, or a constant potential of -50 mV (thick dashed lines) was assumed. For comparison, experimental results obtained on platinum (filled spheres, conditions as in Figure 3) and on gold (open triangles, conditions as in Figure 4) are plotted. The experimental curves were shifted along the voltage axes, and the amplitude was rescaled in order to facilitate the comparison.

determined with

f ) kTn(eeψ/kT + e-eψ/kT - 2) -

0 dψ 2 2 dx

( )

The first term is due to the osmotic pressure, and the second represents the Maxwell stress term. f does not depend on x anymore; it is the same for all x. For distances larger than the Debye length the force decays roughly exponentially (Figure 6). For constant potential and constant charge boundary conditions the force amplitude saturated at high potentials. This is demonstrated in Figure 7, which shows the amplitude of the electrostatic force vs the surface potential. For high negative or high positive surface potentials the force amplitude saturated and did not significantly change with varying potential anymore. Between -100 and +100 mV the force amplitude changes by 80%. The shape of the curves in Figure 7 can be directly compared to experimental results plotted in Figures 3 and 4. One could object that the calculations were done for the one-dimensional system of two planar surfaces while the tip has a complex threedimensional structure. However, detailed calculations showed the this does not change the shape of the force curves significantly.26

Raiteri et al. Two aspects of the experimental results agreed with predictions of the Poisson-Boltzmann theory. 1. The steep change of the force observed in region 2 corresponds to the changing force calculated around zero surface potential. Though the steepness of the change was lower in the experiments (80% change of the force occurred within 300 mV rather than 200 mV as calculated), the maximal steepness observed agreed with theory. A reduction of the steepness could be due to electrochemical reactions or to the adsorption of ions. 2. The relatively constant force measured in region 1 agrees with the calculated saturation at high negative potentials. This interpretation implies that the points of zero charge of platinum and gold are approximately at a potential of maximal change in the force amplitude. For gold in 1 mM KCl, KNO3, or KSO4 this was around +0.9 VSHE; for platinum in 1 mM KCl this was at +0.7 VSHE. Values for the point of zero charge reported in the literature are roughly 0 ( 0.4 VSHE for gold21,27,28 and platinum.26,29,30 One reason for our relatively high point of zero charge might be the high pH. Owing to a hydroxylated oxide layer,21,31 the externally applied potential needs to be strongly positive to compensate for negative charges due to dissociated hydroxyl groups on the surface. Results concerning the attraction at positive sample potentials are not clear. It is known that the tip jumps onto the sample surface when the gradient of the attractive force exceeds the spring constant of the cantilever. Attractive forces are the vdW force and at high positive potentials the double-layer force. The vdW force can be approximated by2 FvdW ) AR/6D2 leading to a force gradient of AR/3D2. A is the Hamaker constant, and R is the radius of curvature at the end of the tip. With Hamaker constants of 5 × 10-20 J (for Si3N4/water/Si3N4)32 or 25 × 10-20 J (gold/water/gold),13 a spring constant of 0.09 N/m, and R ) 10 nm the jump-in is expected at 1.2 nm and 2.1 nm, respectively. Hence, the vdW force cannot explain the large jump-in distance of 10-15 nm. To estimate the influence of the electrostatic force, we assumed that the electrostatic attraction at high positive potentials has the same amplitude as the repulsive force at negative potentials of typically 3 nN. Then the force gradient is 3nN/λD × e-D/λD. With a spring constant of 0.09 N/m a jump into contact is expected at a distance of D ) 12 nm. Such jump-into-contact distances were indeed observed at positive sample potentials. At distances larger than 12 nm we should have been able to detect the attractive force vs distance. However, we never observed an attractive force that decayed with the Debye length. Instead, a long-range attraction was observed that cannot be explained with Poisson-Boltzmann theory. Also, the slight increase of the force amplitude with increasing magnitude of the potential observed in region 1 is not predicted by theory. In contrast, owing to the constant potential condition applied for the metal surface, which weakens the repulsion at high negative potentials, the Poisson-Boltzmann theory predicts a slight decrease of the repulsion in region 1. Potential Dependent Structure of Gold. In some experiments we could resolve the molecular structure of the gold surface while changing the potential. At zero potential the original hexagonal (1 × 1) Au(111) structure was observed with a lattice constant of 2.9 Å (Figure 8). Below -0.4 VSHE in the cathodic and -0.2 VSHE in the anodic part of the voltage sweep, stripes of 4.9 ( 0.3 Å spacing were observed. They ran parallel to rows of atoms of the (1 × 1) structure. In some cases these stripes consisted of two parallel stripes each with a thickness of about 2.5 Å. A spacing of 4.9 Å agrees with a x3 spacing of the gold, which is 4.99 Å. In

Electrostatic Forces

Figure 8. Atomic force microscope image of Au(111) in 1 mM KCl at pH 9.5. The potential of the gold surface was changed while scanning. The image was scanned from left to right within 14 s. In this time the potential changed linearly from -0.6 VSHE at the left down to -0.9 VSHE and back to +1.2 VSHE (right). At the left, at negative potentials, stripes of 4.9 Å spacing were observed. After the potential was increased above -0.3 VSHE, the (1 × 1) phase appeared (middle). Above +0.9 VSHE no recognizable structure was observed anymore (right).

the direction along the stripes no features were resolved, which is consistent with the result of Kolb, Schneider, and others33 who proposed a (23 × x3) reconstruction of Au(111) at negative potentials. Above a potential of about +0.8 VSHE the (1 × 1) structure disappeared and no distinct two-dimensional structure was observed anymore. In the cathodic sweep the reverse sequence of structures was imaged and the whole cycle could be repeated. On platinum we never resolved the atomic structure probably because it is not crystalline on the surface. Conclusion Our experiments confirmed two aspects predicted by the Poisson-Boltzmann theory: a steep change of the force within a range 200-300 mV and a strong, approximately constant repulsive force at negative surface potentials. At high negative surface potentials this saturation was not complete. In contrast to the prediction, we observed a slight further increase of the electrostatic repulsion with increasing negative surface potential of the metal. No definite result was obtained for the attractive electrostatic force at high positive sample potentials. Though the tip jumped onto the surface at the expected distance, we could not observe an attractive component that decayed with the Debye length. Instead, a long-range attractive force was observed for which we do not have an explanation. Acknowledgment. We thank Ernst Bamberg, Manfred Jaschke, Markus Preuss, and Subrata Tripathi for their help. This work was partially supported by the VIGONI program. References and Notes (1) Hunter, R. J. Foundations of Colloid Science I+II; Clarendon Press: Oxford, 1986. (2) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1992.

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