Double-Layer Interactions between Self-Assembled Monolayers of ω

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Double-Layer Interactions between Self-Assembled Monolayers of ω-Mercaptoundecanoic Acid on Gold Surfaces Victoria Kane and Paul Mulvaney* Advanced Mineral Products Research Centre, Chemistry School, University of Melbourne, Parkville, Victoria 3052, Australia Received November 28, 1997. In Final Form: April 10, 1998 The atomic force microscope was used to investigate the interaction between 11-mercaptoundecanoic acid surfaces and 2-mercaptoethanesulfonic acid surfaces as a function of electrolyte and pH. The surface potential was found to peak at -80 mV at pH 6-8 in 0.1 mM 1:1 electrolyte. The Hamaker constant for the gold-gold interaction was found to be decreased from the value of 1 × 10-19 J in water to 4 × 10-20 J in ethanol. The dispersion interaction between gold surfaces following derivatization with 11mercaptoundecanoic acid was drastically reduced. The terminal carboxyl groups did not ionize in ethanol. Even in water, extremely low degrees of ionization were observed, with just 1-2% of surface sites being ionized at pH 10. The force curves showed no jump-in nor adhesion above pH 7. We could not reconcile the ψafm-pH results with a simple diffuse layer model for the interface; however the ionization behavior could be explained with sodium ion binding to surface carboxyl groups with a binding constant pKNa ) 6.3. The addition of micromolar amounts of Pb2+ caused almost complete neutralization of charged surface groups. These data could be modeled with KPb ) (1-4) × 10-10. An alternative modeling procedure based on incorporation of a zero-order Stern layer could only explain the experimental values if an extremely low value of the inner layer capacitance was assumed of 1-4 µF cm-2. However, this model may be able to explain the lack of jump-in in alkaline solution and the absence of adhesion at high pH.

Introduction Over the last 30 years, colloids of several materials have been proposed as model systems for double-layer interactions in water. These include silver iodide and monodisperse, functionalized latex particles.1,2 Whilst charge titration and electrophoretic data obtained using these colloids largely support existing double-layer models of the interface, one difficulty has been an accurate determination of the number of ionizable surface sites. This parameter has usually remained a fitted variable when modeling the data. A second problem is the variation in intrinsic dissociation constant of surface sites due to their chemical heterogeneity. Even in the case of latex particles, there can be chemical heterogeneities because the carboxyl groups may be located beneath the actual particle surface within the low-dielectric region of the polymer core or they may protrude out from the surface plane. The position of the ionizable proton will affect its pKa, since the lower polarity within the hydrophobic latex particle core compared to water will increase the pKa of the carboxyl group. The self-assembly of ω-substituted alkanethiols on metal substrates provides an alternative method for creating well-defined surfaces with controllable chemical functionality.3-6 At first sight, SAMs on gold appear to * To whom correspondence should be addressed. Fax: 61-3-93446233. E-mail: [email protected]. (1) (a) Kruyt, H. R. Colloid Science; Elsevier: Amsterdam, 1952; Vol. 1. (b) Lyklema, J. K. Kolloid Z. 1961, 175, 129. (2) (a) Homola, A.; James, R. O. J. Colloid Interface Sci. 1977, 59, 123. (b) Homola, A.; James, R. O.; Healy, T. W. J. Chem. Soc., Faraday Trans 1 1977, 73, 1436. (3) Kim, Y.-T.; McCarley, R. L.; Bard, A. J. Langmuir 1993, 9, 1941. (4) Bain, C. D.; Evall, J.; Whitesides, G. M. J. Am. Chem. Soc . 1989, 111, 7155. (5) Nuzzo, R. G.; Allara, D. L. J. Am. Chem. Soc. 1983, 105, 4481. (6) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559.

obviate some of the earlier modeling difficulties. Evaporated gold surfaces display predominantly Au(111) lattice planes and are almost atomically smooth over large areas of several hundred square nanometers. The alkanethiols adopt a regular (x3 × x3) R30° adlattice on this surface.7 This corresponds to a surface site density of 7.7 × 10-10 mol cm-2.8 This particular value is supported by helium diffraction9 and transmission electron diffraction data,10 and is also consistent with IR studies by Chidsey et al.11 The ability to reproducibly prepare an ionizable surface with the same site density is an important advance in double-layer studies. Because the chain lengths of all adsorbates are equal and the gold surface has a roughness of around 1-2 nm2/µm2, all functional groups will sit at practically the same distance from the surface, leading to homogeneous ionization constants for all surface sites. Contact angle titrations of mercaptoundecanoic acid monolayers on gold agree qualitatively with double-layer models,12 but whilst the wetting of water droplets has been studied as a function of pH, the ionic strength of the droplets was not kept constant, so exact agreement with theory cannot be expected. Although more recent studies have indicated that there is considerable rearrangement of the surface gold atoms following monolayer formation,13 the fresh surfaces remain structurally intact long enough for “hole” formation to be neglected.14 (7) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J. Chem Phys. 1993, 98, 678. (8) Widrig, C. A.; Alves, C. A.; Porter, M. D. J. Am. Chem. Soc. 1991, 113, 2805. (9) Chidsey, C.; Liu, G.-Y.; Rowntree, P.; Scoles, G. J. Chem. Phys. 1989, 91, 4421. (10) (a) Bain, C. D.; Troughton, E. B.; Tao, Y.; Evall, J.; Whitesides, G. M.; Nuzzo, R. J. Am. Chem. Soc. 1989, 111, 321. (b) Strong, L.; Whitesides, G. Langmuir 1988, 4, 456. (11) Chidsey, C. E. D.; Loiacono, B. N. Langmuir 1990, 6, 682. (12) Bain, C. D.; Whitesides, G. M. Langmuir 1989, 5, 1370. (13) Pan, W.; Durning, C. J.; Turro, N. J. Langmuir 1996, 12, 4469.

S0743-7463(97)01296-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 05/23/1998

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In this paper, we measure the double-layer forces between a gold sphere and a gold plate in solution before and after adsorption of 11-mercaptoundecanoic acid. We find that although reproducible potential-pH curves can be obtained, the results cannot be interpreted quantitatively using Gouy-Chapman (GC) theory because of the extraordinarily low degree of ionization. We propose two simple additions to the basic GC model, each of which can explain some of the experimental data more adequately. Experimental Section (i) Chemicals. Analytical grade NaNO3, NaOH, and HNO3 were used without further purification. High-purity nitrogen (99%) and AR grade ethanol were used as supplied. Milli-Q water was used throughout. Gold (99.99%) was obtained from The Australian Bullion Company. All glassware was soaked in hot Decon-90 solution and rinsed vigorously in Milli-Q water. The glassware was then dried in a laboratory oven at 100 °C. The O-ring and plastic tubing were boiled in Milli-Q water for 30 min, rinsed with ethanol, and blown dry with nitrogen before use. 11-Mercaptoundecanoic acid was prepared using the following synthesis. A solution of 11-bromoundecanoic acid (2.28 g, 8.60 mmol), sodium thiosulfate pentahydrate (2.14 g, 8.64 mmol), and 2:1 ethanol/water (50 cm3) was refluxed for 3 h. The solvent was removed, and 10% H2SO4 (30 cm3) was added. The flask was fitted with an air condenser and the mixture heated at 90 °C for 2 h. The cloudy liquid was then extracted with dichloromethane (3 × 70 cm3). The combined dichloromethane extracts were washed with water (2 × 50 cm3), dried over Na2SO4, and filtered. The solvent was removed and the product recrystallized from HPLC grade heptane to give 11-mercaptoundecanoic acid (1.25 g, 67%) as fine colorless crystals. Mp 43-46 °C. 1H NMR (CD2Cl2) δ 1.24 f 1.39 (m, 12H, (CH2)6), 1.36 (t, 1H, SH), 1.59 and 1.61 (both triplet of triplets, both 2H, HSCH2CH2, HO2CCH2CH2-), 2.37 (t, 2H, CH2CO2H), and 2.50 (dt, 2H, HSCH2, J1 ) 7.6 Hz, J2 ) 7.6 Hz). (ii) Preparation of Gold Surfaces and Cantilevers. Microscope slides were cut into approximately 1 cm squares. The slides were washed with a solution of Decon-90 to remove oil from the glass cutter, submerged in 70% nitric acid for 10 min, washed with distilled water, and stored under AR isopropanol. As gold does not bind well to glass, a ∼100 Å chromium layer was initially deposited by sputtering before ∼500 Å of gold was deposited. Gold easily adsorbs organic contaminants, even when exposed to air for short periods.15 When a droplet of water is placed on a freshly prepared surface, the resulting hydrophobic surface gives a large contact angle (∼80°) . To remove the contaminants, the surface was cleaned with “piranha solution” (1:3 H2O2(30%)/ concentrated H2SO4) for 1 min. (WARNING: Piranha solution reacts violently with organic matter, especially when hot, and is extremely corrosive.) The surface was rinsed with water and the contact angle redetermined. If the contact angle approached 0° it was determined to be clean and so was quickly rinsed in ethanol and submerged in the thiol solution. AFM images of the surface before and after cleaning showed the rms line roughness over 1 mm2 decreased from 1.5 to 0.87 nm after cleaning with acid. In Figure 1 we show cross sections of the gold surface before and after acid cleaning. The cantilevers used were manufactured by Digital Instruments, Santa Barbara, CA. Tungsten spheres were attached to V-shaped cantilevers with 24 h Araldite. Under a microscope, a XYZ translational stage was used to guide a copper wire (diameter ∼40 µm) with a small amount of glue onto the tip of the cantilever. Typically, about 10-15 L of Araldite was deposited on the tip. A clean wire was then used to place a tungsten sphere on the tip. The glue was allowed to harden for at least 12 h before a 20.0 ( 0.2 nm layer of gold (99.99%) was deposited by thermal evaporation at a pressure of 1 × 10-5 Torr and a current of 40 A.

(i) Gold-Gold and Thiol-Thiol Interactions. The interaction between two gold surfaces in water has previously been investigated.18 It was found that the van der Waals interaction between clean gold surfaces with zero contact angle for water was 2.5 × 10-1 9 J, close to the values predicted by Lifschitz theory. In this study, the values obtained were consistently lower, around 1 × 10-19 J. Fresh gold surfaces cleaned in Piranha solution were completely wet by aqueous solutions for some 5 min. Thereafter, the contact angle began to rise steadily and drops of fluid spontaneously contracted on the gold surface. This process was attributed to atmospheric adsorption. In ethanol, the interaction between fresh surfaces was attractive at all separations with strong adhesion, as seen from the raw data shown in Figure 2. The apparent Hamaker constant in this case was usually found to be

(14) (a) Sondag-Huethorst, J. A. M.; Scho¨nenberger, C.; Fokkink, G. J. J. Phys. Chem. 1994, 98, 6826. (b) Sondag-Huethorst, J. A. M. Ph.D Thesis, Wageningen University, 1994. (15) (a) Gaines, G. L. J. Colloid Interface Sci. 1981, 79, 295. (b) Kane, V. B.Sc.(hons.) Research Report, University of Melbourne, 1996.

(16) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (17) Sader, J. E.; Larson, I.; Mulvaney, P.; White, L. R. Rev. Sci. Instrum. 1995, 66, 3789. (18) Biggs, S.; Mulvaney, P. J. Chem. Phys . 1994, 100, 8501.

Figure 1. Cross sections of fresh, evaporated gold films on Cr-coated glass before (upper image) and after (lower image) treatment with Piranha solution. Replicate measurements on different glass films consistently showed that the line roughness was less than 1 nm/µm after cleaning. (iii) Thiol Deposition. A solution of 11-mercaptoundecanoic acid (20 mL, 1 mM) was prepared using ethanol as a solvent. If the thiol did not fully dissolve dichloromethane (0.1-0.2 mL) was added. The spring constants were determined by the Cleveland method16 both before and after deposition of gold films onto the cantilevers, allowing for correct placement of spheres on the tip.17 We estimate the overall error in k to be 10%. This translates into an error of approximately 10% in measured surface potential for the typical potentials and ionic strengths encountered in this work. Initially, the deposition was carried out in the fluid cell itself. The fluid cell was assembled and flushed with ethanol. Then 11-mercaptoundecanoic acid in ethanol was injected and allowed to equilibrate within the cell for various lengths of time. Force curves were measured during the equilibration process. Subsequently, the cell was flushed with pure ethanol to remove excess mercaptan and then was flushed with electrolyte. However, it was found to be easier if the cantilever and plate were equilibrated with the thiol prior to cell assembly which reduced contamination of the gold spheres. The surfaces were left submerged in the thiol for 18 h and then were washed with ethanol.

Results

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Figure 3. Normalized experimental force curves for gold surfaces modified with mercaptoundecanoic acid (dotted lines) as a function of pH, together with fitted interaction curves (full lines) at 0.1 mM NaNO3. Fits assume constant surface charge and A ) 4 × 10-20 J. The Debye lengths were all within 10% of the predicted values for the electrolyte concentration at each pH. Note that, at low pH, there is a clear jump-in, which gradually disappears as the pH is raised. Above pH 6, the jumpin is just an inflection in the force curve. The theory curves predict sharp jump-ins at all pH values.

Figure 2. (a) Normalized force curves obtained for interaction of a gold sphere with a gold plate under a variety of conditions. The dotted curves are for approach, and the continuous curves are during retraction. Curve i was obtained with clean gold surfaces in ethanol and shows a typical van der Waals jump-in and strong adhesion. (ii) The same system after injection of 2 mM 11-mercaptoundecanoic acid. The curve was measured 2 min after injection. Similar curves were obtained after the residual alkanethiol was removed by injection of 10 mL of ethanol. The jump-in and adhesion are drastically reduced. There is no electrostatic repulsion evident due to ionization of the SAM carboxyl groups in ethanol. (iii) The same system after flushing with Milli-Q water, showing the generation of a repulsive double-layer interaction. A weak pull-off is observed when the water is freshly injected but disappears after equilibration. (b) Force curves obtained using 1,2-mercaptoethanesulfonate. Dotted lines are data obtained during approach of the surfaces, and continuous lines are data obtained during retraction: (i) gold-gold in ethanol; (ii) 2 min after addition of 1 mM 1,2-mercaptoethanesulfonate in ethanol. The van der Waals interaction and adhesion are strongly reduced, and the sulfonate head groups are uncharged in the ethanol (iii) after injection of 3D water and equilibration for 3 min. A large doublelayer repulsion is evident as soon as the water displaces the ethanol.

around 4 × 10-20 J. Addition of of an ethanolic solution of the alkanethiol caused a dramatic reduction in the attractive interaction, and a concomitant reduction in the adhesion. However, the interaction force remained attractive at all sphere-plate separations. This demonstrates that the carboxyl groups of the alkanethiol do not ionize in ethanol. This explains why dense monolayers can self-assemble in ethanol. Despite the high polarity of ethanol, there is no ionization and head group repulsion does not limit thiol adsorption onto the gold surface. In Figure 2 we also show the interaction observed some hours

later after flushing the cell with ethanol to remove excess adsorbate and subsequent flushing with Milli-Q water. Immediately, strong repulsion is seen, with a long interaction range, due to the low ionic strength. There is a clear jump-in at small separations, and the retraction curve displays no adhesion but follows the extension curve. In the presence of thiol layers, steric repulsion was often observed at small separations, and occasionally pushthroughs were seen at large applied pressures. These were between 1 and 2 nm in thickness and due to interdigitation of the two monolayers on each surface. Importantly, the double-layer interaction remained remarkably stable even after acquisition of 30 force curves from the same surface site, and we do not believe that any irreversible surface damage occurred due to the measurement of the force curves themselves. The inhibition of double-layer charging in ethanol was also found for sulfonate head groups. Typical raw force data for adsorption of 1,2-mercaptoethanesulfonic acid onto gold are shown in Figure 2b. They are remarkably similar to the carboxyl group ionization behavior, in that there is strong reduction of the dispersion interaction in ethanol, after alkanethiol adsorption, and little evidence for ionization of the sulfonate groups. Upon flushing with water, strong repulsion is seen, but surprisingly, the potentials generated are quite small. We were unable to obtain potentials much higher than -80 to -100 mV in dilute electrolyte, despite the fact that the sulfonate pKa is about 2. This may be due to counterion binding or to incomplete surface coverage due to the shorter alkane chain length. (ii) Effect of pH. In Figure 3, we show typical force curves obtained as a function of the solution pH within the fluid cell, at a constant ionic strength of 0.1 mM. As evident from the curves, increased pH leads to a dramatic increase in sphere-plate repulsion, with a constant Debye length of 30 ( 0.5 nm. In each case, a clean jump-in was seen at 2-10 nm separation, and a sharp, unstructured region of constant compliance. The jump-in distance decreased steadily as the pH was increased. At the highest pH, the jump-in became an inflection. Also shown are

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Figure 4. Experimental values of ψafm of the functionalized alkanethiol monolayers as a function of pH at three ionic strengths. Also shown are fits to Model III, discussed in the text. The fits to the model use KNa ) 4 × 10-6, Ka ) 10-6.3, and Ns ) 7.7 × 10-10 mol cm-2, and the Debye length is calculated from the 1:1 electrolyte concentration. Also shown are three values obtained at pH 10 in the presence of CsNO3. The reduction in potential at high pH is due to the increased metal ion concentration.

fits to the data using the known spring constant and particle radius assuming constant surface charge on both surfaces. In Figure 4, we summarize the data obtained from several series of pH titrations at different ionic strengths. In each case, fresh gold surfaces were prepared, and different gold-sphere-mounted cantilevers were employed to avoid difficulties due to thiol rearrangement. In general surfaces aged in the fluid cell for more than 48 h displayed different force behavior from that of fresh samples. For all three ionic strengths, ionization of the carboxyl groups began at between pH 3 and 4, rising rapidly to about pH 7 and then leveling off. Above pH 10, a decrease in potential was observed at lower ionic strengths. The maximum surface potential observed was about -100 mV in distilled water. These results were very reproducible, but higher potentials had been expected because of the high surface density of ionizable groups. At 1 mM salt, the ionization of the surface sites appeared strongly inhibited, with the potential reaching just -30 mV. The changes to the jump-in distance and pull-off distance are shown in Figure 5 for 0.1 mM electrolyte. There is a strong correlation between the two. The jump into contact, which is very pronounced for clean gold surfaces because of the high Hamaker constant, decreases to zero at pH 6.8 and above. At the same time, the adhesion falls off steadily becoming zero above pH 6. The effects of the increased electrolyte concentration on the force profiles are shown in Figure 6. The log plots confirm that the long range interaction is entirely attributable to electrostatic repulsion between the surfaces and hydrophobic interactions between the alkane chains appear to play no role. At higher electrolyte concentrations, there is a clean jump-in, and no apparent steric or short range structural effects are introduced by the higher salt concentrations. (iii) Effect of Heavy Metal Adsorption. The doublelayer repulsion was measured after increasing amounts of lead ions were introduced into the fluid cell at pH 6. Lead is known to adsorb strongly to humic acids in natural

Kane and Mulvaney

Figure 5. Observed jump-in distance (open circles) and adhesion pull-off distance (closed circles) for mercaptoundecanoic acid-modified gold surfaces as a function of pH. The gold sphere had a radius 4.2 µm, and the spring constant was k ) 0.2 N m-1. Electrolyte was 0.1 mM NaNO3.

Figure 6. Force-distance plots obtained from 11-mercaptoundecanoic acid monolayers on gold at pH 6 for three ionic strengths. Note that there is evidence for short range compressible layers at low ionic strength and the clean jump-ins. The short range repulsion seemed to be most apparent at low ionic strength.

waters.19 Humic acids contain both phenolic and carboxylic acid groups. The functionalized alkanethiol surface provides a useful model for the measurement of the relative binding constants of metals to carboxylated surfaces. In Figure 7, the surface potential of the functionalized gold surfaces is shown as a function of both sodium and lead concentration. As is clear, the potential drops rapidly to zero (within experimental error) at a lead level of just 1 µM, some ten thousand times lower than the transition level for sodium. Injections of high sodium concentrations, up to 0.1 M, followed by flushing with distilled water did not lead to increased repulsion. This suggests that lead cannot be desorbed by sodium below 0.1 M. We also found that CsNO3 yielded surface potentials identical to those of sodium within experimental error. To remove Pb2+ from the surface, nitric acid was introduced into the system at pH 2. After 5 min, a solution of 10-4 M NaNO3 at pH 6 was added. The potential was determined to be -50 mV. Therefore, the bound lead was at least partially removed; i.e., we calculate that the (19) Yariv, S.; Cross, H. Geochemistry of Colloid Systems; Springer Verlag: Berlin-Heidelberg, 1979.

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Figure 7. Fitted values of the surface potential (ψafm) of 11mercaptoundecanoic acid monolayers on gold as a function of [NaNO3], [CsNO3] and [Pb(NO3)2] at pH 10. Also shown are fits using Ns ) 7.7 × 10-10 mol cm-2, KNa ) 4 × 10-6, and KPb ) 1 × 10-10 and 4 × 10-10 using eqs 2, 3, and 9-15.

equilibrium

Pb2+(aq) + 2COOH T 2H+(aq) + (COO)2Pb (1) lies on the left for [Pb2+(aq)] ) 10-6 M and [H+] ) 10-2 M. Thus, the adsorption equilibrium with lead can be controlled by pH, with 10 mM acid being sufficient to drive the desorption of lead ions from the surface. Discussion The results presented here are qualitatively consistent with the wetting studies and qualitative chemical adhesion studies reported earlier. However, as will be shown in the next section, the degree of ionization of the surface carboxyl groups is very low. In AFM force measurements, interaction potentials are measured directly; however, surface charge titrations cannot be performed reliably because of the low surface area available for measurement. Consequently, deductions about the charge distribution at the interface are based entirely on the interaction potentials. The work by Larson et al.20 has clearly demonstrated that the apparent interaction potential is numerically almost identical to the ζ or shear plane potential at the boundary of the diffuse layer. In other words, the inner adsorbed ions are not disturbed during approach of the two surfaces, and a naked “surface potential” is not determined. We now consider three models for the interpretation of the ψafm-pH and ψafmelectrolyte data. (i) Model I. The simplest model for the SAM-H2O interface is a diffuse layer model based on chemical ionization equilibrium of the acidic surface sites.21-23 This is illustrated in the upper part of Figure 8. The equilibrium constant for dissociation of an acid site, denoted COOH, is given by

COOH T COO- + H+(surf)

(2)

(20) Larson, I.; Drummond, C. J.; Grieser, F. J. Phys. Chem. 1995, 99, 2114. (21) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci. 1978, 9, 303. (22) Chan, D. Y. C.; Mitchell, D. J. J. Colloid Interface Sci. 1983, 95, 193. (23) Chan, D. Y. C. In Chemical Processes at Mineral Interfaces; Davis, J. A.. Hayes, K. F., Eds.; ACS Symosium Series 323; American Chemical Society: Washington, DC 1986.

Figure 8. Scheme of three double-layer models used to fit the AFM data. Model I is the simple site dissociation-diffuse layer model. Model II is as per Model I, but with a Helmholtz layer of variable capacitance. There is assumed to be no ion binding at the shear plane. Model III is the diffuse layer model with both sodium and proton site dissociation. The variable is pKNa. Location of surface charges and potentials are shown. In Models I and III the fitted potential is assumed to correspond to a plane close to the true surface, whereas, in Model II, the observed potential corresponds to that at the Helmholtz plane.

Ka ) aCOO-aH+(surf)/aCOOH

(3)

We identify surface activities with concentrations, an assumption examined in detail by Healy and White.21 The surface concentration of protons is assumed to be related to the bulk value by

[H+](surf) ) [H+]∞ exp(-y0)

(4)

where y0 ) eψ0/kT is the reduced surface electric potential relative to bulk solution. The charge due to the ionized carboxyl groups is simply σ0 ) -e[COO-], from which it follows that

σ0 ) -eNs/(1 + [H+]/Ka exp(-y0))

(5)

This equation is valid if the equilibrium constant is independent of the degree of ionization at the surface. For the identical chemical sites at the alkanethiol-water interface, this assumption is better met than in almost any other colloid system to date. Equation 5 links the surface charge density to the local potential created by ionization. As sites ionize, the local potential becomes more negative and the local pH decreases, which acts to retard ionization. The dissociation curve vs pH consequently broadens from the value obtainable for the 11mercaptoundecanoic acid molecules freely dispersed in solution. It is important to note that the lower ionization predicted by eq 5 is not due to the change in pKa of the

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Figure 9. Plots of the experimental values of the reduced surface potential yafm ()eψafm/kT), and the calculated y0 values needed to fit the data as a function of pH according to eqs 5 and 6, assuming Ns ) 7.7 × 10-10 mol cm-2, pKa ) 6.3, at 0.03 mM, 0.1 mM, and 1 mM NaNO3. From eqs 5 and 6, the potential at the head group needs to be close to -400 mV at pH 10 to explain the low degree of ionization.

surface sites but to the fact that the local pH differs from the bulk value. If the double layer is purely diffuse, then the electrostatic potential due to the surface charge can be calculated directly from the Poisson-Boltzmann equation. For an electrolyte concentration of N0 ions per unit volume

σ0 ) -σd ) 2κr0kT/e sinh(yafm/2)

(6)

κ ) (2e2N0/r0kT)1/2

(7)

where

is the inverse Debye length or inverse diffuse layer thickness. Equations 5 and 6 provide a unique solution for the surface charge density and potential. Conventionally, Ns is a fitting parameter if charge titrations of the surface have not been carried out. In this case, we adopt a slightly different approach. Ns has been established from independent measurements7-11 but σ0 as a function of pH is not available. From yafm ()eψafm/kT) we calculate σ0 via eq 6. This is the surface charge density necessary to generate the measured diffuse layer potential. However from eq 5, we also can calculate the surface potential required to give this degree of surface ionization using Ns ) 7.7 × 10-10 mol cm-2 and pKa ) 4.84. The results are shown for all three ionic strengths in Figure 9. As is clear, the surface potentials found from eq 5 are vastly higher than those observed experimentally and are largely independent of ionic strength. This is because, to account for low surface ionization at high pH with the large surface site densities associated with the densely packed alkanethiol groups, we need large, negative surface potentials. This discrepancy suggests that the SAM-water interface cannot be adequately described by a simple diffuse layer model. For thiols with bulky terminal groups, the site density may be slightly lower than the value used of 7.7 × 10-10 cm-2, but since we obtain ionization fractions of just 1-2%, even a substantial reduction in Ns does not alter the general conclusion that there is only slight ionization of the surface carboxyl groups. We now attempt to improve the basic diffuse layer model with two embellishments. (ii) Model II. In the first of these modifications (Model II, Figure 8) we adjust the potential distribution by

Figure 10. Calculated values of the inner layer capacitance as a function of pH at three ionic strengths needed to reconcile the potentials in Figure 8, using Model II. The inner layer capacitance required is largely independent of solution ionic strength. Data are for 0.03 mM (open circles), 0.1 mM (full circles), and 1 mM (squares) NaNO3.

incorporation of a Stern layer. We assume that both eqs 5 and 6 are valid but refer to two different planes within the double layer. We assume that the true surface charge is due to ionization of carboxyl groups and that protons can exist coplanar with this surface. Conversely, the adsorbed water molecules produce a Helmholtz layer impenetrable to the diffuse layer of hydrated sodium ions. These ions only reach the shear plane, coincident with the plane whose potential is determined by AFM. With this model, higher potentials are attained at the surface, consistent with the high surface site density, but this potential falls off inside the Helmholtz region to its observed value of ψafm at the shear plane. The free parameter introduced by this procedure is the inner layer capacitance. This capacitance will allow the potential to fall across the inner layer from the “surface potential” curves in Figure 9 down to the ψafm potential curves also shown. As is obvious from those curves, the potential drop across the inner region will have to be 100-300 mV. To avoid the introduction of more than one floating parameter, we do not allow any specific adsorption of cations into the inner region, so this is a zero order Stern (ZOS) correction. The capacitance of this inner layer of thickness β and relative permittivity I is given by

KI ) σd/(ψ0 - ψafm) ) I0/β

(8)

The capacitance remains independent of pH and ionic strength. Failure to remain constant would imply potential-dependent adsorption of counterions at the shear plane. In Figure 10, we show the calculated values for the inner layer capacitance of the alkanethiol surface as a function of pH at three ionic strengths, calculated from eqs 5-8. Remarkably, the capacitance is constant within 40% over the entire range of solution conditions employed but has an extremely low value of 1.0 ( 0.5 µF cm-2. This is an unusually low inner layer capacitance, explicable only with a condenser thickness of at least 15-20 Å, even if we take I to be 2. Further corroboration of the ZOS model is obtained from an analysis of the ionic strength dependence of ψafm. In Figure 11, we show y0, yafm, and the inner layer capacitance required to reconcile the two using the ZOS model. Over a 500-fold change in salt concentration, we find that the incorporation of a constant, very low Stern layer capacitance of 2 ( 1 µF cm-2 will give good agreement with

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where

K ) [H+(surf)]/Ka + [Na+(surf)]/KNa

Figure 11. Calculated values of the experimental surface potential (yafm) and the reduced surface potential (y0) according to Model II as a function of ionic strength at pH 6 using eq 5, and the values of the inner layer capacitance (KI) required to reconcile the surface and measured potentials at each ionic strength.

experiment. In summary, the ionization behavior of ω-mercaptoundecanoic acid can be fitted to a single-site ionization model with a Stern layer. (iii) Model III. The fundamental objection to the ZOS model is the unrealistic value of the capacitance required for agreement with experiment. We therefore now examine an alternative model based on competitive site binding by sodium ions. This model takes the opposite viewpoint. We assume it is the sodium binding that reduces the potential by neutralizing a large number of the ionized carboxyl groups. To again keep the number of free parameters to a minimum, we assume that the sodium ions and protons are coplanar. The AFM potential is now a potential close to the true surface value (y0 ) yafm), with no Stern layer being invoked. To model the counterion binding, we use a mass-action approach for both metal ions and protons.

COOH T COO- + H+(surf)

(2)

Ka ) aCOO-aH+(surf)/aCOOH

(3)

COONa T COO- + Na+(surf)

(9)

KNa ) aCOO-aNa+(surf)/aCOOH

(10)

The surface charge density is now given by

σ0 ) -e[COO-] ) -eNs[COO-]/{[COOH] + [COONa] + [COO-]} (11) ) -eNs/(1 + [H+(surf)]/Ka + [Na+(surf)]/KNa) (12) Upon introducing eqn 4 for the surface concentrations, we obtain

σ0 ) -eNs/{1 + ([H+]∞/Ka + [Na+]∞/KNa) exp(-y0)} (13) Depending on the values of KNa and Ka, either pH or pNa may determine the surface charge density. The maximum surface charge density is found when y0 ) 0:

σ0(max) ) -eNs/(K + 1)

(14)

(15)

It can be seen that if the pH is raised sufficiently and [H+]∞/Ka , [Na+]∞/KNa, the maximum charge density at high pH is simply σ0 (max) ) -eNs/([Na+]∞/KNa + 1), which is independent of the acidity of the surface sites. Again eqs 6 and 13 for the diffuse layer charge density provide unique solutions for σ0 and ψafm for any pH and pNa, once KNa and Ka are specified. In Figure 4, we show the results of the fitting to the ψafm-pH curves using a single value of KNa ) 4 × 10-6, but with Ka shifted from its nominal value of pKa ) 4.84 to pKa ) 6.3. The fits are remarkably good given the simplicity of the fitting procedure. We consistently noted strong reductions in ψafm at high pH at 0.03 mM, which are now explicable and are a result of the increasing sodium ion concentration. Sodium is now “a potential determining ion”, so it not only increases ionic strength but also begins to neutralize ionized sites strongly above pH 10. Changing the pKa to 6.3 moves all the curves to higher pHs, which is necessary since there is little ionization below pH 5. This higher pKa may reflect the fact that the strongly packed carboxyl groups cannot hydrogen bond as efficiently to surface water as when they are dispersed molecularly in solution. Good fits were obtained for values of pKa ) 6.3 ( 0.1. The value of KNa primarily determines the maximum potential reached at any ionic strength, whilst the pKa determines the pH regime where dissociation occurs. It is important to recognize that the shift in pKa is not because of the negative surface potential generated by ionization. The effect of the increasing potential on the degree of ionization is already explicitly included through eq 13. The increase in pKa reflects the different dielectric environment experienced by densely packed carboxyl groups in the SAM, compared to the fully hydrated environment of molecularly dispersed carboxylic acid molecules. In Figure 7, we show the fit to the change in potential as a function of added NaNO3, at the constant pH of 10. The fit is adequate but importantly involves the same parameters as the pH modeling.There is no adjustable parameter in the fit, since we have fitted the pH data using KNa ) 4 × 10-6. We have also tried fitting the reduction in potential observed when lead is added. The binding constant for lead was fitted without allowing for the fact that it probably neutralizes two sites. Good agreement was found for the same acidity constant, pKa ) 6.3, with KPb ) (1-4) × 10-10, and we conclude that the binding constant of lead is 103 times higher than that for sodium and acid binding. From these results, sodium plays a dominant role in determining the double-layer structure at the surface of organic acid-coated materials, such as proteins, humic acids, and latex colloids. However to differentiate between the two models presented more convincingly, we require either surface charge titrations of these monolayers or direct electrochemical measurement of the interfacial capacitance. The surface area is too small when plates are used, but titration of alkanethiol-derivatized colloids may provide important substantiation of the site binding model used here, particularly with respect to the apparent shift in pKa. Other groups have likewise proposed that the intrinsic pKa is shifted in surface acid-base chemistry.24-26 Such titration data can also confirm whether (24) Thomas, R. R. Langmuir 1996, 12, 5247.

3310 Langmuir, Vol. 14, No. 12, 1998

the high charge densities of 7.7 × 10-10 mol cm-2 used here represent the true titratable charge at the surface. In modeling the data, we have tried two simple embellishments to explain the low ionization behaviour of the densely packed thiol groups at the SAM-water interface. Other groups have previously inferred strong shifts in the acidity of carboxyl groups in functionalized monolayers, on the basis of contact angle titrations12 and QCM “frequency-titrations”. Wang et al. found that HS(CH2)15COOH monolayers had unusually large pKa values and proposed that two effects might account for the shift.27 These were changes in hydrogen bonding and low dielectric constants at the surface of the monolayer. A decrease in local dielectric constant with increasing pH, due to increased rotational polarization of surface water, could help to explain the low ionization. Wang et al. also found that the viscosity of the water layer adjacent to the QCM appeared to decrease as the pH was raised, and they inferred that there were large changes in water structure associated with the ionization of the SAMs.27 The lack of a jump-in at high pH values and the disappearance of surface adhesion for ionized monolayers observed in our work could be explained by an increase in the viscosity of a 4-6 nm thick water layer as the pH is raised. Wang et al. actually predicted a decrease in water viscosity at high pH, because the QCM frequency shifted upward. But the key point of their results is that the mechanical properties of fluid layers adjacent to surfaces may be coupled to the double-layer charge. Such an effect may be of general importance in unraveling the short range “hydration” or “steric” forces that appear between some charged surfaces. For example, a number of groups have previously reported strong, short range repulsion between surfaces that have adsorbed carboxylate groups such as citrate ions.28 In each case, the jump-in due to van der Waals forces was apparent at low pH but disappeared in alkaline solution. In those cases, where the stabilizing ion was adsorbed to the surface, multilayers of adsorbed ions may be involved, and an extended hydrogen-bonded network of carboxylic acid molecules may perhaps form, but in the case of SAMs in indifferent electrolytes, the short range force must be attributed to water structuring alone. Note that surface roughness does not account for the lack of a jump-in, since the jump-in reappears as soon as the pH is lowered once more to less than pH 5. At least four to five layers of water must be held firmly enough on each surface to account for the fact that the two surfaces do not experience any significant dispersion interaction before constant compliance is reached. Invoking anomalous water structure is necessary to account for both the lack of a jump-in and the absence of any measurable adhesion. This suggests that the Helmholtz or inner region expands as the surface potential rises, due to solvent or sodium ion ordering, and one may contend that the Stern layer model in fact accounts for these effects better than the competitive site binding model. As the Stern layer expands, the shear plane potential stays low, by virtue of its increasing separation from the surface. As a consequence, since constant compliance occurs at the shear plane, the dispersion interaction and the adhesion (25) Chatelier, R. C.; Drummond, C. J.; Chan, D. Y. C.; Vasic, Z. R.; Genegenbach, T. R.; Griesser, H. J. Langmuir 1995, 11, 4122. (26) Holmes-Farley, S. R.; Bain, C. D.; Whitesides, G. M. Langmuir 1994, 10, 741. (27) Wang, J.; Frostman, L. M.; Ward, M. D. J. Phys. Chem. 1992, 96, 5224. (28) Biggs, S.; Mulvaney, P.; Zukoski, C. F. ; Grieser, F. J. Am. Chem. Soc. 1994, 116, 9150.

Kane and Mulvaney

both disappear at higher pH. A surface-potential-dependent water viscosity would likewise explain the stability and peptization behavior of thiol-stabilized gold colloids at high pH and low salt concentrations.29 A source of surface charge not considered in the models presented here is electrical charge. We have assumed that there is protonic equilibrium between the functional groups and the solution, but we have ignored redox reactions as a source of surface charge. The two reactions that may play a role are oxygen reduction and solvent reduction. Chemical ionization raises the electrochemical potential of conduction electrons within the metal, and consequently, the rates of interfacial redox reactions are coupled to the protonic acid-base equilibria. The ionization of carboxyl groups acts as a cathodic bias on the metal. There is limited experimental data to test the importance of this charging hypothesis, though the contact potential measurements of Crooks et al.30 do suggest that ionization is affected by electrode potential. Electrons on the metal can respond to the increasing degree of ionization at high pH values by transferring to oxygen or water. This metal charge would retard ionization of the carboxyl groups at high pH. Alternatively, actual electron transfer may not be necessary. Fawcett and co-workers have calculated the total differential capacitance of the metal-SAMwater interface and find that the SAM layer has a potential-dependent capacitance, whose origin appears to be the image charge on the metal induced by the ionization of the carboxyl groups at the SAM-water interface.31,32 This image charge itself acts to retard ionization of the acid sites at high pH. We note that it is well-established that the overpotential for electron transfer on metal oxide surfaces is coupled directly to the solution pH, which, in turn, is the primary factor controlling the surface potential.33 Conclusions ω-Substituted alkanethiol monolayers on gold appear to be model surfaces for double-layer studies. The doublelayer forces measured in this work are in reasonable accord with the wetting studies carried out by previous workers. However, the interfacial electrostatics are not completely consistent with simple DLVO theory. For example, there are strong reductions in the measured composite Hamaker constant for the coated gold surfaces, that are not due to simple shielding of the metal-metal dispersion interaction. The surface potential is independent of the nature of the (monocationic) counterion in solution, but divalent metals (Pb2+ and Zn2+) bind very strongly. Consistent with earlier colloid electrophoresis results, we find that, despite high surface site densities, there is little ionization of carboxyl groups in basic solution. We have fitted the data to two modified double-layer models. The inclusion of an inner or Stern layer can be used to reconcile the low ionization values, but only at the expense of an unrealistically low inner layer capacitance of 1-2 µF cm-2. Of course, given that there is strong evidence for water structuring at high pH, it may well be that the Stern layer is much thicker than is usually postulated, perhaps even 20-30 Å thick. Such a thickness would explain the absence of a van der Waals jump-in at high pH, the lack of adhesion, and the low apparent surface potential. (29) Giersig, M.; Mulvaney, P. Langmuir 1993, 9, 3408. (30) Crooks, R. M.; Ricco, A. J. Langmuir 1993, 9, 1775. (31) Andreu, R.; Fawcett, W. R. J. Phys. Chem. 1994, 98, 12753. (32) Janek, R. P.; Fawcett, W. R.; Ulman, A. J. Phys. Chem. B 1997, 101, 8550. (33) Mulvaney, P. Zeta Potential and Colloid Reaction Kinetics. In Nanoparticles in Solids and Solutions: Preparation, Characterization and Applications; Fendler, J., Ed.; VCH: New York, 1998.

SAMs of ω-Mercaptoundecanoic Acid

However, we have likewise shown that a simpler model based on strong cation binding will give good agreement. Even allowing for the fact that ionization is retarded by the local negative potential as a consequence of ionization, it is necessary to increase the intrinsic pKa of the carboxyl groups to 6.3 ( 0.1 to rationalize the pH dependence of the interaction force. This value is in remarkable agreement with the contact angle data in ref 24, collected on a much more poorly defined surface. This competitive ion binding model does not explain the loss of adhesion and the disappearance of a jump-in at high pH, but this alternative model does explain the rapid decrease in surface potential at pH 10-11, which diffuse layer compression alone cannot explain. A choice between these two models may be possible if charge titration data on alkanethiol-modified gold colloids

Langmuir, Vol. 14, No. 12, 1998 3311

can yield independent values for Ns and pKa, an avenue we are currently pursuing. Alternatively, differential capacitance and dielectric response meaurements may provide a means to differentiate between the models presented here. We suggest that electron-transfer equilibria may play a role in determining the overall charge distribution at the gold-SAM-water interface. Acknowledgment. The authors thank Frank Caruso for an initial sample of 11-mercaptoundecanoic acid and D. Y. Chan and L. R. White for useful discussions. The support of the Australian Research Council and the Advanced Mineral Products Research Centre is also gratefully acknowledged. LA971296Y