The Titration of Carboxyl-Terminated Monolayers Revisited: In Situ

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Langmuir 2008, 24, 9440-9448

The Titration of Carboxyl-Terminated Monolayers Revisited: In Situ Calibrated Fourier Transform Infrared Study of Well-Defined Monolayers on Silicon D. Aureau,* F. Ozanam, P. Allongue, and J.-N. Chazalviel Physique de la Matie`re Condense´e, E´cole Polytechnique, CNRS, 91128 Palaiseau, France ReceiVed April 18, 2008. ReVised Manuscript ReceiVed June 6, 2008 The acid-base equilibrium at the surface of well-defined mixed carboxyl-terminated/methyl-terminated monolayers grafted on silicon (111) has been investigated using in situ calibrated infrared spectroscopy (attenuated total reflectance (ATR)) in the range of 900-4000 cm-1. Spectra of surfaces in contact with electrolytes of various pH provide a direct observation of the COOH T COO- conversion process. Quantitative analysis of the spectra shows that ionization of the carboxyl groups starts around pH 6 and extends over more than 6 pH units: ∼85% ionization is measured at pH 11 (at higher pH, the layers become damaged). Observations are consistently accounted for by a single acid-base equilibrium and discussed in terms of change in ion solvation at the surface and electrostatic interactions between surface charges. The latter effect, which appears to be the main limitation, is qualitatively accounted for by a simple model taking into account the change in the Helmholtz potential associated with the surface charge. Furthermore, comparison of calculated curves with experimental titration curves of mixed monolayers suggests that acid and alkyl chains are segregated in the monolayer.

1. Introduction The confinement of molecules in the pores or at the surface of a solid often gives rise to unexpected properties. Nanotechnologies currently take advantage of this specificity for many different technological applications (chemical and biological sensors, electroluminescent devices, microelectronics, molecular electronics, etc.). In this context, acid surfaces are of special interest because they have specific binding properties or can be used as the starting point of multistep schemes for the surface functionalization. For such purposes, it is generally of prime importance to control the reactivity and ionization state of these acid monolayers. As a matter of fact, the titration of acid moieties confined at a solid surface has been investigated in many distinct systems during the last two decades. Namely, the dissociation of carboxyl groups at monolayer surfaces was investigated at self-assembled acid-terminated monolayers prepared by silanization on silicon oxide,1 by adsorption of thiols on gold,2 or direct grafting on silicon.3 The main characterization techniques used were capacitance measurements,4 voltammetry,5 chemical force microscopy measurements,6,7 and wetting angle measurements via a “contact angle titration” method.2a,8 Studies usually reported a single surface pKa, but with a value larger than that in solution (∼5). However, these data span a wide range, between 5.5 and 9, and the shape of the titration curves seems to be strongly dependent on the characterization technique. These facts point * Corresponding author. E-mail:[email protected]. (1) Wasserman, S. R.; Tao, Y. T.; Whitesides, G. M. Langmuir 1989, 5, 1074– 1087. (2) (a) Troughton, E. B.; Bain, C. D.; Whitesides, G. M.; Nuzzo, R. G.; Allara, D. L.; Porter, M. D. Langmuir 1988, 4, 365–385. (b) Bain, C. D.; Whitesides, G. M. Langmuir 1989, 5, 1370–1378. (3) Liu, Y. J.; Navasero, N. M.; Yu, H. Z. Langmuir 2004, 20, 4039–4050. (4) Kakiuchi, T.; Iida, M.; Imabayashi, S.; Niki, K. Langmuir 2000, 16, 5397– 5401. (5) Zhao, J; Luo, L.; Yang, X.; Wang, E.; Dong, S. Electroanalysis 1999, 11, 1108–1113. (6) Vezenov, D.; Noy, A.; Rozsnyai, L. F.; Lieber, C. M. J. Am. Chem. Soc. 1997, 119, 2006–2015. (7) Hu, K.; Bard, A. J. Langmuir 1997, 13, 5114–5119. (8) Creager, S. E.; Clarke, J. Langmuir 1994, 10, 3675–3683.

to the limitations inherent to the use of methods that are only an indirect characterization of the ionization state of the surface. Infrared spectroscopy is certainly the most relevant laboratory technique to study the COOH T COO- equilibrium at surfaces,9–12 because the IR bands related to each species are clearly different, which, in principle, allows for a direct determination of the ionization degree of the surface at any step of the titration.10,11 The first IR studies were conducted on hardly controlled systems called polyethylene carboxylic acid PE-CO2H.9 Studies on SAMs on gold have only been performed ex situ12 with the intrinsic disadvantage that dehydration of the layer occurs after removal of the sample from the acid/base medium. To the best of our knowledge only two groups have used IR spectroscopy for in situ titration of carboxyl-terminated siloxane monolayers on oxidized silicon. Sukenik and coworkers10 published a first detailed paper in which the titration spreads over several pH units. A more recent work by Gershevitz et al.11 reported the existence of two pKa values assigned to carboxyl monomers (pKa ) 4.9) and hydrogen bonded carboxyl groups (pKa ∼ 9). However, none of the mentioned studies is truly quantitative, as the IR bands were not calibrated in intensity. In order to clarify these issues, we undertook calibrated in situ Fourier transform infrared (FTIR) measurements for a truly quantitatiVe study of the surface equilibrium COOH T COO-. In other words, we measured the surface concentrations of COOH and COO- sites on acid-terminated monolayers prepared by photochemical hydrosilylation on atomically flat Si(111) surfaces.13 This system presents several key advantages: (i) The chemical composition of the starting acid monolayer, including (9) Holmes-Farley, S. R.; Reamey, R. H.; McCarthy, T. J.; Deutch, J.; Whitesides, G. M. Langmuir 1985, 1, 725–740. (10) Cheng, S. S.; Scherson, D. A.; Sukenik, C. N. Langmuir 1995, 11, 1190– 1195. (11) (a) Gershevitz, O.; Sukenik, C. N. J. Am. Chem. Soc. 2004, 126, 482–483. (b) Gershevitz, O.; Osnis, A.; Sukenik, C. N. Isr. J. Chem. 2005, 45, 321–336. (12) Tominaga, M.; Maetsu, S.; Kubo, A.; Taniguchi, I. J. Electroanal. Chem. 2007, 603, 203–211. (13) Faucheux, A.; Gouget-Laemmel, A. C.; Henry de Villeneuve, C.; Boukherroub, R.; Ozanam, F.; Allongue, P.; Chazalviel, J.-N. Langmuir 2006, 22, 153–162.

10.1021/la801219u CCC: $40.75  2008 American Chemical Society Published on Web 08/02/2008

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mixed monolayers, has been quantitatively determined.13 (ii) Dense monolayers are reproducibly obtained and offer a superior chemical robustness because water is excluded at the nanometer scale.14,15 (iii) As mentioned in refs 10 and 11, the attenuated total reflectance (ATR) geometry provides superior sensitivity and flexibility for in situ measurements.16 (iv) As shown below, the calibration method of the different IR bands related to anchored moieties can be made routine. Thanks to this advanced approach, we show from in situ and calibrated titration curves of carboxyl-terminated monolayers of various compositions that the acid-base equilibrium is strongly influenced at the surface by a reduced solvation as well as electrostatic interactions. A physical model is presented, which allows for disentangling the above-mentioned factors responsible for the differences observed between titration at surfaces and in solutions.

2. Experimental Section General Information. Undecylenic acid (98%), 1-decene (97%), and ammonium sulfite monohydrate (92%) were purchased from Aldrich. All cleaning (H2O2 30%, H2SO4 96%, acetic acid 100%) and etching (NH4F 40%) reagents were of VLSI grade and supplied by Merck. Phosphoric acid 85% and potassium hydroxide 85% were purchased from SDS; boric acid 99.5%, potassium phosphate monobasic 99% and dibasic 99% were from Merck, and tribasic 95% was purchased from Fluka. Ultrapure water was provided by a Millipore station that ensures a resistivity of 18.2 MΩ cm. Preparation of the Silicon Surface. The silicon samples were cut from 〈111〉 oriented n- or p-type double-sided polished silicon wafers (0.2° misorientation toward 〈112j〉, float zone F ) 130-150 Ω cm for n-type silicon and F ) 30-40 Ω cm for p-type silicon) and shaped as ATR prisms (15 × 15 × 0.5 mm3, approximately 45° bevels). For an accurate calibration of the IR band intensity, the bevel angles were measured using laser deflection. All ATR samples used in this work were 500 µm thick and exhibited 48° bevels. The samples were initially cleaned in “piranha” solution, a 3:1 mixture of concentrated H2SO4 (98%) and H2O2 (30%), in order to remove all organic contaminations. This wet oxidation was followed by copious rinsing with ultrapure water. Cleaned silicon samples were then chemically etched for 12 min in oxygen-free 40% NH4F (ca. 0.05 mol L-1 ammonium sulfite was added to the etching solution) to remove native oxide and obtain atomically smooth H-terminated surfaces with flat terraces of ca. 100 nm width.17 After etching, the surface was rinsed with ultrapure water. Formation of Alkyl Monolayers on Silicon By Photochemical Hydrosilylation. A one-step procedure was used to prepare welldefined mixed decyl/10-carboxydecyl organic monolayers on H-Si (111) via direct photochemical hydrosilylation of undecylenic acid and 1-decene mixtures. The neat mixture of undecylenic acid/1decene was outgassed under argon in a Schlenk tube at 90 °C for 30 min and then cooled to room temperature under continuous argon bubbling to insert the freshly prepared H-terminated silicon sample. Grafting was performed for 3 h in a UV reactor (312 nm, 6 mW cm-2). The functionalized surface was then rinsed in oxygen-free hot acetic acid (60-70 °C) under argon during 15 min (to desorb the hydrogen-bonded undecylenic acid molecules).13 Infrared Spectroscopy. ATR-FTIR spectra were recorded in sand p-polarization using a Bomem MB100 FTIR spectrometer equipped with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) photovoltaic detector. In order to obtain data over an extended spectral range (900-4000 cm-1, 4 cm-1resolution), we used small ATR samples (15 mm width, 500 µm thickness) to reduce the optical (14) Wallart, X.; Henry de Villeneuve, C.; Allongue, P. J. Am. Chem. Soc. 2005, 127, 7871–7878. (15) Gorostiza, P.; Henry de Villeneuve, C.; Sun, Q. Y.; Sanz, F.; Wallart, X.; Boukherroub, R.; Allongue, P. J. Phys. Chem. B 2006, 110, 5576–5585. (16) Chazalviel, J.-N.; Erne´, B. H.; Maroun, F.; Ozanam, F. J. Electroanal. Chem. 2001, 509, 108–118. (17) Munford, M. L.; Corte`s, R.; Allongue, P. Sens. Mater. 2001, 13, 259.

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Figure 1. Scheme of the flow cell for in situ infrared measurements: (a) front view of the ATR silicon prism; (b) side view of the flow cell.

path length in silicon and minimize the effect of the residual bulk silicon absorption below 1500 cm-1. In usual ex situ configuration (at air contact), this geometry provides a reasonable number of internal reflections (around 30 for typical samples). In all of the figures presented for ex situ measurements, the reference spectrum was taken with an H-Si (111) surface, and the quantitative analysis used to derive the molecular concentration followed the method presented by Faucheux et al.13 Flow Cell and Solutions. In situ measurements were conducted with a specially designed 100 µL flow cell (Figure 1), which allowed for varying the pH by fast exchange of electrolyte without re-exposing the surface to air. In all of the figures dealing with in situ FTIR, the spectrum at pH 2 was taken as the reference. The spectra for s- and p-polarization were quantitatively analyzed, as exposed in the next section. Because of the O-ring diameter (10 mm), in situ absorbance corresponds to 10 internal reflections only (corresponding to the effective surface area of the sample in contact with electrolytes). The spectra were recorded at open-circuit potential. Applying a potential had only a weak effect on the band intensities. To minimize the unwanted contributions from the pH buffer, low-concentrated solutions (ionic strength 10-2 M) of inorganic buffers were used in this study, except for the solution of pH 14. The buffer solution composition was as follows: pH 2-3, phosphoric acid/potassium phosphate monobasic; pH 6-7-8, potassium phosphate monobasic/ potassium phosphate dibasic; pH 9-10, boric acid/potassium hydroxide; pH 10-11, potassium phosphate dibasic/potassium phosphate tribasic; pH 12-14, potassium hydroxide.

3. Results All samples were first characterized ex situ by infrared spectroscopy to quantify the composition of monolayers. This preliminary measurement allowed us to check the quality of the surface, and especially to make sure that the unreacted adsorbed molecules had been removed after the final rinse in hot acetic acid.13 The exact surface concentration of carboxyl terminal groups that will be in contact with solutions is therefore known from this initial calibration. Our preparation procedure yields dense mixed carboxyl/methyl-terminated monolayers, with surface concentrations of organic chains in the range 2.5-3 × 1014 cm-2, corresponding to a surface coverage referred to the initial number of SiH bonds 0.3-0.4 close to the maximum coverage 0.5.13–15 In the following, the samples are designated by the relative concentration of acid groups in the grafted layers. For instance, a 30% acid monolayer corresponds to a mixed monolayer composed of 30% acid chains and 70% alkyl chains. The measured surface concentration of COOH sites is indicated in each case. Spectrum Analysis. Figure 2 shows typical raw infrared sand p-polarized spectra of the νCdO absorption region (1300-1800 cm-1) before any correction. This example corresponds to a 100% acid-terminated surface (NCOOH ) 2.5 × 1014 cm-2) in contact with a solution of pH ) 11. The reference spectrum is that recorded in a solution of pH ) 2. Four bands are clearly identified. The band around 1720 cm-1 is characteristic

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Figure 2. Typical uncorrected s- and p-polarized IR spectra showing the change in IR absorption at pH 11 compared to pH 2 in the case of a 100% acid monolayer (NCdO ) 2.5 1014 cm-2).

of the νCdO absorption of the COOH groups in contact with aqueous solutions. The fact that it is negative indicates that the concentration of COOH groups has been reduced by increasing the pH. Simultaneously, the positive absorption bands at 1400 and 1550 cm-1, characteristic of the COO- group, indicate the formation of ionized sites on the surface. The band around 1640 cm-1 is unambiguously attributed to the δOH2 mode of the water molecule. This positive band is likely arising from an increasing density of water molecules close to the surface. Its amplitude is not totally reproducible, but it systematically tends to increase with increasing pH in the course of a given pH-dependent study. This behavior is in full agreement with several contact angle measurement studies, which evidenced that surface wettability increases with increasing pH.1–3 However, these observations could not be quantitatively exploited (the increasing wettability is sometimes accompanied with the progressive removing of small air bubbles initially trapped at the electrode surface, a phenomenon that is hardly reproducible). Nontrivial dependencies on IR polarization (see Figure 2) make it mandatory to make a quantitative analysis of s- and p-polarized spectra. Since the number and assignment of spectral components in the spectra is perfectly known, the spectra were decomposed in the range 1470-1800 cm-1 as the linear superposition of five components used as a basis set. The five components were a linear baseline, a typical spectrum of atmospheric water present in the environment of the spectrometer, and three Voigt functions to account for the δOH2 band of water molecule (1640 cm-1), the νCO band of COOH (1720 cm-1), and the asymmetric COOstretching band (1550 cm-1). Using this five-component model, we found that, among the carboxyl bands, that at 1550 cm-1 turns out to be the most robust for quantitative analysis, i.e., its parameters (position, intensity, width) exhibit the minimum cross-correlation with that of the other spectral components. In addition, the calibration with carboxylate salts with long chains was more reliable, as they are better soluble than the corresponding fatty acids (ionic species in a polar solvent). By comparison, the position and width of the COOH band appeared more sensitive to fitting. First, there is a greater overlap of the water absorption band at 1640 cm-1 with the νCOOH band at 1720 cm-1 than with the νCOO- absorption band at 1550 cm-1, as shown in Figure 2. In addition, the comparison with calibration experiments may be affected by the fact that this band is sensitive to the environment of the CdO group. Solvation by hydrogen bonding with water for an acid in solution significantly differs from that of an acid at the interface

Figure 3. pH-dependent IR spectra after water and baseline correction for a 100% acid monolayer. (NCdO ) 2.5 1014 cm-2) s- and p-polarization. Reference spectrum taken at pH 2. The buffer ions at pH 9 (borates) exhibit an extra absorption at 1400 cm-1, which adds to the νsCOOmode of the carboxylates.

between alkyl chains and aqueous solutions. In conclusion, for a quantitative study of the dissociation equilibrium, the integrated intensity of the νasCOO- band at 1550 cm-1 provides a more accurate basis than that of the νCdO band of COOH at 1720 cm-1. Figure 3 shows a series of spectra recorded in situ between pH 3 and 11 (reference spectrum at pH 2). For a better examination of the acid-base processes, these spectra were drawn after subtraction of the linear baseline and the contribution of the band associated with water absorption determined by the analysis procedure. When pH is increased, there is a conspicuous and continuous decrease of the νCdO absorption around 1720 cm-1 (disappearance of COOH groups), correlated with an increase of the absorption bands at 1400 and 1550 cm-1(formation of COOgroups). One also notices a strong polarization dependence of the νsCOO- band, whereas the νasCOO- and νasCOOH bands are only weakly dependent on the polarization. This result will be used to discuss the monolayer structure. pH Stability Range. For a reliable quantitative study of acid-base equilibrium, it is mandatory to determine the pH domain in which the acid-terminated monolayers on Si (111) are totally stable and check the reversibility of the acid-base equilibrium. Figure 4a compares two wide-range IR spectra obtained at pH 2 after exposing the acid surface for about 15 min to a solution of pH 11 (bottom spectrum) and of pH 14 (top spectrum). After the treatment in 1 M KOH, two negative bands appear and are ascribed to losses in COOH (1715 cm-1) and CH2 (2800-2900 cm-1). Integration of these bands indicates that about 1/3 of the monolayer has been removed, most likely by chemical etching of the silicon substrate initiated at monolayer point defects as observed in the case of alkyl monolayers in 40% NH4F.15 Silicon (111) is indeed chemically etched in strong bases.18 The positive band at 900-1200 cm-1 (Si-O-Si bridges) is assigned to oxidation of the newly exposed silicon surface as one reduces the solution pH. In contrast to the above observations, the spectrum is essentially featureless after treatment in the buffer solution of (18) Allongue, P.; Costa-Kieling, V.; Gerischer, H. J. Electrochem. Soc. 1993, 140, 1009–1018.

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Figure 5. Change in the surface concentration of COOH and COOgroups as a function of pH for a mixed layer (75% acid monolayer) grafted on Si(111). The initial concentration of COOH groups is NCdO ) 1.9 × 1014 cm-2. The solid line is calculated according to eq 4, assuming segregation of acid and alkyl chains (see discussion), and the dotted line represents the complementary variation for NCOOH.

Figure 4. (a) In situ IR spectra (s-polarization) in the range 900-3050 cm-1 measured in a solution of pH 2 for a 75% acid surface after exposure to 1 M KOH (pH 14) (top) and after exposure to phosphate buffer at pH 11 (bottom). The reference spectrum was measured at pH 2 before treatment. The initial concentration of COOH groups is NCdO ) 1.9 × 1014 cm-2. The negative bands corresponding to CdO and CH bonds (bottom spectrum) indicate that the interface was damaged by the treatment in 1 M KOH. (b) pH dependence of in situ IR spectra (spolarization) focusing on the νasCdO band of a 75% acid surface. Notice the increase in the amount of ionized groups up to pH 14. The reference spectrum was measured at pH 2.

pH 11. This demonstrates the complete stability of the monolayer (no loss in CH) and the total reversibility of the COOH T COOequilibrium (no change in CO band). In addition, we note the absence of significant oxidation at the Si-molecule interface. The same behavior is found for solutions of pH < 11. We studied the pH-dependence of the νasCO band. Figure 4b indicates a monotonic increase of the band intensity up to pH 14. This demonstrates that the conversion of the acid layer continues at pH > 11. Unfortunately, in these conditions, the integrity of the monolayer is no longer preserved, and the data of Figure 4b cannot be used for a reliable quantitative analysis. Therefore, in the following, we will restrict the titration study within the pH range 2-11 because the monolayer is totally stable in this pH domain. The reader should nevertheless bear in mind that full ionization of the acid monolayer is not achieved at pH 11. Quantitative Surface Titration. Figure 5 shows the pH dependence of surface concentration (expressed in cm-2) of COO- and COOH sites at the surface of the monolayer. The general behavior is consistent with expectations for an acid-base titration; the increase in surface concentration of COO- groups is quantitatively associated with a decrease in surface concentra-

tion of COOH groups. The negative correlation is, however, not perfect. As discussed above, the precision on NCOO- is much better than for NCOOH (see error bars in Figure 5) due to a strong overlap of the COOH band with the band associated with water absorption. In the following, only variations of COO- site concentration will be considered. The titration onset, defined as the pH at which the monolayer reaches a 10% ionization degree, is close to pH 6. Moreover, the ionization appears to be much more progressive than that for a titration curve in homogeneous solution. In previous semiquantitative studies,8–12 the surface was assumed to bear COOH functions only at low pH and COO- functions only at high pH, corresponding to a full ionization of the layer. Here the high-pH limit is not so clear. Our calibration indicates that surface ionization is not complete at pH 11: the surface concentration of COO- groups amounts to 1.6 × 1014 per cm2 only, which is about 85% of the initial concentration of COOH groups measured with the dry surface (1.9 × 1014 per cm2 for this surface). This quantitative calibration confirms the results of Figure 4b. Figure 6 presents titration curves between pH 2 and pH 11 for mixed carboxyl/alkyl monolayers with different surface compositions. The curves exhibit a similar shape for various dilutions of COOH groups in the alkyl monolayer. The ionization onset is at pH 6, independently of the layer composition. As in Figure 5, the process extends over a pH range much wider than would naively be expected from a classical titration curve in solution, and the “average” pKa appears higher than expected, as it was shown previously on different systems of monolayers at surfaces.10,19,20 Also, the inset of Figure 6 shows that the absolute concentration of NCOO- measured at pH 11 is systematically smaller than the initial concentration NCOOH of ionizable groups. For all of the mixed monolayers, ionization at pH 11 amounts on average to ca. 85% of the COOH sites available. Influence of Chain Length. In view of investigating the influence of the organic layer composition on its ionization capability, we also considered mixed acid monolayers prepared by grafting samples from a solution obtained by mixing 1 volume of undecylenic acid with 2 volumes of n-alkenes of different chain lengths. Figure 7 presents infrared spectra obtained at pH (19) Whitesides, G. M.; Biebuyck, H. A.; Folkers, J. P.; Prime, K. L. J. Adhes. Sci. Technol. 1991, 5, 57–69. (20) Aoki, K.; Kakiuchi, T. J. Electroanal. Chem. 1999, 478, 101–107.

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Figure 6. Titration curves for mixed layers. The numbers on the curves give the relative concentration of acid groups in the grafted layer. The arrows on the right-hand side give the initial concentration of COOH groups as measured on the dry surfaces. (The systematically low intensity values measured at pH 9 are an artifact induced by the borate buffer used for this pH. In the range we are interested in, this buffer exhibits an infrared absorption that disturbs the fitting of the experimental spectra). The solid lines are computed according to eq 4, assuming segregation of acid and alkyl chains. Inset: plot of the concentration NCOO- measured at pH 11 against the initial concentration NCOOH of ionizable groups.

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electrolyte. Typically, in a binary salt solution of concentration c ) 0.1 mol/L, the mean distance between ions of the same charge is c-1/3 ) 25 Å, whereas that between carboxyl groups on a 100% acid-grafted Si surface is NS-1/2 ) 7 Å (NS ) 2.5 × 1014 cm-2). Furthermore, in 3D, the electrostatic interactions are efficiently reduced by Coulomb screening (the Debye-Hu¨ckel screening length is 10 Å for a monovalent salt in 0.1 M concentration), a mechanism less efficient in 2D than in 3D. The interaction between surface charges is a common problem in electrochemistry.22,23 At an electrode surface, these interactions tend to make the ionization of the acid groups more difficult than in solution. This can be understood as the consequence of the negative charging of the electrode surface, which induces a negative potential δφS relative to the bulk electrolyte. This effect increases with the fraction R of ionized groups. As a result, the proton concentration close to the surface is larger than that in the electrolyte bulk, according to Boltzmann statistics:

[H+]S ) [H+]0 exp(-eδφS⁄kBT)

(1)

where kB is the Boltzmann constant, T is the temperature, e is the elementary charge, and [H+]S and [H+]0 are the proton concentrations at the surface and in the electrolyte bulk, respectively. Writing the acid-base equilibrium constant at the surface Ka ) 10-pKa ) [H+]S × R/(1 - R), it becomes

pH ) pKa + log

R 1 eδφS 1 - R 2.3 kBT

(2)

The first two terms in the above expression represent the usual relation for titration in solution. The third term arises from the electrostatic interaction among groups. The actual extent to which electrostatic interactions take place and are screened at the surface and in the electrolyte determines the relationship between δφS and R. Detailed models of double layer effects have been worked out in the case of molecular films containing acidic head groups.24,25 Using the formalism developed for oxide-semiconductor electrodes,26 we simply write that δφS is equal to the Helmholtz potential δφH, i.e., the diffuse layer effects are not explicitly considered (Figure 8). Within this approach, a simple expression is obtained for δφS:

-eNSR ) CHδφS Figure 7. Infrared spectra (s-polarization) at pH 11 referred to pH 2 for 42% monolayers from 1:2 mixtures of undecylenic acid with hexene (C6), octene (C8), and decene (C10).

11 in the case of acid chains (C11) diluted in hexane (C6), octane (C8) and decane (C10) monolayers. The spectra show that the amount of carboxyl groups ionized at pH 11 is independent of the alkyl chain length. This point will be discussed below.

4. Discussion Model for Surface Titration. The above FTIR data indicate that the surface equilibrium strongly differs from the equilibrium in the homogeneous phase. The ionization onset of COOH on the surface (pH ∼ 6) is higher than the pKa (around 5) of fatty acids in solution27 (Figures 5 and 6). It corresponds to a shift of ∼2 pH units comparing to usual acids in solution. Furthermore, the titration of COOH groups on the surface extends over more than 6 pH units (Figures 5 and 6). Electrostatic interactions between ionized groups have already been invoked in order to account for this spreading of the titration curves.4,20,21 Electrostatic interactions in two dimensions (2D), i.e., on a surface, are much more critical than in three dimensions (3D), in the bulk of an (21) Smith, C. P.; White, H. S. Langmuir 1993, 9, 1–3.

(3)

where NS is the surface concentration of ionizable sites (carboxyl + carboxylate) and CH is the Helmholtz capacitance. Substituting δφS from eq 3 into eq 2 leads to a relationship between pH and R:

pH ) pKa + log

2 R 1 e NSR + 1 - R 2.3 CHkBT

(4)

This relationship is essentially linear when NS is large enough. Figure 9 shows calculated plots of RNS vs pH using CH and pKa as the only adjustable parameters. To best simulate the set of experimental plots in Figure 6, we used pKa ) 6.5 and CH ) 175 µF/cm2. With these parameter values, there is a good agreement between the experimental results for the concentrated (>75%) (22) Bockris, J. O. M.; Reddy, A. K. N. Modern Electrochemistry; Plenum: New York, 1970; Vol. 2, Chapter 7. (23) Chazalviel, J.-N. Coulomb Screening by Mobile Charges: Applications to Materials Science, Chemistry and Biology; Birkha¨user: Basel, Switzerland, 1999. (24) Fawcett, W. R.; Fedurco, M.; Kovacova, Z. Langmuir 1994, 10, 2403– 2408. (25) Schweiss, R.; Welzel, P. B.; Werner, C.; Knoll, W. Langmuir 2001, 17, 4304–4311. (26) Gomes, W. P.; Cardon, F. Prog. Surf. Sci. 1982, 12, 155–215. (27) Kanicky, J. R.; Shah, D. O Langmuir 2003, 19, 2034–2038.

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Figure 8. Scheme of the charge distribution and corresponding potential profile across the interface.

Figure 9. Calculated change in COO- concentration as a function of pH, for different concentrations NS of acid groups assumed to be randomly diluted in the mixed organic layer.

acid-terminated surface and the calculated pH dependence in COO- concentration, which supports the proposed model. The agreement is only fair for more diluted mixed layers, which calls for refining the model, as discussed below. Although there are no available data about CH at acid-terminated silicon electrodes, the value of 175 µF/cm2 seems large compared to expectations. In other words, this 2D model tends to overestimate the electrostatic interactions between COO- groups at the surface. A plausible explanation is that the surface charges are partially screened by a limited incorporation of solution and ionic species at the top of the monolayer. Recent capacitance measurements13 have indeed evidenced partial penetration of molecular water at the top of COOH-terminated monolayers grafted on Si(111). The value pKa ) 6.5, larger than the pKa value of usual fatty acid solutions,27 indicates that ion solvation is affected by the immediate neighborhood. In an organic monolayer, the carboxyl groups suffer from a restricted access to the outer space, which hinders their ionization and increases the pKa, leading to the high value of the “surface” or “effective” pKa. To summarize, electrostatic interactions between the ionized groups lead to a spreading of the titration curve over a wide pH range, and a reduced solvation of ionized groups at the surface

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is responsible for a shift of the ionization onset by 1.5 pH units. As a result, the ionization of surface carboxyl groups is not complete up to pH 11. Conformation of Acid Chains in the Monolayer. As noticed in Figure 3, the two bands related to COO- sites exhibit distinct dependencies on the polarization of the IR beam. In particular, the νsCOO- band (1400 cm-1), associated with the symmetric CO stretching mode, is much weaker in s-polarization than in p-polarization. This clearly indicates that the carboxylate group is nearly perpendicular to the surface. In the case of the νasCOOband (1550 cm-1, antisymmetric COO- stretching mode) the p/s ratio is about 1.1. From this value one can extract an average tilt angle θ of the dynamic dipole with respect to the surface normal. Using the sensitivity coefficients along the three directions (Ix ) 1.75, Iy ) 2.11, Iz ) 2.40, see Appendix), and using the fact that the p/s intensity ratio is rps ) (2Iz cos2 θ + Ix sin2 θ)/ (Iy sin2 θ) for a random distribution of the azimuthal dipole orientation, the tilt angle is given by θ ) tan-1{[2Iz/(rpsIy Ix)]1/2}. Using the experimental rps values gives an average tilt angle of θ ∼ 70° for νasCOO-. This value does not exactly match the θ ) 90° picture expected from the polarization dependency of the νsCOO- band (Figure 10b). Tentatively, we infer that this tilt angle of 70° arises from the averaging of the distribution due to a non negligible fluctuation of the COO- head orientations around the surface normal. The νCO mode of the COOH group exhibits a p/s ratio of ∼1.3. Considering that the dynamic dipole of the νCdO mode is collinear to the CdO bond, a tilt angle of 65° is deduced, which is consistent with the geometrical bisector of the OdC-OH group close to the surface normal. As a whole, these observations are therefore consistent with an all-trans structure of the monolayers (see Figure 10a). As shown in Figure 7, the ionization of carboxyl groups appears independent of the alkyl chain length, i.e., affecting the neighborhood of the acid groups does not change the surface pKa. The simple picture sketched in Figure 11a (corresponding to all-trans acid chains homogeneously distributed in the grafted layer) is obviously in contradiction with this result, because COOH groups are not better solvated when the difference in chain length is as large as four carbons, which corresponds to a height difference of 4 Å, on the order of the hard sphere diameter of molecular water (2.5 Å). The geometry sketched in Figure 11b corresponds to acid chains homogeneously distributed in the grafted layer with the upper part lying on the surrounding methyl terminations, hence minimizing the hydrophobic interactions. This kind of conformation has been inferred by others.2a On one hand, the latter geometry could explain the insensitivity of the surface pKa to the alkyl chain length. On the other hand, the constraint to keep the OdC-OH group close to the surface normal (notice the very small intensity of the νsCOO- band at 1400 cm-1 in all of the s-polarized spectra of Figure 7) appears to induce an extra elastic energy cost for this conformation. Therefore, these considerations call for reconsidering the hypothesis of a homogeneous distribution of acid chains in the monolayer, implicitly assumed up to now. Distribution of Acid Chains in the Mixed Monolayers. The distribution of acid chains in mixed alkyl/acid monolayers is sketched in Figure 12 in two limiting cases. Figure 12a represents the case of the homogeneous distribution of acid chains that has been considered up to now. In this picture, the electrostatic interactions between ionized groups are expected to be a function of the acid chain surface concentration, as indicated by the different spreading of the calculated titration curves in Figure 9. The geometry sketched in Figure 12b corresponds to a monolayer in which the alkyl and acid chains are segregated on

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Figure 10. (a) Orientation of COO- in contact with aqueous electrolyte. (b) Stretching modes of the CO bonds. The bottom arrows indicate the directions of the associated dynamic dipoles.

Figure 11. Conformation of acid chains when they are longer than the alkyl ones, in the picture of homogeneously distributed acid chains. (a) All trans conformation. (b) Chains twisted in their upper part.

Figure 13. Calculated change in COO- concentration as a function of pH, for different concentrations NS of acid groups segregated in the mixed organic layer as sketched in Figure 12b.

Figure 12. Limiting cases for the distribution of COOH-terminated chains in mixed acid/alkyl monolayers. (a) homogeneously distributed acid chains (b) segregated acid chains.

the microscopic scale. In this case, the acid heads in mixed layers behave as in a compact 100% acid layer because their local environment is independent of the dilution, and remains the same as for a 100% acid layer, except at the boundaries of acid domains. The spreading of the titration curves is then expected to be the same for all dilutions, as shown by the calculated curves in Figure 13. All curves are simply proportional to one another, the R(pH) relation being given by eq 4, where the value of NS is that for a 100% acid layer. Comparing the experimental titration curves with the calculated ones suggests that (microscopic) segregation occurs because the calculated curves in Figure 13 fit the data of Figure 6 much better than those calculated within the homogeneous assumption (Figure 9). As a matter of fact, the solid lines in Figure 6 are computed similarly to the curves shown in Figure 13, with pKa ) 6.5 and CH ) 175 µF/cm2. In particular, the experimental progressive character of the ionization at every dilution is now well accounted for. Moreover, the structure in Figure 12b is consistent with an identical behavior for the mixed layers with various alkyl chain lengths (Figure 7). We hence infer from Figure 6 and the absence

of chain length effect that acid chains are segregated in mixed monolayers. The above suggestion raises a fundamental question about the formation mechanisms of mixed monolayers. In the case of thiol self-assembled monolayers on gold, intermolecular chain interactions and surface mobility play a major role.28 In the case of silicon and in our conditions (photochemical reaction at ∼50 °C), the Si-C bond is too energetic to be cleaved, which suppresses any surface rearrangement after molecular grafting. We therefore suspect that the surface segregation is bound to a phase separation at molecular scale in the grafting solution, due to H-bonding between -COOH head groups. Confirming the surface segregation calls for some independent evidence. Such investigations are presently underway.

5. Conclusion Calibrated in situ FTIR establishes that titration of carboxyl groups is largely modified in two dimensions. The process presents a single pKa but solvation constraints at the surface explain a shift of pKa by one to two pH units. Moreover, electrostatic interactions between ionized acid groups are responsible for the spreading of the titration curve over more than six pH units. Quantitative modeling of the titration curves and complementary results from polarized IR spectroscopy clearly suggest that in the (28) (a) Laibinis, P. E.; Nuzzo, R. G.; Whitesides, G. M. J. Phys. Chem. 1992, 96, 5097–5105. (b) Tielens, F.; Costa, D.; Humblot, V.; Pradier, C.-M. J. Phys. Chem. C 2008, 112, 182–190.

Titration of Carboxyl-Terminated Monolayers

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present case, acid and alkyl chains tend to segregate at the surface during the grafting. Taking into account the electrostatic interactions between surface species is of high importance in many surface reactions. As a matter of fact, acid terminated surfaces are often used in procedures to immobilize a probe molecule (chemical or biochemical) onto solid surfaces,29,30 and it appears clear that the usual mild operating conditions for biochemical applications (neutral or weakly alkaline)29 correspond to a surface in which acid groups are only partially deprotonated. In these conditions, deprotonation of the monolayer is reversible and does not affect the integrity of the monolayer. Furthermore, the immobilization of biomolecules at such a surface often implies the reaction of amine compounds, also partially ionized in the same operating conditions. As for the acid-base titration, the electrostatic interactions between these species also appear to markedly affect the kinetics of the immobilization reaction,31 underlining the generic importance of this phenomenon. Supporting Information Available: Typical infrared spectra in the range of 1300-1800 cm-1 for carboxylate ions in aqueous solution. Concentration dependence of COO- absorbance for different carboxylate ions. This material is available free of charge via the Internet at http://pubs.acs.org.

Appendix: Calibration of IR Bands Related to COOH and COO– Groups The absorption intensities of the νCO bands were calibrated from the absorption of acid salts soluble in aqueous solution. IR absorption of the grafted layer can be analyzed by describing this layer as a slice of thickness δ and effective dielectric function ε ) ε′ + iε′′ at the interface between a solid of refractive index ns (3.42 for silicon) and a medium of refractive index nl (1.33 for water). The absorbance can be written at wavelength λ in sand p-polarization (formulas are always written per reflection).32

1 2π as ) I ε′′δ λ ns cos φ y y ap )

(

(A1)

)

nl4 1 2π Ixε′′x δ + Iz ′2 ε′′δ ′′2 z λ ns cos φ ε +ε z

z

band of an aqueous solution containing various carboxylate salts in variable concentrations. In practice, carboxylate ions with short saturated chains (1 to 5 carbons) have been chosen because they are soluble in water. In the calibration experiments, the infrared absorption of the liquid is measured in the ATR geometry at the interface between the same solid and the liquid of complex refractive index n˜ ) nl + ik. k is supposed to be small enough to neglect the change in the depth d of the evanescent wave due to absorption. Consequently, the liquid absorption is written

a′p )

(29) (a) Wagner, P.; Nock, S.; Spudich, J. A.; Volkmuth, W. D.; Chu, S.; Cicero, R. L.; Wade, C. P.; Linford, M. R.; Chidsey, C. E. D. J. Struct. Biol. 1997, 119, 189–201. (b) Strother, T.; Cai, W.; Zhao, X.; Hamers, R. J.; Smith, L. M. J. Am. Chem. Soc. 2000, 122, 1205–1209. (c) Voicu, R.; Boukherroub, R.; Bartzoka, V.; Ward, T.; Wojtyk, J. T. C.; Wayner, D. D. M. Langmuir 2004, 20, 11713– 11720. (30) (a) Bo¨cking, T.; James, M.; Coster, H. G. L.; Chilcott, T. C.; Barrow, K. D. Langmuir 2004, 20, 9227–9235. (b) Perring, M.; Dutta, S.; Arafat, S.; Mitchell, M.; Kenis, P. J. A.; Bowden, N. B. Langmuir 2005, 21, 10537–10544. (c) Chi, Y. S.; Choi, I. S. Langmuir 2005, 21, 11765–1772.

(A3)

1 2π d (I + I )2n k λ ns cos φ x z l 2

(A4)

To obtain the sought calibration, assumptions have to be made to relate ε and n˜. We assume that the high-frequency real dielectric response of the grafted layer is isotropic and identical to that of the liquid (that means nl ≈ (ε′x)1/2 ≈ (ε′y)1/2 ≈ (εz′ )1/2) and that the proportionality constant between the absorption coefficient of the CO mode and the vibrator concentration is the same in the layer and in the liquid (same optical absorption cross-section). These assumptions physically mean that the environment of COO- vibrators is similar in the layer in contact with the electrolyte and in the liquid, as it was aimed at by the use of carboxylate salts. Denoting C as the concentration of vibrators, we obtain

N⊥ ⁄ δ ε′′z ) C⁄3 2knl

(A5)

ε′′y N| ⁄ 2δ ε′′x ) ) C⁄3 2knl 2knl

(A6)

After simple algebra, taking the ratio between the absorbance of the layer and that measured for the carboxylate salts in solution, it becomes

as C As C d) ′ d ′ 3 a A 3

(A7)

Iyap - Ixas C d IyAp - IxAs C d ) 32 32 I a′ I A′

(A8)

N| )

(A2)

where φ is the angle of incidence and Ix, Iy, and Iz are numerical coefficients depending on ns, nl, and φ only. For ns) 3.42 (silicon), nl ) 1.33 (water), and φ ) 48°, Ix ) 1.75, Iy ) 2.11, and Iz ) 2.40. ε has been taken as a tensor in order to possibly account for anisotropic effects due to the adsorbate configuration. With respect to this possibility, it is useful to consider N| the surface concentration of vibrators corresponding to the projection of the dynamic dipole of the vibrational modes in the interfacial plane, and N⊥ corresponding to the projection of the dynamic dipoles along the z direction. The actual surface concentration of vibrators is simply given by N ) N| + N⊥. In order to calibrate the intensity of the νasCOO- band, we applied the method developed by Faucheux et al. in the case of acid-terminated layers.13 Using the same total internal reflection geometry, we measured the intensity of the νasCOO- absorption

1 2π d I 2n k λ ns cos φ y l 2

a′s )

s

N⊥ )

z s

s

z s

where the above expressions have been extended to integrated absorbances per reflection As,p and A′s,p, the smoothly varying parameters Ix, Iy, and Iz, and length d being evaluated at the center of the considered band. Typical infrared spectra of aqueous carboxylate solutions and the concentration dependence of COO- absorbance for different carboxylate ions are given in the Supporting Information. The linear variation of the νasCO band intensity (the straight line passes through the origin) ascertains that calibration is not biased by specific surface adsorption. Calling γ the slope of this plot, the fact that the same value of γ is measured for butanoate and pentanoate solutions is a strong indication that the absorption cross section of COO- becomes independent of chain length above four carbons, whereas using acetate would lead to an erroneous calibration. Therefore, the carboxylate-terminated chains grafted on silicon were calibrated from butanoate and pentanoate solutions. Taking the experimental slope γs ) A′s/C ) 3 cm-1 mol-1 L (γp ) A′p/C ) 5.5 cm-1 mol-1 L) and d ) 0.474 µm at 1550 cm-1, we end up for the surface concentration of the carboxylate

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groups in the grafted layers (expressed in cm-2 and As,p in cm-1, for φ ) 48°):

N| ) (3.17 × 1015)As

(A9)

N⊥ ) (6.60 × 10 ) × (2.11 × Ap - 1.75 × As)

(A10)

14

where As,p are computed using the natural logarithm. Thanks to this calibration, the surface concentrations corresponding to the

parallel and perpendicular components for each band were deduced and combined in order to derive the total amount of each species. LA801219U (31) Moraillon, A.; Gouget-Laemmel, A. C.; Ozanam, F.; Chazalviel, J.-N. J. Phys. Chem. C 2008, 112, 7158–7167. (32) Chabal, Y. J. Surf. Sci. Rep. 1988, 8, 211–357.