Analytical Expressions for Proton Transfer Voltammetry: Analogy to

Mar 27, 2013 - Department of Chemistry, The University of the West Indies, Mona Campus, Kingston 7, Jamaica. Anal. Chem. , 2013, 85 (9), pp 4475–448...
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Analytical Expressions for Proton Transfer Voltammetry: Analogy to Surface Redox Voltammetry with Frumkin Interactions Juan José Calvente,*,† Antonio M. Luque,† Rafael Andreu,† Willem H. Mulder,‡ and José Luis Olloqui-Sariego† †

Departamento de Química Física, Universidad de Sevilla, 41012 Sevilla, Spain Department of Chemistry, The University of the West Indies, Mona Campus, Kingston 7, Jamaica

‡

S Supporting Information *

ABSTRACT: Theory for interfacial proton transfer voltammetry of a molecular film containing any acid/base loading has been developed under equilibrium conditions. Diagnostic criteria to disentangle the interplay between diffuse layer and ionization effects are outlined. Easy-to-use analytical expressions for the voltammetric features are derived for the particular case of an invariant diffuse layer effect, which turn out to be entirely analogous to those for a surface redox conversion with Frumkin interactions. It is demonstrated that, regardless of the electrolyte concentration, significant ionization of the external acid groups located nearby the diffuse layer is sufficient for the fulfillment of this relevant particular case. A strategy is outlined to determine the amount, the intrinsic pKa, and the burial depth of the voltammetrically active groups from the surface concentration dependence of the main voltammetric features. Self-assembled monolayers of 11-mercaptoundecanoic acid deposited on Au(111), containing higher amounts of buried carboxylic groups than previously reported, have been studied to assess more critically the influence of electrostatic effects on the ionization process. Preliminary evidence suggests that the protonation/deprotonation voltammetric wave involves physisorbed rather than chemisorbed thiol molecules. Application of the present theoretical approach to this system reveals that the voltammetrically active carboxylic groups are located close to the electrode surface and become more acidic upon increasing their surface concentration.

S

waves than those predicted by Smith’s and White’s model. The first experimental evidence of a reversible voltammetric wave associated with the protonation/deprotonation of an ionizable SAM was reported by White et al.13 for a mixed monolayer of 11-mercaptoundecanoic (MUA) and decanethiol deposited on Ag(111), which displays some of the qualitative trends predicted by previous theoretical models. Since then, similar voltammetric responses have been reported for MUA,14,30 4mercaptobenzoic acid,15 and 3-mercaptopropylphosphonic acid31 monolayers deposited on gold electrodes. In spite of these efforts, there are still some fundamental aspects of the potentiostatic ionization of acidic SAMs that remain poorly understood. For instance, an estimate of the intrinsic pKa value of the immobilized acid groups is still required, since in most instances only the apparent pK1/2 value (i.e., the pH at which half-ionization occurs) is experimentally accessible. As will be shown here, an estimate of the intrinsic pKa can be obtained from the voltammetric peak potential together with some extrathermodynamic considerations. Also, a direct estimate of the amount of voltammetrically active acid groups from their voltammetric features is still lacking due to

elf-assembled monolayers (SAMs) of thiols bearing acid/ base groups are of fundamental and applied interest. They are a well suited model to study the factors that govern interfacial proton transfers and are also commonly used for anchoring biomolecules,1−4 controlling surface wettability5 and crystal nucleation,6 and for electroanalysis.7−9 Most of these applications are based on their capability to vary the interfacial charge with the solution pH. The acidity of ionizable SAMs has been probed with a large number of techniques.10−26 The reported pKa values for typical carboxylic acid-terminated SAMs span a range from 4.5 to 10.3. This broad scatter may be due to limitations of the techniques that probe indirectly the degree of ionization of SAMs, but it may also reflect the complexity of these interfacial systems. Electrochemical techniques offer some advantages for the quantitative characterization of ionizable SAMs as they can be readily used to both drive and probe interfacial proton transfers under conditions of thermodynamic and kinetic control. Smith and White27 were the first to recognize that potentiostatic ionization of an acid SAM leads to a variation of the interfacial capacitance that should appear as a maximum in the voltammetric response. This seminal theoretical work was subsequently refined by Fawcett et al.28,29 who considered the discreteness-of-charge effect and the presence of a Stern layer adjacent to the monolayer, to produce narrower voltammetric © 2013 American Chemical Society

Received: January 2, 2013 Accepted: March 27, 2013 Published: March 27, 2013 4475

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criteria for their applicability are established. The feasibility of this approach is proven by studying the voltammetric ionization of MUA-modified Au(111) electrodes containing up to fifteen times more buried carboxylic groups than previously reported. By increasing the amount of embedded groups, the ionizationinduced voltammetric broadening is amplified, which allows for a more precise determination of the location of the ionization plane.

the nonfaradaic nature of the interfacial ionization process. A strategy is developed here to estimate it from the area and the full width at half-maximum of the voltammetric wave. On the other hand, the shift of the voltammetric peak potential with pH has been commonly taken as evidence of the presence of a protonation/deprotonation process. However, experimental Ep vs pH slopes are often more negative than the expected −0.059 V/pH. For instance, slopes within the [−0.065, −0.070 V/pH] interval have been reported for MUA14,30 and 4-mercaptobenzoic15 SAMs deposited on gold. In a recent work, we have developed a two-population model for ionizable SAMs, which has shed light on some fundamental aspects of their electric field-driven ionization.30 First, it has been shown that only buried ionizable groups contribute perceptibly to the voltammetric wave, their contribution increasing with their burial depth into the monolayer. Second, only when these buried groups are in close contact with the electrode surface does the estimated Ep vs pH slope equal −0.059 V/pH, whereas more negative slopes are predicted upon decreasing the burial depth. In order to keep the mathematics tractable, the analysis was restricted to low loadings of buried acid groups so that interfacial potential profiles remain nearly linear along the voltammetric scan. However, this approach is likely to fail upon increasing the number of buried acid groups since piecewise linear potential profiles are expected to develop when these groups become increasingly ionized (Figure 1).

■

EXPERIMENTAL SECTION 11-Mercaptoundecanoic acid (MUA), sodium hydroxide, and high purity Puratronic sodium fluoride were purchased from Aldrich, Fluka, and Alfa Aesar, respectively, and used without further purification. Water was purified with a Millipore Milli-Q system (resistivity 18 MΩ cm). The solution pH was adjusted to 8.5 in the electrochemical cell by adding a few drops of a freshly prepared ∼1 mM NaOH solution to the previously deaerated 5 mM NaF solution. The pH was continuously monitored with an Orion 8102BN electrode connected to an Orion 420A pH meter. An Au(111) single crystal electrode (Metal Crystals and Oxides), with a geometric basal surface area of 0.225 cm2, was used to form MUA self-assembled monolayers. MUA SAMs with different loadings of buried carboxylic groups were deposited by immersing the gold surface in ethanolic solutions containing different concentrations of MUA from 1 mM to 80 mM, during a variable deposition time in the interval 0.5−24 h. The modified electrode was first rinsed with ethanol and then with the 5 mM NaF aqueous solution at pH 8.5. Contact of the MUA-coated Au(111) surface with the electrolyte solution in the electrochemical cell was made by the pendant meniscus configuration, and it was allowed to equilibrate with the solution for ca. 5 min before acquisition of the voltammograms. Voltammetric measurements were carried out in a waterjacketed glass cell, thermostatted at 25.0 ± 0.2 °C with a Haake D8.G circulator thermostat. A Ag|AgCl|NaCl (sat’d) electrode and a Pt wire were used as reference and auxiliary electrodes, respectively. The reference electrode made electrical contact with the cell solution via a salt bridge filled with the same solution. Electrolyte solutions were deaerated with a presaturated argon stream prior to the measurements, and a positive argon pressure was maintained over the solution during the measurements. Three-cycle voltammograms were acquired with an Autolab PGSTAT30 (Eco Chemie), and only the steadystate voltammograms corresponding to the third scan are reported. All potential values are referred to the Ag|AgCl|NaCl (sat’d) electrode.

■

Figure 1. Schematic illustration of the interfacial potential profile of an ionizable SAM with two acid populations, located at planes a and d, for distinct ionization degrees of the buried population in the absence (upper panel) or presence (lower panel) of external ionized groups at plane d.

THEORY Following our previous work,30 we consider a modified electrode with two populations of acid groups (Figure 1), one located at plane a inside the monolayer, and the other located at the boundary of the diffuse layer (plane d). Although the need to consider a buried population of carboxylic groups comes from the electrostatic analysis of the voltammetric response,30 some experimental findings suggest that these buried groups can be ascribed to physisorbed molecules embedded in a partially disordered film. Previous studies based on NEXAFS, XPS, and infrared reflection−absorption measurements have shown that carboxylic-terminated SAMs prepared from high thiol concentrations exhibit a high degree of disorder and the presence of physisorbed thiol molecules on

In the present work, the theory for reversible proton transfer voltammetry of molecular films containing any amount of buried ionizable groups is developed, aimed at using the surface concentration dependence of the voltammetric features to determine the location, amount, and intrinsic acidity of the buried groups. Analytical expressions for the voltammetric features of these molecular films for the commonly found case of an invariant diffuse layer effect are derived, and diagnostic 4476

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top of the underlying chemisorbed film.32−36 This physical adsorption has been shown to be disrupted in the presence of small molecules capable of forming hydrogen bonds with the carboxylic/carboxylate groups, such as acetic acid.33,35,36 The absence of the protonation/deprotonation voltammetric wave for a mercaptobenzoic monolayer formed in the presence of acetic acid15 is consistent with the involvement of these physisorbed molecules in the development of the voltammetric peak. Within this scenario, incorporation of a fraction of the carboxylate groups of physisorbed molecules into the underlying disordered film can be driven by a combination of (i) the favorable interfacial electric field as the electrode becomes more positively charged, (ii) the poor solvation of the hydrocarbon chain by the aqueous solution,37 and (iii) the affinity of the carboxylate group toward the metal surface, resulting from electrostatic image interactions (not captured by a description based on the mean-field approximation).38−40 Once the carboxylate moiety is close to the metal surface, reversal of the electrode potential to more negative values drives its protonation. The carboxylic group may then remain inside the monolayer by a combination of hydrogen bonding and van der Waals interactions. The general, albeit numerical, solution for the voltammetric response associated with the potentiostatic protonation/ deprotonation of the two populations of ionizable groups is derived in the Supporting Information. As demonstrated there (Figure S-1), the degree of ionization of the external acid population remains almost invariant along the potential window where full ionization of the internal population occurs. In what follows, we make use of this approximation by considering that only the protonation state of the internal population can be varied potentiostatically. Let ΓaT be the surface concentration of buried acid groups (ΓaT = ΓaROH + ΓaRO−) and ΓdRO− the potential-independent surface concentration of the external ionized groups. The fractions of the neutral (ROH) and ionized (RO−) forms of the buried acid groups, θi = Γai /ΓaT, are given by a θROH =

aH+ ; a H + + Kaξ a

a − = θRO

Kaξ a a H + + Kaξ a

concentrations cele or whenever ΓdRO− ≫ ΓaRO−, the diffuse layer potential ϕd remains nearly invariant along the voltammetric scan, and its value approaches the potential of zero charge of the modified electrode in the absence of internal ionization ϕmpzc,0 (Figures S-2 and S-3 in the Supporting Information). Under these conditions, dϕd/dϕm ≈ 0, and the expression for the voltammetric current (eq S-16) reduces to i = vK md + ωaFv ΓTa

m ϕm = ϕ1/2,0 +

ωa(1 − ωa)F ΓTa a θRO− K md

a ⎫ RT ⎧ ⎛ θRO− ⎞ a a −⎬ ⎨ln⎜ a ⎟ + g Γ T ωaθRO ωaF ⎩ ⎝ 1 − θRO− ⎠ ⎭ ⎪

⎪

⎪

⎪

(4)

ϕm1/2,0

where g = (1 − ωa)F /(KmdRT), and is the half-ionization potential (where θaRO− = θaROH = 1/2) in the limit ΓaT = 0, which is related to the solution pH by 2

m ϕ1/2,0 =

(1 − ωa) m 2.3RT (pK a − pH) − ϕpzc ,0 ωaF ωa

(5)

where it has been assumed that ϕd ≈ ϕd1/2 ≈ ϕmpzc,0. By differentiating eq 4 with respect to θaRO−, and taking into a m a −1 account that dθRO = (dϕm/dθRO , the following − /dϕ −) expression is obtained for the voltammetric current density from eq 3 i = vK md +

a a −(1 − θ ωa2F 2v ΓTa θRO RO−) a a −(1 − θ RT 1 + g ΓTa ωaθRO RO−)

(6)

where the first term on the RHS represents the contribution of the flat capacitive baseline (ibl), and the second term stands for the contribution of the potentiostatic interfacial proton transfer (icor). It should be noted that the second term is analogous to the current derived for a Frumkin surface redox conversion,41,42 with the parameters ωa and g replacing the number of electrons exchanged per molecule and the repulsive intermolecular interaction parameter, respectively. The voltammetric response associated with the i.d.l.s. case can be computed in a straightforward manner from eqs 4 and 6 by using θaRO− as the independent variable instead of ϕm. Analytical expressions for the peak potential ϕmp , peak current density icor,p, and full width at half-maximum (f whm) of the baseline-corrected voltammetric wave can be derived from eqs 4 and 6 as described in the Supporting Information:

(1)

a

ϕa = ωaϕm + (1 − ωa)ϕd −

(3)

where v is the potential scan rate. An explicit expression for the relationship between θaRO− and m ϕ can now be obtained by combining eqs 1 and 2 and the material balance θaROH + θaRO− = 1

where ξ = exp(Fϕ /RT), Ka is the acid dissociation constant, aH+ is the hydronium ion bulk activity, and ϕa is the mean-field potential at the inner dissociation plane, which is given by (Supporting Information) a

a − dθRO m dϕ

(2)

where ωa = Kmd/Kad is the ratio of the integral capacitance of the monolayer (Kmd) to that of the dielectric slab bounded by plane a and the diffuse layer boundary d (Kad), so that 0 < ωa < 1, and ϕm and ϕd are the average potentials at the metal and plane d, respectively. The presence of ϕd in eq 2 precludes the formulation of explicit analytical expressions for the voltammetric current, which must be calculated numerically as described in the Supporting Information. However, analytical expressions for the voltammetric features are readily obtainable for the commonly found experimental situation where ϕd remains invariant along the voltammetric scan. We will refer to this particular case as the invariant dif f use layer scenario (i.d.l.s.). Voltammetric Response within the Invariant Diffuse Layer Scenario. As will be shown later, for high electrolyte

m ϕpm = ϕ1/2,0 +

icor , p =

(1 − ωa)F a ΓT 2K md

ωa2F 2v ΓTa RT (4 + g ΓTa ωa)

fwhm =

(8)

⎫ RT ⎧ ⎛ 1 + Ψ ⎞ a ⎟ + gω ΨΓ ⎬ ⎨2 ln⎜ a T ⎝ ⎠ ⎭ ωaF ⎩ 1−Ψ

gωaΓaT)/(8

(7)

(9)

where Ψ = ((4 + + By combining eqs 4 and 6-8, the following expressions are obtained for the normalized baseline-corrected voltammetric wave in terms of θaRO−: 4477

gωaΓaT))1/2.

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Figure 2. Protonation/deprotonation cyclic voltammograms calculated for the indicated values of ωa, cele, and ΓdRO− under equilibrium conditions with the general solution, eqs S-1, S-11, S-12, S-14, and S-15 with σd = −FΓdRO− (solid lines), and the expressions for the i.d.l.s. case, eqs 4 and 6 (dashed lines). Green and pink lines correspond to ωa = 0.8, whereas red and blue lines correspond to ωa = 0.5. Other parameter values: ΓaT = 5 pmol cm−2, pKa = 4.0, Kmd = 3 μF cm−2, εs = 78.5, pH = 8, and T = 298 K. Green triangles mark the location of the potential of zero charge in the absence of internal ionization. m

ϕ −

ϕpm

a ⎫ RT ⎧ ⎛ θRO− ⎞ a a − ⎬ ⎨ln⎜ = a ⎟ + g Γ T ωa(θRO − 0.5) ωaF ⎩ ⎝ 1 − θRO− ⎠ ⎭ ⎪

⎪

⎪

⎪

along the voltammetric scan. Upon increasing either cele or ΓdRO−, the capacitive baseline minimum disappears, and the voltammetric wave approaches the expected i.d.l.s. behavior, which is indicative of either a negligible (for high cele values) or constant (for high ΓdRO− values) contribution of the diffuse layer potential to the ionization of buried acid groups. The extent of the diffuse layer effect also depends on the ωa value, which for a dielectrically uniform monolayer is determined by the relative location of the buried acid groups within the monolayer. In general, an increase of ωa results in the narrowing of the voltammetric wave, that may be accompanied by a shift of the peak potential toward more negative (ϕmp > ϕmpzc,0, Figure 2a) or more positive (ϕmp < ϕmpzc,0, Figure 2c) values. In the case of a significant diffuse layer effect (Figure 2b), the increase of ωa also reduces its impact on the voltammetric features as evidenced by the voltammetric wave approaching the i.d.l.s. behavior. According to this analysis, the absence of a minimum in the capacitive baseline can be taken as an indicator for the applicability of the analytical expressions derived for the i.d.l.s. case. The ionization of the internal groups is expected to affect the voltammetric wave shape as their surface concentration ΓaT increases. Figure 3A illustrates this influence under conditions where the diffuse layer effect remains invariant along the voltammetric scan. For low enough ΓaT values, σa is so small that it does not perturb significantly the linear potential profiles predicted in the absence of internal ionization. Under these conditions, the terms containing the gΓaT factor in eqs 4 and 6 can be neglected, so that ideal, Nernstian-like voltammetric waves characterized by a f whm of 90.6/ωa mV at 298 K are predicted. An increase of ΓaT results in a greater accumulation of charge at the proton transfer plane during ionization of the buried groups, with the subsequent decrease of ϕa that gives rise to piecewise linear potential profiles. Under these conditions, the main contribution to ϕa is the ionization term (third term on the RHS of eq 2), so that more positive potentials on the metal are required to further ionize the buried groups. This situation is reflected in a broadening of the voltammetric wave that eventually takes a truncated-bell shape. For high enough ΓaT values, the voltammetric broadening becomes so large that sigmoidal-like voltammograms are obtained in the commonly

(10)

icor

■

icor , p

=

(4 + 1+

a a −(1 − θ g ΓTa ωa)θRO RO−) a a −(1 − θ g ΓTa ωaθRO RO−)

(11)

RESULTS AND DISCUSSION Interplay between Diffuse Layer and Ionization Effects. For a given solution pH, the degree of ionization of the buried acid groups depends on the local potential at the plane of dissociation ϕa (eq 1). Two factors contribute to the value of ϕa for a given applied potential on the metal; namely, the diffuse layer potential ϕd (second term on the RHS of eq 2) and the charge developed at the plane of dissociation σa = −FΓaTθaRO− (third term on the RHS of eq 2). In practice, the relative contribution of ϕd and σa to ϕa can be controlled by varying the electrolyte concentration cele, the amount of buried acid groups ΓaT, and the number of ionized external groups ΓdRO−. In this section, we shall first consider the scenario where only one factor, either the ionization or the diffuse layer effect, contributes significantly to the voltammetric response (i.e., the case of weak diffuse-layer/ionization coupling), and then we will discuss the case where both of them affect the voltammetric features (i.e., the case of strong diffuse-layer/ionization coupling). Weak Diffuse-Layer/Ionization Coupling. For a given dielectric structure of the monolayer (i.e., for fixed values of ωa and Kmd), the diffuse layer effect can be modulated by varying cele or ΓdRO−. Figure 2 illustrates how these two variables affect the voltammetric response of a modified electrode containing a low number of buried acid groups, so that their ionization does not affect significantly the interfacial potential profile. Under these conditions, the voltammetric response can be decomposed into the voltammetric wave, associated with the interfacial proton transfer, and the capacitive baseline of the modified electrode, which is independent of the internal ionization degree. For low cele and ΓdRO− values, the capacitive baseline develops a minimum at the potential of zero total charge, and the voltammetric wave (solid lines in Figure 2) deviates from that predicted for the i.d.l.s. case (dashed lines in Figure 2), reflecting the variation of the diffuse layer potential 4478

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the diffuse layer potential to the interfacial proton transfer makes it difficult to determine the relevant system parameters (ωa and pKa) from a fit of the voltammetric wave. This problem persists even when the nonzero contribution of the diffuse layer remains invariant along the voltammetric scan (second term on the RHS of eq 5). However, we have found that this complication can be circumvented by taking advantage of the variation of the voltammetric features with the amount of buried ionizable groups ΓaT. In a practical situation, determination of ΓaT from the integral of the voltammetric wave requires the prior knowledge of ωa. Thus, instead of using ΓaT as the independent variable representing the amount of buried ionizable groups, it is more convenient to employ the charge (per unit electrode surface area) that circulates through the external circuit during the ionization process, Qp/dp, which is related to ΓaT and can be determined in a straightforward manner by integrating the baseline-corrected voltammetric wave: Q p / dp = ωaF ΓTa =

1 | v

∫ icordϕm|

(12)

(see eq S-17). Figure 4 depicts the dependence of the peak potential ϕmp , peak current icor,p, and full width at half-maximum f whm of the baseline-corrected voltammetric wave on Qp/dp, for distinct values of ωa, cele, and ΓdRO−. As can be observed, both ϕmp and Figure 3. Anodic trace of protonation/deprotonation cyclic voltammograms calculated for the indicated surface concentrations of buried acid groups in the (A) presence (ΓdRO− = 8 × 10−10 mol cm−2) or (B) absence (ΓdRO− = 0) of external ionized groups (solid red lines). Other parameter values: pKa = 4.0, Kmd = 3 μF cm−2, ωa = 0.8, εs = 78.5, cele = 1 mM, pH = 8, and T = 298 K. Green dashed lines represent the contribution of the capacitive baseline (first term on the RHS of eq S-16) to the overall voltammetric current. Purple solid line in the lower panel represents the anodic trace in the absence of internal ionization. Insets represent the potential profiles within the monolayer for ϕm = −0.2 V and distinct values of ΓaT: 1, 15, 90, and 1000 pmol cm−2 (upper panel), and 1, 25, and 100 pmol cm−2 (lower panel).

accessible experimental potential window. Under these circumstances, gΓaTωaθaRO−(1 − θaRO−) ≫ 1 in the plateau region, and applying this condition to eq 6, the baseline-corrected plateau current density is given by ωavKmd/(1 − ωa). Strong Diffuse-Layer/Ionization Coupling. A strong mutual influence of the ionization and diffuse layer effects is expected for low electrolyte concentrations whenever ΓaT ≫ ΓdRO−. Under these circumstances, the increase of ΓaT not only shifts and broadens the voltammetric wave but also decreases the underlying capacitive baseline on the positive side of the voltammetric wave, due to the effect of the internal ionization on the diffuse layer potential (Figure 3B). As illustrated in the lower panel of Figure 3B, the capacitive baseline (green dashed lines) deviates from that calculated in the absence of internal ionization (purple solid lines), so that the latter should not be used as a reference baseline to isolate the proton transfer voltammetric wave from the raw voltammograms. In this case, a quantitative characterization of the voltammetric protonation/ deprotonation process should rely on digital simulation. Determination of System Parameters from the Voltammetric Features. The electrostatic contribution of

Figure 4. Peak potential (upper panels), full width at half-maximum (middle panels) and scan rate-normalized peak current (lower panels) as a function of the charge under the baseline-corrected voltammetric wave for the indicated values of cele, ΓdRO−, and ωa. Other parameter values: pKa = 4.0, Kmd = 3 μF cm−2, εs = 78.5, pH = 8, and T = 298 K. 4479

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f whm vary linearly with Qp/dp, whereas icor,p shows a nonlinear dependence, consisting of a linear behavior at low Qp/dp values that gradually levels off upon increasing Qp/dp. Bearing in mind the general expression for the peak potential ϕpm =

(1 − ωa) d 2.3RT (pK a − pH) − ϕp + ωaF ωa

(1 − ωa) p / dp Q 2K mdωa

ϕmp

(13) p/dp

ϕdp

the linearity of the vs Q plot indicates that is rather insensitive to ΓaT. This is a consequence of the fact that, for a fixed acid/base conversion, the variation of the charge accumulated at the proton transfer plane upon increasing ΓaT is compensated by the corresponding variation of the charge at the metal surface, so that ϕdp remains constant. According to eq 13, the slope of the ϕmp vs Qp/dp graph is given by (1 − ωa)/ (2Kmdωa), which can be used to determine ωa. Conversely, the intercept of the ϕmp vs Qp/dp plot depends on both cele and ΓdRO−, its variation decreasing upon increasing ωa. An estimate of the intrinsic pKa of the buried acid groups can be obtained from this intercept value, provided that an independent estimate of ϕdp is available, which is not often the case. However, we have found that for high values of either cele or ΓdRO−, ϕdp approaches the value of the potential of zero charge of the modified electrode in the absence of internal ionization ϕmpzc,0. The error in the estimate of pKa from the ϕmp values by using the approximation ϕdp ≈ ϕmpzc,0 in eq 13 is less than ±0.25(1 − ωa) at 298 K whenever ΓdRO− ≥ 100 pmol cm−2 or cele ≥ 0.5 M (see the Supporting Information). On the other hand, the linear dependence of f whm on Qp/dp is somewhat surprising, even for the i.d.l.s. case, due to the apparent nonlinearity of eq 9 with respect to ΓaT. For this particular case, we have found that the numerical fwhm values computed from eq 9 can be reproduced with the following linear expression: fwhm =

1.075(1 − ωa) p / dp 3.525RT + Q ωaF K mdωa

Figure 5. Third scan of three-cyclic voltammograms recorded for a MUA-coated Au(111) electrode in contact with a 5 mM NaF aqueous solution of pH 8.5 at 298 K as a function of the deposition time in a 50 mM MUA ethanolic solution (left panel) or the time elapsed in the electrochemical cell in contact with the electrolyte solution (right panel). Scan rate 0.05 V s −1. Electrode surface area 0.225 cm2. Green inverted triangles indicate the open circuit voltage EOC.

experimental conditions (i.e., low electrolyte concentration and solution pH 8.5) have been chosen to slow down such a deactivation process. It should also be noted that the use of a relatively high MUA concentration in the deposition solution produces much larger voltammetric waves than those previously reported, so that electrostatic effects can be more critically assessed. In general, an increase in the amount of buried carboxylic groups results in a broadening of the voltammetric wave and a shift of its peak potential toward more negative values. The fact that the voltammetric wave develops at more negative potentials than the open circuit voltage (green inverted triangle in Figure 5) indicates that, prior to the application of a cell voltage, the buried carboxylic groups are deprotonated at pH 8.5. As illustrated in Figure 6a, the f whm of the anodic wave varies linearly with the charge developed during the ionization of the buried acid groups Qp/dp, in line with the theoretical predictions depicted in Figure 4 (similar results were obtained for the cathodic wave). By inserting the intercept and slope values of this linear dependence into the corresponding terms of eq 14, and using the experimental value of Kmd = 2.8 μF cm−2, the ωa parameter takes a value of 0.986, which confirms that ionization of the buried acid groups occurs close to the electrode surface. Moreover, this ωa value also reproduces both the nonlinear dependence of the anodic peak current with Qp/dp (Figure 6b) and the normalized anodic voltammetric waveshape for distinct values of ΓaT (Figure 6c). Once the ωa value is known, the amount of voltammetrically active carboxylic groups ΓaT can be estimated from the area under the baseline-corrected voltammetric wave by using eq 12. It has been found that ΓaT increases from 3 to 120 pmol cm−2 upon increasing the deposition time from 1 to 24 h in a 50 mM MUA ethanolic solution. Taking into account that under the present experimental conditions the formation of a monolayer of chemisorbed MUA molecules takes less than an hour, these results suggest that the protonation/deprotonation voltammetric wave is originated in physisorbed rather than chemisorbed MUA molecules. This is further supported by the need of using higher MUA concentrations than those employed in previous studies to increase the number of

(14)

As can be seen in Figure 4, the slope of the f whm vs Qp/dp plot is insensitive to cele and ΓdRO− and coincides with the value predicted for the i.d.l.s. case, namely 1.075(1 − ωa)/(Kmdωa); whereas the intercept varies slightly with cele and ΓdRO−. Comparison with Experiments. Self-assembled monolayers of 11-mercaptoundecanoic acid (MUA) deposited on gold electrodes are well suited to investigate electric field-driven interfacial proton transfers.13−15,30 Having developed in the previous section the theory for any acid/base loading, we now compare the theoretical predictions with experimental results, to assess the influence of the number of buried acid groups on the potential-induced protonation/deprotonation process. Figure 5 depicts the voltammetric response of a MUAmodified gold electrode in a 5 mM NaF aqueous solution of pH 8.5 for different amounts of the buried carboxylic groups, that have been achieved by varying either the deposition time from a 50 mM MUA ethanolic solution (left panel, Figure 5), or the time elapsed in the electrochemical cell (right panel, Figure 5), where a slow deactivation process takes place. A similar deactivation has been thoroughly studied by Burgess et al.15 for 4-mercaptobenzoic (MBA) SAMs, who ascribed it to the disruption of hydrogen bonding between MBA molecules by interaction with the electrolyte cations. In the present study, 4480

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predictions are likely to be due to a variation of the pKa toward more acidic values upon increasing the loading of the buried acid groups (ΔpKa ∼ −1.1 for ΔΓaT ∼ 120 pmol cm−2). This pKa shift is consistent with the greater disorder reported for mercaptohexadecanoic SAMs when they were prepared from more concentrated thiol solutions than those employed in earlier studies.33 An estimate of the pKa from the Ep values requires the transformation of the theoretical ϕm-potential scale to the experimental E-potential scale, which can be done according to the following expression: m E = ϕm + (Epzc − ϕpzc ) ,0

(15)

In a previous work, a value of −0.170 V has been reported for the Epzc of a MUA-modified Au(111) in a pH 8.5 aqueous solution containing 0.2 M NaClO 4 and 5 mM sodium phosphate buffer.18 On the other hand, according to the reported values for the apparent pK1/2 of the terminal carboxylic groups, more than half a monolayer should be ionized at pH 8.5 (i.e., 4 × 10−10 mol cm−2 < ΓdRO− ≤ 8 × 10−10 mol cm−2).10,11,13,14,17−20,26 The theoretical values of ϕmpzc,0 for the two limits of the ΓdRO− interval are −0.138 V and −0.178 V, respectively (eq S-12 with ϕd = ϕmpzc,0 and −σdif = σd = −FΓdRO−). By applying eq 15 to the peak potential (i.e., E = Ep and ϕm = ϕmp ), combining it with eq 13, and inserting the above estimates of Epzc and ϕmpzc,0 in the resulting expression, an estimate of pKa within the interval 4.7 ≤ pKa ≤ 5.2 is obtained for the ionization of the buried groups in the limit ΓaT → 0. These estimates are close to the pKa value reported for the ionization of typical carboxylic acids in aqueous solutions, which is consistent with the aforementioned fact that under open circuit conditions (green inverted triangle in Figure 5) the population of buried carboxylic groups is deprotonated at pH 8.5. This result suggests that the buried carboxylic groups are in a less hydrophobic environment than that expected for a tight SAM, a fact that is consistent with the highly disordered structure reported for 16-mercaptohexadecanoic SAMs prepared from high thiol concentrations.33

Figure 6. (a) Full width at half-maximum and (b) scan ratenormalized peak current recorded for a MUA-coated Au(111) electrode in a 5 mM NaF aqueous solution of pH 8.5 at 298 K with a scan rate of 0.05 V s−1 as a function of the charge under the baselinecorrected anodic voltammetric wave, which was modulated by varying the MUA concentration in the deposition ethanolic solution from 1 to 80 mM and the deposition time from 0.5 to 24 h. (c) Normalized baseline-corrected anodic voltammetric waves recorded for the indicated amounts of buried carboxylic groups. Inset in part c depicts the peak potential as a function of the anodic charge. Symbols are experimental data and solid lines represent the theoretical predictions computed from (a) eq 9, (b) eq 8, and (c) eqs 10 and 11 (for the normalized voltammetric waves) and eqs 7 and 15 (for the peak potential in the inset), with the following parameter values: ωa = 0.986, Kmd = 2.8 μF cm−2, ϕm1/2,0 + (Epzc − ϕmpzc,0) = −0.228 V, and T = 298 K.

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CONCLUSIONS Theory for proton transfer voltammetry of molecular films containing any loading of buried ionizable groups has been developed, and analytical expressions for the commonly found case of an invariant diffuse layer effect have been derived under equilibrium conditions. These expressions have been found to be entirely analogous to those reported for a surface redox conversion with Frumkin intermolecular interactions. It has also been shown that the dependence of the voltammetric features on the acid/base loading can be used to determine the amount, intrinsic acidity, and location of the buried ionizable groups within the monolayer. Particularly useful are the linear variations predicted for both the peak potential and full width at half-maximum with the acid/base loading, whose slopes provide information on the location of the ionization plane regardless of the diffuse layer effect. This information is critical to determining the amount of buried ionizable groups from the integrated voltammetric wave. An estimate of the intrinsic pKa from the peak potential value requires the prior knowledge of the potential of zero charge of the modified electrode. Preliminary evidence is given that the protonation/ deprotonation voltammetric wave of the 11-mercaptoundecanoic acid self-assembled monolayer deposited on Au(111) involves physisorbed rather than chemisorbed thiol molecules.

voltammetrically active carboxylic groups. A more detailed study of the physisorption process is underway and will be reported in a forthcoming communication. With regard to this point, three factors are envisaged to contribute to the incorporation of a fraction of the physisorbed carboxylic/ carboxylate groups to a plane close to the electrode surface, namely, (i) the electrostatic interaction of the negatively charged carboxylate group with the mean interfacial electric field, whenever the electrode becomes positively charged, (ii) its own image charge which it induces on the metal surface, and (iii) the hydrogen bonding between the carboxylic and anchored sulfur moieties. In spite of the ability of the present approach to reproduce the normalized voltammetric waveshape, it has been found that it cannot account for the variation of the peak potential with the amount of buried carboxylic groups (inset Figure 6c). Bearing in mind that the peak potential depends also on the pKa and the potential of zero charge values (eqs 7 and 5), and that for the present system the contribution of the latter is quite small because (1 − ωa)/ωa = 0.014 in eq 5, the observed deviations of the peak potential with respect to the theoretical 4481

dx.doi.org/10.1021/ac303661g | Anal. Chem. 2013, 85, 4475−4482

Analytical Chemistry

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Application of the derived theory reveals that the voltammetrically active carboxylic groups lie close to the electrode surface and that their pKa presumably decreases upon increasing the number of buried carboxylic groups. Additional work is underway to understand this unexpected finding. Overall, the present work represents a step forward in the quantitative characterization of the potentiostatic ionization of molecular films containing acid/base groups by means of cyclic voltammetry. From a conceptual point of view, it also contributes to the unified treatment of redox and acid/base voltammetries, as they share mathematical solutions of the same form.

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ASSOCIATED CONTENT

S Supporting Information *

General solution for the voltammetric response, applicability of relevant approximations, voltammetric peak parameters for the invariant diffuse layer scenario. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +34-954557177. Fax: +34-954557174. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Spanish MICINN under Grant CTQ2008-00371 and by the Junta de Andalucia under Grant FQM02492.

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dx.doi.org/10.1021/ac303661g | Anal. Chem. 2013, 85, 4475−4482