A Dielectric Model of Self-Assembled Monolayer Interfaces by

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A Dielectric Model of Self-Assembled Monolayer Interfaces by Capacitive Spectroscopy† Márcio S. Góes,‡ Habibur Rahman,§ Joshua Ryall,§ Jason J. Davis,*,§ and Paulo R. Bueno*,‡ ‡

Instituto de Química, Institute of Chemistry, Physical Chemistry Department, Universidade Estadual Paulista, São Paulo State University, UNESP, CP 355, 14800-900 Araraquara, São Paulo, Brazil § Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, United Kingdom ABSTRACT: The presence of self-assembled monolayers at an electrode introduces capacitance and resistance contributions that can profoundly affect subsequently observed electronic characteristics. Despite the impact of this on any voltammetry, these contributions are not directly resolvable with any clarity by standard electrochemical means. A capacitive analysis of such interfaces (by capacitance spectroscopy), introduced here, enables a clean mapping of these features and additionally presents a means of studying layer polarizability and Cole−Cole relaxation effects. The resolved resistive term contributes directly to an intrinsic monolayer uncompensated resistance that has a linear dependence on the layer thickness. The dielectric model proposed is fully aligned with the classic Helmholtz plate capacitor model and additionally explains the inherently associated resistive features of molecular films.

and d is the thickness of the dielectric layer, A the electrode area, εm the Self-Assembled Monolayer (SAM) dielectric constant and ε0 the permittivity of free space. The presence of a nanometer-thick SAM on an electrode surface considerably reduces the interfacial capacitance from that associated with the bare surface (typically by an order of magnitude). Though the electronic “blocking” characteristics of these films have been acknowledged for some time,12 only recently has it been recognized that alkanethiol SAMs in solution behave as leaky capacitors, with a resistance dependent on the electrode potential.11a,13 There is, notably, experimental evidence that eq 1 does not hold completely for alkanethiol SAMs across a range of temperatures, for example.13 Furthermore, εm may not, in fact, be constant but may decrease as the layer thickness increases,14 accompanying changes in structural ordering and the degree of hydration. It has also been reported that shortchain alkanethiols have capacitances that are higher than would be expected, an observation that has been explained by an increase in ionic permeability associated with a reduction in film crystallinity, a suggestion further corroborated by XPS,15 FT-IR,16 ellipsometry,16a and electrochemistry.16a,17 Recently, Gooding et al. have shown that the capacitance of an alkanethiol film is affected by the potential.18 In the 0−500 mV vs Ag/AgCl region, alkanethiol capacitance was observed to be 2−5 μF cm−2 but to increase rapidly at potentials above +600 mV, an observation assigned to increased ionic permability as SAM fluidity increases. It is important to note that although the capacitative characteristics of monolayer films have been analyzed in some

1. INTRODUCTION Organized monolayers are single-molecule-thick films in which the constituents share a common orientation.1 A frequent depiction of these is one of molecules with identifiable head and tail groups, aligned perfectly on a smooth surface.1 Such interfaces have attracted significant attention in recent years largely because they present a facile means of engineering surface properties through their adsorption from solution or vacuum.2 They accordingly provide a powerful and flexible means of generating sensory or responsive interfaces (such as those capable of biosensing), fundamental building blocks in molecular electronics, and have numerous applications in inorganic (opto)electronic devices. They have been extensively investigated by a number of research groups.3−9 One key relevant characteristic of these films is their response to an applied (external) or inherent (dipole-based) electric field. An understanding of such features is critical if one seeks to use them as component building blocks within more functional biomimetic devices or micronanoelectronic configurations where, for example, an interfacial recognition process, redox state change, or movement is transduced by the underlying electrode surface. Importantly, the “structural” characteristics of an adsorbate film and its interactions with the environment also inherently contribute to the “electrical” characteristics of the subsequently derived final film.10 These films are, almost invariably, considered to be dielectric layers and are typically modeled within a parallel plate capacitor depiction of the solid/liquid interface,11 where ε εA Cm = m 0 (1) d

Received: March 28, 2012 Revised: May 15, 2012

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Originally scheduled to be part of the Bioinspired Assemblies and Interfaces special issue. © XXXX American Chemical Society

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dx.doi.org/10.1021/la301281y | Langmuir XXXX, XXX, XXX−XXX

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Figure 1. (a) Schematic representation of the classical picture of electrochemical double-layer capacitance, with a positively polarized Au−metal interface. The orange line depicts the potential decay (here taking the Au work function (ϕ) as the reference) through the layer. The inset represents the IHP. (b) Dielectric model proposed for hydrated SAM-modified interfaces. Note the existence of dipoles and solvated ions in the SAM layer (see the upper inset). The resultant capacitance in electrolyte media is the series capacitance, Cm, according to eq 3. IHP and OHP refer to the inner and outer Helmholtz planes respectively.

detail,11a,b,13,19 their relaxation characteristics under the influence of an applied field have not been previously resolved. Herein we depart from the parallel plate capacitor model enshrined within eq 1 and use a capacitive spectroscopy approach, electrochemical impedance spectroscopy (EIS),12a,19f,20 to resolve directly, in frequency and for the first time, the Debye-type dipolar relaxation characteristics of SAMs on gold (though this is a generalized model applicable to any adlayer on a metallic surface). These observations, which are in agreement with the acknowledged capacitive features of such organic layers, form part of a spectroscopic framework that can provide a powerful means of monitoring SAM structural changes (through temperature or solution composition, for example or a recognition process). The analyses are modeled through an appropriate equivalent circuit12a encompassing a simple RC series circuit, including solution resistance in series with double layer and monolayer capacitance, with the latter moving away from the model of eq 1 and including the layer polar dynamic polarization (its inherent and electrolyte-derived polar features and their response to an imposed static or dynamic electric field).21

Several theories have been proposed to explain the origin and magnitude of the Helmholtz capacity.11a,b,12a,19d,e Though differing in detail, recent treatments agree that this contains contributions both from the metal and from the solution at the interface (i.e., from both electronic and ionic phases).11a,b,19d,e Significantly, because of the finite size of the ions and solvent molecules, the solution shows considerable structure at the metal interface and the surface potential of the metal varies with the adsorbed ionic charge.23 The modification of this simple, classic, interfacial model in the presence of a monolayer film, spanning the solid (electronic) and the electrolyte (ionic), is depicted in Figure 1b. The presence of this intervening hydrated dielectric layer modifies the doublelayer capacitance in generating a new term, Cm, according to: 1 1 1 = + Cm Cb Cdl

where Cb, the bulk capacitance of the monolayer (the expected layer capacitance without ionic ingress), is the expected capacitance of the layer without electrolyte or proton ions (or associated ions). The resultant capacitance Cm can be treated as that of a plate (eq 1). If Cdl > Cb, the latter dominates the interfacial capacitive response and Cb then approaches Cm (i.e., Cb ≈ Cm). Equation 3, then, summarizes a general capacitive picture for SAM-modified electrodes.1,11a,b,13,19a,c−f The utilization of this model, however, does not provide any information about the polar dynamics/relaxation characteristics or structure-dependent polarization dynamics that arise from the ingress of solutionphase ions into the film. A more realistic model of such interfaces is arrived at by considering, in the first instance, its inherent dipoles. For alkylthiol films, it is known that the monolayer−air interface lies 500−700 mV positive of the metal−thiol interface (with the negatively charged thiol headgroup residing close to the metal and the more dominant alkane (δ+)−S(δ−) dipoles pointing down towards the gold).14,24 Though the monolayer dipole magnitudes are unchanged in a small-amplitude applied field, their (torque-driven) orientation is responsive, with a time scale dependent on the surrounding local viscosity.13 These features are, ideally, described by a Debye or Cole−Cole relaxation function.21c In addition to these inherent (molecular adlayer)

2. A SELF-ASSEMBLED MONOLAYER DIELECTRIC MODEL 2.1. Metal/Liquid and Metal/SAM/Liquid Interfaces. A schematic representation of the double-layer capacitance model of a solid/liquid interface according to the Gouy−Chapman− Stern (GCS) approach is shown in Figure 1a.22 Within this model, Cdl is the resultant capacitance formed by the two series capacitances such that: 1 1 1 = + Cdl CH CD

(3)

(2)

where CH and CD are the Helmholtz-layer and diffuse-layer capacitances, respectively. Although highly simplified in the sense that the solution is modeled as being composed of point ions embedded in a solvent dielectric continuum above a perfectly conducting metal electrode, this simple model is surprisingly good at describing the metal−solution interface. The distribution of the ions near the interface can be calculated from electrostatics and statistical mechanics.22 B


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features will be dynamics associated with the flux of electrolyte ions into/out of the film as a function of the potential.21b,c,25 Indeed, ionic relaxation comprises ionic conductivity and interfacial and space charge relaxation processes, characteristics that predominate at low frequencies and make contributions to the electric loss that are orders of magnitude larger than the response due to polarization fluctuations.21b,c,25 In seeking to resolve and analyze these features in terms of polar and ionic relaxation,21,25 we are proposing here to use capacitance spectroscopy (CS), where any dipolar (and coupled ionic) changes are associated with a resolved characteristic frequency (ωc/2π) (associated with the reciprocal of the angular characteristic time constant (τc = 1/ωc). These dynamic features not only constitute part of a more complete picture of such interfaces but are also inherent in both the layer ionic conductance and the uncompensated resistance present in transient electroanalytical techniques.26 Typically, this intrinsic resistance contributes in parallel to charge-transfer resistance in redox analyses at SAM-modified electrodes, potentially distorting the results.27 The SAMCS approach introduced here aims to provide a resolved SAM “fingerprint” (in terms of the capacitance and associated resistance) that is readily distinguishable (subtractable) from any redox analyses subsequently carried out. 2.2. Dielectric Model of Metal/SAM/Liquid Interfaces. Spectrally resolved electrochemical impedance spectroscopy (EIS) is powerful in revealing the complexities contributing to the current responses at electrochemical interfaces and within electroactive materials, where the charge-transfer resistance, faradaic kinetics, double-layer capacitance, diffusion-controlled reactions, and ionic mobility terms, for example, can be resolved.22 Under the conditions of high charge transfer resistance typical at modified electrode surfaces, however, SAM dielectric contributions are not directly resolved by conventional techniques.27 The acquired data can, however, be utilized in generating capacitance spectra (from the complex impedance function). The derived capacitance complex function highlights the storage characteristics of the interface rather than the resistive terms, as emphasized in normal EIS.28 Mathematically, the terms are phasorially related. Specifically, Z*(ω)Z′ + jZ″ (where ω = 2πf is the angular frequency and j = (−1)1/2) and its inverse, the admittance, Y*(ω) = 1/Z*(ω), are related phasorially to the capacitance function according to:

C*(ω) = (jω)−1Y *(ω) C*(ω) =

jY ′ Y″ − = C′ + jC″ ω ω

In an ideal, perfectly homogeneous Debye system, this is describable by a single function f(t) = e−t/τc, where τc is the characteristic relaxation time of the process. The interface is, however, more realistically describable by a distribution of functions, a Cole−Cole formalism, and a spread of exponentials. In such circumstances, one has a net stretched exponential function f(t) = e−(t/τc)β where β quantifies, in effect, the degree of dispersion of relaxation dynamics within the film or the film homogeneity. The complex capacitive response of the interfacial relaxations as a function of frequency are represented by eqs 6 and 7, where the dynamics are perfectly homogeneous (Debye) or distributed (Cole−Cole), respectively. C*(ω) = Cm +

C*(ω) = Cm +

C t − Cm 1 + (jωτc)

(6)

C t − Cm 1 + (jωτc)1 − α

(7)

in which 0 < α < 1. Note that the Ct − (Cm/1) + (jωτc) term occurs in parallel to the Cm capacitive term21c and vanishes if data acquisition occurs at a frequency beyond that at which polar constituents of the molecular layer can respond (Cm is the limitig capacitance at high frequency). At practical perturbation frequencies of 100 kHz < ωc < 1 MHz, the Rt and Ct terms contribute in a nonzero manner. The features of the polarization described by eqs 6 and 7 are better visualized when such functions are represented in terms of an equivalent circuit. (See below.) β is related to eq 7 by β = 1 − α. Implicit (because τc = RtCt) in eqs 6 and 7 is the existence of a resistive contribution. (See the equivalent circuit description below.) This resistive term, Rt, couples with the capacitive term Ct to contribute to a resolvable time constant for relaxation as stated. The capacitive characteristics in Debye and Cole−Cole cases are summarized in Figures 2 and 3. To summarize thus far, the interfacial capacitance of a SAMmodified electrode has important and resolvable contributions from its constituent polar or charged features to any applied field. The time domains of these are directly visualized in complex capacitance (C*) Bode plots. If sufficient geometric knowledge of the interface, namely, the SAM layer thickness and underlying electrode surface area, can be obtained, then the complex capacitance (C*) can be reported in terms of a dielectric complex function (ε*) (i.e., considering the Au/SAM interface to be plate capacitor model according to the Helmholtz model):

(4)

(5)

ε*(ω) =

The real part (C′) of the complex capacitance function is related to the imaginary part of the admittance (C′ = Y″/ω), and the imaginary part (C″) is related to the real part of the admittance (C″ = Y′/ω). As noted, the capacitance characteristics of a SAM interface are defined by the response of its inherent or field-induced dipoles and ionic field to electrode potential. The equivalent circuit representation of this will be discussed in the next section, where two terms, Rt and Ct, accounting for the resistance (of the molecular layer/associated ions to field-induced reorientation) and capacitance (dipoles and ions) of the SAM layer, respectively, will be introduced, in addition to the Cm and electrolyte resistance Re. The relaxation processes in a modulating imposed field have associated dynamics that are exponential in the time domain.

d C*(ω) ε0A

(8)

From a consideration of non-redox-active solid/SAM/liquid junctions (where only nonfaradaic processes are active), the dynamic model described in eqs 6 to 8 makes predictions about resolvable capacitive terms that report directly on the electrostatic dynamics within the film. In the next section, an equivalent circuit model will be introduced from which these terms can be segregated and subsequently subtracted from any additional faradaic activity (i.e., they can be compensated for to highlight redox features).27 2.3. Equivalent Circuit Model for Metal/SAM/Liquid Interfaces. The on-electrode assembly and analysis of redoxactive films provides a powerful means of analyzing the thermodynamics and kinetics associated with molecular electron C


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Figure 2. (a) Nyquist complex capacitance and (b) Bode capacitive diagrams of an ideal Debye relaxation process derived from eq 5. Here Ct = 0.9 mF (equivalent to the diameter of the semicircle in part a) and Cm = 0.1 mF (in practical situations, this high-frequency monolayer capacitance is lower than low-frequency capacitance Ct).21a In part b, the steplike function with two plateaus is the real part of the capacitive complex function (i.e., the C″ component). Note that the imaginary component of the complex capacitance C″ is also shown and its peak indicates the value of τc. Both components in part b are represented in millifarads and on a logarithmic scale. (c) Bode capacitive plot of the imaginary component only (i.e., C″ is on a nonlogarithmic abscissa scale. The resolved characteristic frequency is highlighted in c. where the value of τc can be obtained. Note that the Cm and Ct terms are visualized in C′ and their time scales are resolved in C″.

Figure 3. (a) Nyquist complex capacitance and (b) Bode capacitive diagrams of a Cole−Cole relaxation process describable by eq 6, with α = 0.3 (β = 0.7). In all plots Ct = 0.9 mF and Cm = 0.1 mF. (c) Bode capacitive diagram of the imaginary componentonly (i.e., C″ with a nonlogarithmic scale on the abscissa). Note that, in comparison to Figure 2, the semicircle has a depressed format and the C″ pattern in parts b and c is broadened by the the dispersive/stretch effects of the α and/or β terms. Physically, this is interpretable in terms of a distribution of polar relaxation times.

transfer, and an enormous amount of work has now been published with a diverse array of surface-assembled films. It is important, then, to address how the introduced SAM dynamic features can contribute to behavior often observed and commonly either ignored or ascribed loosely to uncompensated effects.27 As previously noted, the introduction of a SAM both perturbs Cdl and introduces polar relaxation terms Rt and Ct with an associated relaxation time τc. The perturbation of Cdl (and its replacement) generates an equivalent capacitance term Cm (eq 3). The dipolar dynamics introduced by the SAM can then be expressed with respect to the equivalent circuit by, in the first instance, a generic black-box term parallel to high-frequency capacitance Cm (Figure 4). In the ideal Debye scheme, this encompasses only Rt and Ct. For the non ideal (Cole− Cole) case, Rt spans a distribution of values and is represented by a CPE (constant-phase element) defined explicitly by Qt(jω)−α. Note that when α = 0 (meaning no τc distributive feature) Qt = Rt. The traditional picture of the Helmholtz model (a parallel plate capacitor with an intervening dielectric) models the interface as comprising an electrolyte resistance in series with a capacitor. It does not, however, differentiate between the capacitances of the monolayer and the double layer, both of which appear in series with the electrolyte resistance. The model proposed herein predicts an ability to resolve all of these contributions experimentally in a manner that not only reports on the structural characteristics of a SAM but also provides a

Figure 4. (a) Equivalent circuit depiction of the Au/solution interface summarizing the contributions from nonfaradaic processes. (b) Equivalent depiction with a SAM modification (Cm and black box element,with the the latter representing the ionic dipolar SAM terms). The ideal response of a dipolar layer is represented by series resistive and capacitive terms Rt and Ct, respectively. A nonideal response can be represented in terms of an equivalent circuit by series capacitive term Ct and a Qt term that account for a Gaussian distribution of resistances (i.e., a Gaussian distribution of dipolar orientation energies with respect to the alternating electric field).

facile means of removing the effects of uncompensated resistance in any associated redox chemistry. D


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Figure 5. (a) Theoretical Nyquist impedimetric plot of a SAM-modified interface for different magnitudes of Ct where it is evident that the impedance representation provides little information. (b) The same theoretical interface presented as a Nyquist capacitive diagram where Ct is directly visualized from the diameter of the semicircle in part b or the plateau value in part c (20, 10, or 5 μF). In parts c and d are shown the Bode diagrams of the real and imaginary parts of the complex capacitive function, C*, respectively. In part d, it is important to observe that the magnitude of the relaxation process (visualized by the magnitude of the C″ peak) attributed to the dipolar/electrostatic features of the SAM layer decreases with decreasing Ct (i.e., with decreasing τc according to τc = ωc−1). Note that Cm was set as null here for convenience.

3. SAM CAPACITANCE SPECTROSCOPY The analysis of either the fundamental (eq 4) complex capacitance response or its geometrical normalization by d/ε0A according to eq 8 of a SAM/liquid interface will be herein referred to as SAMCS. Figure 5 depicts simulated SAMCS spectra of a Debye-like (homogeneous) SAM/interface taking Cm as null (in practice, Ct > Cm). Under these conditions, the Debye equation (eq 6) becomes: C*(ω) =

Ct 1 + (jωτc)

It is expected that there will be a progression toward higher frequency, ω c, as Ct ̀ decreases (Figure 5d), according to τ c = ω c−1. Fundamentally, one expects an increasing monolayer thickness to be associated with a decrease in the Ct capacitance term according to the generalized Helmholtz model (although the model does not consider a physical picture of specific polar or ionic contributions) and an increase in the Rt term (the resistance of the layer dipoles and ionic field to further field-induced perturbation). As shown above (Figure 6), these changes are readily resolvable in SAMCS but not in impedance Nyquist plots. The Ct and Rt terms are coupled, and the resonance within the Bode plots represents the time scale τc = RtCt. The evolution of this resonance with SAM thickness represents the result of the opposing Ct and Rt contributions. In Figure 6d, the net effect is observed to be a displacement toward lower frequencies with increasing chain length, although the magnitude of the peak does not change. To summarize thus far, SAMCS is expected to resolve the polarization dynamics of SAMs on metallic electrodes in a manner that is both invisible to standard EIS analyses and a sensitive function of film thickness. The methodology can, additionally, be applied in the study of film heterogeneity through resolving the dispersion in τc. Heterogeneities contribute to a perturbation away from ideal Debye behavior in a manner quantified through α. The effects of the existence of a distribution of polar relaxations in the film are shown in Figure 7, where it is evident that α does not affect Ct or Cm but causes a

(9)

in which monolayer dipolar features dominate the response (i.e., Ct, τc and implicitly Rt (τc = RtCt). Figure 5 extends the theoretical predictions introduced into Figure 3 across a range of Ct magnitudes where it is evident (Figure 5a) that an impedimetric Nyquist representation resolves little over and above reporting a large impedance, but the Nyquist capacitance directly reports Ct (Figure 5b). The onset of this semicircle directly reports Cm (here set to zero), and the diameter of the semicircle equates to Ct. Bode plots of the imaginary part of the complex function provide a facile means of quantifying the Ct contribution and thus the layer dielectric polarizability as a function of frequency (with the plateau at low frequency corresponding to the sum of Ct and Cm, Figure 5c). Bode plots of the imaginary part of C* directly report ωc, the angular characteristic frequency of polar relaxation (identified as the frequency of the peak). E


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Figure 6. (a) Theoretical Nyquist impedimetric analyses of a SAM-modified electrode for a range of Rt values at constant Ct. In part a, it can be seen again that the EIS response is largely insensitive. (b) Nyquist capacitive diagram where the value of Ct can be evaluated from the diameter of the semicircle. In parts c and d, the associated Bode diagrams of real and imaginary complex capacitive function, C* are shown. In part d, it is important to note that the intensity of the relaxation process attributed to the polar features of the SAM layer is constant with increasing Rt (i.e., with decreasing τc). As expected, the frequency of the peak increases because τc = ωc−1. scanning between −0.5 V and ca. 1.3 V vs Ag/AgCl at a sweep rate of 100 mV s−1. Electrodes were finished by cycling in the negative potential range (−0.5 to −1 V vs Ag/AgCl) before being used immediately for SAM formation. After incubation electrodes were thoroughly rinsed in ethanol and ultrapure water and inserted into the electrochemical cell, which was previously deoxygenated by bubbling with argon for 20 min; deareated conditions were maintained by flushing with argon throughout data acquisition. Cyclic voltammetry and electrochemical impedance spectroscopy measurements were carried out with an Autolab PGSTAT 12 instrument (Echo Chemie, Utrecht, The Netherlands) equipped with an FRA2 module. All EIS measurements were carried out at a hold potential of 0.22 V versus Ag/AgCl in aqueous solutions of 0.5 M NaClO4 as the supporting electrolyte at room temperature using a typical three-electrode cell setup. Platinum mesh and Ag/AgCl counter and reference electrodes, respectively, were used. AC frequencies for impedance experiments ranged from 1 MHz to 10 mHz with an amplitude of 10 mV. The complex Z*(ω) (impedance) function was converted to C*(ω) (capacitance) through the physical definition Z*(ω) = 1/jωC*(ω) in which ω is the angular frequency.27 All obtained impedance data were checked against the constraints of linear systems theory by Kramers−Kronig using the appropriate routine of the FRA Autolab software. Zview equivalent circuit modeling software was employed for data fitting using a built-in complex element or RC circuit.

displacement of the relaxation resonance peak toward higher frequencies and lower magnitude. This behavior is similar to that observed with decreasing Rt. The next sections of this article are concerned with an experimental exemplification of the introduced concepts across a range of alkylthiol SAMs.

4. EXPERIMENTAL PROCEDURE All working electrodes were 1-mm-diameter polycrystalline gold disks (Bioanalytical Systems, BAS), prepared as previously reported29 by a series of mechanical and electrochemical polishing steps, separated by sonication for short intervals in Milli-Q water. Electroactive areas were evaluated by the integration of the cathodic peak from gold electropolishing voltammograms and converted to the real surface area using a conversion factor of 482 μC cm−2.30 Typically, areas of 0.02−0.03 cm2 were obtained, corresponding to a roughness, measured as the ratio of electroactive and geometrical areas, of 1.5−2.5. SAM formation was carried out on freshly prepared electrode surfaces by overnight incubation at room temperature in 1 mM solutions of 1-butanethiol (C4, n = 3), 1-hexanethiol (C6, n = 5), 1-octanethiol (C8, n = 7), 1-decanethiol (C10, n = 9), and 1-dodecanethiol (C12, n = 11) in HPLC grade ethanol. Prior to SAM formation, all electrodes were treated with hot piranha solution (70% H2SO4/30% H2O2) followed by mechanical polishing to a mirror finish using aluminum oxide disks (Buehler, Fibrmet Discs) with polishing progressing from coarse (3 μm) to fine (0.3 μm). (CAUTION! Piranha solution can react violently with organic materials and should be handled with extreme caution! Piranha solution should not be stored in tightly sealed containers.) This was followed by electrochemical polishing in 0.5 M sulfuric acid and potential

5. RESULTS AND DISCUSSION As mentioned in the Experimental Procedure section, the complex Z*(ω) (impedance) function is convertable to C*(ω) F


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Figure 7. (a) Theoretical Nyquist impedimetric plot (i.e., the EIS response of a SAM-blocking interface). Here, Ct is fixed and a dispersion in the resistance is taken into account through a nonzero α value. In a, it can be seen that the EIS response does not provide information on the capacitive changes in the SAM layer interface, as expected. (b) The same theoretical response as in part a but presented in Nyquist capacitive form where Ct is reported through the semicircle diameters. In parts c and d are shown the Bode diagrams of the real and imaginary components, respectively. In part d, it is important to observe that the intensity of the relaxation process decreases with an increase in α (i.e., with an increase in dispersion).

(capacitance) by C*(ω) = 1/jωZ*(ω). Practically, this involves taking the data resolved in a standard impedance analysis (Z*(ω)), sampled across a range of frequencies at any steadystate potential, and converting it phasorially into a complex capacitance (C*(ω)) with its real and imaginary components. In processing Z*(ω) data sets in this way, one obtains the imaginary part of the capacitance by noting that C″ = φZ′ and C′ = φZ″, where φ = (ω|Z|2)−1 and |Z| is the modulus of Z*. 5.1. SAM Capacitance Spectroscopy: Separating Experimental and SAM Relaxation Characteristics. Before this conversion of complex impedance to complex capacitance, the solution resistance (Re) can be subtracted from the spectrum by means of Z′(ω) − Re.27 Note that this process normally requires the determination of Re,22,31 but this is not required here because this contribution is clearly visualized from the beginning of the real part of Z′ at high frequency in Nyquist plots and is thereafter subtracted (Figure 8a). This is equivalent to the (partial, see below) iR drop correction in transient techniques. The Re term is obviously reflective, not of the SAM interface but of the experimental configuration. Without its prior removal, the relaxation characteristics resolved in a Bode plot of C″ (Figure 8d) are ascribable (see equivalent circuit in Figure 4) to a series RC monolayer term where the resistance component is the sum of Re and Rt. A subtraction of the Re contribution leads (yellow curve) to a clean resolution of the SAM Rt and Ct contributions as theoretically predicted. The impedance-derived C*(ω) function thus reports on two parallel processes: Cm resolved at high frequency (Figures 2, 4,

and 5−7) and the incremental resistance and capacitance (RtCt) terms arising from the constituent polar SAM relaxation processes resolvable at frequencies >10 kHz. One can refine the C*(ω) function further through the elimination of Cm contributions to capacitive spectra by means of C′(ω) − Cm. Practically, this requires only a horizontal displacement in Nyquist capacitive plots. (The semicircle related to the dipolar relaxation departs from a non-null value initially but is zeroed through this process (Figures 5−7).) 5.2. SAM Capacitance Spectroscopy: Resolving the Effects of the Chain Length (Layer Thickness). In this section, we extend the previous demonstration to a range of alkylthiol films, with a particular focus on the evolution of polar relaxation features with film thickness. These analyses, as before, are carried out in the absence of a redox probe. Figure 9 summarizes the Nyquist impedimetric and capacitive characteristics of three films. As expected from theory, the Nyquist impedance diagrams (Figure 9a) report only on the progression of general resistive effects. The individual layer dipolar characteristics are clearly resolved by the Nyquist capacitive plot (Figure 9b), where a Ct decrease with increasing chain length is clear and in accordance with previously noted predictions.12a (See also Figure 7b.) Nyquist capacitance plots resolve, in addition to the semicircle reporting Ct, a straight line at lower frequencies, associated with ionic diffusion (as shown in Figure 9b as opposed to fieldinduced ionic fluctuation within the SAM). This aspect of the spectra will not be discussed herein. G


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Figure 8. (a) Nyquist impedimetric plot for a 1-butanethiol (C4, n = 3) SAM-modified electrode. (b) Magnified Nyquist impedimetric plot showing the series resistance, here stated as Re (the Z′ axis intercept). (c, d) Real and imaginary parts of the complex capacitance represented in Bode form. The yellow curve is the response after Re correction. Although Re contributes to the relaxation process, this is not the only contribution present because of ionic and dipolar relaxation processes operating inside the monolayer (i.e., due to Rt coupled to Vt).

Figure 9. (a) Nyquist impedimetric plots for 1-hexanethiol, 1-decanethiol, and 1-dodecanethiol. The inset highlights the response at high frequency, where there polar relaxation is observed, highlighting the inability of impedance to detect layer effects. (b) Corresponding Nyquist capacitive diagrams. The red line corresponds to a fitting to the dielectric model proposed herein (Figure 4b and eq 7). The resolved semicircles in the high-frequency regime summarized (inset) directly report Ct (and εm through eq 8). As stated previously, Ct can be obtained from the diameter of the semicircle in part b, as indicated for the C6 film. The data has been normalized by the effective electrode area.

range of monolayer films, one can resolve a progressive decrease in Ct and an increase in Rt (Figure 11). It is evident that the capacitive spectral analyses reported in Figure 11 cleanly resolve a progressive linear decrease in Ct with increasing chain length. As noted previously, the origin of this capacitive term is both dipolar and ionic in nature, with the latter being dominant and decreasing with increasing film crystallinity. The trend in Rt, not resolvable nor readily removed

A capacitive Bode analysis of these interfaces is presented in Figure 10, where an increase in the frequency dispersion associated with SAM relaxation with SAM thickness is apparent. A more complete interpretation of this forms part of ongoing work. Significantly, these analyses not only resolve Ct but, through the time domain of the relaxation process τc, the Rt contribution (through τc = RtCt). In extending these analyses across a greater H


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Figure 10. Bode diagrams of the (a) real and (b) imaginary parts of the complex capacitance for three alkylthiol SAMs. The progressive decrease in Ct with chain length is resolvable through the plateau heights in part a. In part b, the characteristic SAM relaxation frequencies and intensities are evident. The frequency axis is reported here as the base 10 exponents for clarity. As stated previously, Ct in the Bode diagram can be obtained for the 0.1−1 kHz plateau resolved in part a. τc is obtained from the frequency of the peak resolved in part b.

As noted within eq 1, in treating the interface as a plate capacitor the resolved Ct values (obtained here from the fitting of SAMCS spectra to the dielectric model or equivalent of Figure 4b) can be used to calculate the film εm from: εm = d

C t, A ε0

(10)

(where Ct,A is Ct per unit area). As depicted in Figure 11d, both the absolute values of εm14 and the trend across different SAMs are entirely in line with expectations of progressive increases in the film hydrophobic character and decreases in ionic permeability14,24d as the methylene numbers increase, with a step change occurring between n = 7 and 9 films. Though there have been numerous reports of an alkanethiol SAM dielectric, prior determinations invariably are reported as averages over a range of chain lengths (as determined from the gradient of 1/C versus chain length) and span 2.1−2.616a,19f,24d,32,33 in value. We believe the current report to be the first experimental verification of structure-related dielectric variance.

6. FINAL REMARKS AND CONCLUSIONS When an organic SAM layer is introduced between a metallic interface and a liquid electrolyte, one expects not only a doublelayer-based capacitance decrease but, in addition, new dipolar dynamic trends associated with ionic fluctuation within the film and molecular-scale polarizability. We have introduced here the theoretical basis of SAMCS, which is fully aligned with but more detailed than the Helmholtz plate capacitor model of such interfaces, and exemplified it with a range of alkanethiol films. The interface, in such cases, is most appropriately considered to consist of two parallel impedance terms, a high-frequency (typically >100 kHz) Cm capacitance and SAM-based Rt and Ct terms. The relaxation time τc = RtCt represents a fingerprint of the SAM and enables Rt to be determined directly. In the case of additional redox events, this term is then readily removed from subsequent (kinetic) analyses (cleanly negating the effects of uncompensated resistance). Because Ct and Rt are structuredependent, this form of capacitance spectroscopy is readily applied to the analysis of SAM structure and ionic ingress from solution as a function of pH, temperature, surface potential, and electrolyte strength, for example.

Figure 11. Evaluation of parameters of the SAM dielectric model as a function of chain length. All data was acquired from the fitting (exemplified in Figures 9b and 10, red lines) of SAMCS plots according to the dielectric model discussed. The errors indicated are fitting errors generated from the use of mean data acquired from three different measurements.

in standard ac or dc voltammetric methods, deserves attention because this term contributes directly to what is referred to as (undefined) uncompensated resistance in electroanalyses involving SAM layers and is thus a source of error in kinetic analyses.26 The breadth of the resonance peaks resolved in Figure 10b is a signature of Cole−Cole rather than Debye adlayer character and reports on a dispersion of polarization characteristics within the film that can be quantified through α (and confirmed through curve fitting). The linear decrease in τc in Figure 11c is a consequence of Ct being a more sensitive reporter of film thickness than Rt (i.e., changes in τc are dominated by Ct, which falls). The distribution of the polar relaxation times, quantified through α, is ∼0.3 here and constant across all films. I


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the São Paulo state research funding agency (FAPESP) and São Paulo State University (UNESP) and CNPq grants.

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