Canadian Journal of Chemistry
An Electrochemical Immittance Analysis of the Dielectric Properties of Self-Assembled Monolayers
Journal: Canadian Journal of Chemistry
Manuscript ID cjc-2020-0005.R1
Manuscript Type: Article
Date Submitted by the 27-Feb-2020 Author:
Complete List of Authors: Dionne, Eric; Université de Montréal, Chimie Ben Amara, Fadwa; Université de Montréal, Chimie Badia, Antonella; Université de Montréal, Chimie Is the invited manuscript for Draft consideration in a Special University of Montreal Issue?:
self-assembled monolayer, dielectric properties, ionic insulator, Keyword: electrochemical impedance spectroscopy
Note: The following files were submitted by the author for peer review, but cannot be converted to PDF. You must view these files (e.g. movies) online. cjc-2020-0005r2_figures.docx
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An Electrochemical Immittance Analysis of the
Dielectric Properties of Self-Assembled Monolayers
Eric R. Dionne, Fadwa Ben Amara, and Antonella Badia
Département de chimie, Université de Montréal, C.P. 6128, succursale Centre-ville,
Montréal, QC H3C 3J7 CANADA Draft
Corresponding author: Antonella Badia ([email protected])
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Abstract
The ability of organic self-assembled monolayers (SAMs) to act as insulating barriers to
charge and ion transport or molecular diffusion is critical to their application in a variety of
technologies. The use of appropriate analytical tools to characterize the dielectric
properties of these molecular thin films is important for the control of structural defects
and establishing structure–property relations. In this context, we analyze the ionic
permeability and dielectric response of SAMs formed from a homologous series of n- Draft alkanethiolates (CH3(CH2)nS, where n = 9, 11, 13, 15, 17, and 19) on gold using the immittance quantities of the complex impedance, capacitance, and permittivity available from the same electrochemical impedance spectroscopy (EIS) measurement. The most sensitive parameters and frequency range for characterizing the capacitive behavior and assessing the ion-blocking quality of the SAMs under non-faradaic conditions are identified. We also investigate the effect of chain length on the interfacial capacitance and dielectric constant of ionic insulating SAMs. The advantages of the capacitance quantity and related permittivity data over traditional impedance representations and equivalent electric circuit modeling are discussed.
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Key words: self-assembled monolayer, dielectric properties, ionic insulator,
electrochemical impedance spectroscopy
Draft
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Introduction
Organothiols chemisorb to noble metal surfaces, forming well-defined two-dimensional
(2D) films coined "self-assembled monolayers" (SAMs).1-4 These monomolecular layers are integral components of nanotechnology,2 in organic/molecular electronics
(capacitors, gate dielectrics for low-voltage FETs, junctions),5 soft lithography,6 and surface-based biomolecular sensors7, 8. The density of structural defects and pinholes in the SAM (i.e., sites for molecular and ion penetration or electron transport to the Draft underlying metal surface) must be low for this nanometer thick film to act as an effective barrier to chemical etchants, non-specific adsorption, charge accumulation or charge transfer. Electrochemical methods to characterize the structural integrity and insulating character of SAMs include cyclic voltammetry (i.e., oxidoreduction of soluble redox species, gold oxide formation/stripping, and underpotential deposition/stripping of metals) and electrochemical impedance spectroscopy (EIS).9 The latter ac technique measures the resistive and capacitive properties of electrochemical cells.10 It can be used to characterize ionic or electronic conductors as well as dielectric materials.11 The frequency-resolved aspect of EIS is especially powerful as it probes conduction (electrical
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and ionic) and electron transfer processes occurring at material/electrolyte interfaces over
time scales of microseconds (MHz) to seconds (Hz to subHz).12 Non-faradaic EIS has
been used to investigate the permeability of SAMs to electrolyte ions, their
electrochemical stability, the effect of substrate roughness, and potential-induced change
in the SAM microstructure.13-25
A library of mathematically-related immittance functions is available from a single EIS
measurement (i.e., complex impedance,Draft admittance, capacitance, permittivity, and dielectric modulus).10, 12, 26 Analyses of film-modified electrodes generally consider only
the raw complex impedance data.13-22, 24 However, an immittance approach more fully
captures the dielectric signature and ionic conductivity of the SAM. Specifically, the
complex impedance representation emphasizes values at low frequency and is often
used to identify Faradaic processes parallel to the double-layer capacitance.10 By
contrast, complex admittance and capacitance representations emphasize values at high
frequency and are better suited to the analysis of blocking electrodes, for which
information is ultimately sought on the system capacitance, or parallel processes whose
time constants differ due to different resistive components.10, 11 For example, Góes et al.
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demonstrated the unique capability of capacitance spectra to separate field-induced ion
migration within the film at low frequency from the ionic dipolar relaxation of the SAM at
higher frequency for Au/SAM/electrolyte interfaces behaving as leaky capacitors.23
Additionally, in a study of potential-induced defects in SAMs, Boubour and Lennox observed a sharp increase in the absolute magnitude of the permittivity at low frequency due to the penetration and accumulation of ions and solvent into the low dielectric
16 hydrocarbon region of the SAM. TheseDraft investigations clearly demonstrate the greater sensitivity of the impedance-derived capacitance and permittivity quantities over the measured impedance at exposing the ionic permeability of low conductivity structures like
SAMs.
The present work uses the complex impedance, capacitance, and permittivity functions
to analyze the dielectric behavior of SAMs of n-alkanethiolates (CH3(CH2)nS) on gold at
a structurally non-perturbing applied dc potential and in the absence of a redox probe.
The focus is on the capacitance and relative permittivity as these properties are used as
figures of merit to characterize the performance of organic dielectric layers.27, 28 We first
consider the responses of CH3(CH2)11SAu SAMs with varying degrees of ionic
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permeability or leakiness to establish the most sensitive parameters and relevant
frequency range for characterizing the capacitive behavior and evaluating the ion-
blocking quality of the SAM. We then investigate the effect of chain length on the
interfacial capacitance and dielectric constant of ionic insulating SAMs. This work differs
from previous investigations employing EIS to characterize the dielectric characteristics
of CH3(CH2)nSAu SAMs in the broader frequency range probed (0.1 Hz–1 MHz) to assess
13-17, 19, 20, 22, 24, 25 the SAM permeability Draft and the use of ion-blocking SAMs with near-ideal capacitor behavior for the study of the chain length dependence23.
BACKGROUND
Relationship between Impedance, Capacitance, and Relative Permittivity
EIS applies a low-amplitude, sinusoidal ac potential (typically 5–10 mV peak-to-peak)
of a given frequency with a dc-offset potential to the electrochemical cell.10, 26 The
response to this potential perturbation is an ac current signal. The impedance Ẑ can be
expressed mathematically as the complex (frequency-dependent) ratio of the input
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potential and measured current output.10, 29, 30 Ẑ is generally represented as a complex
number:
Ẑ () = Z′() + jZ″()
(1)
where Z′ and Z″ are the real and imaginary parts, j is the imaginary unit (-1)1/2, and is the angular frequency of the potential (i.e., ω = 2πf where f is the applied frequency in
Hz). Z′ is the resistance of the systemDraft to current flow and Z″, the reactance, describes the
opposition to changes in the current flow. The absolute impedance magnitude Z| is given
by:
2 2 Z()| = 푍() + 푍() (2)
Mathematical equations for Z′() and Z″() of the equivalent electric circuits commonly
used to fit the impedance response of SAM-modified electrodes are given in Table 1.
Analogous expressions for the complex capacitance Ĉ() and complex relative
permittivity 휖 (), also commonly referred to as the complex dielectric constant, are given
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in Table 2. C′ corresponds to the effective double-layer capacitance and ϵ´ is the relative
permittivity. At low frequency, ϵ´ and C′ adopt static values. The imaginary components
C″ and ϵ are associated with losses in the form of energy dissipation. Ẑ () is related
phasorially to Ĉ():10, 23, 31
1 Ĉ(휔) = (3) Ẑ ()(푗)
The real part C′ is related the imaginary part Z′′ and the imaginary part C′′ is related to the
real part Z′. Assuming a HelmholtzDraft parallel plate capacitor model for the
gold/SAM/electrolyte interface, Ĉ() can be reported in terms of 휖 ():
휖(휔)휀표퐴 퐶(휔) = 푑 (4)
-12 -1 where o is the permittivity of free space (8.85419 × 10 F m ), A is the electrode area,
and d is the SAM film thickness.23, 29, 30 The primary impedance data, Z′() and Z′′(), can
thus be used to generate capacitance and relative permittivity spectra (Table 2), which
highlight the electrical energy storage and dissipative characteristics of the system rather
than its resistive properties (impedance).
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The other impedance-related quantities are the complex admittance (푌 ) and dielectric
modulus (푀 ). These quantities are merely the reciprocals of Ẑ and 휖 , respectively,26 and
are not considered here.
Equivalent Electric Circuit Representations of the SAM-Modified Metal Interface
The equivalent circuits employed to fit the non-faradaic impedance response of SAM-
modified metal electrodes at a structurally non-perturbing dc potential and examples of
impedimetric complex plane plots (DraftZ vs Z) are shown in Fig. 1. The Helmholtz-type equivalent circuit I, consisting of a solution resistance Re in series with a constant phase
element (CPE), describes defect-free ion-blocking SAMs.13, 15, 20, 32 SAMs presenting
defect sites for ion permeation are modeled using the Randles-type circuit II, which
18, 21, 22, 33 8 2 includes a resistance RSAM in parallel with the CPE. When RSAM ~10 cm ,
the impedance response of the SAM can be fit using circuit I.
The use of a CPE in the place of a capacitor to model the interfacial capacitance C
significantly improves the quality of the fits of the experimental data. The CPE is a power
law-dependent parameter that accounts for deviations from pure capacitor behavior. The
impedance of a CPE ẐCPE() is given by the relation:
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1 Ẑ CPE( ) = 푇(푗휔)훼 (5)
where T is the parameter related to the electrode capacitance and is the constant phase
exponent (0 ˂ 1).26 When = 1, the impedance of the CPE is equivalent to that of an
ideal capacitor. In practice, a deviation from unity (e.g., 0.9 1) is almost always
observed, even for a near-perfect blocking film, due to the nanoscale surface roughness
and polycrystallinity of the underlying solid electrode causing local variations of the
current density in the double layer.15,Draft 19 When ≳ 0.99, C is assigned the value of T and
the difference in the units of T (F s1- cm-2) and C (F cm-2) is ignored.34
The total electrochemical capacitance of the SAM-modified electrode is approximated
by two capacitors in series:
-1 -1 -1 C = CSAM + CD (6)
where CSAM is the capacitance of the SAM and CD is the concentration-dependent diffuse
9, 13, 21, 23, 24 layer capacitance of the electrolyte solution. For densely-packed SAMs, CD is
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at least an order of magnitude larger than CSAM so that its contribution to the total
capacitance and T can be neglected, as demonstrated experimentally by prior studies.13,
21
Experimental
Materials
The following n-alkanethiols and reagents were purchased and used without further
purification: 1-decanethiol (CH3(CHDraft2)9SH, 96%, Sigma-Aldrich), 1-dodecanethiol
(CH3(CH2)11SH, ≥ 97%, Fluka), 1-tetradecanethiol (CH3(CH2)13SH, ≥ 98%, Fluka), 1-
octadecanethiol (CH3(CH2)17SH, 98% Sigma-Aldrich), and sodium perchlorate (≥ 98%, Sigma-
Aldrich). 1-Hexadecanethiol (CH3(CH2)15SH, > 95%, Sigma-Aldrich) was purified by column
chromatography prior to use (SiO2, hexane:pentane (1:1 v/v), Rf = 0.75). 1-Eicosanethiol
(CH3(CH2)19SH) was synthesized from CH3(CH2)19OH (98%, Sigma-Aldrich) by refluxing with
35 48% HBr to produce CH3(CH2)19Br followed by reaction with thiourea. Ultrapure water with a
resistivity of 18.2 MΩ cm and total organic carbon of ≤ 5 ppb (MilliQ Gradient) was used to
prepare the electrolyte solution, rinse all surfaces, and as the probe liquid in the contact angle
measurements.
Preparation of CH3(CH2)nSAu SAMs for Electrochemical Impedance Spectroscopy
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Gold bead electrodes (99.99%) of surface area of 0.20 to 0.28 cm2 were used for the
electrochemical measurements. The electrodes were first sonicated in a 2:1 (v/v) mixture of 30%
NH4OH/30% H2O2 for 60 min, rinsed copiously with ultrapure water, and subjected to a 15 min
treatment in an oxygen-plasma cleaner at medium RF power setting (Harrick model PDC-32G).
36 Prior to SAM formation, the gold bead was immersed in dilute aqua regia (3:1:6 HCl/HNO3/H2O)
for ca. 10 min to dissolve away gold and impurities from the bead surface, rinsed copiously with
ultrapure water, and sonicated in ultrapure water for 2 min to remove traces of acid. Finally, the
bead was flame-annealed and quenched in ultrapure water thrice and rinsed thoroughly with
absolute ethanol.
The bead was immersed in an ethanolic solution of 0.2 mM CH3(CH2)nSH for 18–24 h at room
temperature in a sealed incubation vial.Draft2, 9 Prior to use, the SAM-modified bead electrode was
removed from the CH3(CH2)nSH solution, rinsed copiously with absolute ethanol followed by
ultrapure water, and dried with nitrogen.
Preparation of CH3(CH2)nSAu SAMs for Contact Angle Measurements
Premium quality glass slides cut into pieces of 20 mm 25 mm were first cleaned by
immersion in a solution of 3:1 v/v concentrated H2SO4/30% H2O2 (Warning - piranha
solution is a strong oxidizer. Handle with extreme caution!) at room temperature. The
glass slides were rinsed copiously with ultrapure water, sonicated thrice in ultrapure water
to completely remove traces of sulfuric acid, sonicated once in absolute ethanol, and dried
under a stream of nitrogen gas.
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The clean glass slides were coated with titanium and gold by thermal evaporation (VE-90 vacuum evaporator, Thermionics Vacuum Products). The deposition of metal was initiated at a pressure of ∼3 × 10-7 Torr. An adhesion layer of titanium (99.99%) of 5 nm thickness was first deposited onto the glass at a constant rate of 0.01 nm s-1. The substrates were heated to ~200 oC with a UV lamp before the start of the gold evaporation. A 150 nm layer of gold (99.99%) was deposited while gradually varying the rate from 0.1 nm s-1 for the deposition of the first 65 nm to
0.01 nm s-1 for the final 40 nm. The substrate temperature was maintained between 200 oC and
240 oC during the gold deposition process by regulating the intensity of the UV lamp.
After cooling down to room temperature, the gold-coated glass slides were removed from the evaporator chamber and immediately immersed in ethanolic solutions of 0.2 mM CH3(CH2)nSH.
The gold substrates were incubated forDraft 16–24 h at room temperature in sealed incubation vials.
Prior to a measurement, the SAM-functionalized gold-coated slide was removed from the incubation solution, thoroughly rinsed with pure ethanol followed by ultrapure water, and dried under nitrogen.
Electrochemical Impedance Spectroscopy (EIS)
EIS measurements on the CH3(CH2)nSAu SAMs formed on gold bead electrodes were carried out using a three-electrode glass cell thermostatted with a circulation water bath and SP-200 potentiostat (BioLogic Science Instruments) equipped with an impedance analyzer. The electrolyte solution, 1.0 M NaClO4(aq), was deoxygenated by bubbling nitrogen into the electrochemical cell for 20 min before the start of an experiment. Measurements were carried out under a blanket of nitrogen at 22.0 ± 0.1 oC. Impedance spectra were acquired over a frequency span of 7 decades, from 1 MHz to 0.1 Hz, at 32 points per decade using an ac voltage amplitude of 10 mV and an
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applied voltage of -0.185 V versus Ag/AgCl, which is positive of the potential of zero charge
37 measured for CH3(CH2)nSAu SAMs in 0.1 M HClO4(aq) (-0.53 V to -0.51 V for n = 9–17) . SAMs
behave as ionic insulators at this dc potential.14 ZView software (version 3.4f, Scribner Associates)
was employed for complex nonlinear least-squares (CNLS) fitting of the impedance data to an
appropriate electrical equivalent circuit.
Contact Angle Measurements
Static contact angle measurements were carried out using a homemade setup consisting of a
micrometer syringe (Oakton Gilmont) to manually dispense a 2.0 L droplet of probe liquid onto
the SAM surface and a USB digital microscope to capture images of the liquid droplets on the
surface. 8–10 droplets of ultrapure waterDraft were deposited on each SAM-modified gold-coated slide.
Images of the droplets were analyzed using the contact angle plugin of Image J (NIH) to determine
the contact angle formed between the SAMs and water droplets.
Results and Discussion
Immittance Spectra of Ionic Insulating versus Leaky SAMs
We begin by comparing the impedance responses of three CH3(CH2)11SAu SAMs
whose degree of ionic permeability or leakiness follows the order SAM 3 SAM 2 SAM
1 (Table 3). The impedimetric complex plane plot (Fig. 2a) of the insulating (ion-blocking)
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SAM 1 is a nearly vertical line parallel to the y-axis that can described by the equivalent
circuit I, Re + CPE, over the entire frequency range of 1 MHz to 0.1 Hz. We also fitted the
impedance data of this SAM using the circuit II, Re + CPE|RSAM, to show that its resistance
to ion permeation is a factor of 10–100 higher than that of the leaky SAMs 2 and 3 (Table
3). By contrast, the Z–Z plots of the leaky SAMs 2 and 3 deviate from the vertical line
and exhibit pronounced curvature at frequencies ~10 Hz. These SAMs behave as a
capacitor contaminated by a resistiveDraft component related to current leakage at defect sites and must be fit using the equivalent circuit II.
Bode plots of the impedance magnitude Z of the three SAMs show no significant
differences (Fig. 2b). Z at 0.1 Hz is high at 2–3 M cm2. The slopes of the region of linear
dependence of Z on the logarithm of frequency (0.1 Hz–10 kHz) are -0.991, -0.989, and
-0.997 for SAMs 1, 2, and 3, respectively. The slope corresponding to purely capacitive
10 behavior is -1. The measured impedance is dominated by the solution resistance Re at
high frequencies so that Z becomes independent of frequency. A look at the frequency
dependence of the individual Z and Z components (Fig. 2c) reveals that the magnitudes
of Z at 0.1 Hz are comparable for SAMs 1 and 2, while that of the leakier SAM 3 is lower.
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The Z values at 0.1 Hz of the leakier SAMs 2 and 3 are significantly larger than that of
the ion-blocking SAM 1. The magnitude of Z follows the fitted value of RSAM, where a
2 2 higher RSAM corresponds to a lower Z: RSAM = 380 M cm (1), 13 M cm (2), and 3.9
M cm2 (3). This difference between the leaky SAMs 2 and 3 and insulating SAM 1 is
lost in the Bode plots of Z because the magnitude of Z is much larger than that of Z,
and in the case of the leakier SAM 3, a higher Z compensates the lower Z".
o Most significantly, the insulating SAMDraft 1 presents a phase angle of 89 between 1.0 and 0.1 Hz (Fig. 2d). An ideal capacitor exhibits of 90o at all frequencies. Current
leakage through the dielectric layer of the capacitor results in a deviation from 90o. The
phase angles of the leaky SAMs exhibit such a deviation; for SAM 2 decreases from
88o at 1.0 Hz to 83o at 0.1 Hz while for SAM 3 varies from 87o at 1.0 Hz to 73o at 0.1
Hz. The phase angle approaches zero at higher frequencies when Re dominates the total
impedance. Boubour and Lennox previously considered SAMs exhibiting a phase angle
≥ 88o at 1–10 Hz to be effectively free of defects.15 The minimum frequency they probed
was 1 Hz. We however find that a more stringent discrimination between insulating and
leaky SAMs requires probing lower frequencies, i.e., between 1 and 0.1 Hz. These
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frequencies are more in line with the rate of ionic conduction (permeation) processes in
-1 SAMs 2 and 3, given by the product (RSAMT) , which falls between 0.01 and 0.1 Hz. For example, although of SAM 2 is 88o at 1–10 Hz, it behaves as a leaky capacitor at lower
frequencies, and a Helmholtz-type model cannot be used to describe its impedance
response (Fig. 2a). Our analysis of more than 130 CH3(CH2)nS-modified gold electrodes
establishes that a of ≳ 89o at 1 Hz is generally required for the Au/SAM/electrolyte
15 interface to behave as a near ideal capacitorDraft down to 0.1 Hz. We now turn to the real C and imaginary C components derived from Z and Z,
respectively (Table 2), to reveal differences in the capacitive behavior of the three
CH3(CH2)11SAu SAMs. The capacitive complex plane plots (Fig. 3a) show semicircles of
similar diameters for SAMs 1 and 2, and hence directly report that these SAMs have
nearly identical capacitances, while SAM 3 has a larger (diameter) capacitance. The C
values at 0.1 Hz (Fig. 3b) yield static capacitances of 1.08 F cm-2 for the insulating SAM
1, and 1.07 F cm-2 and 1.30 F cm-2 respectively for the leaky SAMs 2 and 3. These
values are in close agreement with the T values obtained from CNLS fits of the impedance
data to the equivalent circuit II (Table 3). In addition to the semicircle, the complex plane
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plots of the leaky SAMs exhibit straight lines at low frequencies due to ion diffusion into
the films.23 A concomitant rise in C with decreasing frequency is observed at frequencies
~1 Hz (Fig. 3c). The maximum amplitudes of the relaxation peaks centered around 100
kHz in the Bode diagrams of C are approximately equal to one-half of the C values at
low frequency (indicative of a near homogeneous dielectric relaxation).38
The complex plane and Bode plots of the real ϵ and imaginary ϵ parts of the complex
relative permittivity 휖 (Fig. 3d-f) mirrorDraft those of the complex capacitance components. The ϵ values at 0.1 Hz (Fig. 3e) immediately show that the insulating SAM 1 and the less
leaky SAM 2 have nearly identical static dielectric constants, ϵSAM 1 = 2.00 and ϵSAM 2 =
1.96. The leakier SAM 3 has a higher dielectric constant, ϵSAM 3 = 2.35, due to the
presence of ions and water molecules in the SAM.
Overall, the frequency dependence of the different dielectric parameters shows that leaky and
insulating SAMs display differences at frequencies 10 Hz, especially between 1 and 0.1 Hz.
Notably, the immittance data indicates that, depending on the degree of ion permeability, leaky
and insulating SAMs do not always present significant differences in the static capacitance and
dielectric constant. These properties are not reliable indicators of the ionic insulating quality of the
SAM. Of the three measured parameters, Z, Z, and , the most direct diagnostic indicator of ion
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permeability is the phase angle at low frequencies. SAMs with a phase angle ≳ 89o at frequencies of 0.1–1 Hz can be considered defect-free for practical purposes, meaning that current leakage at monolayer defect sites is negligible.
Effect of the CH3(CH2)nS Chain Length on the Dielectric Properties of the SAM
Representative impedance plots of gold electrodes modified with CH3(CH2)nS SAMs of n = 9,
11, 13, 15, 17, and 19 are presented in Fig. 4a-c. Here we consider only SAMs that exhibit of
~89o at 1 Hz and behave as ionic insulatorsDraft to limit the alteration of the SAM dielectric response by current leakage at defect sites. A trend is not immediately apparent from the primary impedance data. By contrast, the corresponding capacitance plots (Fig. 4d-f) clearly resolve the chain length differences in the SAM dielectric characteristics. Both the diameters of the semicircles in the CC plots (Fig. 4d) and the C values at frequencies
~1 kHz (Fig. 4e), where C is largely independent of frequency, show outrightly the decrease of the static capacitance with increasing n expected for an increasing layer thickness (eq 4).39 The chain length dependence observed in the Bode plots of C extends to the Bode plots of C, where the maximum peak amplitude decreases with increasing n
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(Fig. 4f). The complex plane and Bode plots of ϵ and ϵ (Fig. 4g-i) show that 휖 spans a
narrow range.
Fig. 5a presents chain length dependent plots of the reciprocal of the capacitance of
the SAM derived from the (i) fitted T values ( = 0.991–0.994), referred to as CT, and (ii)
C values at 0.1 Hz, referred to as C0.1Hz. First, CT (1/CT) and C0.1Hz (1/C0.1Hz) are
statistically indistinguishable for a given n (95% confidence level). Second, the reciprocal
of the SAM capacitance variesDraft linearly with n, indicating that the
Au/S(CH2)nCH3/electrolyte interface obeys the Helmholtz ideal capacitor model, as per
eq 4. Dielectric constants were determined for each n from CT and C0.1Hz using the SAM
film thickness d calculated assuming a 30o tilt from the surface normal of all-trans
extended alkyl chains and a Au-S layer thickness of 0.19 nm.40, 41 Both capacitance
parameters yield mean ϵSAM values that are the same (within error) for a given n (Fig. 5b).
ϵSAM increases linearly from ~2.01 at n = 9 to ~2.20 at n = 15 and tends towards a limiting
value at longer chain lengths. ϵSAM is ~2.26 at n = 19. Values of ϵSAM determined using
23, 37, electrochemical or optical methods range from 2.0 to 2.6 for CH3(CH2)nSAu of n 9.
39, 41, 42
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The optical (high-frequency) dielectric constant of CH3(CH2)nSH liquids increases by
~0.003 per CH2 due to the higher dielectric constant of CH2 (ϵ = 2.164) versus CH3 (ϵ =
43, 44 1.399). The linear variation of ϵSAM of ~0.03 per CH2 from n = 9 and 15 is however a
factor of 10 greater, suggesting that the chain length dependence of ϵSAM stems from the
supramolecular organization within the SAM. Theoretical studies indicate that the density
of the surface-tethered alkyl chains influences the value of ϵ.27, 45, 46 Surface IR
spectroscopy measurements by PorterDraft and coworkers reveal that the conformational disorder of the alkyl chains, in the form of gauche bond defects, progressively decreases
with chain length, stabilizing at n ≳ 15, for which the CH2 peak positions indicate that the
chains are in a crystalline-like environment.39 The water contact angle (hydrophobicity)
also shows an evolution of the SAM structure and associated interface with chain length
o (Fig. 6). The chain length dependence of mirrors that of ϵSAM. plateaus at 109.6 0.3
for n ≳ 15, signaling a constant SAM structure for the longer chains, in agreement with the findings of Chen et al.47. A greater conformational order should favor closer packing
of the polymethylene chains in the SAMs and lead to a higher dielectric constant. The
dielectric constants of SAMs formed from the longest-chain n = 17 and 19 approach the
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48 value of 2.32 reported for high-density polyethylene. The observed increase in ϵSAM as
a function of n likely reflects an evolution of the alkyl chain order and packing density
within the SAM.
In contrast to our findings, Góes et al. report a decrease in ϵSAM from n = 7 to n = 11
for leaky SAMs as the ionic permeability decreases with chain length.23 This clearly
different chain length dependency highlights the need to use insulating SAMs for the
electrochemical determination of theDraft dielectric constant of the organic film.
Conclusions
We compared the non-faradaic electrochemical impedance response of the
CH3(CH2)nS-modified gold electrode with the mathematically-derived complex
capacitance and relative permittivity to characterize the ionic insulating and dielectric
properties of the SAM. The most unambiguous and direct indicator of the SAM leakiness
is the measured phase angle at low frequencies. SAMs with a phase angle ≳ 89o at
frequencies of 0.1–1 Hz effectively behave as ionic insulators, whose complex plane plots
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of the impedance and capacitance can be fit using a Helmholtz-type equivalent circuit.
The real parts C and ϵ respectively of the complex capacitance and relative permittivity derived from the imaginary part Z" of the complex impedance at low frequency (0.1 Hz) directly yield the static interfacial capacitance and SAM dielectric constant, eliminating the need to model the Au/SAM/electrolyte interface with an appropriate equivalent electric circuit. The complex plane and Bode plots of the real and imaginary components C and
C" resolve outrightly the chain lengthDraft dependence of the interfacial capacitance, unlike the analogous representations of the impedance components.
For ionic insulating SAMs, the reciprocal of the capacitance varies linearly with the
number of methylene units in the CH3(CH2)nS across the chain lengths investigated of n
= 9–19, indicating that the Au/SAM/electrolyte interface behaves as an ideal capacitor.
The SAM dielectric constant determined from the capacitance using the Helmholtz model increases with n and approaches the value reported for high-density polyethylene at n ≳
17. The chain length dependence of ϵSAM is consistent with the evolution of the alkyl chain conformation and packing within the SAM indicated by a previous surface IR
39 spectroscopy study and our contact angle measurements. The variation of ϵSAM with n
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has implications for SAM thicknesses measured by ellipsometry, in which a single
dielectric constant is typically used for all chain lengths.39, 49, 50
Our findings demonstrate that frequency-resolved capacitive (C, C") and permittivity
(ϵ, ϵ) analyses are more effective than traditional representations and equivalent circuit
modeling of the measured impedance at revealing the structure-related charging capacity
and dielectric characteristics of an organic film-modified electrode/electrolyte interface.
Future work will focus on characterizingDraft the density and size of the defects in SAMs presenting different degrees of leakiness and non-Faradaic immittance signatures by
using a redox probe in solution (Faradaic EIS).17, 51, 52
ACKNOWLEDGEMENTS
This research was supported by NSERC (Discovery and Discovery Accelerator
Supplement to A.B.). F.B.A. thanks the Tunisian Ministry of Higher Education and
Scientific Research for a scholarship.
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Draft
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Table 1. Impedance of Helmholtz- and Randles-type circuits53, 54
Table 2. Conversion of the measured impedance to capacitance and relative
permittivity10, 31, 38
Table 3. Fitted results of the Randles circuit elements for CH3(CH2)11SAu SAMs exhibiting
different ionic insulating character
Draft
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Figure 1. Schematic of the Au/S(CH2)nCH3/aqueous electrolyte interface at an applied potential positive of the potential of zero charge. Equivalent circuits used to fit the impedance response of a defect-free SAM (I) and SAM presenting sites for ion
permeation (II). Re is the electrolyte solution resistance, CPE is a constant phase element
used to model the capacitance of the SAM-modified interface, and RSAM is the resistance
to ion transport in the SAM. Complex plane impedance plots calculated using the
-7 -1 equivalent circuits I and II and the parametersDraft Re = 10 , T = 2 10 F s , = 0.993, 7 and RSAM = 5 10 . The lower highlighted inset is a zoom of the impedance data between 1
MHz and 1 Hz.
Figure 2. Impedance responses for CH3(CH2)11SAu SAMs of differing ionic permeability. (a)
Impedimetric complex plane plot. (b) Bode plot of the impedance magnitude |Z|. (c) Bode plot of
Z′ and Z′′. (d) Bode plot of the phase angle φ. Impedance spectra were acquired at -0.185 V vs
Ag/AgCl in 1.0 M NaClO4(aq). Symbols are the experimental data and solid lines are the results of
CNLS fits of the data using the equivalent circuit Re + RSAM∥CPE.
Figure 3. Capacitance (C′, C′′) and relative permittivity (ϵ′, ϵ′′) spectra of
CH3(CH2)11SAu SAMs of differing ionic permeability. (a) Capacitive complex plane plot.
(b) Bode plot of the real component C′. (c) Bode plot of the imaginary component C′′: dark
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symbols are the raw data and light symbols are the data after subtraction of Re. (d)
Complex plane plot of the relative permittivity. (e) Bode plot of the real component ϵ′. (f)
Bode plot of the imaginary component ϵ′′. Symbols are the experimental data and solid
lines are the results of CNLS fits of the impedance data using the equivalent circuit Re +
RSAM∥CPE.
Draft Figure 4. Immittance spectra of gold electrodes modified with CH3(CH2)nS of n = 9, 11,
13, 15,17, and 19. (a)–(c) Impedance, (d)–(f) capacitance, and (g)–(i) relative permittivity.
Impedance spectra were acquired at -0.185 V vs Ag/AgCl in 1.0 M NaClO4(aq). Symbols are the
experimental data and solid lines are the results of CNLS fits of the impedance data using the
equivalent circuit Re + RSAM∥CPE.
-1 -1 - Figure 5. Chain length dependence of (a) reciprocal of the capacitance C (CT or C0.1Hz
1 ) and (b) SAM dielectric constant ϵSAM determined from CT or C0.1 Hz and the SAM
thickness calculated for all-trans extended chains tilted by 30o from the surface normal.
Each data point is the mean value of at least 12 different SAMs. Error bars represent the
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-1 95% confidence intervals. Dashed line in (a) is a linear regression of the CT vs n data: r2 = 0.9984. Dashed line in (b) is a guide to the eye.
Figure 6. Comparison of the chain length dependencies of the static contact angle of
water and SAM dielectric constant ϵSAM. Inset shows the contact angle of a sessile water drop on the SAM-functionalized gold surface. Each data point for is the mean value of at least 4 different SAMs. Error bars represent the 95% confidence intervals.
Dashed line is a guide to the eye. Draft
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Table 1. Impedance of Helmholtz- and Randles-type circuits53, 54
α 푐훼 푅SAM (1 + (ωTRSAM) cα) 푍′(휔) = + 푅 훼 e Z(ω) = α 2α + 푅e 푇휔 1 + 2(ωTRSAM) cα + (ωTRSAM)
푠훼 푍(휔) = ― α 푇휔훼 Draft 푅SAM(ωTRSAM) sα Z(ω) = α 2α 1 + 2(ωTRSAM) cα + (ωTRSAM)
The angular frequency ω = 2πf, where f is the frequency in Hz. T and are the CPE
parameter and exponent (eq 5). c = cos(/2) and s = sin(/2).
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Table 2. Conversion of the measured impedance to capacitance and relative permittivity10, 31, 38
Complex quantity Real part Imaginary part
Z() Z() Ĉ() = C′() + jC″() ― ― C'( ) = 2 C″( ) = 2 ωZ(ω) ωZ(ω)
휖() = ϵ′() + 휖 ― Z ( ) d 휖 ― Z ( ) d (ω) = 2 (ω) = 2 jϵ″() ωZ(ω) oA ωZ(ω) oA Draft - ω = 2πf, where f is the frequency in Hz. o is the permittivity of free space (8.85419 × 10 12 F m-1), A is the electrode area, and d is the film thickness.
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Table 3. Fitted results of the Randles circuit elements for CH3(CH2)11SAu SAMs exhibiting different ionic insulating character
SAM Re RSAM CPE φ 1Hz φ 2 2 o / Ω cm / MΩ cm / 0.1Hz / T o / μF sα-1 cm-
2
2.06±0.0 0.9912±0.000 1 380±293 1.09±0.01 89 89 1 1
3.07±0.0 0.9893±0.000 2 12.9±0.3 1.09±0.00 88 83 1 1
2.73±0.0 0.9976±0.000 3 3.9±0.1 1.31±0.02Draft 87 73 The 3 1
uncertainties in Re, RSAM, T, and are from the CNLS fits of the impedance data.
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