Demonstration of Superiority of the Marcus-Hush Electrode Kinetic

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Demonstration of Superiority of the Marcus-Hush Electrode Kinetic Model in the Electrochemistry of Dissolved Decamethylferrocene at a Gold Modified Electrode by Fourier Transformed Alternating Current Voltammetry Jiezhen Li, Gareth F. Kennedy, Alan M. Bond, and Jie Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01324 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry

Demonstration of Superiority of the Marcus-Hush Electrode Kinetic Model in the Electrochemistry of Dissolved Decamethylferrocene at a Gold Modified Electrode by Fourier Transformed Alternating Current Voltammetry Jiezhen Li,† Gareth F. Kennedy,† Alan M. Bond*,†,‡ and Jie Zhang*,†,‡ † School of Chemistry, Monash University, Victoria 3800, Australia ‡ ARC Centre of Excellence for Electromaterials Science, School of Chemistry, Monash University Corresponding Author *[email protected] *[email protected]

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ABSTRACT Fourier transformed alternating current voltammetry is used to compare the applicability of the Butler-Volmer (BV) and Marcus-Hush (MH) models of electrode kinetics (k0) to an outer sphere electrode process where both oxidized and reduced species are soluble. According to numerical simulations, differences between the two models can be revealed clearly by analysis of the AC harmonics when the values of k0 and reorganization energy are sufficiently small. Experimentally an Au electrode coated with self-assembled octanethiol monolayers was introduced to decrease the rate of the DmFc0/+ (DmFc = decamethylferrocene) process, a wellknown outer sphere process. Based on a comparison of the computationally generated best fits, it was demonstrated that the MH model provides substantially better agreement with the experimental data than the BV model for the DmFc0/+ process, unlike some other examples in the literature that favor the BV model.


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INTRODUCTION In dynamic forms of electrochemistry, the empirical Butler-Volmer (BV)1-2 theory is widely to describe the potential dependence of the kinetics of electron transfer processes. Advantages include mathematical simplicity and the fact that it commonly provides an acceptable prediction of current-potential relationships determined experimentally for dissolved and surface confined electroactive species under voltammetric conditions. In the BV theory3, the electrode kinetics is related to the standard electron transfer rate constant (k0) at the formal reversible potential (Ef0) and the electron transfer coefficient (α). For a simple one-electron oxidation process, R ⇌ O + e ( , )

(1)

the oxidation and reduction rate constants ( , ) are functions of , α, Ef0 and applied potential (E):

= ()

(2)

=

(3)

where = ( − )/ , F is the Faraday constant, R is the universal gas constant and T is the absolute temperature. A more advanced theory available to describe the kinetics of electron transfer process is known as the Marcus-Hush (MH) model,3 which relates and to the reorganization energy (λ). According to the MH model, the greater the λ value, the greater the activation energy and the smaller the standard rate constant, and vice versa.3 In the MH model, the oxidation and reduction rate constants are described by the relationships: &

((,)∗ )

%$ = ' ((,)∗ ) &

((,)∗ )

%$ = ' ((,)∗ )

(4) (5)


3


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where +∗ is dimensionless reorganization energy, defined as +∗ = +/ ; I(, +∗ ) is an integral of the form: 1(21&)'

∗)

-(, +

=

; / [ 34∗ ] 1 cm/s)23 and small λ (~0.8 eV) values in dimethylformamide (0.1M tetrabutylammonium hexafluorophosphate)24. Importantly, the bulky methyl groups on the two cyclopenadienyl rings can minimize the probability of DmFc penetrating into the monolayer layer (pinhole effect). The use of FTACV provides access to data on a widely varying time scale from a single experiment,25 which provides information needed (up to six harmonics) to distinguish the two models. Previously, most comparisons of experimental and simulated FTACV data used to extract kinetic parameters were undertaken by a time-consuming heuristic method,26-27 and the results subject to the criteria used by the operator to determine the best agreement between experiment and simulation. In this study, by scripting the simulation software to cover wide ranges of kinetic parameters, the best fit can be found automatically and far faster to produce a result with the required statistical significance.28

EXPERIMENTAL SECTION


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Chemicals All chemicals used were of reagent grade quality or better. Decamethylferrocene (DmFc, 97 %, Sigma-Aldrich), propylene carbonate (≥ 99 %, Sigma-Aldrich), acetonitrile (CH3CN, 97 %, Sigma-Aldrich) and octanethiol (≥ 98.5 %, Sigma-Aldrich), ethanol (≥ 99.5 %, Univar), nitric acid (HNO3, 65 % – 70 %, Univar) and hydrochloric acid (HCl, 32 %, Univar) were used as supplied by the manufacturer. Tetrapropylammonium tetrafluoroborate ([TPA][BF4]) was prepared by a metathesis reaction between sodium tetrafluoroborate (Na[BF4], Sigma-Aldrich) and tetrapropylammonium bromide ([TPA]Br, Sigma-Aldrich) in CH3CN and recrystallized from ethanol. Preparation of Octanethiol Modified Au Electrodes Prior to the modification with octanethiol, the Au electrodes were polished with an aqueous 0.05 mm alumina slurry on a clean polishing cloth, rinsed with water, sonicated thoroughly in water to remove alumina, and etched using dilute aqua regia (3:1:4 concentrated HCl : concentrated HNO3 : H2O) for approximately 5 min. Immediately after being etched, the electrodes were rinsed with ethanol and then immersed in a 50 mM solution of the octanethiol in ethanol for no less than 12 h to form the desired coating. Electrochemical Experiments Following self-assembly, the octanethiol modified Au electrode was carefully rinsed with ethanol and then transferred into the electrochemical cell. Direct current (DC) cyclic voltammetric experiments were undertaken with a CHI 760E electrochemical workstation (CH Instruments, Texas, USA). Large amplitude Fourier transformed alternating current voltammetry (FTAC) voltammetric experiments were undertaken with a home built instrument29 using an applied sine wave perturbation superimposed onto the DC potential ramp. After data collection,


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the total DC plus AC current was subjected to Fourier transformation to obtain the power spectrum. After selection of the frequency band of interest, inverse Fourier transformation was used to generate the required DC or AC harmonic components.29 All electrochemical studies were carried out at 22 ± 2 °C using a standard three electrode electrochemical cell setup. The working electrode was gold (Au, nominal diameter = 1.0 mm, eDAQ) for electrode kinetic studies or glassy carbon (GC, nominal diameter = 1.0 mm, eDAQ) for diffusion coefficient measurements. Platinum wires were used as the auxiliary and quasi-reference electrodes. The quasi-reference electrode potential was calibrated against that for the DmFc0/+ process. The effective electrode area (A) of the Au electrode (0.0082 cm2) was calculated from analysis of a plot of DC peak current versus the square root of scan rate for the oxidation of 1.0 mM Fc in CH3CN (0.1 M [Bu4N][PF6]) using the Randles-Sevcik relationship3 and the known diffusion coefficient (D) of 2.24 × 10-5 cm2 s-1 for Fc30 under these conditions. Simulations of the FTACV data were undertaken with MECSim (Monash Electrochemistry Simulator) software (http://www.garethkennedy.net/MECSim.html). DC cyclic voltammetric simulations were undertaken using DigiSim software (version 3.03, Bioanalytical Systems, Inc.) A least-squares correlation (LS) was used to quantify the agreement between experimental and simulated data. LS definition along with the procedure of theory-experiment comparison by computer can be found in Supporting Information.

RESULTS AND DISCUSSION Theoretical Comparison Between the MH and BV Models by FTACV Comparisons between the MH and BV models were initially investigated theoretically for the reaction given in Equation (1) with both O and R being soluble in order to guide the choice of optimal parameters for experimental evaluation. Figure 1 shows the theoretical FTACV 6th


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harmonic component comparisons of the MH model with λ = 1.0 eV and the BV one with > = 0.50. For a large k0 value (Figure 1(a)), the difference in the two models is essentially indistinguishable since the process is close to reversible, but with decreasing k0 values (Figure 1(b to d)) the differences become increasingly more obvious. In all cases, the current magnitudes derived from the MH model are smaller than those predicted by the BV one. In Figure 2, the 6th harmonic components of FTACV derived from the MH model as a function of + value as well as that obtained from the BV model with > = 0.50 for a process with k0 of 0.0020 cm s−1 are shown for comparison. Clearly, for small + values, differences between the BV and MH models are more apparent under the conditions described in the figure caption. From evaluation of Figures 1 and 2, it is concluded that slow electrode kinetics and small reorganization energy are required in order to readily differentiate the models.

Figure 1. Simulated 6th harmonic FTACV for BV (blue), > = 0.50 and MH (red), λ = 1.0 eV. Other simulation parameters are frequency (f) = 10.0 Hz, amplitude (∆E) = 160 mV, uncompensated resistance (Ru) = 0 Ω, capacitance (Cdl) = 0 µF cm−2, diffusion coefficient (D) =


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1.0 × 10-5 cm2 s−1, electrode area (A) = 0.010 cm2, C = 1.0 mM, v = 0.05 V s−1, T = 295 K, Ef0 = 0 V, k0 = 0.050 (a), 0.010 (b), 0.0050 (c) and 0.0020 (d) cm s−1. The effects of k0 and > for the BV model, along with k0 and λ for MH model with FTACV are shown in Figures S1 to S4. In Figure S1, the current magnitude decreases with a decrease in the k0 value from 1st to 6th harmonic components with the BV model. Changing the > value (Figure S2) only affects the symmetry of the forward and backward processes. That is the shapes change from symmetrical (> = 0.50) to asymmetrical (> = 0.60 or 0.40) while the current magnitudes remain similar. Both k0 and λ values can affect the current magnitude in the MH model with smaller k0 or λ values both giving smaller currents (Figures S3 and S4). However, it should be noted that variation of the λ value does not alter the symmetry. Consequently, if an experimental system is fitted accurately using the MH model (e.g. with k0 = 0.0020 cm s-1 under the conditions given above), then it is not likely that a set of parameters exists which will enable the same data to be accurately fitted using the BV model. BV

Increasing λ


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Figure 2. Simulated 6th harmonic FTACV for BV (dotted line), > = 0.50 and MH (solid lines), λ = 5.0 eV, 2.0 eV, 1.0 eV and 0.50 eV. k0 = 0. 0020 cm s−1 and the values for other simulation parameters are given in the caption to Figure 1. Stability of Octanethiol on Au Electrode in Propylene Carbonate It has been reported that attempts to maintain alkanethiolate monolayers as blocking layers in organic solvents were problematic, due to a tendency of the alkanethiolates to detach from the surface.21 In this literature report, a DC cyclic voltammetric process with large peak-to-peak separation was initially observed at an alkenthiolate modified Au electrode for the Fc0/+ process that is fast at a bare Au electrode, confirming that the alkenthiolate monolayer impedes electron transfer between the electrode and the redox couple. As the potential was cycled, the separation between the oxidation and reduction peaks decreased and eventually had the characteristics predicted for a reversible electron transfer process, indicating that the alkenthiolate monolayer gradually becomes detached from the electrode surface. In order to prevent detachment, 500 µM of octanethiol was added to the propylene carbonate electrolyte solution.21 Given the strong affinity of thiols for gold, even such a small concentration of octanethiol in solution can be used to effectively prevent octanethiol from leaving the electrode surface (Figures S5−S7), thereby maintaining the monolayer intact. Consequently, with 500 µM of octanethiol presented in the solution, a stable DC cyclic voltammogram without any peak shift is observed for at least 10 cycles for the DmFc0/+ process as shown in figure S8. In addition, any pinhole effect if present also can be revealed from analysis of the higher order harmonics. The high kinetic sensitivity associated with higher order harmonics will allow a reversible electron transfer process at pinholes to be detected even when the pinhole density is low. Figure S9 shows a comparison of simulated 6th harmonic FTACV data for a reversible case and a slow kinetics with same k0 value


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as measured in this study. The difference in current magnitude between these two processes is significant. The ratio of peak currents between the reversible and quasi-reversible processes is as high as 250. Experimental Comparison Between the MH and BV Models to DmFc0/+ Process on an Octanethiol Modified Au Electrode by FTACV The DmFc0/+ couple exhibits a reversible one-electron process at a bare glassy carbon (GC) electrode (facile electron transfer kinetics).23 The diffusion coefficients (D) of DmFc in propylene carbonate (0.10 M tetrapropylammonium tetrafluoroborate ([TPA][BF4])) was found to be 2.4 × 10−6 cm2 s−1 based on the Randles-Sevcik equation,3 in good agreement with the literature value31 of 1.8 × 10−6 cm2 s−1 in propylene carbonate (0.50 M tetrabutylammonium perchlorate). A reversible process with a similar D value was also obtained with a bare Au electrode. The k0 values associated with the DmFc0/+ process in propylene carbonate (0.10 M [TPA][BF4]) at an octanethiol modified Au electrode were determined by FTAC voltammetry using a sine wave perturbation with ∆E = 160 mV and f = 3.99 Hz (The reason for choosing large ∆E and low f values can be found in Figures S10−S11 and the relevant text). The k0 values were extracted from

comparisons of experimental and simulated data undertaken

computationally using a bash script to provide a wide range of kinetic parameters in order to find the best fit (see Experimental Section for the details of parameter optimization). In this case, the unknown kinetic parameters are k0 and > with the BV model or λ with the MH model with Ef0 known from reversible data obtained at a bare GC/Au electrode. The uncompensated resistance (Ru) was determined accurately from impedance analysis and taken into account in the simulations. The agreement between experiment and simulation was quantified by the least-


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squares correlation (LS). Figure 3 shows an example of a LS comparison between experimental and simulated data based on the MH model, with the best fit given by a white circle. Figure 4 shows the experimental data along with simulations with the computationally derived best fit values for the BV and MH models. Parameters used in the experiment-simulation comparisons are provided in Table 1. For the BV model (Figure 4 (a-g)), a k0 value of 0.001 cm s-1 and a > value of 0.50 were obtained by LS analysis with a maximum LS value of 74.5 %. Figure 4 (h-n) shows the significantly superior agreement between experiment and simulation across all DC and AC components using the MH model. k0 and λ values were estimated to be 0.0017 cm s-1 and 0.40 eV. This simulation yielded a LS value of 93.5 %, which is far superior to that achieved with the BV fit. The derived λ value is in good agreement with the estimated λ (0.53 eV) calculated from Marcus theory taking the radius of DmFc to be 6.5 Å.31 Since the Au electrode is covered by octanethiol, electron have to tunnel a long distance.6 Therefore, this increased distance reduces the electronic coupling between the DmFc and the electrode surface resulting in(favoring) a non-adiabatic electron transfer.32


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Figure 3. Least squares comparison between simulation results based on the MH model and experimental data obtained from 1.0 mM DmFc in propylene carbonate (0.10 M [TPA][BF4], 500 µM octanethiol) at an octanethiol modified Au electrode, as a function of two unknown parameters, k0 and λ. Best fit (k0 = 0.0017 cm s-1 and λ = 0.40 eV) based on the parameters optimization are shown as a white circle. FTAC voltammetric data were also acquired with a lower bulk concentration of DmFc, 0.2 mM, in order to lessen the influence of the IRu effect. The results are summarized in Table 1 and comparisons of experimental and simulated data using the BV and MH models are presented in Figure S12 in the Supporting Information. Again, the BV model gives a much large discrepancy in the higher order harmonics (LS = 76.5 %) while excellent agreement (LS = 94.3 %) is observed between experiment and simulation using the MH model, giving a best fit k0 value of 0.0017 cm s-1 and λ of 0.37 eV, both values being very similar to those obtained with a 1.0 mM concentration.


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Figure 4. Comparison of the simulated (red) data based on the BV (a-g) or the MH model (h-n) with experimental (blue) FTAC voltammograms, obtained from 1.0 mM DmFc in propylene carbonate (0.10 M [TPA][BF4], 500 µM octanethiol) at an octanethiol modified Au electrode. (a, h) aperiodic DC component, (b–g, i-n) 1st to 6th AC harmonic components. The simulation parameters are f = 3.99 Hz, ∆E=160 mV, Ru = 2020 Ω, Cdl = 3 µF cm-2, T = 295 K, A = 8.2 × 10-3 cm2, D = 2.4 × 10-6 cm s-1, Ef0 = 0 V vs. DmFc0/+, k0 = 0.0010 cm s−1 and > = 0.50 for BV model and k0 = 0.0017 cm s−1 and λ = 0.40 eV for MH model.

Model

C (mM)

Ru (Ω)

ACS Paragon Plus Environment 0

Cdl (µF cm-2)

Ef (V)

(cm s-1)

a

λ(eV)

15


BV

MH

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1.0

2020

3.0

0

0.0010

0.50

naa

0.20

1980

2.8

0

0.0009

0.50

naa

1.0

2020

3.0

0

0.0017

naa

0.40

0.20

1980

2.8

0

0.0017

naa

0.37

Table 1. Electrode kinetic parameters used to simulate the voltammetry obtained at an octanethiol modified Au electrode for DmFc (1.0 mM) in propylene carbonate (0.10 M [TPA][BF4], 500 µM octanethiol). a

na = not applicable

CONCLUSION In summary, the electrode kinetics of the DmFc0/+ process in propylene carbonate at an octanethiol modified Au electrode has been evaluated by FTACV and the suitability of the BV and MH models for electrode kinetics was compared. Under the relevant conditions, FTACV provides a strong distinction between the two models. The use of the thiol layer slows the electrode kinetics allowing significant differences to be observed for the two models. Moreover, the presence of the thiol layer minimizes the double layer effect, enabling the electrode kinetics to be measured without requiring a double layer correction. By comparing the computationally generated best fits to the experimental data, it is convincingly demonstrated that the MH model provides superior agreement with the experimental data. In addition, the MH model provides a more insightful model from which the physically meaningful λ parameter can be derived. It is concluded that the MH model is substantially preferred for an ideal outer sphere process where both reduced and oxidized forms are soluble.

ASSOCIATED CONTENT


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Supporting Information Theory-Experiment Comparison, Conditions optimization and Figures S1-S12 (PDF) AUTHOR INFORMATION Corresponding Author *[email protected] *[email protected] ORCID Alan M. Bond: 0000-0003-2493-5209 Jie Zhang: 0000-0002-1113-5205 Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The authors gratefully acknowledge the Australian Research Council for financial support.

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Demonstration of Superiority of the Marcus-Hush Electrode Kinetic

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