Technology Report pubs.acs.org/jchemeduc
Development and Use of an Open-Source, User-Friendly Package To Simulate Voltammetry Experiments Shuo Wang,*,†,‡ Jing Wang,§ and Yanjing Gao†,‡ †
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China § School of Physical Science and Technology, Shanghai Tech University, Shanghai 201204, China ‡
S Supporting Information *
ABSTRACT: An open-source electrochemistry simulation package has been developed that simulates the electrode processes of four reaction mechanisms and two typical electroanalysis techniques: cyclic voltammetry and chronoamperometry. Unlike other open-source simulation software, this package balances the features with ease of learning and implementation and can run on mainstream operating systems. In an elctroanalysis lecture for graduate students, we have simulated the cyclic voltammetry of an electron transfer reaction with varied scan rates. The dynamical concentration profiles were demonstrated in an animation to help students understand the relation between currents and evolving concentration profiles, and the relations between peak currents and scan rates were also discussed. KEYWORDS: Upper-Division Undergraduate, Graduate Education/Research, Chemical Engineering, Computer-Based Learning, Electrochemistry, Kinetics
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INTRODUCTION
THEORETICAL BACKGROUND The model contains a single one-dimensional domain of length L = 6 Dt , where D is diffusion coefficient of the analyte and t is the simulation time. In the presence of a large quantity of supporting electrolyte, the transport and reaction of the chemicals in the bulk solution are described by the diffusion reaction equation:
Voltammetry is based on the variation of the potential of the working electrode in the electrolyte solution as electrons are transferred between the electroactive species and the electrode, with the resulting current being recorded. For design and research, voltammetry is a valuable technique because information about both the electrochemical reactivity and the transport properties of a system can be extracted simultaneously. For all its importance, voltammetry is a difficult technique to understand. Especially for students without good training in mathematical physics, it is not easy to understand the influence on the voltammograms of either the different kinetic parameters of the reactions (electrochemical rate constant, diffusion coefficient, chemical reaction rate, etc.) or the experimental conditions (electrode potential, scan rate, etc.). For these reasons, a number of toolkits have been developed to simulate voltammetry. For example, Stephania Messersmith has introduced a chemistry experiment that utilizes DigiSim software to simulate cyclic voltammetry for upper-division undergraduate students.1 However, commercial software is expensive and may be cost-prohibitive for many students or teachers. A literature review shows a number of open-source toolkits for simulation.2,3 Carlo Nervi has developed a program to perform general electrochemical simulations and fitting of experimental data.4 Jay Brown has created an Excel spreadsheet to simulate cyclic voltammetry.5,6 Herein we describe an opensource, user-friendly voltammetry simulator that demands no special computational skills from the user and thus is suitable for physical chemistry, instrumental analysis, or upper-division electrochemistry courses. © XXXX American Chemical Society and Division of Chemical Education, Inc.
∂c = DΔc + R(c) ∂t
(1)
where c is the concentration of the chemical species and R(c) is the consumption or generation rate of the chemicals due to reaction. At the bulk boundary, x = L, we assume that there is no mass flux, i.e., ∂c =0 ∂x
(2)
At the electrode surface, x = 0, the current for the electron transfer reaction (O + ne− = R) is given by the Butler−Volmer equation: ⎡ ⎛ α nFη ⎞ ⎛ −αcnFη ⎞⎤ ⎟ − c exp⎜ ⎟⎥ I = AFk 0⎢c R exp⎜ a O ⎝ BT ⎠ ⎝ BT ⎠⎦ ⎣
(3)
where A is the electrode area, k0 is the heterogeneous rate constant of the reaction, αa is the anodic charge transfer coefficient, αc is the cathodic transfer coefficient, n is the number of electron transferred, B is the gas constant, F is the Received: December 19, 2016 Revised: August 13, 2017
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DOI: 10.1021/acs.jchemed.6b00986 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Technology Report
Figure 1. User interface of the simulator.
Faraday constant, T is the absolute temperature, and η is the overpotential at the working electrode: η = E − E°
The main features of this software are summarized in Table 1. Brief documentation is given in the Supporting Information.
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Table 1. Main Features of the Software
where E is the potential applied to the working electrode and E° is the standard reduction potential of the redox couple of species O and R. According to Faraday’s laws of electrolysis, the flux of the reactant species is −N =
I AFn
Feature
Description
Reaction mechanisms
Four predefined reaction mechanisms (see details in the text). The reactants are adsorbed on the surface of the electrode or distributed in the bulk solution. Initial concentration of the reactant, standard redox potential, rate of electron transfer, concentration, diffusion coefficient, homogeneous rate constants, temperature, and experimental techniques, including cyclic voltammetry and chronoamperometry. Find the peaks in a voltammogram; fit the experimental voltammogram manually to get the reaction parameters Save simulation parameters and results; read simulation parameters. Create the current versus time curve or current versus potential curve; output a video of the dynamical concentration profiles. Superposition of multiple plots.
Simulation parameters
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The applied potential for voltammetry studies is either a triangular cyclic form (cyclic voltammetry simulation) or a step function (chronoamperometry simulation). The above model (eqs 1−5) was implemented in MATLAB and incorporated into a graphical user interface (see the Supporting Information for the source code). The whole program was compiled to obtain a standalone application that can run on mainstream operating systems. The user interface of the simulator is shown in Figure 1. Four reaction mechanisms are included in this simulator: (1) a simple electron transfer reaction (E); (2) an electron transfer reaction followed by a chemical reaction (EC); (3) an electron transfer reaction followed by a chemical reaction and then an electron transfer reaction (ECE); (4) an electron transfer reaction followed by a catalysis reaction (EC′). The mechanisms are presented with following reactions: E:
R → O + e−
EC:
R → O + e− , −
Analysis tools File commands Results outputs Results view
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A CLOSER LOOK AT THE CYCLIC VOLTAMMETRY OF AN ELECTRON TRANSFER REACTION In an electroanalysis lecture for graduate students, we took the example of the cyclic voltammetry of the reversible electron transfer reaction R → O + e−. As shown in Figure 2, four voltammograms were simulated at four successive scan rates, from 1 mV/s to 1 V/s. The current increases with the scan rate, but the voltammograms have a similar qualitative “doublepeaked” appearance. To help understand this feature, the dynamical concentration profiles were demonstrated in an animation. Initially, at reducing potentials, the oxidation reaction is not driven, and the current is negligible. As the potential moves toward the reduction potential of the redox couple, the oxidation reaction is accelerated, and the current
O → products S → T + e−
ECE: R → O + e ,
O → S,
EC′ : R → O + e−,
O + Y → R + products B
DOI: 10.1021/acs.jchemed.6b00986 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Technology Report
Figure 2. Simulated cyclic voltammograms of a reversible electron transfer reaction recorded at different scan rates from 1 V/s to 1 mV/s (bottom to top). It should be noted that the peaks of all anodic currents are located at about 33 mV.
Figure 3. Snapshots of diffusion profiles for the reversible electron transfer reaction at 32.7 mV (when the peak currents occur): (a) scan rate = 1 V/ s; (b) scan rate = 0.1 V/s.
To understand the dependence of the peak current on the scan rate, the concentration profiles at 32.7 mV (where the peak current occurs) for different scan rates (1 V/s and 0.1 V/ s) are compared in Figure 3. For the higher scan rate, the concentration varies from the bulk to the surface over a narrow region, i.e., a shorter-ranged diffusion layer is established, which gives rise to a larger current. The students were asked to do the simulation themselves, comparing the videos to gain insight into the relation between the current and the evolving concentration profile. They should
increases. In the dynamical concentration profiles (Figure 3), one can see that the oxidation reaction has consumed the reactant at the electrode surface, and the current becomes limited by the rate of transport of R toward the working electrode. Therefore, a peak current is observed. Upon sweeping back toward more reducing potentials, the reconversion of O into the original R gives a cathodic current. The depletion of O causes a cathodic peak current, and reconversion thereafter proceeds at a diffusion-controlled rate. C
DOI: 10.1021/acs.jchemed.6b00986 J. Chem. Educ. XXXX, XXX, XXX−XXX
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note that as the current increases, the concentration at the electrode surface (x = 0) is driven to almost zero, after which the concentration gradient decreases under diffusion, as does the current. The peak current (Ip) is an important indicator in electroanalysis: since the magnitudes of the two peak currents are equal for a reversible reaction, Ip is a common diagnostic variable in voltammetry. Its value is theoretically given by the Randles−Ševciḱ equation:7,8 ⎛ nFvD ⎞1/2 ⎟ Ip = 0.4463nFAc0⎜ ⎝ RT ⎠
Technology Report
REFERENCES
(1) Messersmith, S. J. Cyclic Voltammetry Simulations with DigiSim Software: An Upper-Level Undergraduate Experiment. J. Chem. Educ. 2014, 91 (9), 1498−1500. (2) Van Ryswyk, H. Simulation of single-step chronoamperometry via spreadsheet. J. Chem. Educ. 1991, 68 (11), A283. (3) Sanchez, G.; Codina, G.; Aldaz, A. A voltammetry experiment by digital simulation. J. Chem. Educ. 1991, 68 (6), 489. (4) Nervi, C. Electrochemical Simulations Package, version 2.4, 1998. http://lem.ch.unito.it/chemistry/esp_manual.html (accessed Aug 8, 2017). (5) Brown, J. H. Analysis of Two Redox Couples in a Series: An Expanded Experiment To Introduce Undergraduate Students to Cyclic Voltammetry and Electrochemical Simulations. J. Chem. Educ. 2016, 93 (7), 1326−1329. (6) Brown, J. H. Development and Use of a Cyclic Voltammetry Simulator To Introduce Undergraduate Students to Electrochemical Simulations. J. Chem. Educ. 2015, 92 (9), 1490−1496. (7) Bard, A. J.; Faulkner, L. R.; Leddy, J.; Zoski, C. G. Electrochemical Methods: Fundamentals and Applications; Wiley: New York, 1980; Vol. 2. (8) Compton, R. G.; Banks, C. E. Understanding Voltammetry; World Scientific: Singapore, 2007.
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where v is the scan rate and c0 is the initial concentration of the electroactive species. The students were encouraged to do the simulation of a quasi-reversible electron transfer reaction (k0 = 10−5 m/s) with different scan rates. They should find that the peak current still scales with the square root of the scan rate, but the exact value of the current deviates from the Randles−Ševciḱ equation (see this example in the student handout). This square root relation is a common verification that the current is diffusion-controlled, which breaks as the electroactive species adsorb on the electrode surface, as can be easily verified using this simulator.
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CONCLUDING REMARKS We have developed a voltammetry simulation package with a graphical user interface that is helpful for lecturing on some basic electrochemical processes. We have used this package in an electroanalysis lecture to help students gain insight into chemistry in a voltammogram. By simulation of cyclic voltammetry at different scan rates, different transport phenomena were observed with different time scales. This package can also help chemists to compare voltammetry with theoretical simulations to get quantitative information from experiments. We hope to incorporate more reaction mechanisms and improve the fitting function in a future work.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.6b00986. Instructor’s notes and student handout (PDF, DOCX) Details about installation and use of the simulator (PDF, DOCX) Source code for the simulator (ZIP) Supporting files for the simulator (ZIP) CSV files for various examples (ZIP)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Shuo Wang: 0000-0003-4895-376X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S.W thanks Rong Wang (Shanghai Normal University) for useful discussions about the development of the software and the anonymous reviewers for their suggestions. D
DOI: 10.1021/acs.jchemed.6b00986 J. Chem. Educ. XXXX, XXX, XXX−XXX
