Visualization of Electrochemical Behavior under Finite Conditions using JAVA and its Application for Assisted Learning
Hidenobu SHIROISHI, Tomoyo NOMURA, Kazunori ISHIKAWA, Sumio TOKITA and Masao KANEKO
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1 Introduction
Polymercoated electrodes dispersing functional molecules have been studied during the last two decades [1  4]. These electrodes have wide application such as chemical sensors [5], electrocatalysis [6], and energy conversion devices [7]. It is important to study the charge propagation in polymer membranes for developing highperformance devices.
Needlesstosay a polymer layer coated on an electrode has a finite thickness. This causes a discrepancy in electrochemical results between the finite condition and the infinite condition from which equations in the solution system are derived. Another difference between these two systems is that the diffusion of molecules in a polymer layer is much slower than that in a solution. The contribution of the charge hopping mechanism to the whole charge propagation in a polymercoated electrode would become greater than that in a solution system, so that equations in a solution cannot be applied to the polymercoated electrode system depending on the situation. Under such finite conditions, it is difficult to solve diffusion equations, when the condition is altered a little. Thus an environment to analyze an electrochemical behavior easily and simply is needed.
In an educational respect, it is a problem to teach electrochemistry attractively because of a lot of abstruse equations. It is instructive to make an environment where every student can perform virtual electrochemical measurements using a network. Such a program has to satisfy the following requirements.

Calculations should be performed in each computer to prevent the concentration of calculations on the server.

The program should be distributed to each computer easily.

The program should be platformindependent for wide use.
JAVA is the best language to meet the above conditions.
In the present paper, we have developed a platformindependent program, called ES1 (Electrochemical Simulator), written in JAVA language, which can calculate electrochemical behavior under finite conditions. This program is intended for a beginner using a modified electrode.
2 Method
2. 1 Theory of the Electrochemical Simulation
Figure 1 shows the scheme of a polymercoated electrode in which functional molecules were dispersed. In an electrodecoated polymer layer, functional molecules (redox center) are randomly dispersed. The electrode is dipped in an electrolyte solution. Electrochemical measurement is performed by the conventional three electrode system. A conventional diffusion equation including firstorder catalytic reaction was used for the simulation:
where C( x, t) (mol cm^{3}) is the concentration of the oxidized molecule at the time t (s), k (s^{1}) is the firstorder rate constant for the catalysis by the oxidized molecule, D (cm^{2} s^{1}) is the diffusion coefficient of the charge. Assuming that a functional molecule(M) can catalyze a reaction, the firstorder catalytic reaction is expressed by
where M_{ox} and M_{red} are the oxidized and reduced forms of the redox center, respectively, S is a substrate, P is a product.
Figure 1. Scheme of a polymercoated electrode with dispersed functional molecules
Assuming that the concentration of the redox species obeys a Nernstian equation [8], a boundary condition on the electrode (x = 0) is represented as
where C_{T} (mol cm^{3}) is the total concentration of the molecule, E is the applied potential on the electrode, E° is the redox potential of the molecule, n is the number of electrons, F (C mol^{1}) is the Faraday constant. Another boundary condition under finite conditions is represented as
where l is the thickness of the polymer layer. A finite differential method (FDM) was used for the simulation.
2. 2 Implementation
We used a PC9821 machine (NEC) in which Microsoft Windows 2000 was installed for developing ES1 with the Microsoft Visual J++ version 6(SP3). However, we didn't use a Windows Foundation Class library (WFC) to keep a platformindependent feature. ES1 was tested using IBM/AT compatible with Internet Explorer version 5.5.
3 Results and Discussion
3. 1 The Feature of ES1
Figure 2 shows the combination of the ES1 and electrochemical texts written in HTML. Students can learn electrochemistry by electrochemical text blended with the simulation program smoothly[9]. ES1 has only one button in the control panel. Simple operation is very important for use in an electrochemistry class because most of the time in class should be spent for teaching electrochemistry itself, and not for teaching the usage of the program. The numerical results are put into a text area since JAVA applets are prohibited from accessing any local disks. The results in the text area can be copied by using a shortcut key ([Ctrl]+[C]).
Figure 2. Combination of the ES1 and electrochemical texts written in HTML. Upper window illustrates the concentration distribution of the oxidized molecule. Lower window shows the cyclic voltammogram of the molecule.
3. 2 Results of the Simulation
Figure 3 shows the time dependence of R_{CT} estimated by absorption spectral change at potential step measurement using ITO/Nafion[Ru(bpy)_{3}^{2+}] electrode. A curve calculated with ES1, shown in Figure 3, coincides with the actual measurement suggesting that the simulation is reasonable. The diffusion coefficient used in the simulation was estimated by conventional equation in the solution system in the initial time region.
Figure 3. Time dependence of R_{CT} estimated by absorption spectral change at potential step measurement from 0.6V (versus AgAgCl) to 1.4V using ITO/Nafion[Ru(bpy)_{3}^{2+}] electrode in 0.1mol dm^{3} KNO_{3} (pH 1). The solid line was calculated with ES1. ( D = 3.2 × 10^{10} cm^{2}s^{1}, l = 1 × 10^{4} cm, C_{T} = 4.2 × 10^{4} mol cm^{3} )
Students can see the electrochemical behavior shown below using ES1. Figure 4(a) shows a series of cyclic voltammograms at various thicknesses of a finite layer. The increase of the layer thickness raised the anodic current beyond the potential at the peak current, where the anodic current is derived from the diffusion of charges, but reduces the cathodic current on the reverse scan. This is because a thinner layer makes a steeper concentration gradient of the redox molecules.
Figure 4. Virtual electrochemical measurements of a material (D = 3×10^{10}cm^{2}s^{1}, k = 0 s^{1}, E° = 1.1 V vs. a standard electrode) at various thicknesses using ES1. (a) Cyclic voltammogram from 0.7 V to 1.5 V at 20mV/s. , l = 0.5 ×10^{4} cm;   , 1.0 ×10^{4} cm ; ..., 2.0 ×10^{4} cm ;  .  3.0 ×10^{4} cm. (b) The plots of R_{CT} vs. t^{1/2}l^{1} at applied potential from 0.7V to 1.5V. , A simulated curve under finite condition;   , calculated by eq.3 (under infinite condition).
The equation of the time dependent R_{CT} value under infinite conditions is represented by eq. 3 [10, 11], where R_{CT} is the fraction of the redox molecule that accepted a charge.
Figure 4(b) shows the plots of R_{CT} vs. t^{1/2}l^{1} simulated by ES1. The simulated curve under the finite conditions deviated from the curve calculated by eq. 3 above R_{CT} 0.5.
Figure 5(a) shows a series of cyclic voltammograms at various k values. The anodic current beyond the redox potential increased with the k value. Time dependence of R_{CT} under finite conditions at various k values in potential step measurement is shown in Figure 5(b). The increase of k value reduced the time to reach the plateau, and also lowered the plateau value.
Figure 5. Virtual electrochemical measurements of a material (D = 3×10^{10}cm^{2}s^{1}, E° = 1.1 V vs. a standard electrode) at various k values using ES1. , k = 0 s^{1};   , 5 ×10^{3} s^{1} ; ..., 5 ×10^{2} s^{1} ;  .  5 ×10^{1} s^{1}. (a) Cyclic voltammogram from 0.7 V to 1.5 V at 20mV/s. (b) Time dependence of R_{CT} at an applied potential from 0.7V to 1.5V.
4 Conclusion
An electrochemical simulator (ES1) under finite conditions for redox centers confined in an electrode coated polymer layer was developed for an electrochemistry class. ES1 was written in JAVA language which has characteristics of platformindependence, an easy cooperation with HTML and small load on a server computer. The R_{CT} value under finite conditions deviated from that under infinite conditions above R_{CT} 0.5.
The authors acknowledge a GrantinAid for JAERI's Nuclear Research Promotion Program (JANP) from Japan Atomic Energy Research Institute.
References
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[ 9] This program embedded in HTML can be seen at
http://klab01.sci.ibaraki.ac.jp/~kanekolab/electrochem.html
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