Chapman University Field of Electrocatalysis Catalyst Nanoparticles MatLab

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1) solution on paper with steps.

2) .m files containing the MATLAB code developed.

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Problem 1 (Individual) In the field of electrocatalysis catalyst nanoparticles, of 3 nm in size are dispersed over a highsurface are of electronically conductive support, such as carbon. Electrochemical reaction takes place at the surface of the electrocatalyst and one wants to maximize the surface exposed to reactive species. To prevent nano-particles agglomeration and to expose maximum amount of surface area the carbon black, with high surface area is used. Such an example for Pt nanoparticles on carbon black support is shown below in TEM image and a schematic. Figure 1. a) A schematic of Pt supported on carbon and oxygen reduction reaction reactants (O2 and H+, e-). b) A TEM image of Pt dispersed on carbon. As can be seen in Figure 1, Pt is very well dispersed on carbon support. This electrocatalyst is used in polymer electrolyte fuel cells, where oxygen reduction reaction (ORR) takes place in cathode. Oxygen, protons and electrons react on Pt surface to form water. For fuel cells to be cost effective you want to minimize Pt loading in the catalyst layer. Suppose you are given Pt on carbon (Pt/C) electrocatalyst to evaluate for fuel cell applications. It is deposited onto a membrane and its geometric area is 25 cm2. Furthermore, you are given the Pt loading in this catalyst to be 0.3 mg/cm2geo. (the geo stands for geometric). You want to determine the electrochemical surface area (ECSA) of Pt dispersed on carbon. To do this you run an experiment called “cyclic voltammetry” (CV), where you use Pt/C as your working electrode. You polarize it by applying potential sweep from ~0.05 V to 0.8 V and record the current, and then you sweep back the potential from 0.8 V to 0.05 V and record negative values for current. You are using sweep rate of 40 mV/s. In the region from ~0.05 to ~0.4 V the measured current is due to hydrogen adsorption from water onto Pt surface. If we assume one monolayer of H adsorbed on the surface: Had = H+ + e-, this resulted in charge transport and the collected current can directly be correlated to surface area of Pt. You can integrate the obtained curve to calculate the ECSA with the following equations to determine the area in the H adsorption region of the CV: 𝐸𝐶𝑆𝐴 ( where 𝑐𝑚2 𝑚𝑔 )= 𝑄( 𝑚𝐶 ) 𝑐𝑚2 𝑚𝑔 𝑚𝐶 )∗𝑐ℎ𝑎𝑟𝑔𝑒 𝑝𝑒𝑟 𝑚𝑜𝑛𝑜𝑙𝑎𝑦𝑒𝑟 ( 2 ) 𝑐𝑚 𝑐𝑚2 𝑔𝑒𝑜 𝑙𝑜𝑎𝑑𝑖𝑛𝑔 ( (1) 𝑚𝐶 𝑄( 𝑐𝑚2 )= [𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝑎𝑟𝑒𝑎 (𝑚𝐴.𝑉)−𝐷𝑜𝑢𝑏𝑙𝑒 𝑙𝑎𝑦𝑒𝑟 𝑎𝑟𝑒𝑎 (𝑚𝐴.𝑉)] 𝑚𝑉 𝑆𝑤𝑒𝑒𝑝 𝑟𝑎𝑡𝑒 ( 𝑠 )∗𝐴𝑔𝑒𝑜 (𝑐𝑚2 ) (2) The charge per monolayer of H+ on Pt during a CV is 0.210 mC/cm2 . Figure 2 (and excel sheet) shows the CV and H adsorption region, as well as double layer region. Somewhere above 0.4 V the current levels off and we enter into “double layer” region, as H no longer adsorbs on the surface and the only current measured is due to capacitive charging. Figure 2. CV of Pt/C electrocatalyst. 1) Use raw data from excel sheet to plot this CV. Develop a Matlab code that will automatically: a) Detect left-hand-side of curve intercept with x-axis (starting point), and find the righthand-side of the curve, where H region is merging into double layer region. The right point generally cannot be determined too precisely. The left-hand-side point generally shifts from CV to CV, it is approximately at 0.05 V but can be at 0.1V. Hence having automatic algorithm for detection of this point is critical. b) Develop algorithm and will integrate the area of the H adsorption, and that subtracts the double layer region to arrive at “Integrated area – double layer area”. You may want to use any of the algorithms covered in class for integration. c) Use Equation 1 and 2 to calculate the value of the ECSA. d) Describe what type of errors are present in the above integration process. 1.27E-01 1.17E-01 1.02E-01 8.87E-02 7.53E-02 6.13E-02 4.77E-02 3.67E-02 3.03E-02 3.56E-02 3.66E-02 3.77E-02 3.86E-02 3.97E-02 4.07E-02 4.17E-02 4.27E-02 4.36E-02 4.47E-02 4.56E-02 4.66E-02 4.77E-02 4.87E-02 4.96E-02 5.07E-02 5.17E-02 5.26E-02 5.36E-02 5.53E-02 5.70E-02 5.80E-02 5.90E-02 5.99E-02 6.10E-02 6.20E-02 6.30E-02 6.40E-02 6.50E-02 6.59E-02 6.70E-02 6.79E-02 6.90E-02 7.00E-02 7.10E-02 7.20E-02 7.30E-02 7.40E-02 7.50E-02 -4.71E+03 -4.71E+03 -4.71E+03 -4.71E+03 -4.71E+03 -4.71E+03 -4.71E+03 -4.71E+03 -4.55E+03 -2.68E+03 -2.19E+03 -1.80E+03 -1.48E+03 -1.21E+03 -1.00E+03 -8.32E+02 -6.68E+02 -5.37E+02 -4.37E+02 -3.39E+02 -2.45E+02 -1.84E+02 -1.27E+02 -6.01E+01 -2.23E+01 1.05E+01 5.27E+01 8.18E+01 1.20E+02 1.57E+02 1.65E+02 1.77E+02 1.98E+02 2.00E+02 2.06E+02 2.20E+02 2.22E+02 2.25E+02 2.31E+02 2.36E+02 2.37E+02 2.40E+02 2.48E+02 2.48E+02 2.49E+02 2.57E+02 2.58E+02 2.60E+02 7.60E-02 7.70E-02 7.80E-02 7.90E-02 8.00E-02 8.10E-02 8.20E-02 8.29E-02 8.40E-02 8.50E-02 8.60E-02 8.70E-02 8.80E-02 8.90E-02 9.00E-02 9.10E-02 9.20E-02 9.30E-02 9.39E-02 9.50E-02 9.60E-02 9.70E-02 9.80E-02 9.90E-02 9.99E-02 1.01E-01 1.02E-01 1.03E-01 1.04E-01 1.05E-01 1.06E-01 1.07E-01 1.08E-01 1.09E-01 1.10E-01 1.11E-01 1.12E-01 1.13E-01 1.14E-01 1.15E-01 1.16E-01 1.17E-01 1.18E-01 1.19E-01 1.20E-01 1.21E-01 1.22E-01 1.23E-01 1.24E-01 2.62E+02 2.65E+02 2.66E+02 2.68E+02 2.68E+02 2.70E+02 2.71E+02 2.74E+02 2.80E+02 2.84E+02 2.84E+02 2.86E+02 2.85E+02 2.84E+02 2.86E+02 2.89E+02 2.90E+02 2.92E+02 2.95E+02 2.98E+02 2.99E+02 3.02E+02 3.04E+02 3.07E+02 3.09E+02 3.11E+02 3.12E+02 3.14E+02 3.16E+02 3.16E+02 3.20E+02 3.23E+02 3.24E+02 3.26E+02 3.29E+02 3.31E+02 3.32E+02 3.35E+02 3.36E+02 3.36E+02 3.39E+02 3.40E+02 3.39E+02 3.43E+02 3.44E+02 3.43E+02 3.45E+02 3.46E+02 3.48E+02 1.25E-01 1.26E-01 1.27E-01 1.28E-01 1.29E-01 1.30E-01 1.31E-01 1.32E-01 1.33E-01 1.34E-01 1.35E-01 1.36E-01 1.37E-01 1.38E-01 1.39E-01 1.40E-01 1.41E-01 1.42E-01 1.43E-01 1.44E-01 1.45E-01 1.46E-01 1.47E-01 1.48E-01 1.49E-01 1.50E-01 1.51E-01 1.52E-01 1.53E-01 1.54E-01 1.55E-01 1.56E-01 1.57E-01 1.58E-01 1.59E-01 1.60E-01 1.61E-01 1.62E-01 1.63E-01 1.64E-01 1.65E-01 1.66E-01 1.67E-01 1.68E-01 1.69E-01 1.70E-01 1.71E-01 1.72E-01 1.73E-01 3.47E+02 3.47E+02 3.45E+02 3.44E+02 3.45E+02 3.42E+02 3.40E+02 3.41E+02 3.39E+02 3.37E+02 3.37E+02 3.35E+02 3.33E+02 3.32E+02 3.30E+02 3.27E+02 3.24E+02 3.24E+02 3.20E+02 3.18E+02 3.18E+02 3.15E+02 3.13E+02 3.12E+02 3.10E+02 3.09E+02 3.07E+02 3.05E+02 3.03E+02 3.02E+02 3.01E+02 2.97E+02 2.96E+02 2.97E+02 2.95E+02 2.93E+02 2.93E+02 2.92E+02 2.91E+02 2.90E+02 2.89E+02 2.87E+02 2.87E+02 2.86E+02 2.83E+02 2.84E+02 2.84E+02 2.82E+02 2.82E+02 1.74E-01 1.75E-01 1.76E-01 1.77E-01 1.78E-01 1.79E-01 1.80E-01 1.81E-01 1.82E-01 1.83E-01 1.84E-01 1.85E-01 1.86E-01 1.87E-01 1.88E-01 1.89E-01 1.90E-01 1.91E-01 1.92E-01 1.93E-01 1.94E-01 1.95E-01 1.96E-01 1.97E-01 1.98E-01 1.99E-01 2.00E-01 2.01E-01 2.02E-01 2.03E-01 2.04E-01 2.05E-01 2.06E-01 2.07E-01 2.08E-01 2.09E-01 2.10E-01 2.11E-01 2.12E-01 2.13E-01 2.14E-01 2.15E-01 2.16E-01 2.17E-01 2.18E-01 2.19E-01 2.20E-01 2.21E-01 2.22E-01 2.82E+02 2.82E+02 2.81E+02 2.80E+02 2.78E+02 2.76E+02 2.77E+02 2.74E+02 2.72E+02 2.73E+02 2.72E+02 2.70E+02 2.70E+02 2.69E+02 2.68E+02 2.67E+02 2.66E+02 2.65E+02 2.63E+02 2.64E+02 2.62E+02 2.61E+02 2.62E+02 2.61E+02 2.59E+02 2.60E+02 2.59E+02 2.59E+02 2.58E+02 2.58E+02 2.56E+02 2.56E+02 2.57E+02 2.55E+02 2.54E+02 2.56E+02 2.55E+02 2.54E+02 2.56E+02 2.55E+02 2.55E+02 2.55E+02 2.55E+02 2.54E+02 2.55E+02 2.55E+02 2.53E+02 2.54E+02 2.55E+02 2.23E-01 2.24E-01 2.25E-01 2.26E-01 2.27E-01 2.28E-01 2.29E-01 2.30E-01 2.31E-01 2.32E-01 2.33E-01 2.34E-01 2.35E-01 2.36E-01 2.37E-01 2.38E-01 2.39E-01 2.40E-01 2.41E-01 2.42E-01 2.43E-01 2.44E-01 2.45E-01 2.46E-01 2.47E-01 2.48E-01 2.49E-01 2.50E-01 2.51E-01 2.52E-01 2.53E-01 2.54E-01 2.55E-01 2.56E-01 2.57E-01 2.58E-01 2.59E-01 2.60E-01 2.61E-01 2.62E-01 2.63E-01 2.64E-01 2.65E-01 2.66E-01 2.67E-01 2.68E-01 2.69E-01 2.70E-01 2.71E-01 2.54E+02 2.54E+02 2.56E+02 2.56E+02 2.57E+02 2.57E+02 2.56E+02 2.56E+02 2.57E+02 2.57E+02 2.56E+02 2.58E+02 2.59E+02 2.58E+02 2.59E+02 2.60E+02 2.61E+02 2.61E+02 2.62E+02 2.61E+02 2.61E+02 2.63E+02 2.62E+02 2.61E+02 2.63E+02 2.63E+02 2.62E+02 2.63E+02 2.63E+02 2.63E+02 2.63E+02 2.63E+02 2.62E+02 2.61E+02 2.62E+02 2.59E+02 2.58E+02 2.58E+02 2.57E+02 2.55E+02 2.55E+02 2.53E+02 2.51E+02 2.49E+02 2.47E+02 2.44E+02 2.41E+02 2.40E+02 2.35E+02 2.72E-01 2.73E-01 2.74E-01 2.75E-01 2.76E-01 2.77E-01 2.78E-01 2.79E-01 2.80E-01 2.81E-01 2.82E-01 2.83E-01 2.84E-01 2.85E-01 2.86E-01 2.87E-01 2.88E-01 2.89E-01 2.90E-01 2.91E-01 2.92E-01 2.93E-01 2.94E-01 2.95E-01 2.96E-01 2.97E-01 2.98E-01 2.99E-01 3.00E-01 3.01E-01 3.02E-01 3.03E-01 3.04E-01 3.05E-01 3.06E-01 3.07E-01 3.08E-01 3.09E-01 3.10E-01 3.11E-01 3.12E-01 3.13E-01 3.14E-01 3.15E-01 3.16E-01 3.17E-01 3.18E-01 3.19E-01 3.20E-01 2.33E+02 2.31E+02 2.27E+02 2.24E+02 2.22E+02 2.18E+02 2.16E+02 2.12E+02 2.07E+02 2.03E+02 2.00E+02 1.97E+02 1.92E+02 1.89E+02 1.86E+02 1.82E+02 1.79E+02 1.77E+02 1.73E+02 1.70E+02 1.67E+02 1.64E+02 1.61E+02 1.59E+02 1.56E+02 1.52E+02 1.51E+02 1.48E+02 1.46E+02 1.44E+02 1.42E+02 1.41E+02 1.39E+02 1.37E+02 1.35E+02 1.34E+02 1.33E+02 1.31E+02 1.29E+02 1.29E+02 1.27E+02 1.26E+02 1.26E+02 1.24E+02 1.24E+02 1.22E+02 1.22E+02 1.20E+02 1.20E+02 3.21E-01 3.22E-01 3.23E-01 3.24E-01 3.25E-01 3.26E-01 3.27E-01 3.28E-01 3.29E-01 3.30E-01 3.31E-01 3.32E-01 3.33E-01 3.34E-01 3.35E-01 3.36E-01 3.37E-01 3.38E-01 3.39E-01 3.40E-01 3.41E-01 3.42E-01 3.43E-01 3.44E-01 3.45E-01 3.46E-01 3.47E-01 3.48E-01 3.49E-01 3.50E-01 3.51E-01 3.52E-01 3.53E-01 3.54E-01 3.55E-01 3.56E-01 3.57E-01 3.58E-01 3.59E-01 3.60E-01 3.61E-01 3.62E-01 3.63E-01 3.64E-01 3.65E-01 3.66E-01 3.67E-01 3.68E-01 3.69E-01 1.20E+02 1.18E+02 1.17E+02 1.17E+02 1.16E+02 1.15E+02 1.15E+02 1.14E+02 1.15E+02 1.14E+02 1.13E+02 1.12E+02 1.12E+02 1.12E+02 1.10E+02 1.10E+02 1.10E+02 1.09E+02 1.09E+02 1.09E+02 1.08E+02 1.08E+02 1.08E+02 1.07E+02 1.06E+02 1.07E+02 1.06E+02 1.05E+02 1.05E+02 1.05E+02 1.04E+02 1.04E+02 1.05E+02 1.04E+02 1.04E+02 1.04E+02 1.02E+02 1.02E+02 1.03E+02 1.02E+02 1.01E+02 1.02E+02 1.01E+02 1.00E+02 1.00E+02 1.00E+02 1.00E+02 9.92E+01 9.94E+01 3.70E-01 3.71E-01 3.72E-01 3.73E-01 3.74E-01 3.75E-01 3.76E-01 3.77E-01 3.78E-01 3.79E-01 3.80E-01 3.81E-01 3.82E-01 3.83E-01 3.84E-01 3.85E-01 3.86E-01 3.87E-01 3.88E-01 3.89E-01 3.90E-01 3.91E-01 3.92E-01 3.93E-01 3.94E-01 3.95E-01 3.96E-01 3.97E-01 3.98E-01 3.99E-01 4.00E-01 4.01E-01 4.02E-01 4.03E-01 4.04E-01 4.05E-01 4.06E-01 4.07E-01 4.08E-01 4.09E-01 4.10E-01 4.11E-01 4.12E-01 4.13E-01 4.14E-01 4.15E-01 4.16E-01 4.17E-01 4.18E-01 9.84E+01 9.82E+01 9.85E+01 9.76E+01 9.70E+01 9.79E+01 9.71E+01 9.68E+01 9.71E+01 9.64E+01 9.69E+01 9.57E+01 9.54E+01 9.46E+01 9.45E+01 9.50E+01 9.36E+01 9.39E+01 9.42E+01 9.34E+01 9.29E+01 9.37E+01 9.28E+01 9.29E+01 9.28E+01 9.24E+01 9.17E+01 9.19E+01 9.18E+01 9.06E+01 9.10E+01 9.14E+01 9.05E+01 9.04E+01 9.09E+01 9.02E+01 9.00E+01 9.04E+01 8.97E+01 8.94E+01 8.97E+01 8.93E+01 8.84E+01 8.91E+01 8.90E+01 8.87E+01 8.85E+01 8.89E+01 8.85E+01 4.19E-01 4.20E-01 4.21E-01 4.22E-01 4.23E-01 4.24E-01 4.25E-01 4.26E-01 4.27E-01 4.28E-01 4.29E-01 4.30E-01 4.31E-01 4.32E-01 4.33E-01 4.34E-01 4.35E-01 4.36E-01 4.37E-01 4.38E-01 4.39E-01 4.40E-01 4.41E-01 4.42E-01 4.43E-01 4.44E-01 4.45E-01 4.46E-01 4.47E-01 4.48E-01 4.49E-01 4.50E-01 4.51E-01 4.52E-01 4.53E-01 4.54E-01 4.55E-01 4.56E-01 4.57E-01 4.58E-01 4.59E-01 4.60E-01 4.61E-01 4.62E-01 4.63E-01 4.64E-01 4.65E-01 4.66E-01 4.67E-01 8.82E+01 8.85E+01 8.80E+01 8.77E+01 8.83E+01 8.79E+01 8.71E+01 8.79E+01 8.75E+01 8.71E+01 8.75E+01 8.74E+01 8.82E+01 8.71E+01 8.77E+01 8.70E+01 8.70E+01 8.75E+01 8.68E+01 8.68E+01 8.73E+01 8.69E+01 8.68E+01 8.72E+01 8.70E+01 8.72E+01 8.70E+01 8.72E+01 8.68E+01 8.69E+01 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1.00E+03 0.00E+00 -1.00E+03 -2.00E+03 -3.00E+03 -4.00E+03 -5.00E+03 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01 5.00E-01 6.00E-01 7.00E- n-title 1 5.00E-01 6.00E-01 7.00E-01 8.00E-01 9.00E-01
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Explanation & Answer

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Final solution
%declaring of variables
A_geo=25;
voltage1=0.05:0.8;
voltage2=0.8:0.05;...


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