48 lines
1.4 KiB
Python
48 lines
1.4 KiB
Python
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#!/usr/bin env python3
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from formulasheet import *
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from scipy.constants import gas_constant, Avogadro, elementary_charge
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Faraday = Avogadro * elementary_charge
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@np.vectorize
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def fbutler_volmer_left(ac, z, eta, T):
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return np.exp((1-ac)*z*Faraday*eta/(gas_constant*T))
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@np.vectorize
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def fbutler_volmer_right(ac, z, eta, T):
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return -np.exp(-ac*z*Faraday*eta/(gas_constant*T))
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def fbutler_volmer(ac, z, eta, T):
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return fbutler_volmer_left(ac, z, eta, T) + fbutler_volmer_right(ac, z, eta, T)
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def butler_volmer():
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fig, ax = plt.subplots(figsize=size_half_third)
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ax.set_xlabel("$\\eta$")
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ax.set_ylabel("$i/i_0$")
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etas = np.linspace(-0.1, 0.1, 400)
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T = 300
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z = 1.0
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# other a
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alpha2, alpha3 = 0.2, 0.8
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i2 = fbutler_volmer(0.2, z, etas, T)
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i3 = fbutler_volmer(0.8, z, etas, T)
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ax.plot(etas, i2, color="blue", linestyle="dashed", label=f"$\\alpha={alpha2}$")
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ax.plot(etas, i3, color="green", linestyle="dashed", label=f"$\\alpha={alpha3}$")
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# 0.5
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ac = 0.5
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irel_left = fbutler_volmer_left(ac, z, etas, T)
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irel_right = fbutler_volmer_right(ac, z, etas, T)
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ax.plot(etas, irel_left, color="gray")
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ax.plot(etas, irel_right, color="gray")
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ax.plot(etas, irel_right + irel_left, color="black", label=f"$\\alpha=0.5$")
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ax.grid()
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ax.legend()
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ylim = 6
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ax.set_ylim(-ylim, ylim)
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return fig
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if __name__ == '__main__':
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export(butler_volmer(), "ch_butler_volmer")
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