def test_ErCi(nu, C, k_f):
sim = ecs.Simulation(True)
sim.env.setTemperature(T)
sim.el.disk(r)
red = ecs.Species('red', C, D)
ox = ecs.Species('ox', 0.0, D)
prod = ecs.Species('prod', 0.0, D)
rdx1 = ecs.Redox(ox, red, n, 0.0, 10.0, alpha).enable()
sim.sys.addRedox(rdx1)
rxn1 = ecs.Reaction(ox, None, prod, None, k_f, 0.0).enable()
sim.sys.addReaction(rxn1)
sim.exper.setScanPotentials(-0.5, [0.5], -0.5)
sim.exper.setScanRate(nu)
[potential, current] = sim.run()
metrics = sim.metrics()
# Savéant (Elements of ...) page 83:
i_p_theoretical = 0.496 * F * (np.pi * r * r) * C * np.sqrt(f * nu * D)
print(metrics[0], i_p_theoretical)
E_p_theoretical = (0.78 - np.log(k_f / nu / f) / 2) / f
print(metrics[1], E_p_theoretical)
i_p_err = np.abs(2 * (i_p_theoretical - metrics[0]) /
(i_p_theoretical + metrics[0]))
E_p_diff = np.abs(E_p_theoretical - metrics[1]) / np.abs(potential[0] -
potential[1])
assert i_p_err < 0.025 # less than 2.5% error in peak current
assert E_p_diff < 1.0 # peak potential within step potential
def test_Er(T, r, nu, n, alpha, C, Dred, Dox):
global R, F
f = float(n)*F/R/T
sim = ecs.Simulation(False)
sim.setPotentialSizing(0.2/float(n)) # TODO: this should happen inside the algorithm
sim.env.setTemperature(T)
sim.el.disk(r)
ox = ecs.Species('ox', 0.0, Dox)
red = ecs.Species('red', C, Dred)
rdx1 = ecs.Redox(ox, red, int(n), 0.0, 10.0, alpha).enable()
sim.sys.addRedox(rdx1)
sim.exper.setScanPotentials(-0.5, [0.5], -0.5)
sim.exper.setScanRate(nu)
[potential, current] = sim.run()
metrics = sim.metrics()
# Bard & Faulkner chapter 6:
i_p_theoretical = 0.4463*float(n)*F*(np.pi*r*r)*C*np.sqrt(f*nu*Dred) # Randles-Sevcik equation
E_half = np.log(np.sqrt(Dred/Dox)) / f
E_p_theoretical = E_half + 1.109 / f
i_p_err = np.abs(2*(i_p_theoretical - metrics[0])/(i_p_theoretical + metrics[0]))
E_p_diff = np.abs(E_p_theoretical - metrics[1]) / np.abs(potential[0]-potential[1])
assert i_p_err < 0.01 # less than 1% error in peak current
assert E_p_diff < 1.0 # peak potential within step potential
def test_ErCr(nu, C, k_f, k_b):
sim = ecs.Simulation(True)
sim.env.setTemperature(T)
sim.el.disk(r)
red = ecs.Species('red', C, D)
ox = ecs.Species('ox', 0.0, D)
prod = ecs.Species('prod', 0.0, D)
rdx1 = ecs.Redox(ox, red, n, 0.0, 10.0, alpha).enable()
sim.sys.addRedox(rdx1)
rxn1 = ecs.Reaction(ox, None, prod, None, k_f, k_b).enable()
sim.sys.addReaction(rxn1)
sim.exper.setScanPotentials(-1.0, [0.5], -1.0)
sim.exper.setScanRate(nu)
#sim.setPotentialSizing(0.1)
[potential, current] = sim.run()
metrics = sim.metrics()
# Savéant (Elements of ...) page 85:
i_p_theoretical = 0.4463 * F * (np.pi * r * r) * C * np.sqrt(
f * nu * D) # Randles-Sevcik equation
print(metrics[0], i_p_theoretical)
E_p_theoretical = (1.109 - np.log(1 + k_f / k_b)) / f
print(metrics[1], E_p_theoretical)
i_p_err = np.abs(2 * (i_p_theoretical - metrics[0]) /
(i_p_theoretical + metrics[0]))
E_p_diff = np.abs(E_p_theoretical - metrics[1]) / np.abs(potential[0] -
potential[1])
assert i_p_err < 0.015 # less than 2.5% error in peak current
assert E_p_diff < 1.0 # peak potential within 2 step potential
def test_Ei(T, r, nu, alpha, k_e, C, Dred, Dox):
global R, F
f = (1 - alpha) * F / R / T
sim = ecs.Simulation(False)
sim.env.setTemperature(T)
sim.el.disk(r)
ox = ecs.Species('ox', 0.0, Dox)
red = ecs.Species('red', C, Dred)
rdx1 = ecs.Redox(ox, red, 1, 0.0, k_e, alpha).enable()
sim.sys.addRedox(rdx1)
sim.exper.setScanPotentials(-0.5, [2.0], -0.5)
sim.exper.setScanRate(nu)
[potential, current] = sim.run()
metrics = sim.metrics()
# Bard & Faulkner chapter 6 (section 6.3.2):
i_p_theoretical = 0.4958 * F * (np.pi * r * r) * C * np.sqrt(f * nu * Dred)
print(metrics[0] * 1.0e6, i_p_theoretical * 1.0e6)
E_p_theoretical = (0.780 + np.log(np.sqrt(Dred * nu * f) / k_e)) / f
i_p_err = np.abs(2 * (i_p_theoretical - metrics[0]) /
(i_p_theoretical + metrics[0]))
E_p_diff = np.abs(E_p_theoretical - metrics[1]) / np.abs(potential[0] -
potential[1])
assert i_p_err < 0.01 # less than 1% error in peak current
assert E_p_diff < 1.0 # peak potential within step potential
def test_CE_KP(nu, C, k_f, k_b):
sim = ecs.Simulation(True)
sim.env.setTemperature(T)
sim.el.disk(r)
red = ecs.Species('red', 0.0, D)
ox = ecs.Species('ox', 0.0, D)
prod = ecs.Species('prod', C, D)
rdx1 = ecs.Redox(ox, red, n, 0.0, 10.0, alpha).enable()
sim.sys.addRedox(rdx1)
rxn1 = ecs.Reaction(prod, None, red, None, k_f, k_b).enable()
sim.sys.addReaction(rxn1)
sim.exper.setScanPotentials(-0.5, [0.5], -0.5)
sim.exper.setScanRate(nu)
[potential, current] = sim.run()
metrics = sim.metrics()
# Savéant (Elements of ...) page 93:
i_p_theoretical = F * (np.pi * r * r) * C * np.sqrt(D * k_b) * (k_f / k_b)
print(metrics[0], i_p_theoretical)
i_p_err = np.abs(2 * (i_p_theoretical - metrics[0]) /
(i_p_theoretical + metrics[0]))
assert i_p_err < 0.01 # less than 1% error in plateau current
def simulate_Eq(T, r, nu, alpha, k_e, C, Dred, Dox, deltaTheta=0.2):
sim = ecs.Simulation(True)
sim.env.setTemperature(T)
sim.el.disk(r)
ox = ecs.Species('ox', 0.0, Dox)
red = ecs.Species('red', C, Dred)
rdx1 = ecs.Redox(ox, red, 1, 0.0, k_e, 1 - alpha).enable()
sim.sys.addRedox(rdx1)
sim.exper.setScanPotentials(-0.2, [], 1.0)
sim.exper.setScanRate(nu)
sim.setPotentialSizing(deltaTheta)
[potential, current] = sim.run()
return [potential, current, sim.metrics()]
import matplotlib as mpl
import matplotlib.pyplot as plt
import pyecsim as ecs
if __name__ == '__main__':
sim = ecs.Simulation(True) # bool verbosity
A = ecs.Species('A', 1.0, 1.0e-9)
B = ecs.Species('B', 0.0, 1.0e-9)
C = ecs.Species('C', 0.0, 1.0e-9)
rxn1 = ecs.Reaction(B, None, C, None, 10.0, 0.0).enable()
sim.sys.addReaction(rxn1)
rdx1 = ecs.Redox(A, B, 1, -0.5, 10.0, 0.5).enable()
sim.sys.addRedox(rdx1)
sim.el.disk(1.0e-3)
sim.exper.setScanPotentials(0.0, [-0.7], 0.0)
sim.exper.setScanRate(1.0)
k_fs = np.logspace(-5.0, 9.0, num=10)
E_pc = []
cmap_conc = mpl.cm.get_cmap('nipy_spectral')
plt.figure()
for index, k_f in enumerate(list(k_fs)):
cval = 1.0 - index / 10