# The ImpedanceFitter is a package to fit impedance spectra to equivalent-circuit models using open-source software.
#
# Copyright (C) 2021 Julius Zimmermann, julius.zimmermann[AT]uni-rostock.de
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from scipy.constants import epsilon_0 as e0
from .suspensionmodels import eps_sus_MW, bhcubic_eps_model
[docs]def particle_model(omega, ep, kp, kmed, emed, p, c0):
r"""Single particle in suspension model
Parameters
-----------
omega: :class:`numpy.ndarray`, double
list of frequencies
c0: double
value for :math:`c_0`, unit capacitance in pF
ep: double
particle permittivity, value for :math:`\varepsilon_\mathrm{p}`
kp: double
particle conductivity, value for :math:`\sigma_\mathrm{p}` in :math:`\mu`\ S/m
emed: double
medium permittivity, value for :math:`\varepsilon_\mathrm{med}`
kmed: double
medium conductivity, value for :math:`\sigma_\mathrm{med}`
p: double
volume fraction
Returns
-------
:class:`numpy.ndarray`, complex
Impedance array
Notes
-----
.. warning::
The unit capacitance is in pF!
The particle conductivity is in uF/m!
"""
c0 *= 1e-12 # use pF as unit
kp *= 1e-6
epsi_med = emed - 1j * kmed / (e0 * omega)
epsi_p = ep - 1j * kp / (e0 * omega)
esus = eps_sus_MW(epsi_med, epsi_p, p)
Ys = 1j * esus * omega * c0 # suspension admittance spectrum
Z_fit = 1 / Ys
return Z_fit
[docs]def particle_bh_model(omega, ep, kp, kmed, emed, p, c0):
r"""Single particle in Bruggeman-Hanai suspension model
Parameters
-----------
omega: :class:`numpy.ndarray`, double
list of frequencies
c0: double
value for :math:`c_0`, unit capacitance in pF
ep: double
particle permittivity, value for :math:`\varepsilon_\mathrm{p}`
kp: double
particle conductivity, value for :math:`\sigma_\mathrm{p}` in :math:`\mu`\ S/m
emed: double
medium permittivity, value for :math:`\varepsilon_\mathrm{med}`
kmed: double
medium conductivity, value for :math:`\sigma_\mathrm{med}`
p: double
volume fraction
Returns
-------
:class:`numpy.ndarray`, complex
Impedance array
Notes
-----
.. warning::
The unit capacitance is in pF!
The particle conductivity is in uF/m!
"""
c0 *= 1e-12 # use pF as unit
kp *= 1e-6
epsi_med = emed - 1j * kmed / (e0 * omega)
epsi_p = ep - 1j * kp / (e0 * omega)
esus = bhcubic_eps_model(epsi_med, epsi_p, p)
Ys = 1j * esus * omega * c0 # suspension admittance spectrum
Z_fit = 1 / Ys
return Z_fit