def gammas(self):
r'''Calculate and return the activity coefficients of a liquid phase
using an activity coefficient model.
.. math::
\gamma_i = \exp\left(\frac{\frac{\partial n_i G^E}{\partial n_i }}{RT}\right)
Returns
-------
gammas : list[float]
Activity coefficients, [-]
Notes
-----
'''
try:
return self._gammas
except:
pass
# Matches the gamma formulation perfectly
GE = self.GE()
dG_dxs = self.dGE_dxs()
if self.scalar:
dG_dns = dxs_to_dn_partials(dG_dxs, self.xs, GE)
RT_inv = 1.0 / (R * self.T)
gammas = [exp(i * RT_inv) for i in dG_dns]
else:
gammas = gibbs_excess_gammas(self.xs, dG_dxs, GE, self.T)
self._gammas = gammas
return gammas
def dnGE_dns(self):
r'''Calculate and return the partial mole number derivative of excess
Gibbs energy of a liquid phase using an activity coefficient model.
.. math::
\frac{\partial n G^E}{\partial n_i}
Returns
-------
dnGE_dns : list[float]
First partial mole number derivative of excess Gibbs entropy of the
liquid phase, [J/(mol)]
Notes
-----
'''
return dxs_to_dn_partials(self.dGE_dxs(), self.xs, self.GE())
def dgammas_dT(self):
r'''Calculate and return the temperature derivatives of activity
coefficients of a liquid phase using an activity coefficient model.
.. math::
\frac{\partial \gamma_i}{\partial T} =
\left(\frac{\frac{\partial^2 n G^E}{\partial T \partial n_i}}{RT} -
\frac{{\frac{\partial n_i G^E}{\partial n_i }}}{RT^2}\right)
\exp\left(\frac{\frac{\partial n_i G^E}{\partial n_i }}{RT}\right)
Returns
-------
dgammas_dT : list[float]
Temperature derivatives of activity coefficients, [1/K]
Notes
-----
'''
r'''
from sympy import *
R, T = symbols('R, T')
f = symbols('f', cls=Function)
diff(exp(f(T)/(R*T)), T)
'''
try:
return self._dgammas_dT
except AttributeError:
pass
d2nGE_dTdns = self.d2nGE_dTdns()
dG_dxs = self.dGE_dxs()
GE = self.GE()
dG_dns = dxs_to_dn_partials(dG_dxs, self.xs, GE)
T_inv = 1.0/self.T
RT_inv = R_inv*T_inv
self._dgammas_dT = dgammas_dT = []
for i in self.cmps:
x1 = dG_dns[i]*T_inv
dgammas_dT.append(RT_inv*(d2nGE_dTdns[i] - x1)*exp(dG_dns[i]*RT_inv))
return dgammas_dT
def dnSE_dns(self):
r'''Calculate and return the partial mole number derivative of excess
entropy of a liquid phase using an activity coefficient model.
.. math::
\frac{\partial n S^E}{\partial n_i}
Returns
-------
dnSE_dns : list[float]
First partial mole number derivative of excess entropy of the liquid
phase, [J/(mol*K)]
Notes
-----
'''
dnSE_dns = dxs_to_dn_partials(self.dSE_dxs(), self.xs, self.SE())
if not self.scalar and type(dnSE_dns) is list:
dnSE_dns = array(dnSE_dns)
return dnSE_dns