Activity Coeff. Models (polykin.thermo.acm)¤
Overview¤
This module implements activity coefficient models (ACMs) used in polymer reactor modeling. All models are formulated in terms of the molar excess Gibbs energy,
\[ g^{E} = g^{E}(T, x_i) \]
with all relations evaluated at constant pressure. Only multicomponent models are considered.
From \(g^E\), “all other thermodynamic properties can be obtained. For instance, the excess entropy and enthalpy are given by:
\[\begin{aligned}
s^{E} &= -\left(\frac{\partial g^{E}}{\partial T}\right)_{P,x_i} \\
h^{E} &= -R T^2 \left(\frac{\partial (g^{E}/RT)}{\partial T} \right)_{P,x_i}
\end{aligned}\]
A regular solution satisfies \(s^{E}=0\), while an atermal solution satisfies \(h^{E}=0\).
The activity coefficients are given by:
\[ \ln \gamma_i = \frac{1}{RT} \left( \frac{\partial (n g^E)}{\partial n_i} \right)_{T,P,n_j} \]
with:
\[ g^{E} = RT \sum_i x_i \ln \gamma_i \]