The UNIQUAC segment activity coefficient model (UNIQUAC-SAC) is an activity coefficient model used to calculate the Gibbs free energy of a non-ideal system ^[1] . It is a modification to the UNIQUAC model and it defines the activity coefficient $\gamma_I$ as a function of the molar composition $x_I$. In UNIQUAC-SAC the activity coefficient is defined in a way that:

\[ln \gamma_I = ln \gamma_I^C + ln \gamma_I^R\]

Where $ln \gamma_I^C$ and $ln \gamma_I^R$ are the combinatorial and residual contributions to the activity coefficient of molecule $I$. The combinatorial contribution $ln \gamma_I^C$ is defined as:

\[ln \gamma_I^C = ln \dfrac{\phi_I}{x_I} + \dfrac{z}{2} q_I ln \dfrac{\theta_I}{\phi_I} + l_I - \dfrac{\phi_I}{x_I} \sum_{J} {x_J l_J}\]

and

\[\theta_I = \dfrac{x_I q_I}{\sum_J {x_J q_J}}\]

\[\phi_I = \dfrac{x_I r_I}{\sum_J {x_J r_J}}\]

\[l_I = \dfrac{z}{2} (r_I - q_I) - (r_I - 1)\]

\[r_I = \sum_K{v_K^I R_K}\]

\[q_I = \sum_K{v_K^I Q_K}\]

The variables $r_I$ and $q_I$ are the volume and surface parameters of molecule $I$ that are calculated using the segment surface area, $Q$ , and segment volume, $R$ , parameters as well as the number of occurrences of the segment on each molecule $v^I_K$. $\theta_I$ and $\phi_I$ are surface and volume fraction of component $I$ in the mixture, respectively. The residual part in the term of segment activity coefficient is written as:

\[ln \gamma_I^R = ln \gamma_I^{lc} = \sum_k{v_{k}^I [ln \Gamma_k - ln \Gamma_k^I]}\]

\[ln \Gamma_k = Q_k[1 - ln \sum_m {\Theta_m \Psi_{m k}} - \sum_m{\dfrac{\Theta_m \Psi_{m k}}{\sum_n{\Theta_n \Psi_{n m}}}}]\]

\[\Theta_m = \dfrac{Q_m X_m}{\sum_n {Q_n X_n}}\]

\[\Psi_{m n} = exp^{-\dfrac{U_{m n} - U_{n m}}{RT}} = exp^{-\dfrac{a_{m n}}{T}}\]

\[X_m = \dfrac{\sum_J {v_m^J x_J}}{\sum_J \sum_n v_n^J x_J}\]

$x_I$ and $x_J$ are the mole fractions of component $I$ and $J$, respectively, and the subscripts $m$, $n$, and $k$ denote the segment-base species indices. $X_m$ and $X_m^I$ are the segment-based mole fractions of segment species in solution and in pure component $I$, respectively.