在博文混合溶剂中的高分子凝胶理论推导中，渗透压计算是按照各组分均匀分布来计算的。在一般情况下，各组分不是均匀分布，那该如何计算渗透压呢？

对于混合溶剂中的高分子凝胶，由于体积不可压缩性约束条件，三种组分不是独立的，我们把独立组分选为凝胶和一种溶剂。自由能密度为

\begin{equation*}
\begin{split}
f(\phi_{2},\phi_3)=&(1-\phi_{2}-\phi_3)\ln(1-\phi_{2}-\phi_3)+\phi_{2}\ln\phi_{2}\\
&+\chi_{12}(1-\phi_{2}-\phi_3)\phi_2 +\chi_{13}(1-\phi_{2}-\phi_3)\phi_3+\chi_{23}\phi_2\phi_3
\end{split}
\end{equation*}

渗透压为

\begin{equation*}
\Pi=\phi_2\frac{\partial f}{\partial \phi_2}+\phi_3\frac{\partial f}{\partial \phi_3}-f(\phi_{2},\phi_3)
\end{equation*}

第一项

\begin{equation*}
\begin{split}
\phi_2\frac{\partial f}{\partial \phi_2}=&\phi_2\left [-\ln(1-\phi_{2}-\phi_3)+\ln\phi_{2}+\chi_{12}(1-\phi_{2}-\phi_3)-\chi_{12} \phi_{2}-\chi_{13}\phi_3+\chi_{23}\phi_3\right ]\\
=&-\phi_2\ln(1-\phi_{2}-\phi_3)+\phi_2\ln\phi_{2}+\chi_{12}(1-\phi_{2}-\phi_3)\phi_2-\chi_{12} \phi_{2}^2-\chi_{13}\phi_2\phi_3+\chi_{23}\phi_2\phi_3
\end{split}
\end{equation*}

第二项

\begin{equation*}
\begin{split}
\phi_3\frac{\partial f}{\partial \phi_3}=&\phi_3\left [-\ln(1-\phi_{2}-\phi_3)-1-\chi_{12}\phi_{2}-\chi_{13}\phi_3+\chi_{13}(1-\phi_{2}-\phi_3)+\chi_{23}\phi_2\right ]\\
=&-\phi_3\ln(1-\phi_{2}-\phi_3)-\phi_3-\chi_{12}\phi_{2}\phi_3-\chi_{13}\phi_3^2+\chi_{13}(1-\phi_{2}-\phi_3)\phi_3+\chi_{23}\phi_2\phi_3
\end{split}
\end{equation*}

于是渗透压为

\begin{equation*}
\begin{split}
\Pi=&\phi_2\frac{\partial f}{\partial \phi_2}+\phi_3\frac{\partial f}{\partial \phi_3}-f(\phi_{2},\phi_3)\\
=&-\ln(1-\phi_{2}-\phi_3)-\phi_3-\chi_{12}\phi_{2}\phi_3-\chi_{12}\phi_{2}^2-\chi_{13}\phi_2\phi_3 -\chi_{13}\phi_3^2+\chi_{23}\phi_2\phi_3 \\
=&-\ln(1-\phi_{2}-\phi_3)-\phi_3-\chi_{13}\phi_3^2-\chi_{12}\phi_{2}^2+G\phi_2\phi_3
\end{split}
\end{equation*}

其中

\begin{equation*}
G=\chi_{23}-\chi_{12}-\chi_{13}
\end{equation*}

本体溶液自自由能密度

\begin{equation*}
f_s(\phi_{2s})=(1-\phi_{2s})\ln(1-\phi_{2s})+\phi_{2s}\ln\phi_{2s}+\chi_{12}(1-\phi_{2s})\phi_{2s}
\end{equation*}

渗透压为

\begin{equation*}
\Pi_s=\phi_{2s}\frac{\partial f_s}{\partial \phi_{2s}}-f_s(\phi_{2s})-\ln(1-\phi_{2s})-\chi_{12}\phi_{2s}^2
\end{equation*}

其他体系的渗透压计算与此类似。