Shcherbakova Nataliya, Gerbaud Vincent, Roger Kevin
Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INP, UPS, 31432 Toulouse, France.
Entropy (Basel). 2023 Sep 13;25(9):1329. doi: 10.3390/e25091329.
Phase diagrams are powerful tools to understand the multi-scale behaviour of complex systems. Yet, their determination requires in practice both experiments and computations, which quickly becomes a daunting task. Here, we propose a geometrical approach to simplify the numerical computation of liquid-liquid ternary phase diagrams. We show that using the intrinsic geometry of the binodal curve, it is possible to formulate the problem as a simple set of ordinary differential equations in an extended 4D space. Consequently, if the thermodynamic potential, such as Gibbs free energy, is known from an experimental data set, the whole phase diagram, including the spinodal curve, can be easily computed. We showcase this approach on four ternary liquid-liquid diagrams, with different topological properties, using a modified Flory-Huggins model. We demonstrate that our method leads to similar or better results comparing those obtained with other methods, but with a much simpler procedure. Acknowledging and using the intrinsic geometry of phase diagrams thus appears as a promising way to further develop the computation of multiphase diagrams.
相图是理解复杂系统多尺度行为的有力工具。然而，实际上确定相图既需要实验也需要计算，这很快就会变成一项艰巨的任务。在此，我们提出一种几何方法来简化液 - 液三元相图的数值计算。我们表明，利用双节线曲线的内在几何形状，可以将该问题表述为扩展四维空间中的一组简单常微分方程。因此，如果从实验数据集已知诸如吉布斯自由能之类的热力学势，那么整个相图，包括旋节线曲线，都可以轻松计算出来。我们使用修正的弗洛里 - 哈金斯模型在四个具有不同拓扑性质的三元液 - 液相图上展示了这种方法。我们证明，与其他方法相比，我们的方法能得出相似或更好的结果，但计算过程要简单得多。认识并利用相图的内在几何形状因此似乎是进一步发展多相图计算的一种有前景的方法。
