The gas–liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor–liquid interface, we apply our recently developed approach (Phys. Chem. Chem. Phys., 2018, 20, 16238) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas–liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks–Chandler–Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas–liquid dividing line and the corresponding line tensions.

中文翻译：

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通过多尺度方法捕获的模型Langmuir单层的气液相平衡†

Langmuir单层的气-液膨胀相变发生在非常低​​的表面浓度下，这使得在有限的三维（3D）原子模拟中探索该现象极为昂贵。与两亲性表面活性剂的3D模型的参考系统起始于2D气液界面，我们应用我们的最近开发的方法（物理学。化学式化学物理。，2018，20，16238）和整个系统映射到一个有效的2D系统表面活性剂质量中心投影到界面平面上。通过获得的粗粒相互作用势然后使用来自3D模拟的力匹配方案来预测相应的Langmuir单层的2D气相-液相平衡。在吉布斯系综中进行蒙特卡罗模拟，以计算单层内气相和液相共存相的面密度，化学势和表面压力。我们将这些模拟与基于Weeks–Chandler–Anderson微扰理论的2D密度泛函方法的结果进行比较。我们还使用这种方法来确定气液平衡分界线上的密度分布和相应的线张力。