限制条件下相行为的Minkowski泛函
Minkowski functionals for phase behavior under confinement
摘要：
在这项工作中，闵可夫斯基泛函作为一个框架来研究如何形态（即结构的形状）和拓扑结构（即如何连接不同的结构）影响壁吸附和毛细凝聚下紧约束。基于经典的密度泛函理论（DFT）的数值模拟运行了各种各样的几何形状，使用硬球和Lennard-Jones流体。这些DFT计算相比，使用Minkowski泛函得到的结果。结果表明，Minkowski泛函可以很好地描述Lennard-Jones流体的行为。此外，通过自由能的分解，闵可夫斯基泛函提供了一个很好的框架，以更好地理解什么是一个系统的物理学的主要贡献。最后，在研究作为闵可夫斯基泛函的函数的相位包络移位时，发现拓扑结构具有不同的效果，取决于所考虑的相变是否是一阶或二阶转变。
英文摘要：
In this work, the Minkowski functionals are used as a framework to study how morphology (i.e. the shape of a structure) and topology (i.e. how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (DFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These DFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the physics of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a first- or a second-order transition.
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