关于封闭流体结晶的Gibbs-Thomson方程
On the Gibbs-Thomson equation for the crystallization of confined fluids
摘要：
Gibbs-Thomson（GT）方程描述了作为孔径的函数的受限流体相对于本体的结晶温度的偏移。虽然这个百年关系式成功地用于分析实验，但在文献中发现的它的推导往往依赖于成核理论的论点（即动力学而不是热力学）或未能陈述其假设，因此导致相似但不同的表达式。在这里，我们重温GT方程的推导，以澄清系统定义，相应的热力学系综，以及沿途所作的假设。我们还讨论了外部库中的热力学条件对最终结果的作用。然后，我们转向一个模型系统的数值模拟，独立计算进入GT方程的各项，并比较后者的预测与熔化温度下确定的限制通过超平行回火巨正则蒙特卡罗模拟。我们强调了一些困难有关的限制下的模拟结晶取样。总的来说，尽管它的局限性，GT方程可以提供一个有趣的替代路线来预测大孔中的熔化温度，使用分子模拟来评估进入该方程的相关量。例如，这种方法可以用于研究最近在原子力显微镜的尖端和基底之间实验观察到的离子液体的纳米级毛细管冷冻。
英文摘要：
The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e. kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation, and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores, using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could for example be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an Atomic Force Microscope and a substrate.
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