液体中的分子尺度气泡：超越毛细近似的形成自由能
Molecular-sized bubbles in a liquid: free energy of formation beyond the capillarity approximation
AI总结：
本文通过分子模拟研究简单液体中瞬态气泡的形成自由能，修正了基于体积表征的玻尔兹曼关系，并发现小气泡自由能需在毛细近似基础上增加与半径成线性的额外项。
摘要：
我们利用分子模拟研究了简单液体中自发出现的瞬态气泡。目标是通过玻尔兹曼分布假设，从气泡尺寸分布 $p(s)$ 推导出气泡的形成自由能 $W(s)$：$W(s) = -kT \ln p(s)$。气泡的检测与表征采用一种基于叠加在液体上的网格的方法，该方法对于大于网格尺度的气泡效率较高。我们首先研究了网格选择对结果的影响，并表明使用多个网格值可以在最小计算成本下检测宽尺寸范围内的气泡。随后可以推导出大范围尺寸的气泡形成自由能，特别关注此前研究中很少涉及的趋于消失的气泡区域。我们首先表明，当气泡尺寸由其体积表征时，通常的玻尔兹曼关系必须加以修正。特别是，气泡体积分布在气泡趋于消失时发散，在利用上述公式计算其形成自由能之前应考虑这一点。一个适用于任意相互作用的球形分子的解析展开证实了这一观察。我们随后表明，毛细近似对于小气泡失效：必须在通常的二次（表面）项和三次（体积）项之外，增加一个与气泡半径成线性关系的额外贡献。这一额外项很可能与微小气泡的不规则形状有关。
英文摘要：
We investigate the transient bubbles that spontaneously appear in a simple liquid using molecular simulations. The objective is to deduce the free-energy of formation of the bubbles $W(s)$ from the bubble size distribution $p(s)$ through the hypothesis of a Boltzmann distribution: $W(s) = -kT \ln p(s)$. The bubbles are detected and characterized using a method based on a grid superimposed on the liquid, efficient for bubbles larger than the grid mesh. We first investigate how the results are affected by the mesh choice, and show that using several mesh values allows to detect bubbles in a wide range of sizes with minimal computing cost. The free-energy of formation of a bubble can then be deduced for a large range of sizes, with particular emphasis in the region of vanishing bubbles scarcely investigated in previous works. We first show that the usual Boltzmann relation has to be modified when the bubble size is characterized by its volume. In particular, the bubble volume distribution diverges for a vanishing bubble, which should be taken into account before calculating its free-energy of formation from the above formula. An analytical expansion, valid for any interacting spherical molecules, confirms this observation. We then show that the capillarity approximation fails for small bubbles: an extra contribution, linear with the bubble radius, has to be added to the usual quadratic (surface) and cubic (volume) contributions to the free-energy. This extra term most probably relates to the irregular shape of the tiny bubbles.
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