Nanotechnology. 2019 May 24;30(21):215701. doi: 10.1088/1361-6528/ab061f. Epub 2019 Feb 11.
Graphene nanobubbles (GNBs) are formed when a substance is trapped between a graphene sheet (a 2D crystal) and an atomically flat substrate. The physical state of the substance inside GNBs can vary from the gas phase to crystal clusters. In this paper, we present a theoretical description of the gas-liquid phase transition of argon inside GNBs. The energy minimization concept is used to calculate the equilibrium properties of the bubble at constant temperature for a given mass of captured substance. We consider the total energy as a sum of the elastic energy of the graphene sheet, the bulk energy of the inner substance and the energy of adhesion between this substance, the substrate and graphene. The developed model allows us to reveal a correlation between the size of the bubble and the physical state of the substance inside it. A special case of a GNB that consists of argon trapped between a graphene sheet and a graphite substrate is considered. We predict the 'forbidden range' of radii, within which no stable GNBs exist, that separates bubble sizes with liquid argon inside from bubble sizes with gaseous argon. The height-to-radius ratio of the bubble is found to be constant for radii greater than 200 nm, which is consistent with experimental observations. The proposed model can be extended to various types of trapped substances and 2D crystals.
石墨烯纳米气泡（GNBs）是在物质被捕获在石墨烯片（二维晶体）和原子级平坦基底之间时形成的。GNB 内物质的物理状态可以从气相到晶体团簇变化。在本文中，我们提出了 GNB 内氩气的气液相变的理论描述。能量最小化概念用于计算在给定捕获物质质量下的恒定温度下气泡的平衡性质。我们将总能量视为石墨烯片的弹性能量、内部物质的体能量以及该物质、基底和石墨烯之间的粘附能的总和。所开发的模型允许我们揭示气泡的大小与其中物质的物理状态之间的相关性。考虑了由捕获在石墨烯片和石墨基底之间的氩气组成的 GNB 的特殊情况。我们预测了“禁止范围”的半径，在该范围内不存在稳定的 GNB，该范围将内部有液态氩气的气泡的大小与内部有气态氩气的气泡的大小分开。发现气泡的高度与半径之比对于大于 200nm 的半径是恒定的，这与实验观察结果一致。所提出的模型可以扩展到各种类型的捕获物质和二维晶体。
