Micro- and nano-sized blisters can form spontaneously when two-dimensional (2D) crystals are transferred onto substrates because liquid molecules that are initially adsorbed on 2D material and substrate surfaces can be squeezed and trapped by interfacial forces. In this work, we use a combination of experiments, continuum theories, and coarse-grained molecular dynamics (CGMD) simulations to investigate the shape characteristics of spontaneously formed blisters under 2D crystals with heights ranging from a few ångströms to tens of nanometers. We show three distinct regimes in which the height-to-radius ratios (i.e., aspect ratios) of liquid-filled 2D crystal blisters are size-independent, rough linearly proportional, and inversely proportional to the blister radius. We reveal that the blister shape characteristics are governed by three factors: the 2D crystal elasticity, the interfacial interactions, and the phases of confined substances. The characteristic length scales (to which comparing the blister height or radius can define the boundary between these different regimes) are also discussed. We also provide approximate analytical solutions to the blister aspect ratios, which, together with complementary CGMD simulation results, agree with our experimental measurements.

当二维 (2D) 晶体转移到基板上时，微米和纳米尺寸的气泡会自发形成，因为最初吸附在二维材料和基板表面上的液体分子会被界面力挤压和捕获。在这项工作中，我们结合实验、连续介质理论和粗粒度分子动力学 (CGMD) 模拟来研究高度从几埃到几十纳米的二维晶体下自发形成的水泡的形状特征。我们展示了三种不同的方案，其中充满液体的 2D 晶体水泡的高度与半径比（即纵横比）与尺寸无关，大致呈线性比例，并且与水泡半径成反比。我们发现水泡形状特征受三个因素控制：二维晶体弹性、界面相互作用和受限物质的相。还讨论了特征长度尺度（比较水泡高度或半径可以定义这些不同制度之间的边界）。我们还提供了泡罩纵横比的近似解析解，与互补的 CGMD 模拟结果一起，与我们的实验测量结果一致。