Multiplicity of thermodynamic states of van der Waals gas in nanobubbles

The gas-containing nanobubbles have attracted extensive attention due to their remarkable properties and extensive application potential. However, a number of fundamental aspects of nanobubbles, including thermodynamic states for the confined gas, remain still unclear. Here we theoretically demonstrate that the van der Waals (vdW) gases confined in nanobubbles exhibit a unique thermodynamic state of remarkably deviating from the bulk gas phase, and the state transition behavior due to the size-dependent Laplace pressure. In general, the vdW gas inside nanobubbles present multiple stable or transient states, where 0–2 states are for supercritical gas and 0–4 for subcritical gas. Our further analysis based on Rayleigh–Plesset equation and free energy determination indicates that the gas states in nanobubbles exhibits different levels of stability, from which the coexistence of multiple bubble states and microphase equilibrium between droplets and bubbles are predicted. This work provides insight to understand the thermodynamic states appeared for gas in nanobubbles.