Gas–droplet–liquid transitions and fluctuations in soft nano-confinement

One permanent characteristic of the thermodynamics of small systems is environment-dependence, also known as ensemble-dependence. Fluid molecules in soft (deformable) nano-confinement offer a special ensemble that acts as a bridge between classical isobaric (NPT) and isochoric (NVT) ensembles. Here, we discuss the gas–liquid transition taking place in a soft nano-confinement where the cell volume is not fixed but changes when the system pressure is changed. The free energy of the system is calculated as a function of the size of the liquid droplet that appears in the gas phase. We discuss how the phase behavior changes when the condition of the confinement changes from rigid confinement to very soft confinement. For the simple fluid model studied, the coexistence and critical phase behaviors are found to be uniquely determined by αK (αK is the dimensionless elasticity constant of the wall of confined space and is proportional to its ability to resist deformation), and the confinement with moderate softness exhibits richer phase behavior. We then study the fluctuations of pressure, volume, and droplet size for fluid in soft confined spaces, which is again closely related to the wall softness. Under moderate softness, large fluctuations in both fluid pressure and volume are seen in the transition region where fluid pressure increases with volume expansion, accompanied by the strengthened fluctuation of droplet size.