Fluids under extreme confinement can deviate substantially in their thermodynamic and transport properties from their bulk counterparts. Specifically, fluids subject to confinement in carbon nanotubes (CNTs) of precise diameters less than 2 nm demonstrate remarkable properties that can be leveraged for critical nanofluidic applications. However, their metrology is experimentally difficult due to extreme synthesis conditions. The pioneering advancement by Travalloni et al. of a series of fluid Equations of State (EOS) for extreme confinement provides an opportunity to describe and design experimentally realizable measurements at the nanometer scale and extract valuable thermodynamic property data for these exotic systems. In this work, we derive and analyze the EOS predictions for water, methanol, n-butane, n-hexane, n-decane, benzene, and carbon dioxide under confinement through simulated thermally driven phase transitions at constant pressure, or isobars. Both the van der Waals (vdW) and Peng Robinson (PR) EOS are considered. At the boundary of the model system, the confined fluid is considered connected to a constant pressure reservoir. We also consider the case where there is a thermal gradient connecting the fluid to an ambient pressure and temperature reservoir, consistent with a fluid in a heated, semi-infinite nanotube. In order to model such a system, we derive and validate a quasi-equilibrium condition for nanoconfinement to relate the gradient of the chemical potential and temperature in a bulk and confined phase. These temperature-driven isobars are experimentally tractable measurements that can enable thermodynamic properties, such as the enthalpy of phase transition and the phase transition critical temperature, to be reliably measured for fluids under extreme confinement. Using the EOS formulations, we show the explicit effects of the molecule-CNT interaction on these important thermodynamic parameters. We further model fluid mixtures and separation behaviors in CNTs. Finally, we predict the capillary pressure of fluids inside CNTs, showing that the PR EOS is able accurately capture the well-known maximum in capillary pressure that occurs at CNT diameters between 1.2 and 1.4 nm. The predictive capabilities of the nanoconfined EOS are an important engineering tool to modeling the phase behavior of any fluid in carbon nanomaterials, and can help better inform the rational design of nanofluidic devices.
