Analytical attractive functions and their derivatives in bulk and nanoconfined pores

Abstract

In this paper, two new analytical attractive (alpha) functions and their derivatives in bulk and nanoconfined pores are developed based on the virial equation of state (EOS) and statistical thermodynamics and are evaluated at different conditions for the first time. A cubic EOS is modified to nanometer scale and applied to predict the thermodynamic and phase properties in bulk and nanoconfined pores coupled with the new analytical alpha functions. The nanoscale‐extended EOS coupled with the analytical alpha functions are validated to be accurate by means of the experimental data for the thermodynamic and phase calculations. The alpha functions and dimensionless attractive term A for the O2, Ar, CO2, N2, and C1‐C10 are always positive and monotonically decrease with the temperature increases at T ≤ 2000 K in the bulk phase, whereas the second virial coefficients (B2) are always negative and increase with the temperature increases. Moreover, the alpha functions, A, and B2 for all of components remain constant with the decreasing pore radius until rp = 50 nm, the former two of which decrease while the latter one increases by further reducing the pore radius. It should be noted that the intermolecular attractive force (ie, A) is a function of the pressure, which is gradually increased at P ≤ 10 MPa though drastically increases afterwards. Also, the enhanced confinement effects lead the same‐component intermolecular attractive forces to be smaller. The analytical formulations in the SRK type slightly outperform in the gaseous or light component cases, while those in the PR type are better for the heavy component cases in terms of the thermodynamic property calculations, both of which are compatible with the modified EOS and analytical alpha functions.