Van der Waals chain-molecule fluid in self-consistent field approximation: Some thermal properties

The van der Waals equation for a monomer is used to derive the equation of state for a fluid consisting of chain molecules of equal length. The evolution of a part of the diagram of state pertaining to liquid-vapor equilibrium is treated for the case of an increase in the number of links in a molecule. The dependences on the number of links n are found for the following properties of polymer fluid: the critical temperature $T_c$, the critical pressure $p_c$, the critical density $\rho_c$, the critical compressibility $z_c$, the temperature of normal boiling, the Riedel parameter of similarity $\alpha$, the acentric factor $\omega$, and the enthalpy of vapor formation $\Delta H_\nu$. A comparison with the experimental data for $n$-alkanes and $1$-alkanols reveals that the obtained dependences reflect qualitatively correctly the variation of the above-identified properties with an increase of the number of links in a molecule. For long chains $(n\gg1)$, the scaling dependences are determined for the properties of a chain-molecule fluid: $T_c\sim1-n^{-1/2}$, $p_c\sim n^{-3/2}$, $\rho_c\sim n^{-1/2}$, $z_c\sim n^{-1}$, $\alpha\sim n$, $\omega\sim n^{2/3}$, $\Delta H_\nu\sim n$.