Modelling the solid–liquid–vapour phase behaviour of n-alkanes in a TPT-1 framework

Abstract

We study the global phase behaviour of n-alkanes applying Wertheim's first order thermodynamic perturbation theory (TPT1). The molecules are modelled as homonuclear chains comprised of m freely jointed spherical segments interacting via the Lennard-Jones potential. Vega et al. [J. Chem. Phys. 116, 17 (2002)] have shown that the TPT1 is suitable to treat solid phases as well as fluid phases when model chains are considered, but that the adoption of a fully flexible chain model leads to the under-prediction of triple point temperatures and overestimation of the fluid ranges in comparison to experiment. Here, we propose a model in which a different number of segments are used to treat the fluid and the solid phase. The number of segments used to model the molecules in the fluid phase $m_{\mathrm{f}}$, and the LJ monomer potential parameters σ and ε are taken from published soft-SAFT values, whereas in the case of the solid phase a reduced temperature-dependent effective chain length $m_{\mathrm{s}}(T^{\ast })$ is determined through a minimisation between theoretical and experimental liquid-solid phase equilibrium data. We refer to this model as effective-solid TPT1 (es-TPT1). We use the model proposed to calculate the solid–liquid–vapour phase diagrams of several n-alkanes and compare with experimental data. In the approach proposed, the conformation of chains in the solid phase is decoupled from the fluid phase, and an excellent description of the melting properties, as well as accurate predictions of the triple point temperatures for the n-alkanes examined is obtained. This simple solution provides an avenue to model the solid–liquid–vapour phase behaviour of other real substances in a TPT1 framework, and hence within the SAFT family of equations.

GRAPHICAL ABSTRACT

Keywords:

• n-alkanes
• phase behaviour
• solid–liquid equilibrium
• TPT1

Acknowledgments

We gratefully acknowledge Luis Alcázar-Vara and Eduardo Buenrostro-González (Instituto Mexicano del Petróleo, México) for very usefull discussions and information about experimental data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We acknowledge support from the University of Guanajuato [grant number CIIC 151/2022] and CONACYT (México) for a PhD scholarship (VRC). Amparo Galindo acknowledges support from the Royal Academy of Engineering and Eli Lilly and Company for support of a Research Chair [grant number RCSRF1819\7\33].