Development of SAFT-Based Coarse-Grained Models of Carbon Dioxide and Nitrogen

We develop coarse-grained models for carbon dioxide (CO₂) and nitrogen (N₂) that capture the vapor-liquid equilibria of both their single components and their binary mixtures over a wide range of temperatures and pressures. To achieve this, we used an equation of state (EoS), namely Statistical Associating Fluid Theory (SAFT), which utilizes a molecular-based algebraic description of the free energy of chain fluids. This significantly accelerates the exploration of the parameter space, enabling the development of coarse-grained models that provide an optimal description of the macroscopic experimental data. SAFT creates models of fluids by chaining together spheres, which represent coarse-grained parts of a molecule. The result is a series of fitted parameters, such as bead size, bond length, and interaction strengths, that seem amenable to molecular simulation. However, only a limited set of models can be directly implemented in a particle-based simulation; this is predominantly due to how SAFT handles overlap between bonded monomers with parameters that do not translate to physical features, such as bond length. To translate such parameters to bond lengths in a coarse-grained force-field, we performed Wang-Landau transition-matrix Monte Carlo (WL-TMMC) simulations in the grand canonical ensemble on homonuclear fused two-segment Mie models and evaluated the phase behavior at different bond lengths. In the spirit of the law of corresponding states, we found that a force field, which matches SAFT predictions, can be derived by rescaling length and energy scales based on ratios of critical point properties of simulations and experiments. The phase behavior of CO₂ and N₂ mixtures was also investigated. Overall, we found excellent agreement over a wide range of temperatures and pressures in pure components and mixtures, similar to TraPPE CO₂ and N₂ models. Our proposed approach is the first step to establishing a more robust bridge between SAFT and molecular simulation modeling.