Binary Mixture Vapor-Liquid Equilibria

Simulations were performed on six of binary mixtures to assess the transferability of the optimized potential parameters for noble gases. These mixtures included: argon+krypton, krypton+xenon, methane+krypton, methane+xenon, krypton+ethane, and xenon+ethane. These systems cover the complete range of interactions necessary to evaluate the transferability of the potential parameters between systems composed of non-polar molecules. Calculations were performed using the standard Lorentz-Berthelot combining rules without modification of unlike molecule interaction parameters. Each of these systems exhibits type I phase behavior, with small deviations from ideal solution behavior. The predictions of simulation for the pressure-composition diagrams for methane+xenon, and krypton+ethane are presented

in supplemental material in Figures 4.21 and 4.22, respectively [211]. Tabulated data may be found Tables 4.17-4.18 [211]. In each case, close agreement with experiment was observed, confirming the consistency of the optimized parameters for the Mie potentials. A more detailed discussion is provided in subsequent paragraphs for mixtures of argon+krypton, krypton+xenon, methane+krypton, and xenon+ethane.

The argon+krypton mixture is the most studied of this group. It has been used to assess the accuracy of potentials derived from ab initio calculations [185], and the role of three-body interactions [220] on the predicted phase behavior. In Figure 4.7, the pressure-composition diagrams for argon+krypton predicted by the optimized Mie potentials are shown, with comparisons to experimental data [158, 159] and prior simulations [171, 185]. More detailed comparisons may be found in Figure S12 [211]. When both components are subcritical, the predictions from the optimized Mie potentials are an exact match to experiment. At temperatures above the critical temperature of argon (150.86 K), the mole fraction of argon in the gas phase is over-predicted slightly near the critical point of the mixture. These results are a significant improvement over ab initio derived two and three body potentials [185], and similar in performance to the three-body potentials proposed by Wang and Sadus [220].

The krypton+xenon mixture exhibits type I phase behavior similar to that of argon+krypton. In Figure 4.8, the predictions of the optimized Mie potentials for 165.6 K ≤ 𝑇 ≤ 268.69 K are presented in comparison to experimental data [160].

As expected, the accuracy of the simulation data for this mixture is identical to the predictions of simulation for the argon+krypton system, illustrating the consistency of the parameterizations for noble gases. When both components are sub-critical, excellent agreement with experiment is achieved. At temperatures above the critical temperature of krypton, the mole fraction of krypton in the gas phase was over-predicted. Liquid phase mole fractions and vapor pressures were in close agreement with experiment for all temperatures studied. Previous modeling of the pressure-composition behavior of this mixture with the Peng-Robinson equation of state using a binary interaction parameter of 𝑘𝑖𝑗= −0.0051 produced

conditions, simulations produced more accurate predictions for the liquid compositions compared the Peng- Robinson equation of state.

Figure 4.8: Pressure-composition diagram for krypton+xenon binary system. Black lines represent

experimental data [160]; red symbols denote the predictions of NPT Gibbs ensemble Monte Carlo simulations using the optimized Mie potentials.

Of the mixtures studied here, methane+krypton most closely approaches ideal solution behavior. Experimentally, methane+krypton has a very small negative excess volume of 0.07%, and similarly small excess Gibbs free energy [161, 221]. The pressure composition diagram is razor thin, and provides a stringent test of both the accuracy of the force field, and the simulation methodology. The predictions of the Mie potentials are shown in Figure 4.9, with the experimental data of Calado et al. for comparison [161]. For all temperatures, including isotherms where CH4 is supercritical, excellent agreement was

achieved between simulation and experiment.

The xenon+ethane mixture has been well-studied experimentally [163, 165], with theory [165] and computer simulation [167]. This mixture presents an unusual case where all four excess functions

(𝑉𝐸, 𝐻𝐸, 𝐺𝐸, 𝑆𝐸 are negative, implying an unexpected stronger attraction between simple molecules that otherwise do not exhibit strong interactions, such as hydrogen bonding. Xenon and ethane have similar critical temperatures, 289.7 K (xenon) and 305.4 K (ethane), implying their intermolecular interactions are of similar strength. Prior modeling using statistical associating fluid theory for potentials of variable range (SAFT-VR) showed that parameters for xenon were close to those used for ethane [165, 169].

Figure 4.9: Pressure-composition diagram for methane-krypton binary system. Black lines represent

experimental data [161]; red symbols denote the predictions of NVT Gibbs ensemble Monte Carlo simulations for the optimized Mie potentials.

In Figure 4.10, the pressure composition diagrams predicted by the Mie potentials are presented and compared to experimental data [163] for 182.34 ≤ 𝑇 ≤ 284.31 K. For temperatures below 250 K, the predictions of simulation are in close agreement with experimental data and have an accuracy similar to the predictions of SAFT-VR [165]. As the critical point is approached, mixture vapor pressures are over-

predicted by 1-2%. This is the due to the xenon force field, which was found to over-predict the vapor pressure of pure xenon near the critical point by approximately 2%.

Figure 4.10: Pressure-composition diagram for xenon-ethane binary system. Black lines represent

experimental data [163]; red symbols denote the predictions of NVT Gibbs ensemble Monte Carlo simulations using the optimized Mie potentials.

Additional Gibbs ensemble calculations were performed for an equimolar mixture of xenon+ethane with the cross-interactions reduced by 1%. These calculations produced a positive excess Gibbs free energy, illustrating how small changes in the intermolecular potential may alter the sign of the excess functions. This result suggests that although all four excess functions are negative for this system, the deviation from ideal solution behavior is very small.