J. Richard Elliott

VAPOR-LIQUID EQUILIBRIA OF SQUARE-WELL SPHERES

Results of molecular dynamics (MD) simulations on square-well fluids with λ=1.25, 1.375, 1.5, 1.75, and 2.0 are presented. The calculation of vapor-liquid equilibrium was performed by isochoric integration of the liquid NVE data to obtain the free energy of the liquid and equating this to the vapor free energy from a modified virial equation. The saturation pressure was investigated and compared with that from Monte Carlo simulation and second-order analytical perturbation theory. The vapor pressures from the isochoric integration technique are shown to be smoother than previous results, permitting accurate estimation of the effect of the square-well width on acentric factor. With the saturated properties from molecular dynamics, the f value used in Kofke’s Gibbs-Duhem integration was calculated and was found to be nearly constant. The related integration of the Clapeyron equation was implemented as a check on thermodynamic consistency. Vapor pressures presented here are consistent to within 2%.

Investigation on the Solubility of SO2 and CO2 in Imidazolium-Based Ionic Liquids Using NPT Monte Carlo Simulation

The solubility of sulfur dioxide (SO(2)) and carbon dioxide (CO(2)) at P = 1 bar in a series of imidazolium-based room-temperature ionic liquids (RTILs) is calculated by Monte Carlo simulation in NPT ensemble using the OPLS-UA force field and Widom particle insertion method. The studied ILs were 1-butyl-3-methylimidazolium ([bmim](+)) tetrafluoroborate ([BF(4)](-)), [bmim](+) hexafluorophosphate ([PF(6)](-)), [bmim](+) bromide ([Br](-)), [bmim](+) nitrate ([NO(3)](-)), [bmim](+) bis-(trifluoromethyl) sulfonylimide ([Tf2N](-)), and 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF(4)]). To validate the simulations, the liquid density of studied ILs and the solubility of CO(2) in [bmim][PF(6)] was compared with corresponding experimental and theoretical studies reported in the literature, and a good agreement was obtained. The results of SO(2) solubility demonstrate that the SO(2) gas has the highest solubility in [bmim][NO(3)] and [bmim][Br] ILs and the lowest solubility in [bmim][PF(6)]. To describe the solubility order of polar gases such as SO(2) and nonpolar gases like CO(2), we have simulated the SO(2)/IL and CO(2)/IL mixtures which made possible to investigate the interaction of solute molecules with anions and cations in the liquid phase. We introduced the ratio of solute-IL interaction over cation-anion interaction energy density as an index for solubility of gases in ILs. The results show that the proposed index can describe the solubility order of SO(2) as well as CO(2) and it might be used as an alternative to standard methods of infinite dilution Henrys constant calculations when the solubility order is desired.

Phase envelopes for variable width square well chain fluids

Discontinuous Molecular Dynamics (DMD) and Thermodynamic Perturbation Theory (TPT) have been used to study square-well (SW) chain molecules with variable well-width SW potentials. Well widths of 1.5, 1.8, and 2.0 are considered for united atom models of ethane, n-hexane, and n-octane. The properties studied are the acentric factor, vapor pressure, and liquid density. DMD of purely repulsive potentials was applied to record the number of interaction sites in different wells, giving estimates of the TPT contributions from the attractive potential. DMD simulations of the complete potential near the coexistence condition were used to refine estimates of the derivative quantities related to the compressibility factor. Evaluations of this approach indicate that it is accurate and efficient at βe>0 and η>0.28. Phase diagrams of pure fluids also indicate quantitative accuracy for DMD/TPT at reduced temperatures less than 0.9. The results show that wider wells improve the representation of thermodynamic properties...

Phase diagrams for a multistep potential model of n-alkanes by discontinuous molecular dynamics and thermodynamic perturbation theory

Discontinuous molecular dynamics simulations and thermodynamic perturbation theory have been used to study thermodynamic properties for chain molecules. A multistep potential model is considered in this work through characterization of the vapor pressure and saturated liquid density for the n-alkanes from ethane to octane. The multistep potential model provides ∼4% accuracy for the entire molecular weight range. By contrast, previous studies of the square-well potential showed that the range of the square-well needed to vary with molecular weight to provide comparable accuracy. Therefore, having multiple steps with different depths for each functional group appears to be an essential part of making the potential model transferable. The depths of the wells vary such that the CH2 potential appears flatter than the CH3 potential, in an apparent attempt to moderate the overlaps implicit in the interaction site model.

Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. I. Homogeneous fluids.

In this work, we aim to develop a version of the Statistical Associating Fluid Theory (SAFT)-γ equation of state (EOS) that is compatible with united-atom force fields, rather than experimental data. We rely on the accuracy of the force fields to provide the relation to experimental data. Although, our objective is a transferable theory of interfacial properties for soft and fused heteronuclear chains, we first clarify the details of the SAFT-γ approach in terms of site-based simulations for homogeneous fluids. We show that a direct comparison of Helmholtz free energy to molecular simulation, in the framework of a third order Weeks-Chandler-Andersen perturbation theory, leads to an EOS that takes force field parameters as input and reproduces simulation results for Vapor-Liquid Equilibria (VLE) calculations. For example, saturated liquid density and vapor pressure of n-alkanes ranging from methane to dodecane deviate from those of the Transferable Potential for Phase Equilibria (TraPPE) force field by about 0.8% and 4%, respectively. Similar agreement between simulation and theory is obtained for critical properties and second virial coefficient. The EOS also reproduces simulation data of mixtures with about 5% deviation in bubble point pressure. Extension to inhomogeneous systems and united-atom site types beyond those used in description of n-alkanes will be addressed in succeeding papers.

Asymptotic trends in thermodynamic perturbation theory

The development of transferable force fields for n-alkanes has enabled molecular-dynamics simulation of the reference (A0) and perturbation (A1,A2) terms in thermodynamic perturbation theory (TPT) over a broad range of chain length. The implied equations of state yield 9.1% average error in vapor pressure and 4.7% error in liquid density for compounds ranging from propane to triacontane. Further simulations extend to nC80, but there are no experimental data to which comparisons can be made. With reliable TPT terms from molecular simulation, it is possible to analyze the trends with respect to molecular weight. Each TPT contribution is shown to approach an asymptote in the long chain limit. The asymptotes and the approaches to them are quantitatively characterized. A0 and A1 approach their asymptotes at relatively short chain lengths (nC30). A2, on the other hand, approaches its asymptote slowly (nC80). Simulation-based TPT terms also permit unambiguous interpretation of the number of coarse-grained segments relative to the number of carbons in the chain. Previous attempts have relied on characterizations that included the repulsive and attractive contributions simultaneously in a manner susceptible to a cancellation of errors. In this work, the reference fluid alone provides the characterization and the result is shown to be consistent with expectations for the A1 term. The conclusion is that the number of carbons per segment approaches roughly 10 in the long chain limit, much larger than previously reported. A small adjustment to the chain contribution from Wertheims [J. Stat. Phys. 42, 477 (1986)] TPT1 model is sufficient to provide quantitative accuracy for A0.

Optimized step potential models for n-alkanes and benzene

Abstract Vapor pressure, density, and internal energy data from the literature are correlated in terms of the intermolecular interactions as represented by stepwise potential energies. Discontinuous molecular dynamics simulations are performed for united atom hard chain models of ethane, n-butane, n-hexane, n-octane, and benzene. Assuming square-well attractions ending at r/σ=1.2, 1.5, 1.8, and 2.0, the depths of each well are regressed by computing the physical properties from thermodynamic perturbation theory at each set of trial depths and minimizing the deviations from experimental observation. The result is an equation-of-state for each fluid derived directly from the intermolecular potential model. Because molecular dynamics form the basis for the reference fluid simulations, transport properties may also be derived. Vapor pressure, density, and internal energy are correlated to roughly 1% average absolute deviation. The trends in the resulting potential models suggest that the change in disperse attractions with distance may vary from one functional group to another. For example, the optimized potential model for benzene diminishes to zero more slowly than the model for ethane.

Theory and simulation of chain-molecule fluid structure

Results of NVT molecular-dynamics simulations are reported for modelled n-butane and n-pentane over a range of densities at temperatures of about 430 K. The model potential is the repulsive part of the Lennard-Jones potential with bond angles constrained at 109·47° and bond lengths of 0·153 nm, where σ = 0·3923 nm and e/k = 72 K. Simulation results for average site-site distribution functions are compared with results of an approximate RISM theory. Similarly to the case of diatomic fluids, the accuracy of the approximate theory is only qualitative, but trends of key features of the fluid structure are well represented. The softness of the Lennard-Jones potential appears to play a significant role in smoothing away several potential sources of error in the approximate theory.

Vapor–liquid equilibria of vibrating square well chains

Vibrating square well (SW) 2-mer, 4-mer, and 8-mer with average reduced bond lengths of 0.97±0.03, 0.60±0.03, and 0.40±0.03 were studied by discontinuous molecular dynamics (DMD) simulation in the NVE ensemble. Average bond angles for the reduced bond length of 0.4 were constrained to 127±16° while the longer bond lengths were freely jointed. Vapor–liquid equilibria of the vibrating SW fluids were determined based on DMD simulation by isochoric integration and compared to that of rigid SW chains from Gibbs ensemble Monte Carlo (MC) simulation. The binodals of vibrating chains show a shift to higher temperatures relative to rigid chains, reflecting their less repulsive (more attractive) nature. Vapor pressures of the vibrating chains were computed through isochoric integration with Clausius–Clapeyron consistency to 5% or better. Vapor pressure behavior for each chain model was characterized in terms of critical temperature, critical pressure, and acentric factor. The trend in acentric factor vs. chain length showed that shorter bond lengths gave improved agreement with the experimental trend for n-alkanes. Nevertheless, the trends in acentric factor did not support any molecular model for alkanes which represented methylene segments as individual SW interaction sites. If SW chains are to be applied as models of alkanes, each interaction site must be assigned more than one methylene segment.Vibrating square well (SW) 2-mer, 4-mer, and 8-mer with average reduced bond lengths of 0.97±0.03, 0.60±0.03, and 0.40±0.03 were studied by discontinuous molecular dynamics (DMD) simulation in the NVE ensemble. Average bond angles for the reduced bond length of 0.4 were constrained to 127±16° while the longer bond lengths were freely jointed. Vapor–liquid equilibria of the vibrating SW fluids were determined based on DMD simulation by isochoric integration and compared to that of rigid SW chains from Gibbs ensemble Monte Carlo (MC) simulation. The binodals of vibrating chains show a shift to higher temperatures relative to rigid chains, reflecting their less repulsive (more attractive) nature. Vapor pressures of the vibrating chains were computed through isochoric integration with Clausius–Clapeyron consistency to 5% or better. Vapor pressure behavior for each chain model was characterized in terms of critical temperature, critical pressure, and acentric factor. The trend in acentric factor vs. chain leng...

Attractive-force effects in chain molecular fluids

Molecular-dynamics simulations are used to investigate the effects of attractive forces on the structure of two chain molecular fluids: n-butane and n-pentane. Simulations are performed using the complete site-site Lennard-Jones potential at state points identical with those in previous simulations that used just the repulsive part of the potential. The bond angles are constrained at 109·47° and the bond lengths at 0·153 nm. The potential parameters are σLJ = 0·3923 nm and the e/k = 72 K. Five densities are simulated for butane and four for pentane, all at a constant temperature of 430 K. Comparisons of pressures and the average site distribution functions from simulations for both potential models show an increased effect of attractive forces at low density, very similar to atomic fluids. The magnitude of the attractive-force effect appears to be much greater for chains than for atomic fluids, however, and the magnitude increases with increasing chain length. The simulation results are briefly compared w...