Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres.

In Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] of this series, a methodology was presented for computing the coefficients of a power series of the Helmholtz energy in reciprocal temperature, ß, through density series based on cluster integral expansions. Previously, power series in ß were evaluated by thermodynamic perturbation theory (TPT) using molecular simulation of a reference fluid. The present methodology uses cluster integrals to evaluate coefficients of the density expansion at each individual order of temperature. While Paper I [J. R. Elliott, A. J. Schultz, and D. A. Kofke, J. Chem. Phys. 143, 114110 (2015)] developed this methodology for square well (SW) spheres, the present work extends the methodology to Lennard-Jones (LJ) spheres, where the reference fluid is the Weeks-Chandler-Andersen potential. Comparisons of TPT coefficients computed from cluster integrals to those from molecular simulation show good agreement through third order in ß when coefficients are expressed with effective approximants. Notably, the agreement for LJ spheres is much better than for SW spheres although fewer coefficients of the density series (B2-B5) are available than for SW spheres (B2-B6). The coefficients for Bi(ß) of the reference fluid are shown to follow a simple relationship to the virial coefficients of hard sphere fluids, corrected for the temperature dependency of the equivalent hard sphere diameter. This lays the foundation for a correlation of the second virial coefficient of LJ spheres B2(ß) that extrapolates to infinite order in temperature. This correlation of B2(ß) provides a basis for estimating the low density limit of TPT coefficients at all orders in temperature, facilitating a recursive extrapolation formula to estimate TPT coefficients of fourth order and higher over the entire density range. The applicability of the resulting equation of state is demonstrated by computing the thermodynamic properties for LJ spheres and comparing to standard simulation results.

A simple extrapolation of thermodynamic perturbation theory to infinite order.

Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A3/A2, where A(i) is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT).

Combined temperature and density series for fluid-phase properties. I. Square-well spheres.

Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(ß) η + B3(ß) η(2) + B4(ß) η(3) + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B(i)(ß) coefficients are expanded as a power series in reciprocal temperature, ß, about ß = 0. The methodology is demonstrated for square-well spheres with λ = [1.2-2.0], where λ is the well diameter relative to the hard core. For this model, the B(i) coefficients can be expressed in closed form as a function of ß, and we develop appropriate expressions for i = 2-6; these expressions facilitate derivation of the coefficients of the ß series. Expanding the B(i) coefficients in ß provides a correspondence between the power series in density (typically called the virial series) and the power series in ß (typically called thermodynamic perturbation theory, TPT). The coefficients of the ß series result in expressions for the Helmholtz energy that can be compared to recent computations of TPT coefficients to fourth order in ß. These comparisons show good agreement at first order in ß, suggesting that the virial series converges for this term. Discrepancies for higher-order terms suggest that convergence of the density series depends on the order in ß. With selection of an appropriate approximant, the treatment of Helmholtz energy that is second order in ß appears to be stable and convergent at least to the critical density, but higher-order coefficients are needed to determine how far this behavior extends into the liquid.

Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. II. Confined fluids and vapor-liquid interfaces.

In this work, a new classical density functional theory is developed for group-contribution equations of state (EOS). Details of implementation are demonstrated for the recently-developed SAFT-γ WCA EOS and selective applications are studied for confined fluids and vapor-liquid interfaces. The acronym WCA (Weeks-Chandler-Andersen) refers to the characterization of the reference part of the third-order thermodynamic perturbation theory applied in formulating the EOS. SAFT-γ refers to the particular form of "statistical associating fluid theory" that is applied to the fused-sphere, heteronuclear, united-atom molecular models of interest. For the monomer term, the modified fundamental measure theory is extended to WCA-spheres. A new chain functional is also introduced for fused and soft heteronuclear chains. The attractive interactions are taken into account by considering the structure of the fluid, thus elevating the theory beyond the mean field approximation. The fluctuations of energy are also included via a non-local third-order perturbation theory. The theory includes resolution of the density profiles of individual groups such as CH2 and CH3 and satisfies stoichiometric constraints for the density profiles. New molecular simulations are conducted to demonstrate the accuracy of each Helmholtz free energy contribution in reproducing the microstructure of inhomogeneous systems at the united-atom level of coarse graining. At each stage, comparisons are made to assess where the present theory stands relative to the current state of the art for studying inhomogeneous fluids. Overall, it is shown that the characteristic features of real molecular fluids are captured both qualitatively and quantitatively. For example, the average pore density deviates ∼2% from simulation data for attractive pentadecane in a 2-nm slit pore. Another example is the surface tension of ethane/heptane mixture, which deviates ∼1% from simulation data while the theory reproduces the excess accumulation of ethane at the interface.

Adapting SAFT-γ perturbation theory to site-based molecular dynamics simulation. III. Molecules with partial charges at bulk phases, confined geometries and interfaces.

In Paper I [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 139(23), 234104 (2013)], we showed that how a third-order Weeks-Chandler-Anderson (WCA) Thermodynamic Perturbation Theory and molecular simulation can be integrated to characterize the repulsive and dispersive contributions to the Helmholtz free energy for realistic molecular conformations. To this end, we focused on n-alkanes to develop a theory for fused and soft chains. In Paper II [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 141(2), 024708 (2014)], we adapted the classical Density Functional Theory and studied the microstructure of the realistic molecular fluids in confined geometries and vapor-liquid interfaces. We demonstrated that a detailed consistency between molecular simulation and theory can be achieved for both bulk and inhomogeneous phases. In this paper, we extend the methodology to molecules with partial charges such as carbon dioxide, water, 1-alkanols, nitriles, and ethers. We show that the electrostatic interactions can be captured via an effective association potential in the framework of Statistical Associating Fluid Theory (SAFT). Implementation of the resulting association contribution in assessing the properties of these molecules at confined geometries and interfaces presents satisfactory agreement with molecular simulation and experimental data. For example, the predicted surface tension deviates less than 4% comparing to full potential simulations. Also, the theory, referred to as SAFT-γ WCA, is able to reproduce the specific orientation of hydrophilic head and hydrophobic tail of 1-alkanols at the vapor-liquid interface of water.

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.

On-the-Fly Second Virial Coefficients.

A simple but approximate algorithm is described for computing second virial coefficients based on equilibrated molecular configurations that may be generated during any Monte Carlo or molecular dynamics simulation. The algorithm uses simple quadrature based on sampling every binary pair in the configuration and moving their center-center distances from zero to infinity. Comparisons are made in the literature results using more sophisticated sampling and integration for n-alkanes of ethane through n-dodecane. Accuracy is within the error bars determined by block averaging, and temperature effects can be inferred using a single configurational temperature, including perturbative virial coefficients. Predictably, the accuracy is best at the configurational temperature and when the configurational density is lowest. More notably, good accuracy is achieved from configurations at intermediate densities, and the trend at high density conveys valuable insight about conformational changes. The algorithm is simple enough to assign as a homework problem in an introductory molecular modeling course and reinforces the elementary knowledge of pairwise potentials among multisite molecules, numerical integration, and conformational averaging. The result is also quite valuable on its own merits, especially considering thermodynamic integration to compute phase equilibria. Additionally, the incidental data derived from the computation can provide simple but meaningful insights into the nature of multisite interactions, as demonstrated by relating the Mayer averaged potential to an effective Mie potential. Altogether, the argument is made that the computation of the second virial coefficient should be considered to be a routine metric of any molecular simulation, such as the radial distribution function, pressure, or energy.

Minimization of fermentation inhibitor generation by carbon dioxide-water based pretreatment and enzyme hydrolysis of guayule biomass.

Guayule rubber production leaves >80% biomass as ground bagasse, which can be hydrolyzed to release sugars but also fermentation inhibitors. Here inhibitor generation and sugar conversion by the CO2-H2O pretreatment and enzyme hydrolysis were studied. Different pretreatment conditions: 550-4900 psi, 160-195 °C, 10-60 min and fixed 66.7% water, generated widely varying amounts of inhibitors (per dry-bagasse mass): 0.014-0.252% hydroxymethylfurfural, 0.012-0.794% furfural and 0.17-8.02% acetic acid. The condition (195 °C/3400 psi/30 min) giving highest reducing sugar (86.9 ±â€¯1.5%) and cellulose (99.2 ±â€¯1.3%) conversions generated more inhibitors. Kluyveromyces marxianus fermentation showed complete growth and ethanol production inhibition at ≥14 g/L combined inhibitors. Considering both sugars and inhibitors, the optimum condition was 180 °C, 1800 psi and 30 min, enabling 82.8 ±â€¯2.8% reducing sugar, 74.8 ±â€¯4.8% cellulose and 88.5 ±â€¯6.9% hemicellulose conversions with low levels of hydroxymethylfurfural (0.07%), furfural (0.25%) and acetic acid (3.0%). The optimized CO2-H2O pretreatment gave much lower inhibitor formation and higher sugar conversion than other pretreatment methods.

Effect of surface resistances on the diffusion of binary mixtures in the silicalite single crystal membrane.

Diffusion of methane and argon mixtures through the silicalite single-crystal membrane is studied using the dual-control volume-grand canonical molecular dynamics method to understand how surface resistances alter selectivity and permeance. Comparison of results from intracrystalline transport and entrance simulations for binary mixtures of CH4 and Ar shows that the selectivity of silicalite membranes toward Ar is enhanced in the presence of the surface resistances. In both cases, however, diffusion of faster Ar molecules was inhibited by slower diffusing CH4 molecules, whereas diffusion of the latter remained unaffected. This behavior was explained by the difference between the magnitudes of surface resistances for two molecules, which is much smaller for Ar because of its smaller permeant-crystal interaction size. We find that selectivity of the membrane at the surface depends strongly on total feed pressure and temperature, whereas this dependence is weak for intracrystalline diffusion. Furthermore, we show that the selectivity at the surface diminishes with crystal thickness until a certain thickness is reached, whereas the intracrystalline selectivity remains constant with increasing thickness. Finally, a study of diffusion of C2H6 and CF4 mixtures shows that the diatomic ethane molecules diffuse faster inside the zeolite channels, but their desorption is hindered to a larger extent than that of a spherical molecule with larger diameter and lower heat of adsorption. This observation indicates that the difference in molecular geometry is also a significant factor to explain the exit effect.

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 Henry's constant calculations when the solubility order is desired.

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 Wertheim's [J. Stat. Phys. 42, 477 (1986)] TPT1 model is sufficient to provide quantitative accuracy for A0.

The Mid-Canada Radar Line and First Nations' people of the James Bay region, Canada: an evaluation using log-linear contingency modelling to analyze organochlorine frequency data.

Abandoned radar line stations in the North American arctic and sub-arctic regions are point sources of contamination, especially for PCBs. Few data exist with respect to human body burden of organochlorines (OCs) in residents of communities located in close proximity to these radar line sites. We compared plasma OC concentration (unadjusted for total lipids) frequency distribution data using log-linear contingency modelling for Fort Albany First Nation, the site of an abandoned Mid-Canada Radar Line station, and two comparison populations (the neighbouring community of Kashechewan First Nation without such a radar installation, and Hamilton, a city in southern Ontario, Canada). This type of analysis is important as it allows for an initial investigation of contaminant data without imputing any values. The two-state log-linear model (employing both non-detectable and detectable concentration frequencies and applicable to PCB congeners 28 and 105 and cis-nonachlor) and the four-state log-linear model (using quartile concentration frequencies for Aroclor 1260, PCB congeners [99,118,138,153,156,170,180,183,187], beta-HCH, p,p'-DDT +p,p'-DDE, HCB, mirex, oxychlordane, and trans-nonachlor) revealed that the effects of subject gender were inconsequential. Significant differences (p < 0.05) between the groups examined were attributable to the effect of location on the frequency of detection of OCs or on their differential distribution among the concentration quartiles. In general, people from Hamilton had higher frequencies of non-detections and of concentrations in the first quartile (p < 0.05) for most OCs compared to people from Fort Albany and Kashechewan (who consume a traditional diet of wild meats that does not include marine mammals). An unexpected finding was that, for Kashechewan males, the frequency of many OCs was significantly higher (p < 0.05) in the 4th concentration quartile than that predicted by the four-state log-linear model, but significantly lower than expected in the 1st quartile for beta-HCH. The levels of PCBs found for women in Fort Albany and Kashechewan were greater than those reported for Dene (First Nation people) and Métis (mixed heritage) of the western Northwest Territories (NWT) who did not consume marine mammals, and for Inuit living in the central NWT (occasional consumers of marine mammals). Moreover, the levels of total p,p'-DDT were greater for Fort Albany and Kashechewan women compared to these same aboriginal groups.