Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble

Predicting the Features of Methane Adsorption in Large Pore Metal-Organic Frameworks for Energy Storage

Currently, metal-organic frameworks (MOFs) are receiving significant attention as part of an international push to use their special properties in an extensive variety of energy applications. In particular, MOFs have exceptional potential for gas storage especially for methane and hydrogen for automobiles. However, using theoretical approaches to investigate this important problem presents various difficulties. Here we present the outcomes of a basic theoretical investigation into methane adsorption in large pore MOFs with the aim of capturing the unique features of this phenomenon. We have developed a pseudo one-dimensional statistical mechanical theory of adsorption of gas in a MOF with both narrow and large pores, which is solved exactly using a transfer matrix technique in the Osmotic Ensemble (OE). The theory effectively describes the distinctive features of adsorption of gas isotherms in MOFs. The characteristic forms of adsorption isotherms in MOFs reflect changes in structure caused by adsorption of gas and compressive stress. Of extraordinary importance for gas storage for energy applications, we find two regimes of Negative gas adsorption (NGA) where gas pressure causes the MOF to transform from the large pore to the narrow pore structure. These transformations can be induced by mechanical compression and conceivably used in an engine to discharge adsorbed gas from the MOF. The elements which govern NGA in MOFs with large pores are identified. Our study may help guide the difficult program of work for computer simulation studies of gas storage in MOFs with large pores.

Microscopic Origin of Frictional Rheology in Dense Suspensions: Correlations in Force Space

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (σ_{xy}) and packing fraction (ϕ). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, μ=σ_{xy}/P. We find that μ decreases (i) as ϕ is increased and (ii) as σ_{xy} is increased. Using a new constitutive relation between μ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a discontinuous shear thickening flow diagram that is in good agreement with numerical simulations, and the qualitative features of μ that lead to the generic flow diagram of a discontinuous shear thickening fluid observed in experiments.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Pressure control in interfacial systems: Atomistic simulations of vapor nucleation

A large number of phenomena of scientific and technological interest involve multiple phases and occur at constant pressure of one of the two phases, e.g., the liquid phase in vapor nucleation. It is therefore of great interest to be able to reproduce such conditions in atomistic simulations. Here we study how popular barostats, originally devised for homogeneous systems, behave when applied straightforwardly to heterogeneous systems. We focus on vapor nucleation from a super-heated Lennard-Jones liquid, studied via hybrid restrained Monte Carlo simulations. The results show a departure from the trends predicted for the case of constant liquid pressure, i.e., from the conditions of classical nucleation theory. Artifacts deriving from standard (global) barostats are shown to depend on the size of the simulation box. In particular, for Lennard-Jones liquid systems of 7000 and 13 500 atoms, at conditions typically found in the literature, we have estimated an error of 10-15 k_BT on the free-energy barrier, corresponding to an error of 10⁴-10⁶ s^-1σ^-3 on the nucleation rate. A mechanical (local) barostat is proposed which heals the artifacts for the considered case of vapor nucleation.

Many-body interactions between charged particles in a polymer solution: the protein regime

We study the phase behavior of charged particles in electrolyte solutions wherein non-adsorbing polymers are added to provide an attractive depletion interaction. The polymer has a radius of gyration similar to that of the particle radius, which causes significant many-body effects in the effective polymer mediated interaction between particles. We use a recently developed analytical theory, which gives a closed expression for the full depletion interaction, accounting for all orders of many-body terms in the potential of mean force. We compare with simulations of an explicit polymer model and show that the potential of mean force provides an accurate and computationally efficient description for the charged particle/polymer mixture, over a range of electrolyte concentrations. Furthermore, we demonstrate that the usual pair potential approach is highly inaccurate for these systems. A simple simulation method is used to estimate the limits of stability of the mixture. The pair approximation is shown to predict a much greater region of instability compared with the many-body treatment, due to its overestimation of the polymer depletion effect.

Computational Design of High-χ Block Oligomers for Accessing 1 nm Domains

Molecular dynamics simulations are used to design a series of high-χ block oligomers (HCBOs) that can self-assemble into a variety of mesophases with domain sizes as small as 1 nm. The exploration of these oligomers with various chain lengths, volume fractions, and chain architectures at multiple temperatures reveals the presence of ordered lamellae, perforated lamellae, and hexagonally packed cylinders. The achieved periods are as small as 3.0 and 2.1 nm for lamellae and cylinders, respectively, which correspond to polar domains of approximately 1 nm. Interestingly, the detailed phase behavior of these oligomers is distinct from that of either solvent-free surfactants or block polymers. The simulations reveal that the behavior of these HCBOs is a product of an interplay between both "surfactant factors" (headgroup interactions, chain flexibility, and interfacial curvature) and "block polymer factors" (χ, chain length N, and volume fraction f). This insight promotes the understanding of molecular features pivotal for mesophase formation at the sub-5 nm length scale, which facilitates the design of HCBOs tailored toward particular desired morphologies.

Liquid-Liquid Phase Separation of Patchy Particles Illuminates Diverse Effects of Regulatory Components on Protein Droplet Formation

Recently many cellular functions have been associated with membraneless organelles, or protein droplets, formed by liquid-liquid phase separation (LLPS). Proteins in these droplets often contain RNA-binding domains, but the effects of RNA on LLPS have been controversial. To gain better understanding on the roles of RNA and other macromolecular regulators, here we used Gibbs-ensemble simulations to determine phase diagrams of two-component patchy particles, as models for mixtures of proteins with regulatory components. Protein-like particles have four patches, with attraction strength ε_PP; regulatory particles experience mutual steric repulsion but have two attractive patches toward proteins, with the strength ε_PR tunable. At low ε_PR, the regulator, due to steric repulsion, preferentially partitions in the dispersed phase, thereby displacing the protein into the droplet phase and promoting LLPS. At moderate ε_PR, the regulator starts to partition and displace the protein in the droplet phase, but only to weaken bonding networks and thereby suppress LLPS. At ε_PR > ε_PP, the enhanced bonding ability of the regulator initially promotes LLPS, but at higher amounts, the resulting displacement of the protein suppresses LLPS. These results illustrate how RNA can have disparate effects on LLPS, thus able to perform diverse functions in different organelles.

Transferable Potentials for Chloroethenes: Insights into Nonideal Solution Behavior of Environmental Contaminants

Predicting the nonideal phase behavior of binary and multicomponent systems remains a significant challenge for particle-based simulations. Here, we develop a transferable force field for chloroethenes, common environmental contaminants, that can accurately model the vapor liquid phase equilibria including azeotrope formation. The new all-atom force field reproduces saturated liquid densities, saturated vapor pressures, boiling points, and critical properties within 1, 10, 1, and 1% of the experiment data, respectively. Furthermore, the vapor liquid equilibria of trichloroethylene and 1-propanol binary mixture, which forms a minimum boiling point azeotrope, is predicted with a reasonable accuracy. The microstructure of neat and binary systems is explored using pair correlation functions and spatial distribution functions. As the new force field is consistent with transferable potentials for phase equilibria (TraPPE) force field, it expands the applicability of TraPPE force field to chloroethenes.

Ionic-Functionalized Polymers of Intrinsic Microporosity for Gas Separation Applications

Ionic-functionalized microporous materials are attractive for energy-efficient gas adsorption and separation processes and have shown promising results in gas mixtures at pressure ranges and compositions that are relevant for industrial applications. In this work, we studied the influence of different counterions (Li⁺, Na⁺, K⁺, Rb⁺, and Mg²⁺) on the porosity, carbon dioxide (CO₂) gas adsorption, and selectivity in ionic-functionalized PIM-1 (IonomIMs), a polymer belonging to the class of linear and amorphous microporous polymers known as polymers of intrinsic microporosity (PIMs). It was found that an increase in the concentration of ionic groups led to a decrease in the free volume, resulting in a less porous polymer framework, and Mg²⁺-functionalized IonomIMs exhibited a relatively larger porosity compared to other IonomIMs. The CO₂ adsorption capacity was affected by the different counterions for IonomIM-1, and a higher loading capacity for pure CO₂ was observed for Mg²⁺. Furthermore, the IonomIMs showed an enhanced CO₂ selectivity in CO₂/CH₄ and CO₂/N₂ gas mixtures at conditions used in pressure swing adsorption and vacuum swing adsorption applications. It was also observed that the concentration of ionic groups plays a vital role in changing the CO₂ gas adsorption and selectivity.

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE-D3, BLYP-D3, PBE0-D3, M062X-D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP-D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP-D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO₂ and SO₂ . © 2017 Wiley Periodicals, Inc.

Statistical mechanics of binary mixture adsorption in metal-organic frameworks in the osmotic ensemble

Although crucial for designing separation processes little is known experimentally about multi-component adsorption isotherms in comparison with pure single components. Very few binary mixture adsorption isotherms are to be found in the literature and information about isotherms over a wide range of gas-phase composition and mechanical pressures and temperature is lacking. Here, we present a quasi-one-dimensional statistical mechanical model of binary mixture adsorption in metal-organic frameworks (MOFs) treated exactly by a transfer matrix method in the osmotic ensemble. The experimental parameter space may be very complex and investigations into multi-component mixture adsorption may be guided by theoretical insights. The approach successfully models breathing structural transitions induced by adsorption giving a good account of the shape of adsorption isotherms of CO₂ and CH₄ adsorption in MIL-53(Al). Binary mixture isotherms and co-adsorption-phase diagrams are also calculated and found to give a good description of the experimental trends in these properties and because of the wide model parameter range which reproduces this behaviour suggests that this is generic to MOFs. Finally, a study is made of the influence of mechanical pressure on the shape of CO₂ and CH₄ adsorption isotherms in MIL-53(Al). Quite modest mechanical pressures can induce significant changes to isotherm shapes in MOFs with implications for binary mixture separation processes.This article is part of the theme issue 'Modern theoretical chemistry'.

Transferable Coarse-Grained Models of Liquid-Liquid Equilibrium Using Local Density Potentials Optimized with the Relative Entropy

Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase. CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.

Universal behavior of soft-core fluids near the threshold of thermodynamic stability

We study, by using liquid-state theories and Monte Carlo simulation, the behavior of systems of classical particles interacting through a finite pair repulsion supplemented with a longer range attraction. Any such potential can be driven Ruelle-unstable by increasing the attraction at the expense of repulsion, until the thermodynamic limit is lost. By examining several potential forms, we find that all systems exhibit a qualitatively similar behavior in the fluid phase as the threshold of thermodynamic stability is approached (and possibly surpassed). The general feature underlying the approach to Ruelle instability is a pronounced widening of the liquid-vapor binodal (and spinodal) line at low temperatures, to such an extent that at the stability threshold a vanishing-density vapor would coexist with a diverging-density liquid. We attempt to rationalize the universal pathway to Ruelle instability in soft-core fluids by appealing to a heuristic argument.

Thermodynamic properties of confined square-well fluids with multiple associating sites

In this work, a molecular simulation study of confined hard-spheres particles with square-well (SW) attractive interactions with two and four associating SW sites based on the first-order perturbation form of Wertheim's theory is presented. An extended version of the Gibbs ensemble technique for inhomogeneous fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is used to predict the adsorption density profiles for associating fluids confined between opposite parallel walls. The fluid is confined in four kinds of walls: hard-wall, SW wall, Lennard-Jones (LJ) 12-6 wall potential, and LJ 10-4 wall potential. We analyze the behavior of the confined system for several supercritical temperatures as a function of variation of molecular parameters: potential range λ, bulk densities ρ_b^*, pore width H, cutoff range interaction r_c^*, and range of the potential and depth of the particle-wall (λ_w, ε_w^*). Additionally, we include predictions for liquid-vapor coexistence of bulk associative particles and how their critical properties are modified by the presence of associative sites in the molecule. The molecular simulation data presented in this work are of prime importance to the development of theoretical approaches for inhomogeneous fluids as classical density functional theory. The simulation results presented here are resourceful for predicting adsorption isotherms of real associating fluids such as water.

Precise estimation of transfer free energies for ionic species between similar media

Two-dimensional umbrella sampling is combined with molecular dynamics to calculate correction-free estimates of transfer properties for individual ions.

Field-Theoretic Simulations of the Distribution of Nanorods in Diblock Copolymer Thin Films

Using block copolymer microphases to guide the self-assembly of nanorods in thin films can give rise to polymeric materials with unique optical, thermal, and mechanical properties beyond those found in neat block copolymers. Often the design and manufacture of these materials require exquisite control of the nanorod distribution, which is experimentally challenging due to the large parameter space spanned by this class of materials. Simulation approaches, on the other hand, can access the thermodynamics that contribute to the nanorod distribution and hence offer valuable guidance toward the design and manufacture of the materials. In this work, we employ complex Langevin field-theoretic simulations to examine the thermodynamic forces that govern the assembly of nanorods in thin films of block copolymers with a particular focus on vertically oriented cylindrical and lamellar domains. Our simulations show that the nanorod geometry, the substrate selectivity for the distinct blocks of the copolymer, and the film thickness all play important roles in engineering both the nanorod orientation and spatial distribution in diblock copolymer thin films. In addition, we employ thermodynamic integration to examine how the nanorods alter the stability of vertical and horizontal domains in thin films, where we find that the tendency of the nanorods to stabilize a vertical orientation depends on both the film thickness and the nanorod concentration.

Replica-Exchange and Standard State Binding Free Energies with Grand Canonical Monte Carlo

The ability of grand canonical Monte Carlo (GCMC) to create and annihilate molecules in a given region greatly aids the identification of water sites and water binding free energies in protein cavities. However, acceptance rates without the application of biased moves can be low, resulting in large variations in the observed water occupancies. Here, we show that replica-exchange of the chemical potential significantly reduces the variance of the GCMC data. This improvement comes at a negligible increase in computational expense when simulations comprise of runs at different chemical potentials. Replica-exchange GCMC is also found to substantially increase the precision of water binding free energies as calculated with grand canonical integration, which has allowed us to address a missing standard state correction.

NLDFT Pore Size Distribution in Amorphous Microporous Materials

The pore size distribution (PSD) is one of the most important properties when characterizing and designing materials for gas storage and separation applications. Experimentally, one of the current standards for determining microscopic PSD is using indirect molecular adsorption methods such as nonlocal density functional theory (NLDFT) and N₂ isotherms at 77 K. Because determining the PSD from NLDFT is an indirect method, the validation can be a nontrivial task for amorphous microporous materials. This is especially crucial since this method is known to produce artifacts. In this work, the accuracy of NLDFT PSD was compared against the exact geometric PSD for 11 different simulated amorphous microporous materials. The geometric surface area and micropore volumes of these materials were between 5 and 1698 m²/g and 0.039 and 0.55 cm³/g, respectively. N₂ isotherms at 77 K were constructed using Gibbs ensemble Monte Carlo (GEMC) simulations. Our results show that the discrepancies between NLDFT and geometric PSD are significant. NLDFT PSD produced several artificial gaps and peaks that were further confirmed by the coordinates of inserted particles of a specific size. We found that dominant peaks from NLDFT typically reported in the literature do not necessarily represent the truly dominant pore size within the system. The confirmation provides concrete evidence for artifacts that arise from the NLDFT method. Furthermore, a sensitivity analysis was performed to show the high dependency of PSD as a function of the regularization parameter, λ. A higher value of λ produced a broader and smoother PSD that closely resembles geometric PSD. As an alternative, a new criterion for choosing λ, called here the smooth-shift method (SSNLDFT), is proposed that tuned the NLDFT PSD to better match the true geometric PSD. Using the geometric pore size distribution as our reference, the smooth-shift method reduced the root-mean-square deviation by ∼70% when the geometric surface area of the material is greater than 100 m²/g.

Pressure Enhancement in Confined Fluids: Effect of Molecular Shape and Fluid-Wall Interactions

Recently, several experimental and simulation studies have found that phenomena that normally occur at extremely high pressures in a bulk phase can occur in nanophases confined within porous materials at much lower bulk phase pressures, thus providing an alternative route to study high-pressure phenomena. In this work, we examine the effect on the tangential pressure of varying the molecular shape, strength of the fluid-wall interactions, and pore width, for carbon slit-shaped pores. We find that, for multisite molecules, the presence of additional rotational degrees of freedom leads to unique changes in the shape of the tangential pressure profile, especially in larger pores. We show that, due to the direct relationship between the molecular density and the fluid-wall interactions, the latter have a large impact on the pressure tensor. The molecular shape and pore size have a notable impact on the layering of molecules in the pore, greatly influencing both the shape and scale of the tangential pressure profile.

Comparative Study of the Effect of Defects on Selective Adsorption of Butanol from Butanol/Water Binary Vapor Mixtures in Silicalite-1 Films

A promising route for sustainable 1-butanol (butanol) production is ABE (acetone, butanol, ethanol) fermentation. However, recovery of the products is challenging because of the low concentrations obtained in the aqueous solution, thus hampering large-scale production of biobutanol. Membrane and adsorbent-based technologies using hydrophobic zeolites are interesting alternatives to traditional separation techniques (e.g., distillation) for energy-efficient separation of butanol from aqueous mixtures. To maximize the butanol over water selectivity of the material, it is important to reduce the number of hydrophilic adsorption sites. This can, for instance, be achieved by reducing the density of lattice defect sites where polar silanol groups are found. The density of silanol defects can be reduced by preparing the zeolite at neutral pH instead of using traditional synthesis solutions with high pH. In this work, binary adsorption of butanol and water in two silicalite-1 films was studied using in situ attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy under equal experimental conditions. One of the films was prepared in fluoride medium, whereas the other one was prepared at high pH using traditional synthesis conditions. The amounts of water and butanol adsorbed from binary vapor mixtures of varying composition were determined at 35 and 50 °C, and the corresponding adsorption selectivities were also obtained. Both samples showed very high selectivities (100-23 000) toward butanol under the conditions studied. The sample having low density of defects, in general, showed ca. a factor 10 times higher butanol selectivity than the sample having a higher density of defects at the same experimental conditions. This difference was due to a much lower adsorption of water in the sample with low density of internal defects. Analysis of molecular simulation trajectories provides insights on the local selectivities in the zeolite channel network and at the film surface.