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

Phase behavior of polymer dispersed liquid crystals, comparison between mean-field theory, and coarse-grained molecular dynamics simulations

We report a simulation methodology to quantitatively predict the thermodynamic behaviour (phase diagrams) of polymer mixtures, that exhibit phases with broken orientational symmetry. Our system consists of a binary mixture of short oligomers (NA = 4) and long rod-like mesogens (NB = 8). Using coarse-grained molecular dynamics (CGMD) simulations we infer the topology of the temperature-dependent free energy landscape, from the probability distributions of the components for a range of compositions. The mixture exhibits nematic (N) and smectic phases (Sm-A) as a function of two temperature scales, Tc, that governs the demixing transition, and TNI the nematic-isotropic temperature. Thus in addition to the isotropic (I), a nematic (N) phases observed in simulations of similar systems earlier we report the formation of a new entropy-stabilized phase separated smectic-A (Sm-A) phase with alternating mesogen-rich and oligomer-rich layers. Using the mean-field free energy for polymer-dispersed liquid crystals (PDLCs), with suitably chosen parameter values, we construct a mean-field phase diagram that matches those obtained from CGMD simulations. Our results are applicable to mixtures of synthetic and biological macromolecules that undergo phase separation and are orientable, thereby giving rise to the liquid crystalline phases. Our proposed methodology has a distinct advantage over other computational techniques in its applicability to systems with complex molecular interactions and in capturing the coarsening dynamics of systems involving multiple order parameters.

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

Molecular insights into methane hydrate dissociation: Role of methane nanobubble formation

Understanding the underlying physics of natural gas hydrate dissociation is necessary for efficient CH4 extraction and in the exploration of potential additives in the chemical injection method. Silica being "sand" is already present inside the reservoir, making the silica nanoparticle a potential green additive. Here, molecular dynamics (MD) simulations have been performed to investigate the dissociation of the CH4 hydrate in the presence and absence of ∼1, ∼2, and ∼3 nm diameter hydrophilic silica nanoparticles at 100 bar and 310 K. We find that the formation of a CH4 nanobubble has a strong influence on the dissociation rate. After the initial hydrate dissociation, the rate of dissociation slows down till the formation of a CH4 nanobubble. We find the critical concentration and size limit to form the CH4 nanobubble to be ∼0.04 mole fraction of CH4 and ∼40 to 50 CH4 molecules, respectively. The solubility of CH4 and the chemical potential of H2O and CH4 are determined via Gibbs ensemble Monte Carlo simulations. The liquid phase chemical potential of both H2O and CH4 in the presence and absence of the nanoparticle is nearly the same, indicating that the effect of this additive will not be significant. While the formation of the hydration shell around the nanoparticle via hydrogen bonding confirms the strength of interactions between the water molecules and the nanoparticle in our MD simulations, the contact of the nanoparticle with the interface is infrequent, leading to no explicit effect of the nanoparticle on the dynamics of methane hydrate dissociation.

Monte Carlo molecular simulations with FEASST version 0.25.1

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy.

Liquid-Liquid Transition in a Bose Fluid near Collapse

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this Letter, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum Monte Carlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter η describing its strength. If η exceeds a characteristic value η_{c}, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for η≲η_{c}, finding-in addition to a liquid-vapor transition-a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As η approaches η_{c}, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for η larger than η_{c} our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

Theory and Monte Carlo simulation of the ideal gas with shell particles in the canonical, isothermal-isobaric, grand canonical, and Gibbs ensembles

Theories of small systems play an important role in the fundamental understanding of finite size effects in statistical mechanics, as well as the validation of molecular simulation results as no computer can simulate fluids in the thermodynamic limit. Previously, a shell particle was included in the isothermal-isobaric ensemble in order to resolve an ambiguity in the resulting partition function. The shell particle removed either redundant volume states or redundant translational degrees of freedom of the system and yielded quantitative differences from traditional simulations in this ensemble. In this work, we investigate the effect of including a shell particle in the canonical, grand canonical, and Gibbs ensembles. For systems comprised of a pure component ideal gas, analytical expressions for various thermodynamic properties are obtained. We also derive the Metropolis Monte Carlo simulation acceptance criteria for these ensembles with shell particles, and the results of the simulations of an ideal gas are in excellent agreement with the theoretical predictions. The system size dependence of various important ensemble averages is also analyzed.

MMC: A Monte Carlo laboratory

This Note describes features of the program MMC, several of which are unique to MMC, developed over the past five decades. These include sampling in three different ensembles, biased moves, and some non-conventional analysis techniques.

Adsorption-driven reverse osmosis separation of ethanol/water using zeolite nanosheets

Developing more energy-efficient and cost-effective membrane processes for the separation of ethanol and water represents a strategically important direction to facilitate the production of renewable biofuels. In this study, by employing state-of-the-art molecular simulations, the potential of zeolite nanosheets as reverse osmosis (RO) membranes in ethanol/water separation is investigated. These materials are predicted to offer unprecedentedly high fluxes and more importantly, the ethanol-to-water separation factor can be as large as approximately 800 if the structure is meticulously selected. The separation achieved herein can in fact be considered counter-intuitive as the membrane allows the larger ethanol molecules to permeate through while blocking smaller water molecules. Further investigations reveal that the observed selectivity is strongly correlated with the adsorption selectivity of the bulk materials, suggesting an adsorption-driven mechanism. Promising candidates also appear to have the largest cavity diameter of approximately 6 Å, a size that can be commensurate with the dimensions of ethanol to facilitate its adsorption. The hydrophilicity on the membrane surfaces is as well found to play a non-negligible role. Overall, this study demonstrates the great promise of zeolite nanosheets as RO membranes for extracting anhydrous ethanol from its aqueous mixture and provides guidance toward the selection of promising membrane candidates.

Monte Carlo Simulations of Water Pollutant Adsorption at Parts-per-Billion Concentration: A Study on 1,4-Dioxane

1,4-dioxane, an emerging water pollutant with high production volumes, is a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates the need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for the separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, and MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with a greater affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at a 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption and observe selectivities ranging from 1.1 × 105 in MOR to 8.7 × 106 in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in the aqueous phase at this concentration. This simulation technique can be extended to model other emerging water contaminants such as perfluoroalkyl and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.

Integrating molecular dynamics simulations and experimental data for azeotrope predictions in binary mixtures

An azeotrope is a constant boiling point mixture, and its behavior is important for fluid separation processes. Predicting azeotropes from atomistic simulations is difficult due to the complexities and convergence problems of Monte Carlo and free-energy perturbation techniques. Here, we present a methodology for predicting the azeotropes of binary mixtures, which computes the compositional dependence of chemical potentials from molecular dynamics simulations using the S0 method and employs experimental boiling point and vaporization enthalpy data. Using this methodology, we reproduce the azeotropes, or lack thereof, in five case studies, including ethanol/water, ethanol/isooctane, methanol/water, hydrazine/water, and acetone/chloroform mixtures. We find that it is crucial to use the experimental boiling point and vaporization enthalpy for reliable azeotrope predictions, as empirical force fields are not accurate enough for these quantities. Finally, we use regular solution models to rationalize the azeotropes and reveal that they tend to form when the mixture components have similar boiling points and strong interactions.

Binary phase behavior of select organosulfur compounds in supercritical carbon dioxide: A Monte Carlo molecular simulation study

Pressure-composition binary phase diagrams were determined for methanethiol, dimethyl sulfide, thiophene, benzothiophene, or dibenzothiophene with carbon dioxide at temperatures from 363 to 453 K and pressures from 2 to 20 MPa. Utilizing Gibbs ensemble Monte Carlo molecular simulation, phase coexistence compositions were determined, along with the impact of 4% water cosolvent on select results. Solution structure as a function of pressure and temperature is characterized via radial distribution functions. Comparison to available experimental composition data gives overall mean absolute percentage deviations of 2.2% for thiophene, 37% for methanethiol, and 99% for benzothiophene. Solubilities in a CO2-rich phase are calculated to be sufficient to allow extraction and detection of the compounds studied here via supercritical fluid chromatography and mass spectrometry as a possible analysis approach for future Mars rover missions.

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Sequence dependence of critical properties for two-letter chains

Histogram-reweighting grand canonical Monte Carlo simulations are used to obtain the critical properties of lattice chains composed of solvophilic and solvophobic monomers. The model is a modification of one proposed by Larson et al. [J. Chem. Phys. 83, 2411 (1985)], lowering the "contrast" between beads of different types to prevent aggregation into finite-size micelles that would mask true phase separation between bulk high- and low-density phases. Oligomeric chains of lengths between 5 and 24 beads are studied. Mixed-field finite-size scaling methods are used to obtain the critical properties with typical relative accuracies of better than 10-4 for the critical temperature and 10-3 for the critical volume fraction. Diblock chains are found to have lower critical temperatures and volume fractions relative to the corresponding homopolymers. The addition of solvophilic blocks of increasing length to a fixed-length solvophobic segment results in a decrease of both the critical temperature and the critical volume fraction, with an eventual slow asymptotic approach to the long-chain limiting behavior. Moving a single solvophobic or solvophilic bead along a chain leads to a minimum or maximum in the critical temperature, with no change in the critical volume fraction. Chains of identical length and composition have a significant spread in their critical properties, depending on their precise sequence. The present study has implications for understanding biomolecular phase separation and for developing design rules for synthetic polymers with specific phase separation properties. It also provides data potentially useful for the further development of theoretical models for polymer and surfactant phase behavior.

Computer Simulation of Three-Phase Equilibria for Some Water/n-Alkane Binary Systems

In this work, the vapor-liquid-liquid equilibrium (VLLE) of the water/n-pentane, water/n-hexane, water/n-octane, and water/n-decane binary systems is calculated by computer simulation using the NVT-Gibbs ensemble (in the version of three simulation boxes) combined with the configurational bias Monte Carlo method. The combination of both methods, the molecular potential models used, and the simulation details allowed us to calculate the triphasic equilibrium properties of the systems studied: the densities of the three phases in equilibrium, their compositions, and potential energies. In previous works, these simulations were not carried out at a temperature range nor water/n-alkanes systems simulated in this work, probably because they are highly nonideal systems; so, to the best of our knowledge, this is the first time that this phenomenon is studied in detail. The results from VLLE simulations of the water/n-pentane system for temperatures from 343.2 to 435 K, the water/n-hexane system for temperatures from 373.11 to 473.15 K, the water/n-octane system for temperatures from 310.9 to 500 K, and for the water/n-decane system for temperatures from 374.15 to 525 K are reported here. The temperature range was selected in concordance with the experimental data available for an adequate study of the VLLE simulation results. The subcritical densities (vapor and liquid rich in n-alkane phases) at various temperatures fit well with the scaling law and the law of rectilinear diameters, allowing the estimation of upper critical end point temperature and density of the VLLE. The simulation results show a good prediction with experimental data reports in the literature.

Adsorption of Natural Gas in Metal-Organic Frameworks: Selectivity, Cyclability, and Comparison to Methane Adsorption

Evaluation of metal-organic frameworks (MOFs) for adsorbed natural gas (ANG) technology employs pure methane as a surrogate for natural gas (NG). This approximation is problematic, as it ignores the impact of other heavier hydrocarbons present in NG, such as ethane and propane, which generally have more favorable adsorption interactions with MOFs compared to methane. Herein, using quantitative Raman spectroscopic analysis and Monte Carlo calculations, we demonstrate the adsorption selectivity of high-performing MOFs, such as MOF-5, MOF-177, and SNU-70, for a methane and ethane mixture (95:5) that mimics the composition of NG. The impact of selectivity on the storage and deliverable capacities of these adsorbents during successive cycles of adsorption and desorption, simulating the filling and emptying of an ANG tank, is also demonstrated. The study reveals a gradual reduction in the storage performance of MOFs, particularly with smaller pore volumes, due to ethane accumulation over long-term cycling, until a steady state is reached with substantially degraded storage performance.

Vapor-liquid equilibrium and thermodynamic properties of saturated argon and krypton from Monte Carlo simulations using ab initio potentials

Vapor-liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using ab initio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal-isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor-liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art ab initio pair and nonadditive three-body potentials and quantum effects are accounted for.

Sequestration of Small Ions and Weak Acids and Bases by a Polyelectrolyte Complex Studied by Simulation and Experiment

Mixing of oppositely charged polyelectrolytes can result in phase separation into a polymer-poor supernatant and a polymer-rich polyelectrolyte complex (PEC). We present a new coarse-grained model for the Grand-reaction method that enables us to determine the composition of the coexisting phases in a broad range of pH and salt concentrations. We validate the model by comparing it to recent simulations and experimental studies, as well as our own experiments on poly(acrylic acid)/poly(allylamine hydrochloride) complexes. The simulations using our model predict that monovalent ions partition approximately equally between both phases, whereas divalent ones accumulate in the PEC phase. On a semiquantitative level, these results agree with our own experiments, as well as with other experiments and simulations in the literature. In the sequel, we use the model to study the partitioning of a weak diprotic acid at various pH values of the supernatant. Our results show that the ionization of the acid is enhanced in the PEC phase, resulting in its preferential accumulation in this phase, which monotonically increases with the pH. Currently, this effect is still waiting to be confirmed experimentally. We explore how the model parameters (particle size, charge density, permittivity, and solvent quality) affect the measured partition coefficients, showing that fine-tuning of these parameters can make the agreement with the experiments almost quantitative. Nevertheless, our results show that charge regulation in multivalent solutes can potentially be exploited in engineering the partitioning of charged molecules in PEC-based systems at various pH values.

Molecular Simulation Studies on the Vapor-Liquid Equilibrium of CO2 + 3,3,3-Trifluoropropene (R1243zf) Binary Mixtures

As fourth-generation refrigerants with great development prospects, hydrofluoroolefins (HFOs) can be mixed with other refrigerants, such as carbon dioxide (CO2), to form refrigerant mixtures with low global warming potential (GWP) and zero ozone depleting potential (ODP) while retaining the advantages of each component. Refrigerants can work together to achieve complementary benefits. Combinations of CO2 and HFOs can strengthen the thermodynamic properties of CO2 while inhibiting the flammability of HFOs. At present, relatively few studies have been conducted on the CO2 + 3,3,3-trifluoropropene (R1243zf) mixture. Besides experimental approaches, molecular simulation has grown in importance as a way to determine thermodynamic and transport properties in recent years. In this study, the Gibbs Ensemble Monte Carlo (GEMC) method was used to simulate the vapor-liquid equilibrium (VLE) properties of the CO2 + R1243zf binary mixture in the temperature range of 273.15 to 313.15 K, in which the three-site rigid TraPPE force field and a fully flexible transferable all-atom force field were selected to describe CO2 and R1243zf, respectively. By comparing the GEMC simulation results with the experimental data, it was found that the average deviation of pressure is 2.33%, the average deviation of liquid phase molar fraction Δx is 0.0099, and the mean deviation of gaseous phase molar fraction Δy is 0.0204. The simulation results accord well with the experimental data and the fitting data of the correlation model in the literature, indicating that the molecular models used for CO2 and R1243zf can reliably predict the VLE properties. Finally, the critical parameters of the mixture at a temperature of 313.15 K were predicted, and the radial distribution functions (RDFs) of pure R1243zf and the mixture at 273.15 K and 3.5 MPa were calculated and analyzed by molecular dynamics (MD) simulation.

Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures

The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.

Phase Separation, Reaction Equilibrium, and Self-Assembly in Binary Telechelic Homopolymer Blends

We study a binary blend of telechelic homopolymers that can form reversible AB-type bonds at the chain ends. Reversibly bonding polymers display novel material properties, including thermal tunability and self-healing, that are not found in conventional covalently bonded polymers. Previous studies of reversibly bonding polymer systems have been limited by the computational demand of accounting for an infinite number of possible reaction products in a spatially inhomogeneous, self-assembled structure. We demonstrate that newly developed theoretical models and numerical methods enable the simultaneous computation of phase equilibrium, reaction equilibrium, and self-assembly via self-consistent field theory. Phase diagrams are computed at a variety of physically relevant conditions and are compared with nonreactive analogues as well as previous experimental studies of telechelic polymer blends.

Predicting Critical Properties and Acentric Factors of Fluids Using Multitask Machine Learning

Knowledge of critical properties, such as critical temperature, pressure, density, as well as acentric factor, is essential to calculate thermo-physical properties of chemical compounds. Experiments to determine critical properties and acentric factors are expensive and time intensive; therefore, we developed a machine learning (ML) model that can predict these molecular properties given the SMILES representation of a chemical species. We explored directed message passing neural network (D-MPNN) and graph attention network as ML architecture choices. Additionally, we investigated featurization with additional atomic and molecular features, multitask training, and pretraining using estimated data to optimize model performance. Our final model utilizes a D-MPNN layer to learn the molecular representation and is supplemented by Abraham parameters. A multitask training scheme was used to train a single model to predict all the critical properties and acentric factors along with boiling point, melting point, enthalpy of vaporization, and enthalpy of fusion. The model was evaluated on both random and scaffold splits where it shows state-of-the-art accuracies. The extensive data set of critical properties and acentric factors contains 1144 chemical compounds and is made available in the public domain together with the source code that can be used for further exploration.

Molecular Dynamics Study of the Effect of Charge and Glycosyl on Superoxide Anion Distribution near Lipid Membrane

To examine the effects of membrane charge, the electrolyte species and glycosyl on the distribution of negatively charged radical of superoxide anion (·O₂^-) around the cell membrane, different phospholipid bilayer systems containing ·O₂^- radicals, different electrolytes and phospholipid bilayers were constructed through Charmm-GUI and Amber16. These systems were equilibrated with molecular dynamics by using Gromacs 5.0.2 to analyze the statistical behaviors of ·O₂^- near the lipid membrane under different conditions. It was found that in the presence of potassium rather than sodium, the negative charge of the phospholipid membrane is more likely to rarefy the superoxide anion distribution near the membrane surface. Further, the presence of glycosyl significantly reduced the density of ·O₂^- near the phospholipid bilayer by 78.3% compared with that of the neutral lipid membrane, which may have a significant contribution to reducing the lipid peroxidation from decreasing the ·O₂^- density near the membrane.

Atomistic Insights into the Deposition of Corrosion Products on the Surfaces of Steels and Passivation Films

The deposition of corrosion products on the surface of the steel is a key step for understanding the generation of corrosion products. To clarify the molecular mechanism for corrosion product deposition, the reactive molecular dynamics were utilized to study the deposition process of ferric hydroxide (Fe(OH)₃) on iron and passivation film substrates. It is shown that the deposition phenomenon mainly occurs on the iron surface, while the surface of the passivation film cannot adsorb Fe(OH)₃. Further analysis indicates that the interaction between hydroxyl groups in γ-FeOOH and Fe(OH)₃ is very weak, which is unfavorable to the deposition of Fe(OH)₃. Moreover, the degree of ordered water in the two systems is affected slightly by deposition but the oxygen in water corrodes Fe(OH)₃, breaking its Fe-O bonds, which is more obvious in the Fe system due to its instability. This work has revealed the nanoscale deposition process of corrosion products on the passivation film in a solution environment by reproducing the bonding and breaking of atoms at the molecular level, which is a case in point to the conclusion of the protection of steel bars by passivation film.

Stochastic Monte Carlo Model for Simulating the Dynamic Liquid-Liquid Phase Separation in Bacterial Cells

There is growing evidence showing that many critical biological processes are driven by biomolecule condensates through liquid-liquid phase separation (LLPS). Although the qualitative observation and description of LLPS have been well documented, quantitative simulations of the time-dependent progression of LLPS in live cells are generally lacking. In this work, we build a stochastic Monte Carlo model to simulate the dynamic LLPS process during the formation of bacterial aggresomes. We demonstrate that the size distribution of the protein condensates evolves from an exponential-like to a bimodal-like pattern, and the number of condensates increases at the beginning and then decreases after reaching a maximum. Incorporating diffusion and collision, our simplified model recapitulates the two-step LLPS process in which many smaller condensates are formed in the first step and then merged into a few larger ones. We further reveal that the condensation speed, which can be defined by the condensates formed in unit time during the first step, is mainly determined by both the collision energy barrier and the initial protein density, while the number of condensates at the equilibrium is mainly associated with the dissociation energy barrier. Moreover, the LLPS process is not sensitive to temperature changes ranging around physiological conditions. Additionally, we consider the effect of the nucleation energy barrier on LLPS. We find that a higher nucleation energy barrier brings a slower condensation speed. Overall, we simulate the spatiotemporal dynamics of the LLPS process and provide qualitative guidance for understanding the dynamics of LLPS in bacterial cells, which can faithfully recapitulate experimental observations and facilitate the design of future experimental tests.

Molecular Modeling of Double Retrograde Vaporization Using Monte Carlo Simulations and Equations of State

Vapor-liquid equilibria of binary systems consisting of a low-boiling (i.e., more volatile) and a high-boiling compound may exhibit unexpected behavior near the critical point of the low-boiling compound. Near the critical temperature of the low-boiling compound and for compositions rich in the low-boiling compound, increasing the pressure may result in multiple crossings of the dew- and bubble-point curves. This phenomenon is often called double retrograde vaporization (or condensation) and may play a role in oil field operations and gas transport through pipelines, but the microscopic driving forces for the unusual shape of the dew-point curve are not well understood. Monte Carlo simulations in the constant-pressure, constant-temperature Gibbs ensemble using the united-atom version of the TraPPE force field were carried out for the methane/n-butane mixture at temperatures ranging from 0.95 to 1.05 of the reduced (T/T_c) temperature of methane. The simulations predict a wealth of additional thermodynamic data (densities and free energies of transfer) and structural data that are used to provide much needed molecular-level insights into the fluid properties associated with double retrograde vaporization. Simulated thermodynamic data are also compared with calculations using the Peng-Robinson and PC-SAFT equations of state.

Free energy of critical droplets-from the binodal to the spinodal

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo in the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT), this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at 2.5σ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results for critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to the second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible regions. However, it is imprecise for the smallest droplets and largest metastabilities since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of the formation of critical droplets for the entire metastability range and all temperatures examined and deviates from density gradient theory by less than one k_BT.

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λ_r-6) fluid with a repulsive exponent λ_r from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/T_c from 0.55 to 4.5 and for reduced pressures of up to p/p_c = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.

Field-Theoretic Simulation Method to Study the Liquid-Liquid Phase Separation of Polymers

Liquid-liquid phase separation (LLPS) is a process that results in the formation of a polymer-rich liquid phase coexisting with a polymer-depleted liquid phase. LLPS plays a critical role in the cell through the formation of membrane-less organelles, but it also has a number of biotechnical and biomedical applications such as drug confinement and its targeted delivery. In this chapter, we present a computational efficient methodology that uses field-theoretic simulations (FTS) with complex Langevin (CL) sampling to characterize polymer phase behavior and delineate the LLPS phase boundaries. This approach is a powerful complement to analytical and explicit-particle simulations, and it can serve to inform experimental LLPS studies. The strength of the method lies in its ability to properly sample a large ensemble of polymers in a saturated solution while including the effect of composition fluctuations on LLPS. We describe the approaches that can be used to accurately construct phase diagrams of a variety of molecularly designed polymers and illustrate the method by generating an approximation-free phase diagram for a classical symmetric diblock polyampholyte.

Calculating Binodals and Interfacial Tension of Phase-Separated Condensates from Molecular Simulations with Finite-Size Corrections

We illustrate three methods for calculating the binodals of phase-separated condensates from molecular simulations. Because molecular simulations can only be carried out for small system sizes, correction for finite sizes may be required for making direct comparison between calculated results and experimental data. We first summarize the three methods and then present detailed implementation of each method on a Lennard-Jones fluid. In the first method, chemical potentials are calculated over a range of particle densities in canonical-ensemble simulations; the densities of the dilute and dense phases at the given temperature are then found by a Maxwell equal-area construction. In Gibbs-ensemble Monte Carlo, the exchange between separated dilute and dense phases is simulated to obtain their densities. Lastly, slab-geometry molecular dynamics simulations model the dilute and dense phases in coexistence and yield not only their densities but also their interfacial tension. The three types of simulations are carried out for a range of system sizes, and the results are scaled to generate the binodals corrected for finite system sizes. Size-corrected interfacial tension is also produced from slab-geometry molecular dynamics simulations.

SpiDec: Computing binodals and interfacial tension of biomolecular condensates from simulations of spinodal decomposition

Phase separation of intrinsically disordered proteins (IDPs) is a phenomenon associated with many essential cellular processes, but a robust method to compute the binodal from molecular dynamics simulations of IDPs modeled at the all-atom level in explicit solvent is still elusive, due to the difficulty in preparing a suitable initial dense configuration and in achieving phase equilibration. Here we present SpiDec as such a method, based on spontaneous phase separation via spinodal decomposition that produces a dense slab when the system is initiated at a homogeneous, low density. After illustrating the method on four model systems, we apply SpiDec to a tetrapeptide modeled at the all-atom level and solvated in TIP3P water. The concentrations in the dense and dilute phases agree qualitatively with experimental results and point to binodals as a sensitive property for force-field parameterization. SpiDec may prove useful for the accurate determination of the phase equilibrium of IDPs.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.

Applications of Molecular Dynamics Simulation in Protein Study

Molecular Dynamics (MD) Simulations is increasingly used as a powerful tool to study protein structure-related questions. Starting from the early simulation study on the photoisomerization in rhodopsin in 1976, MD Simulations has been used to study protein function, protein stability, protein-protein interaction, enzymatic reactions and drug-protein interactions, and membrane proteins. In this review, we provide a brief review for the history of MD Simulations application and the current status of MD Simulations applications in protein studies.

Extension of the Aggregation-Volume-Bias Monte Carlo Method to the Calculation of Phase Properties of Solid Systems: A Lattice-Based Cluster Approach

The aggregation-volume-bias Monte Carlo method, which has been successful in the calculation of the formation free energies of liquid clusters, is extended to solid systems. This extension is motivated by early studies where disordered clusters are observed when the original method is applied at a temperature even far below the triple point. In order to avoid the formation of disordered aggregates, the insertion of particles is targeted directly toward those crystal lattice sites. Specifically, the insertion volume used to be defined as a spherical volume centered around a given target molecule is now restricted to be around each of the crystal lattice sites near a given target molecule. The free energies obtained for both liquid and solid clusters are then used to extrapolate bulk-phase information such as the chemical potential of the liquid and solid phases at coexistence. Using the temperature and pressure dependencies of the chemical potential information obtained for both liquid and solid phases, the location of the triple point can be determined. For Lennard-Jonesium, the results were found to be in good agreement with previous simulation studies using other approaches.

Modeling the Phase Equilibria of Associating Polymers in Porous Media with Respect to Chromatographic Applications

Associating copolymers self-assemble during their passage through a liquid chromatography (LC) column, and the elution differs from that of common non-associating polymers. This computational study aims at elucidating the mechanism of their unique and intricate chromatographic behavior. We focused on amphiphilic diblock copolymers in selective solvents, performed the Monte Carlo (MC) simulations of their partitioning between a bulk solvent (mobile phase) and a cylindrical pore (stationary phase), and investigated the concentration dependences of the partition coefficient and of other functions describing the phase behavior. The observed abruptly changing concentration dependences of the effective partition coefficient demonstrate the significant impact of the association of copolymers with their partitioning between the two phases. The performed simulations reveal the intricate interplay of the entropy-driven and the enthalpy-driven processes, elucidate at the molecular level how the self-assembly affects the chromatographic behavior, and provide useful hints for the analysis of experimental elution curves of associating polymers.

Drug Discovery by Automated Adaptation of Chemical Structure and Identity

Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.

Interfacial Properties of Linear Alkane/Nitrogen Binary Mixtures: Molecular Dynamics Vapor-Liquid Equilibrium Simulations

Molecular dynamics simulations were used to investigate the vapor-liquid equilibria (VLE) and interfacial properties of binary mixtures of N2 with either ethane, propane, n-decane, or n-dodecane. Alkanes and N2 were modeled by using the TraPPE-UA and Rivera force fields, respectively. The typically used Lorentz-Berthelot combining rules resulted in liquid phases that are too N2-rich compared to experiment. To improve the accuracy of VLE predictions, the hydrocarbon-nitrogen interactions were fine-tuned, and these improved parameters were used to investigate interfacial properties. Scaling the interaction strength between nitrogen and -CH3 and -CH2- groups by factors of 0.95 and 0.85, respectively, relative to the Lorentz-Berthelot value, was found to minimize error in pressure-composition phase diagrams. These scaling parameters gave excellent agreement with experimental phase diagrams for mixtures of N2 with ethane, propane, or n-dodecane over a range of state points. For ethane/N2 and n-decane/N2 mixtures, trends in surface tension as a function of temperature and pressure are correctly reproduced, although the simulated values are slightly too high compared to experimental values. To assess how the accuracy of hydrocarbon-N2 interaction strength impacts interfacial property predictions, we have compared density profiles and surface tension using several different scaling factors. Using the Lorentz-Berthelot combining rules rather than optimized parameters gave the same qualitative trends, although some quantitative results, such as liquid-phase N2 mole fraction, were found to differ by a factor of ∼1.5. Using the optimized interaction parameters, interfacial behavior was examined by calculating density and free energy profiles. Nitrogen molecules preferentially adsorb at the interfacial region between the liquid and vapor phases. This interfacial adsorption becomes less energetically favorable as either the temperature, pressure, or length of the alkane chain increases.

Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation

The accurate evaluation of free energies within molecular simulations is important to many scientific fields, including fluid and solid phase equilibria, biomolecular condensates, and quantum phase transitions, among others. Unfortunately, free energy estimation is tedious and computationally expensive for molecular models whose degrees of freedom are expressed in particle coordinates. We show that alternative representations of a model as a classical or quantum field theory provide access to a chemical potential operator that can be averaged to yield a direct and low-cost estimate of the Gibbs free energy. The averaging is performed using a “field-theoretic” computer simulation that employs fluctuating fields rather than particles.

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.

Atomistic simulation framework for molten salt vapor–liquid equilibrium prediction and its application to NaCl

Knowledge of the vapor–liquid equilibrium (VLE) properties of molten salts is important in the design of thermal energy storage systems for solar power and nuclear energy production applications. The high temperatures involved make their experimental determination problematic, and the development of both macroscopic thermodynamic correlations and predictive molecular-based methodologies are complicated by the requirement to appropriately incorporate the chemically reacting vapor-phase species. We derive a general thermodynamic-based atomistic simulation framework for molten salt VLE prediction and show its application to NaCl. Its input quantities are temperature-dependent ideal-gas free energy data for the vapor phase reactions and density and residual chemical potential data for the liquid. If these are not available experimentally, the former may be predicted using standard electronic structure software, and the latter may be predicted by means of classical atomistic simulation methodology. The framework predicts the temperature dependence of vapor pressure, coexisting phase densities, vapor phase composition, and vaporization enthalpy. It also predicts the concentrations of vapor phase species present in minor amounts (such as the free ions), quantities that are extremely difficult to measure experimentally. We furthermore use the results to obtain an approximation to the complete VLE binodal dome and the critical properties. We verify the framework for molten NaCl, for which experimentally based density and chemical potential data are available in the literature. We then apply it to the analysis of NaCl simulation data for two commonly used atomistic force fields. The framework can be readily extended to molten salt mixtures and to ionic liquids.

On the dynamically arrested states of equilibrium and non-equilibrium gels: a comprehensive Brownian dynamics study

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas-liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and theαrelaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φvsT) plane.

Thermoresponsive Ionic Liquid/Water Mixtures: From Nanostructuring to Phase Separation

The thermodynamics, structures, and applications of thermoresponsive systems, consisting primarily of water solutions of organic salts, are reviewed. The focus is on organic salts of low melting temperatures, belonging to the ionic liquid (IL) family. The thermo-responsiveness is represented by a temperature driven transition between a homogeneous liquid state and a biphasic state, comprising an IL-rich phase and a solvent-rich phase, divided by a relatively sharp interface. Demixing occurs either with decreasing temperatures, developing from an upper critical solution temperature (UCST), or, less often, with increasing temperatures, arising from a lower critical solution temperature (LCST). In the former case, the enthalpy and entropy of mixing are both positive, and enthalpy prevails at low T. In the latter case, the enthalpy and entropy of mixing are both negative, and entropy drives the demixing with increasing T. Experiments and computer simulations highlight the contiguity of these phase separations with the nanoscale inhomogeneity (nanostructuring), displayed by several ILs and IL solutions. Current applications in extraction, separation, and catalysis are briefly reviewed. Moreover, future applications in forward osmosis desalination, low-enthalpy thermal storage, and water harvesting from the atmosphere are discussed in more detail.

CF4 Capture and Separation of CF4-SF6 and CF4-N2 Fluid Mixtures Using Selected Carbon Nanoporous Materials and Metal-Organic Frameworks: A Computational Study

The adsorption of pure fluid carbon tetrafluoride and the separation of CF₄-SF₆ and CF₄-N₂ fluid mixtures using representative nanoporous materials have been investigated by employing Monte Carlo and molecular dynamics simulation techniques. The selected materials under study were the three-dimensional carbon nanotube networks, pillared graphene using carbon nanotube pillars, and the SIFSIX-2-Cu metal-organic framework. The selection of these materials was based on their previously reported efficiency to separate fluid SF₆-N₂ mixtures. The pressure dependence of the thermodynamic and kinetic separation selectivity for the CF₄-SF₆ and CF₄-N₂ fluid mixtures has therefore been investigated, to provide deeper insights into the molecular scale phenomena taking place in the investigated nanoporous materials. The results obtained have revealed that under near-ambient pressure conditions, the carbon-based nanoporous materials exhibit a higher gravimetric fluid uptake and thermodynamic separation selectivity. The SIFSIX-2-Cu material exhibits a slightly higher kinetic selectivity at ambient and high pressures.