Accurate statistical associating fluid theory for chain molecules formed from Mie segments

Beyond the mean-field approximation for pair correlations in classical density functional theory: Reference inhomogeneous non-associating monomeric fluids for use with SAFT-VR Mie DFT

A free-energy functional is presented to explicitly take into account pair correlations between molecules in inhomogeneous fluids. The framework of classical density functional theory (DFT) is used to describe the variation in the density of molecules interacting through a Mie (generalized Lennard-Jones) potential. Grand Canonical Monte Carlo simulations are performed for the systems to validate the new functional. The statistical associating fluid theory developed for Mie fluids (SAFT-VR Mie) is selected as a reference for the homogeneous bulk limit of the DFT and is applied here to systems of spherical non-associating particles. The importance of a correct description of the pair correlations for a reliable representation of the free energy in the development of the equation of state is duly noted. Following the Barker-Henderson high-temperature expansion, an analogous formulation is proposed from the general DFT formalism to develop an inhomogeneous equivalent of the SAFT-VR Mie free energy as a functional of the one-body density. In order to make use of this new functional in adsorption studies, a non-local version of the DFT is considered, with specific weighted densities describing the effects of neighboring molecules. The computation of these quantities is possible in three-dimensional space for any pore geometry with repulsive or attractive walls. We showcase examples to validate the new functional, revealing a very good agreement with molecular simulation. The new SAFT-DFT approach is well-adapted to describe realistic complex fluids.

Estimating metastable thermodynamic properties by isochoric extrapolation from stable states

The description of metastable fluids, those in local but not global equilibrium, remains an important problem of thermodynamics, and it is crucial for many industrial applications and all first order phase transitions. One way to estimate their properties is by extrapolation from nearby stable states. This is often done isothermally, in terms of a virial expansion for gases or a Taylor expansion in density for liquids. This work presents evidence that an isochoric expansion of pressure at a given temperature is superior to an isothermal density expansion. Two different isochoric extrapolation strategies are evaluated, one best suited for vapors and one for liquids. Both are exact for important model systems, including the van der Waals equation of state. Moreover, we present a simple method to evaluate all the coefficients of the isochoric expansion directly from a simulation in the canonical ensemble. Using only the properties of stable states, the isochoric extrapolation methods reproduce simulation results with Lennard-Jones potentials, mostly within their uncertainties. The isochoric extrapolation methods are able to predict deeply metastable pressures accurately even from temperatures well above the critical. Isochoric extrapolation also predicts a mechanical stability limit, i.e., the thermodynamic spinodal. For water, the liquid spinodal pressure is predicted to be monotonically decreasing with decreasing temperature, in contrast to the re-entrant behavior predicted by the direct extension of the reference equation of state.

Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null

Thermodynamic potentials play a substantial role in numerous scientific disciplines and serve as basic constructs for describing the behavior of matter. Despite their significance, comprehensive investigations of their topological characteristics and their connections to molecular interactions have eluded exploration due to experimental inaccessibility issues. This study addresses this gap by analyzing the topology of the Helmholtz energy, Gibbs energy, Grand potential, and Null potential that are associated with different isothermal boundary conditions. By employing Monte Carlo simulations in the NVT, NpT, and μVT ensembles and a molecular-based equation of state, methane, ethane, nitrogen, and methanol are investigated over a broad range of thermodynamic conditions. The predictions from the two independent methods are overall in very good agreement. Although distinct quantitative differences among the fluids are observed, the overall topology of the individual thermodynamic potentials remains unaffected by the molecular architecture, which is in line with the corresponding states principle-as expected. Furthermore, a comparative analysis reveals significant differences between the total potentials and their residual contributions.

Semiclassical thermodynamic geometry

In this work the thermodynamic geometry (TG) of semiclassical fluids is analyzed. We present results for two models. The first one is a semiclassical hard-sphere (SCHS) fluid whose Helmholtz free energy is obtained from path-integral Monte Carlo simulations. It is found that, due to quantum contributions in the thermodynamic potential, the anomaly found in TG for the classical hard-sphere fluid related to the sign of the scalar curvature is now avoided in a considerable region of the thermodynamic space. The second model is a semiclassical square-well fluid, described by a SCHS repulsive interaction coupled with a classical attractive square-well contribution. The behavior of the semiclassical curvature scalar as a function of the thermal de Broglie wavelength λ_{B} is analyzed for several attractive-potential ranges. A description of the semiclassical R Widom lines, defined by the maxima of the curvature scalar, is also obtained and results are compared with the corresponding classical systems for different square-well ranges.

Assessment of Anharmonicities in Clusters: Developing and Validating a Minimum-Information Partition Function

Precise thermodynamic calculations are essential for understanding the dynamics of cluster systems and new particle formation. However, the widely employed harmonic statistical mechanical approach often falls short in terms of accuracy. In this study, we present an improved statistical model that incorporates vibrational anharmonicity via a novel partition function that requires only one additional system-specific input parameter. In addition to considering vibrational aspects, we also account for anharmonicity related to the configurational space. The role of anharmonicities is thoroughly examined in the case of general clusters, where the complete sets of conformers, mechanically stable spatial arrangements, are known up to clusters composed of 14 monomers. By performing consistent Monte Carlo simulations on these systems, we benchmark the statistical model's efficacy in reproducing key thermodynamic properties (formation free energy and potential energy) in the classical limit. The model exhibits exceptional alignment with simulations, accurately reproducing free energies within a precision of 2kBT and reliably capturing cluster melting temperatures. Furthermore, we demonstrate the significance and applicability of the model by reproducing thermodynamic barriers in homogeneous gas-phase nucleation of larger clusters. The transferability of our developed approach extends to more complex molecular systems and bears relevance for atmospheric multicomponent clusters, in particular.

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Molecular Insights into the Wettability and Adsorption of Acid Gas-Water Mixture

Sequestration of acid gas in geological formations is a disposal method with potential economic and environmental benefits. The process is governed by variables such as gas-water interfacial tension, wetting transition, and gas adsorption into water, among other things. However, the influence of the pressure and temperature on these parameters is poorly understood. This study investigates these parameters using coarse-grained molecular dynamics (CG-MD) simulations and density gradient theory (DGT). Simulations were carried out at 313.15 K and a pressure range of 0-15 MPa. A comparison was made against H2S-water systems to clarify the effects of adsorption on interfacial tension due to vapor-liquid-liquid equilibrium. The predicted H2S-water interfacial tension and phase densities by CG-MD and DGT matched the experimental values well. The adsorption can be quantified via the Gibbs Adsorption function Γ12, which correlated well with the three-phase transition. On the one hand, pressure increments below the three-phase transition revealed a significant adsorption of H2S. On the other hand, above the three-phase transition, the Gibbs Adsorption capacity remained constant, which indicated a saturation of H2S at the water surface due to liquid-liquid equilibrium. Finally, H2S behaves markedly differently in wetting transition, rather than the involved for CO2 to different molecular layers beneath the surface of aqueous solutions. In this respect, H2S is represented by a first-order wetting transition while CO2 presents a critical wetting. Finally, it has also been found that the preferential adsorption of H2S over the H2O interface is greater if compared to that of CO2, due to its strong interaction with water. In fact, we have also demonstrated that CO2 under triphasic conditions strongly influences the wetting of the ternary system.

Prediction of water anomalous properties by introducing the two-state theory in SAFT

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Influence of repulsion on entropy scaling and density scaling of monatomic fluids

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points. Comparisons to equations of state, literature data, and transport property correlations are made. Although the absolute transport property values within a given potential model class may strongly depend on the repulsive exponent, it is found that the repulsive steepness plays a negligible role when entropy scaling is applied. Hence, the plus-scaled transport properties of n, 6 Mie, exponential-six, and Tang-Toennies fluids lie basically on one master curve, which closely corresponds with entropy scaling correlations for the Lennard-Jones fluid. This trend is confirmed by literature data of n, 6 Mie, and exponential-six fluids. Furthermore, entropy scaling holds for state points where the Pearson correlation coefficient R is well below 0.9. The condition R > 0.9 for strongly correlating liquids is thus not necessary for the successful application of entropy scaling, pointing out that isomorph theory may be a part of a more general framework that is behind the success of entropy scaling. Density scaling reveals a strong influence of the repulsive exponent on this particular approach.

Modeling the Thermodynamic Properties of Saturated Lactones in Nonideal Mixtures with the SAFT-γ Mie Approach

The prediction of the thermodynamic properties of lactones is an important challenge in the flavor, fragrance, and pharmaceutical industries. Here, we develop a predictive model of the phase behavior of binary mixtures of lactones with hydrocarbons, alcohols, ketones, esters, aromatic compounds, water, and carbon dioxide. We extend the group-parameter matrix of the statistical associating fluid theory SAFT-γ Mie group-contribution method by defining a new cyclic ester group, denoted cCOO. The group is composed of two spherical Mie segments and two association electron-donating sites of type e1 that can interact with association electron-accepting sites of type H in other molecules. The model parameters of the new cCOO group interactions (1 like interaction and 17 unlike interactions) are characterized to represent target experimental data of physical properties of pure fluids (vapor pressure, single-phase density, and vaporization enthalpy) and mixtures (vapor-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, density, and excess enthalpy). The robustness of the model is assessed by comparing theoretical predictions with experimental data, mainly for oxolan-2-one, 5-methyloxolan-2-one, and oxepan-2-one (also referred to as γ-butyrolactone, γ-valerolactone, and ε-caprolactone, respectively). The calculations are found to be in very good quantitative agreement with experiments. The proposed model allows for accurate predictions of the thermodynamic properties and highly nonideal phase behavior of the systems of interest, such as azeotrope compositions. It can be used to support the development of novel molecules and manufacturing processes.

A molecular density functional theory for associating fluids in 3D geometries

A new free-energy functional is proposed for inhomogeneous associating fluids. The general formulation of Wertheim's thermodynamic perturbation theory is considered as the starting point of the derivation. We apply the hypotheses of the statistical associating fluid theory in the classical density functional theory (DFT) framework to obtain a tractable expression of the free-energy functional for inhomogeneous associating fluids. Specific weighted functions are introduced in our framework to describe association interactions for a fluid under confinement. These weighted functions have a mathematical structure similar to the weighted densities of the fundamental-measure theory (i.e., they can be expressed as convolution products) such that they can be efficiently evaluated with Fourier transforms in a 3D space. The resulting free-energy functional can be employed to determine the microscopic structure of inhomogeneous associating fluids of arbitrary 3D geometry. The new model is first compared with Monte Carlo simulations and previous versions of DFT for a planar hard wall system in order to check its consistency in a 1D case. As an example of application in a 3D configuration, we then investigate the extreme confinement of an associating hard-sphere fluid inside an anisotropic open cavity with a shape that mimics a simplified model of zeolite. Both the density distribution and the corresponding molecular bonding profile are given, revealing complementary information to understand the structure of the associating fluid inside the cavity network. The impact of the degree of association on the preferential positions of the molecules inside the cavity is investigated as well as the competition between association and steric effect on adsorption.

Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

Multiscale simulation of fluids: coupling molecular and continuum

Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In molecular dynamics (MD) simulation, the length and time scales that can be captured are limited, while computational fluid dynamics (CFD) methods are built on a range of assumptions, from the continuum hypothesis itself, to a variety of closure assumptions. To address these issues, the coupling of different methodologies provides a way to retain the best of both methods. Here, we provide a perspective on multiscale simulation based on the coupling of MD and CFD with each a distinct part of the same simulation domain. This style of coupling allows molecular detail to be present only where it is needed, so CFD can model larger scales than possible with MD alone. We present a unified perspective of the literature, showing the links between the two main types of coupling, state and flux, and discuss the varying assumptions in their use. A unique challenge in such coupled simulation is obtaining averages and constraining local parts of a molecular simulation. We highlight that incorrect localisation has resulted in an error in the literature. We then finish with some applications, focused on the simulation of fluids. Thus, we hope to motivate further research in this exciting area with applications across the spectrum of scientific disciplines.

Modeling Sorption of Hydrocarbons in Polyethylene with the SAFT-γ Mie Approach Combined with a Statistical-Mechanical Model to Describe Semicrystalline Polymers

A recently developed statistical-mechanical model is applied systematically to estimate the fraction of tie-molecules (polymer chains linking different crystals directly or via entanglements) in semicrystalline polyethylene (PE) samples. The amorphous domains of the polymer are divided into constrained interlamellar domains and "free" outer-lamellar domains. A set of model parameters is assigned to each sample by correlating previous experimental measurements and minimizing the difference between the predicted solubility of pure hydrocarbons in the sample and the experimental values. We show that the sorption isotherms of multiple pure fluids in each sample can be described by a single parameter set, proving that the polymer-solute interactions (described accurately by the SAFT-γ Mie EoS) are decoupled from the sample-specific properties of the polymer. We find that ∼30% of the crystalline stems in the lamellae of PE are connected to tie-molecules, within the bounds suggested by previous theoretical and computational work. The transferability of the sample-specific parameters is assessed by predicting cosolubility effects and solubility at different temperatures, leading to good agreement with experimental data.

CGCompiler: Automated Coarse-Grained Molecule Parametrization via Noise-Resistant Mixed-Variable Optimization

Coarse-grained force fields (CG FFs) such as the Martini model entail a predefined, fixed set of Lennard-Jones parameters (building blocks) to model virtually all possible nonbonded interactions between chemically relevant molecules. Owing to its universality and transferability, the building-block coarse-grained approach has gained tremendous popularity over the past decade. The parametrization of molecules can be highly complex and often involves the selection and fine-tuning of a large number of parameters (e.g., bead types and bond lengths) to optimally match multiple relevant targets simultaneously. The parametrization of a molecule within the building-block CG approach is a mixed-variable optimization problem: the nonbonded interactions are discrete variables, whereas the bonded interactions are continuous variables. Here, we pioneer the utility of mixed-variable particle swarm optimization in automatically parametrizing molecules within the Martini 3 coarse-grained force field by matching both structural (e.g., RDFs) as well as thermodynamic data (phase-transition temperatures). For the sake of demonstration, we parametrize the linker of the lipid sphingomyelin. The important advantage of our approach is that both bonded and nonbonded interactions are simultaneously optimized while conserving the search efficiency of vector guided particle swarm optimization (PSO) methods over other metaheuristic search methods such as genetic algorithms. In addition, we explore noise-mitigation strategies in matching the phase-transition temperatures of lipid membranes, where nucleation and concomitant hysteresis introduce a dominant noise term within the objective function. We propose that noise-resistant mixed-variable PSO methods can both improve and automate parametrization of molecules within building-block CG FFs, such as Martini.

Molecular modeling of interfacial properties of the hydrogen + water + decane mixture in three-phase equilibrium

The understanding of interfacial phenomena between H2 and geofluids is of great importance for underground H2 storage, but requires further study. We report the first investigation on the three-phase fluid mixture containing H2, H2O, and n-C10H22. Molecular dynamics simulation and PC-SAFT density gradient theory are employed to estimate the interfacial properties under various conditions (temperature ranges from 298 to 373 K and pressure is up to around 100 MPa). Our results demonstrate that interfacial tensions (IFTs) of the H2-H2O interface in the H2 + H2O + C10H22 three-phase mixture are smaller than IFTs in the H2 + H2O two-phase mixture. This decrement of IFT can be attributed to C10H22 adsorption in the interface. Importantly, H2 accumulates in the H2O-C10H22 interface in the three-phase systems, which leads to weaker increments of IFT with increasing pressure compared to IFTs in the water + C10H22 two-phase mixture. In addition, the IFTs of the H2-C10H22 interface are hardly influenced by H2O due to the limited amount of H2O dissolved in nonaqueous phases. Nevertheless, positive surface excesses of H2O are seen in the H2-C10H22 interfacial region. Furthermore, the values of the spreading coefficient are mostly negative revealing the presence of the three-phase contact for the H2 + H2O + C10H22 mixture under studied conditions.

Molecular dynamics simulation of the coalescence of surfactant-laden droplets

We investigate the coalescence of surfactant-laden water droplets by using several different surfactant types and a wide range of concentrations by means of a coarse-grained model obtained by the statistical associating fluid theory. Our results demonstrate in detail a universal mass transport mechanism of surfactant across many concentrations and several surfactant types during the process. Coalescence initiation is seen to occur via a single pinch due to aggregation of surface surfactant, and its remnants tend to become engulfed in part inside the forming bridge. Across the board we confirm the existence of an initial thermal regime with constant bridge width followed by a later inertial regime with bridge width scaling roughly as the square root of time, but see no evidence of an intermediate viscous regime. Coalescence becomes slower as surfactant concentration grows, and we see evidence of the appearance of a further slowdown of a different nature for several times the critical concentration. We anticipate that our results provide further insights in the mechanisms of coalescence of surfactant-laden droplets.

Binding Debye-Hückel theory for associative electrolyte solutions

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Molecular insights into fluid-solid interfacial tensions in water + gas + solid systems at various temperatures and pressures

The fluid-solid interfacial tension is of great importance to many applications including the geological storage of greenhouse gases and enhancing the recovery of geo-resources, but it is rarely studied. Extensive molecular dynamics simulations are conducted to calculate fluid-solid interfacial properties in H2O + gas (H2, N2, CH4, and CO2) + rigid solid three-phase systems at various temperatures (298-403 K), pressures (0-100 MPa), and wettabilities (hydrophilic, neutral, and hydrophobic). Our results on the H2O + solid system show that vapor-solid interfacial tension should not be ignored in cases where the fluid-solid interaction energy is strong or the contact angle is close to 90°. As the temperature rises, the magnitude of H2O's liquid-solid interfacial tension declines because the oscillation of the interfacial density/pressure profile weakens at high temperatures. However, the magnitude of H2O vapor-solid interfacial tension is enhanced with temperature due to the stronger adsorption of H2O. Moreover, the H2O-solid interfacial tension in H2O + gas (H2 or N2) + solid systems is weakly dependent on pressure, while the pressure effects on H2O-solid interfacial tensions in systems with CH4 or CO2 are significant. We show that the assumption of pressure independent H2O-solid interfacial tensions should be cautiously applied to Neumann's method for systems containing non-hydrophilic surfaces with strong gas-solid interaction. Meanwhile, the magnitude of gas-solid interfacial tension increases with pressure and gas-solid interaction. High temperatures generally decrease the magnitude of gas-solid interfacial tensions. Further, we found that the increment of contact angle due to the presence of gases follows this order: H2 < N2 < CH4 < CO2.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.

Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature

This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.

Revised Enskog theory for Mie fluids: Prediction of diffusion coefficients, thermal diffusion coefficients, viscosities, and thermal conductivities

Since the 1920s, the Enskog solutions to the Boltzmann equation have provided a route to predicting the transport properties of dilute gas mixtures. At higher densities, predictions have been limited to gases of hard spheres. In this work, we present a revised Enskog theory for multicomponent mixtures of Mie fluids, where the Barker-Henderson perturbation theory is used to calculate the radial distribution function at contact. With parameters of the Mie-potentials regressed to equilibrium properties, the theory is fully predictive for transport properties. The presented framework offers a link between the Mie potential and transport properties at elevated densities, giving accurate predictions for real fluids. For mixtures of noble gases, diffusion coefficients from experiments are reproduced within ±4%. For hydrogen, the predicted self-diffusion coefficient is within 10% of experimental data up to 200 MPa and at temperatures above 171 K. Binary diffusion coefficients of the CO2/CH4 mixture from simulations are reproduced within 20% at pressures up to 14.7 MPa. Except for xenon in the vicinity of the critical point, the thermal conductivity of noble gases and their mixtures is reproduced within 10% of the experimental data. For other molecules than noble gases, the temperature dependence of the thermal conductivity is under-predicted, while the density dependence appears to be correctly predicted. Predictions of the viscosity are within ±10% of the experimental data for methane, nitrogen, and argon up to 300 bar, for temperatures ranging from 233 to 523 K. At pressures up to 500 bar and temperatures from 200 to 800 K, the predictions are within ±15% of the most accurate correlation for the viscosity of air. Comparing the theory to an extensive set of measurements of thermal diffusion ratios, we find that 49% of the model predictions are within ±20% of the reported measurements. The predicted thermal diffusion factor differs by less than 15% from the simulation results of Lennard-Jones mixtures, even at densities well exceeding the critical density.

Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule-Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the "digital" equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model's internal consistency is successfully assessed using Brown's characteristic curves.

Investigating anionic surfactant phase diagrams using dissipative particle dynamics: development of a transferable model

Dissipative particle dynamics (DPD) provides a powerful coarse-grained simulation technique for the study of a wide range of soft matter systems. Here, we investigate the transferability of DPD models to the prediction of anionic surfactant phase diagrams, taking advantage of fast parameter sweeps to optimise the choice of DPD parameters for these systems. Parameters are developed which provide a good representation of the phase diagrams of SDS (sodium dodecyl sulfate) and three different isomeric forms of LAS (linear alkylbenzene sulfonates) across an extensive concentration range. A high degree of transferability is seen, with parameters readily transferable to other systems, such as AES (alkyl ether sulfates). Excellent agreement is obtained with experimentally measured quantities, such as the lamellar layer spacing. Isosurfaces are produced from the surfactant head group, from which the second moment M of the isosurface normal distribution is calculated for different phase structures. Lyotropic liquid crystalline phases are characterised by a combination of the eigenvalues of M, radial distribution functions, and visual inspections.

Multipolar SAFT-VR Mie Equation of State: Predictions of Phase Equilibria in Refrigerant Systems with No Binary Interaction Parameter

An extension of the SAFT-VR Mie equation of state is proposed to predict the properties of multipolar fluids. The new model, referred to as multipolar M-SAFT-VR Mie, incorporates the general multipolar term developed by Gubbins and co-workers, which accounts for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. A modification of the third order terms in the perturbation theory results in an accurate description of the simulation data for multipolar Lennard-Jones fluids. Both the M-SAFT-VR Mie and polar soft-SAFT models are extended to account for polarizability, and a good agreement is obtained with molecular simulation data. The M-SAFT-VR Mie model is applied to refrigerant systems, and it is found that including both dipole and quadrupole moments in molecular models leads to more accurate results than using only a dipole moment. The new model provides excellent predictions of the vapor-liquid equilibria of zeotropic and azeotropic refrigerant mixtures without the need for binary interaction parameters, making it a valuable tool for formulating low-GWP working fluids.

Determining Brown's Characteristic Curves Using Molecular Simulation

Brown's characteristic curves define lines on the thermodynamic surface where special thermodynamic conditions hold. These curves are an important tool for the development of thermodynamic models of fluids. Yet, practically no experimental data for Brown's characteristic curves is available. In this work, a rigorous and generalized method for determining Brown's characteristic curves based on molecular simulation was developed. As multiple thermodynamic equivalent definitions apply for the characteristic curves, different simulation routes were compared. Based on this systematic approach, the most favorable route for determining each characteristic curve was identified. The computational procedure developed in this work combines molecular simulation, molecular-based equation of state, and the evaluation of the second virial coefficient. The new method was tested on a simple model system (the classical Lennard-Jones fluid) and different types of real substances (toluene, methane, ethane, propane, and ethanol). It is thereby shown that the method is robust and yields accurate results. Moreover, a computer code implementation of the method is presented.

Classical density functional theory for interfacial properties of hydrogen, helium, deuterium, neon, and their mixtures

We present a classical density functional theory (DFT) for fluid mixtures that is based on a third-order thermodynamic perturbation theory of Feynman-Hibbs-corrected Mie potentials. The DFT is developed to study the interfacial properties of hydrogen, helium, neon, deuterium, and their mixtures, i.e., fluids that are strongly influenced by quantum effects at low temperatures. White Bear fundamental measure theory is used for the hard-sphere contribution of the Helmholtz energy functional, and a weighted density approximation is used for the dispersion contribution. For mixtures, a contribution is included to account for non-additivity in the Lorentz-Berthelot combination rule. Predictions of the radial distribution function from DFT are in excellent agreement with results from molecular simulations, both for pure components and mixtures. Above the normal boiling point and 5% below the critical temperature, the DFT yields surface tensions of neon, hydrogen, and deuterium with average deviations from experiments of 7.5%, 4.4%, and 1.8%, respectively. The surface tensions of hydrogen/deuterium, para-hydrogen/helium, deuterium/helium, and hydrogen/neon mixtures are reproduced with a mean absolute error of 5.4%, 8.1%, 1.3%, and 7.5%, respectively. The surface tensions are predicted with an excellent accuracy at temperatures above 20 K. The poor accuracy below 20 K is due to the inability of Feynman-Hibbs-corrected Mie potentials to represent the real fluid behavior at these conditions, motivating the development of new intermolecular potentials. This DFT can be leveraged in the future to study confined fluids and assess the performance of porous materials for hydrogen storage and transport.

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.

A smile is all you need: predicting limiting activity coefficients from SMILES with natural language processing

The knowledge of mixtures' phase equilibria is crucial in nature and technical chemistry. Phase equilibria calculations of mixtures require activity coefficients. However, experimental data on activity coefficients are often limited due to the high cost of experiments. For an accurate and efficient prediction of activity coefficients, machine learning approaches have been recently developed. However, current machine learning approaches still extrapolate poorly for activity coefficients of unknown molecules. In this work, we introduce a SMILES-to-properties-transformer (SPT), a natural language processing network, to predict binary limiting activity coefficients from SMILES codes. To overcome the limitations of available experimental data, we initially train our network on a large dataset of synthetic data sampled from COSMO-RS (10 million data points) and then fine-tune the model on experimental data (20 870 data points). This training strategy enables the SPT to accurately predict limiting activity coefficients even for unknown molecules, cutting the mean prediction error in half compared to state-of-the-art models for activity coefficient predictions such as COSMO-RS and UNIFACDortmund, and improving on recent machine learning approaches.

Soft fundamental measure theory functional for the Weeks-Chandler-Andersen repulsive potential

We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid. We find that this approach is comparable in accuracy to the Barker-Henderson approach combined with the White Bear density functional for the hard-sphere fluid.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Pilot scale assessment of a novel phase-change solvent for energy efficient post -combustion CO2 capture

The proliferation of industrial-scale CO₂ capture technologies requires improvements in existing systems. Absorption/desorption capture processes that employ phase-change solvents (PCS) are promising for energy and cost reduction. Several PCSs have been investigated at bench scale, but very few have been tested in pilot-scale plants. The novel PCS mixture S₁N (N1- cyclohexylpropane-1,3-diamine)/DMCA (Dimethylcyclohexylamine) has previously exhibited desirable performance in equilibrium experiments, economic and sustainability studies. This work presents the pilot-scale evaluation of S₁N/DMCA for the first time, at two different concentrations and various liquid-to-gas ratios. Experimental evidence on key performance indicators is brought forward, including absorption efficiency, cyclic capacity, distance from equilibrium and regeneration energy in comparison to benchmark solvent MEA (monoethanolamine). S₁N/DMCA enables robust operation as it maintains a cyclic capacity of 0.63 mol/kg at different liquid-to-gas ratios, which is about two times higher than that of MEA. It achieves operating loadings close to equilibrium, reaching 1.6 mol/kg, and a regeneration energy of 2.3 GJ/tn CO₂, representing 45% reduction compared to MEA.

Deriving force fields with a multiscale approach:from ab initio calculations to molecular-based equations of state

Using theoretical and computational tools for predicting thermophysical properties of fluid systems and the soft matter has always been of interest to the physical, chemical, and engineering sciences. And certainly, the ultimate goal is to be able to compute these macroscopic properties from first principle calculations beginning with the very atomic constitution of matter. In this work, Mie potential parameters were obtained through dimer interaction energy curves derived from ab initio calculations to represent methane and methane-substituted molecules in a spherical 1-site coarse-grained model. Bottom-up-based Mie potential parameters of this work were compared to top-down-based ones from the statistical associating fluid theory (SAFT) models for the calculation of thermodynamic properties and critical point by molecular dynamics simulations and SAFT-VR Mie equation of state. Results demonstrated that bottom-up-based Mie potential parameters when averaging the Mie potential parameters of a representative population of conformers provide values close to the top-down-based ones from SAFT models and predict well properties of tetrahedral molecules. This shows the level of consistency embedded in the SAFT-VR Mie family of models and confers a status of a purely predictive equation of state for SAFT-VR Mie when a reasonable model is considered to represent a molecule of interest.

Density functional theory for the prediction of interfacial properties of molecular fluids within the SAFT-γ coarse-grained approach

Recently, we have proposed the SAFT-VR Mie MF DFT approach [Algaba et al., Phys. Chem. Chem. Phys., 2019, 21, 11937–11948] to investigate systems that exhibit fluid–fluid interfaces. This formalism is based on the combination of the Statistical Associating Fluid Theory for attractive potentials of variable range using Mie intermolecular potential (SAFT-VR Mie) and a Density Functional Theory (DFT) treatment of the free energy. A mean-field approach is used to evaluate the attractive term, neglecting the pair correlations associated to attractions. This theory has been combined with reported SAFT-γ Coarse-Grained (CG) Mie force fields to provide an excellent description of the vapor–liquid interface of carbon dioxide and water pure fluids. The present work is a natural and necessary extension of this previous study. We assess the adequacy of the proposed methodology for dealing with inhomogeneous fluid systems of large complex molecules, in particular carbon tetrafluoride and sulfur hexafluoride greenhouse gases, the refrigerant 2,3,3,3-tetrafluoro-1-propene, and the long-chain n-decane and n-eicosane hydrocarbons. The obvious diversity of these fluids, their chemical and industrial interest, and the fact of that SAFT-γ CG Mie force fields have been reported for them justify such choice. With the aim of testing the theory, we perform Molecular Dynamics simulations in the canonical ensemble using the direct coexistence technique for the same models. We focus both on bulk, such as coexistence diagrams and vapor pressure curves, as well as interfacial properties, including surface tension. The comparison of the theoretical predictions with the computational results as well as with experimental data taken from the literature demonstrates the reliability and generalization of this method for dealing simultaneously with vapor–liquid equilibrium and interfacial phenomena. Hence, it appears as a potential tool for the interface analysis, with the main advantage over molecular simulation of low computational cost, and solving the experimental difficulties in accurately measuring the surface tension of certain systems.

Comparison of the vapour–liquid surface tensions for substances studied in this work as obtained from SAFT-VR Mie DFT and experiments.