Machine learning potentials for complex aqueous systems made simple.

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex systems such as solid-liquid interfaces. Here we present a machine learning framework that enables the efficient development and validation of models for complex aqueous systems. Instead of trying to deliver a globally optimal machine learning potential, we propose to develop models applicable to specific thermodynamic state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with minimum human effort through a data-driven active learning protocol. Such models can afterward be applied in exhaustive simulations to provide reliable answers for the scientific question at hand or to systematically explore the thermal performance of ab initio methods. We showcase this methodology on a diverse set of aqueous systems comprising bulk water with different ions in solution, water on a titanium dioxide surface, and water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio reference, the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities.

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

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.

Molecular Dynamics Simulation of Polyacrylamide Adsorption on Calcite.

In poorly consolidated carbonate rock reservoirs, solids production risk, which can lead to increased environmental waste, can be mitigated by injecting formation-strengthening chemicals. Classical atomistic molecular dynamics (MD) simulation is employed to model the interaction of polyacrylamide-based polymer additives with a calcite structure, which is the main component of carbonate formations. Amongst the possible calcite crystal planes employed as surrogates of reservoir rocks, the (1 0 4) plane is shown to be the most suitable surrogate for assessing the interactions with chemicals due to its stability and more realistic representation of carbonate structure. The molecular conformation and binding energies of pure polyacrylamide (PAM), hydrolysed polyacrylamide in neutral form (HPAM), hydrolysed polyacrylamide with 33% charge density (HPAM 33%) and sulfonated polyacrylamide with 33% charge density (SPAM 33%) are assessed to determine the adsorption characteristics onto calcite surfaces. An adsorption-free energy analysis, using an enhanced umbrella sampling method, is applied to evaluate the chemical adsorption performance. The interaction energy analysis shows that the polyacrylamide-based polymers display favourable interactions with the calcite structure. This is attributed to the electrostatic attraction between the amide and carboxyl functional groups with the calcite. Simulations confirm that HPAM33% has a lower free energy than other polymers, presumably due to the presence of the acrylate monomer in ionised form. The superior chemical adsorption performance of HPAM33% agrees with Atomic Force Microscopy experiments reported herein.

Defect-Dependent Corrugation in Graphene.

Graphene's intrinsically corrugated and wrinkled topology fundamentally influences its electronic, mechanical, and chemical properties. Experimental techniques allow the manipulation of pristine graphene and the controlled production of defects which allows one to control the atomic out-of-plane fluctuations and thus tune graphene's properties. Here, we perform large scale machine learning-driven molecular dynamics simulations to understand the impact of defects on the structure of graphene. We find that defects cause significantly higher corrugation leading to a strongly wrinkled surface. The magnitude of this structural transformation strongly depends on the defect concentration and specific type of defect. Analyzing the atomic neighborhood of the defects reveals that the extent of these morphological changes depends on the preferred geometrical orientation and the interactions between defects. While our work highlights that defects can strongly affect graphene's morphology, it also emphasizes the differences between distinct types by linking the global structure to the local environment of the defects.

SGTPy: A Python Code for Calculating the Interfacial Properties of Fluids Based on the Square Gradient Theory Using the SAFT-VR Mie Equation of State.

In this work, we showcase SGTPy, a Python open-source code developed to calculate interfacial properties (interfacial concentration profiles and interfacial or surface tension) for pure fluids and fluid mixtures. SGTPy employs the Square Gradient Theory (SGT) coupled to the Statistical Associating Fluid Theory of Variable Range employing a Mie potential (SAFT-VR-Mie). SGTPy uses standard Python numerical packages (i.e., NumPy, SciPy) and can be used under Jupyter notebooks. Its features are the calculation of phase stability, phase equilibria, interfacial properties, and the optimization of the SGT and SAFT parameters for vapor-liquid, liquid-liquid and vapor-liquid-liquid equilibria for pure fluids and multicomponent mixtures. Phase equilibrium calculations include two-phase and multiphase flash, bubble and dew points, and the tangent plane distance. For the computation of interfacial properties, SGTPy incorporates several options to solve the interfacial concentration, such as the path technique, an auxiliary time function, and orthogonal collocation. Additionally, the SGTPy code allows the inclusion of subroutines from other languages (e.g., Fortran, and C++) through Cython and f2py Python tools, which opens the possibility for future extensions or recycling tested and optimized subroutines from other codes. Supporting Information includes a review of the theoretical expressions required to couple SAFT-VR-Mie equation of state with the SGT. The use and capabilities of SGTPy are illustrated through step by step examples written on Jupyter notebooks for the cases of pure fluids and binary and ternary mixtures in bi- and three- phasic equilibria. The SGTPy code can be downloaded from https://github.com/gustavochm/SGTPy.

Equation of state and force fields for Feynman-Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium.

We extend the statistical associating fluid theory of quantum corrected Mie potentials (SAFT-VRQ Mie), previously developed for pure fluids [Aasen et al., J. Chem. Phys. 151, 064508 (2019)], to fluid mixtures. In this model, particles interact via Mie potentials with Feynman-Hibbs quantum corrections of first order (Mie-FH1) or second order (Mie-FH2). This is done using a third-order Barker-Henderson expansion of the Helmholtz energy from a non-additive hard-sphere reference system. We survey existing experimental measurements and ab initio calculations of thermodynamic properties of mixtures of neon, helium, deuterium, and hydrogen and use them to optimize the Mie-FH1 and Mie-FH2 force fields for binary interactions. Simulations employing the optimized force fields are shown to follow the experimental results closely over the entire phase envelopes. SAFT-VRQ Mie reproduces results from simulations employing these force fields, with the exception of near-critical states for mixtures containing helium. This breakdown is explained in terms of the extremely low dispersive energy of helium and the challenges inherent in current implementations of the Barker-Henderson expansion for mixtures. The interaction parameters of two cubic equations of state (Soave-Redlich-Kwong and Peng-Robinson) are also fitted to experiments and used as performance benchmarks. There are large gaps in the ranges and properties that have been experimentally measured for these systems, making the force fields presented especially useful.

Probing the Interfacial Behavior of Type IIIa Binary Mixtures Along the Three-Phase Line Employing Molecular Thermodynamics.

Interfacial properties such as interfacial profiles, surface activity, wetting transitions, and interfacial tensions along the three-phase line are described for a Type IIIa binary mixture. The methodological approach combines the square gradient theory coupled to the statistical associating fluid theory for Mie potentials of variable range, and coarse-grained molecular dynamics simulations using the same underlying potential. The water + n-hexane mixture at three-phase equilibrium is chosen as a benchmark test case. The results show that the use of the same molecular representation for both the theory and the simulations provides a complementary picture of the aforementioned mixture, with an excellent agreement between the molecular models and the available experimental data. Interfacial tension calculations are extended to temperatures where experimental data are not available. From these extrapolations, it is possible to infer a first order wetting transition at 347.2 K, where hexane starts to completely wet the water/vapor interface. Similarly, the upper critical end point is estimated at 486.3 K. Both results show a very good agreement to the available experimental information. The concentration profiles confirm the wetting behavior of n-hexane along with a strong positive surface activity that increases with temperature, contrasting the weak positive surface activity of water that decreases with temperature.

Assembly of porous smectic structures formed from interlocking high-symmetry planar nanorings.

Materials comprising porous structures, often in the form of interconnected concave cavities, are typically assembled from convex molecular building blocks. The use of nanoparticles with a characteristic nonconvex shape provides a promising strategy to create new porous materials, an approach that has been recently used with cagelike molecules to form remarkable liquids with "scrabbled" porous cavities. Nonconvex mesogenic building blocks can be engineered to form unique self-assembled open structures with tunable porosity and long-range order that is intermediate between that of isotropic liquids and of crystalline solids. Here we propose the design of highly open liquid-crystalline structures from rigid nanorings with ellipsoidal and polygonal geometry. By exploiting the entropic ordering characteristics of athermal colloidal particles, we demonstrate that high-symmetry nonconvex rings with large internal cavities interlock within a 2D layered structure leading to the formation of distinctive liquid-crystalline smectic phases. We show that these smectic phases possess uniquely high free volumes of up to ∼95%, a value significantly larger than the 50% that is typically achievable with smectic phases formed by more conventional convex rod- or disklike mesogenic particles.

Molecular Simulation of the Adsorption and Diffusion in Cylindrical Nanopores: Effect of Shape and Fluid⁻Solid Interactions.

We report on molecular simulations of model fluids composed of three tangentially bonded Lennard-Jones interaction sites with three distinct morphologies: a flexible "pearl-necklace" chain, a rigid "stiff" linear configuration, and an equilateral rigid triangular ring. The adsorption of these three models in cylindrical pores of diameters 1, 2, and 3 nm and with varying solid⁻fluid strength was determined by direct molecular dynamics simulations, where a sample pore was placed in contact with a bulk fluid. Adsorption isotherms of Type I, V, and H1 were obtained depending on the choice of pore size and solid⁻fluid strength. Additionally, the bulk-phase equilibria, the nematic order parameter of the adsorbed phase, and the self-diffusion coefficient in the direction of the pore axis were examined. It was found that both the molecular shape and the surface attractions play a decisive role in the shape of the adsorption isotherm. In general, the ring molecules showed a larger adsorption, while the fully flexible model showed the smallest adsorption. Morphology and surface strength were found to have a lesser effect on the diffusion of the molecules. An exceptional high adsorption and diffusion, suggesting an enhanced permeability, was observed for the linear stiff molecules in ultraconfinement, which was ascribed to a phase transition of the adsorbed fluid into a nematic liquid crystal.

Bulk viscosity of molecular fluids.

The bulk viscosity of molecular models of gases and liquids is determined by molecular simulations as a combination of a dilute gas contribution, arising due to the relaxation of internal degrees of freedom, and a configurational contribution, due to the presence of intermolecular interactions. The dilute gas contribution is evaluated using experimental data for the relaxation times of vibrational and rotational degrees of freedom. The configurational part is calculated using Green-Kubo relations for the fluctuations of the pressure tensor obtained from equilibrium microcanonical molecular dynamics simulations. As a benchmark, the Lennard-Jones fluid is studied. Both atomistic and coarse-grained force fields for water, CO2, and n-decane are considered and tested for their accuracy, and where possible, compared to experimental data. The dilute gas contribution to the bulk viscosity is seen to be significant only in the cases when intramolecular relaxation times are in the µs range, and for low vibrational wave numbers (<1000 cm-1); This explains the abnormally high values of bulk viscosity reported for CO2. In all other cases studied, the dilute gas contribution is negligible and the configurational contribution dominates the overall behavior. In particular, the configurational term is responsible for the enhancement of the bulk viscosity near the critical point.

Demixing, surface nematization, and competing adsorption in binary mixtures of hard rods and hard spheres under confinement.

A molecular simulation study of binary mixtures of hard spherocylinders (HSCs) and hard spheres (HSs) confined between two structureless hard walls is presented. The principal aim of the work is to understand the effect of the presence of hard spheres on the entropically driven surface nematization of hard rod-like particles at surfaces. The mixtures are studied using a constant normal-pressure Monte Carlo algorithm. The surface adsorption at different compositions is examined in detail. At moderate hard-sphere concentrations, preferential adsorption of the spheres at the wall is found. However, at moderate to high pressure (density), we observe a crossover in the adsorption behavior with nematic layers of the rods forming at the walls leading to local demixing of the system. The presence of the spherical particles is seen to destabilize the surface nematization of the rods, and the degree of demixing increases on increasing the hard-sphere concentration.

Physical insights into the blood-brain barrier translocation mechanisms.

The number of individuals suffering from diseases of the central nervous system (CNS) is growing with an aging population. While candidate drugs for many of these diseases are available, most of these pharmaceutical agents cannot reach the brain rendering most of the drug therapies that target the CNS inefficient. The reason is the blood-brain barrier (BBB), a complex and dynamic interface that controls the influx and efflux of substances through a number of different translocation mechanisms. Here, we present these mechanisms providing, also, the necessary background related to the morphology and various characteristics of the BBB. Moreover, we discuss various numerical and simulation approaches used to study the BBB, and possible future directions based on multi-scale methods. We anticipate that this review will motivate multi-disciplinary research on the BBB aiming at the design of effective drug therapies.

Extension of the SAFT-VR Mie EoS To Model Homonuclear Rings and Its Parametrization Based on the Principle of Corresponding States.

The statistical associating fluid theory of variable range employing a Mie potential (SAFT-VR-Mie) proposed by Lafitte et al. (J. Chem Phys. 2013, 139, 154504) is one of the latest versions of the SAFT family. This particular version has been shown to have a remarkable capability to connect experimental determinations, theoretical calculations, and molecular simulations results. However, the theoretical development restricts the model to chains of beads connected in a linear fashion. In this work, the capabilities of the SAFT-VR Mie equation of state for modeling phase equilibria are extended for the case of planar ring compounds. This modification proposed replaces the Helmholtz energy of chain formation by an empirical contribution based on a parallelism to the second-order thermodynamic perturbation theory for hard sphere trimers. The proposed expression is given in terms of an extra parameter, χ, that depends on the number of beads, ms, and the geometry of the ring. The model is used to describe the phase equilibrium for planar ring compounds formed of Mie isotropic segments for the cases of ms equals to 3, 4, 5 (two configurations), and 7 (two configurations). The resulting molecular model is further parametrized, invoking a corresponding states principle resulting in sets of parameters that can be used indistinctively in theoretical calculations or in molecular simulations without any further refinements. The extent and performance of the methodology has been exemplified by predicting the phase equilibria and vapor pressure curves for aromatic hydrocarbons (benzene, hexafluorobenzene, toluene), heterocyclic molecules (2,5-dimethylfuran, sulfolane, tetrahydro-2H-pyran, tetrahydrofuran), and polycyclic aromatic hydrocarbons (naphthalene, pyrene, anthracene, pentacene, and coronene). An important aspect of the theory is that the parameters of the model can be used directly in molecular dynamics (MD) simulations to calculate equilibrium phase properties and interfacial tensions with an accuracy that rivals other coarse grained and united atom models, for example, liquid densities, are predicted, with a maximum absolute average deviation of 3% from both the theory and the MD simulations, while the interfacial tension is predicted, with a maximum absolute average of 8%. The extension to mixtures is exemplified by considering a binary system of hexane (chain fluid) and tetrahydro-2H-pyran (ring fluid).

Bottled SAFT: A Web App Providing SAFT-γ Mie Force Field Parameters for Thousands of Molecular Fluids.

Coarse-grained molecular simulation has become a popular tool for modeling simple and complex fluids alike. The defining aspects of a coarse grained model are the force field parameters, which must be determined for each particular fluid. Because the number of molecular fluids of interest in nature and in engineering processes is immense, constructing force field parameter tables by individually fitting to experimental data is a futile task. A step toward solving this challenge was taken recently by Mejía et al., who proposed a correlation that provides SAFT-γ Mie force field parameters for a fluid provided one knows the critical temperature, the acentric factor and a liquid density, all relatively accessible properties. Building on this, we have applied the correlation to more than 6000 fluids, and constructed a web application, called "Bottled SAFT", which makes this data set easily searchable by CAS number, name or chemical formula. Alternatively, the application allows the user to calculate parameters for components not present in the database. Once the intermolecular potential has been found through Bottled SAFT, code snippets are provided for simulating the desired substance using the "raaSAFT" framework, which leverages established molecular dynamics codes to run the simulations. The code underlying the web application is written in Python using the Flask microframework; this allows us to provide a modern high-performance web app while also making use of the scientific libraries available in Python. Bottled SAFT aims at taking the complexity out of obtaining force field parameters for a wide range of molecular fluids, and facilitates setting up and running coarse-grained molecular simulations. The web application is freely available at http://www.bottledsaft.org . The underlying source code is available on Bitbucket under a permissive license.

Nonequilibrium study of the intrinsic free-energy profile across a liquid-vapour interface.

We calculate an atomistically detailed free-energy profile across a heterogeneous system using a nonequilibrium approach. The path-integral formulation of Crooks fluctuation theorem is used in conjunction with the intrinsic sampling method to calculate the free-energy profile for the liquid-vapour interface of the Lennard-Jones fluid. Free-energy barriers are found corresponding to the atomic layering in the liquid phase as well as a barrier associated with the presence of an adsorbed layer as revealed by the intrinsic density profile. Our findings are in agreement with profiles calculated using Widom's potential distribution theorem applied to both the average and the intrinsic profiles as well as the literature values for the excess chemical potential.

Superspreading: mechanisms and molecular design.

The intriguing ability of certain surfactant molecules to drive the superspreading of liquids to complete wetting on hydrophobic substrates is central to numerous applications that range from coating flow technology to enhanced oil recovery. Despite significant experimental efforts, the precise mechanisms underlying superspreading remain unknown to date. Here, we isolate these mechanisms by analyzing coarse-grained molecular dynamics simulations of surfactant molecules of varying molecular architecture and substrate affinity. We observe that for superspreading to occur, two key conditions must be simultaneously satisfied: the adsorption of surfactants from the liquid-vapor surface onto the three-phase contact line augmented by local bilayer formation. Crucially, this must be coordinated with the rapid replenishment of liquid-vapor and solid-liquid interfaces with surfactants from the interior of the droplet. This article also highlights and explores the differences between superspreading and conventional surfactants, paving the way for the design of molecular architectures tailored specifically for applications that rely on the control of wetting.

Modelling the superspreading of surfactant-laden droplets with computer simulation.

The surfactant-driven superspreading of droplets on hydrophobic substrates is considered. A key element of the superspreading mechanism is the adsorption of surfactant molecules from the liquid-vapour interface onto the substrate through the contact line, which must be coordinated with the replenishment of interfaces with surfactant from the interior of the droplet. We use molecular dynamics simulations with coarse-grained force fields to provide a detailed structural description of the droplet shape and surfactant dynamics during the superspreading process. We also provide a simple method for accurate estimation of the contact angle subtended by the droplets at the contact line.

Orientational ordering and phase behaviour of binary mixtures of hard spheres and hard spherocylinders.

We study the structure and fluid-phase behaviour of binary mixtures of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the NPnAT ensemble Monte Carlo (MC) approach in which the normal component of the pressure tensor is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected enhancement of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic NPT ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximations [Malijevský et al., J. Chem. Phys. 129, 144504 (2008)]. In the one-fluid version of the theory, the properties of the mixture are related to an effective one-component HS system, while in the many-fluid theory, the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixture.

Water droplet excess free energy determined by cluster mitosis using guided molecular dynamics.

Atmospheric aerosols play a vital role in affecting climate by influencing the properties and lifetimes of clouds and precipitation. Understanding the underlying microscopic mechanisms involved in the nucleation of aerosol droplets from the vapour phase is therefore of great interest. One key thermodynamic quantity in nucleation is the excess free energy of cluster formation relative to that of the saturated vapour. In our current study, the excess free energy is extracted for clusters of pure water modelled with the TIP4P/2005 intermolecular potential using a method based on nonequilibrium molecular dynamics and the Jarzynski relation. The change in free energy associated with the "mitosis" or division of a cluster of N water molecules into two N/2 sub-clusters is evaluated. This methodology is an extension of the disassembly procedure used recently to calculate the excess free energy of argon clusters [H. Y. Tang and I. J. Ford, Phys. Rev. E 91, 023308 (2015)]. Our findings are compared to the corresponding excess free energies obtained from classical nucleation theory (CNT) as well as internally consistent classical theory (ICCT). The values of the excess free energy that we obtain with the mitosis method are consistent with CNT for large cluster sizes but for the smallest clusters, the results tend towards ICCT; for intermediate sized clusters, we obtain values between the ICCT and CNT predictions. Furthermore, the curvature-dependent surface tension which can be obtained by regarding the clusters as spherical droplets of bulk density is found to be a monotonically increasing function of cluster size for the studied range. The data are compared to other values reported in the literature, agreeing qualitatively with some but disagreeing with the values determined by Joswiak et al. [J. Phys. Chem. Lett. 4, 4267 (2013)] using a biased mitosis approach; an assessment of the differences is the main motivation for our current study.