Calculation of surface tension via area sampling

Revisiting Aspirin Polymorphic Stability Using a Machine Learning Potential

In this study, we present a systematic computational investigation to analyze the long-debated free energy stability of two well-known aspirin polymorphs, denoted as Form I and Form II. Specifically, we developed a strategy to collect training configurations covering diverse interatomic interactions between representative functional groups in aspirin crystals. Utilizing a state-of-the-art neural network interatomic potential (NNIP) model, we trained an accurate machine learning potential to simulate aspirin crystal dynamics under finite temperature conditions with ∼0.46 kJ/mol/molecule accuracy. Employing the trained NNIP model, we performed thermodynamic integration to assess the free energy difference between aspirins I and II, accounting for the anharmonic effects in a large supercell consisting of 512 molecules. For the first time, our results convincingly demonstrated that Form I is more stable than Form II at 300 K, ranging from 0.74 to 1.83 kJ/mol/molecule, aligning with experimental observations. Unlike the majority of previous simulations based on (quasi)harmonic approximations in a small super cell, which often found degenerate energies between aspirins I and II, our findings underscore the importance of anharmonic effects in determining polymorphic stability ranking. Furthermore, we proposed the use of the rotational degrees of freedom of methyl and ester/phenyl groups in aspirin crystals as characteristic motions to highlight rotational entropic contribution that favors the stability of Form I. From the structural perspective, we also found that the subtle free energy difference can be used to explain the distinct thermal expansion responses as observed in both experimental and simulation data. Beyond the aspirin polymorphism, we anticipate that such entropy-driven stabilization can be broadly applicable to many other organic systems, suggesting that our approach holds great promise for stability studies in small-molecule drug design.

Unmasking quantum effects in the surface thermodynamics of fluid nanodrops

The focus of our study is an in-depth investigation of the quantum effects associated with the surface tension and other thermodynamic properties of nanoscopic liquid drops. The behavior of drops of quantum Lennard-Jones fluids is investigated with path-integral Monte Carlo simulations, and the test-area method is used to determine the surface tension of the spherical vapor-liquid interface. As the thermal de Broglie wavelength, λB, becomes more significant, the average density of the liquid drop decreases, with the drop becoming mechanically unstable at large wavelengths. As a consequence, the surface tension is found to decrease monotonically with λB, vanishing altogether for dominant quantum interactions. Quantum effects can be significant, leading to values that are notably lower than the classical thermodynamic limit, particularly for smaller drops. For planar interfaces (with infinite periodicity in the direction parallel to the interface), quantum effects are much less significant with the same values of λB but are, nevertheless, consequential for values representative of hydrogen or helium-4 at low temperatures corresponding to vapor-liquid coexistence. Large quantum effects are found for small drops of molecules with quantum interactions corresponding to water, ethane, methanol, and carbon dioxide, even at ambient conditions. The notable decrease in the density and tension has important consequences in reducing the Gibbs free-energy barrier of a nucleating cluster, enhancing the nucleation kinetics of liquid drops and of bubble formation. This implies that drops would form at a much greater rate than is predicted by classical nucleation theory.

Emerging Trends of Computational Chemistry and Molecular Modeling in Froth Flotation: A Review

Froth flotation is the most versatile process in mineral beneficiation, extensively used to concentrate a wide range of minerals. This process comprises mixtures of more or less liberated minerals, water, air, and various chemical reagents, involving a series of intermingled multiphase physical and chemical phenomena in the aqueous environment. Today's main challenge facing the froth flotation process is to gain atomic-level insights into the properties of its inherent phenomena governing the process performance. While it is often challenging to determine these phenomena via trial-and-error experimentations, molecular modeling approaches not only elicit a deeper understanding of froth flotation but can also assist experimental studies in saving time and budget. Thanks to the rapid development of computer science and advances in high-performance computing (HPC) infrastructures, theoretical/computational chemistry has now matured enough to successfully and gainfully apply to tackle the challenges of complex systems. In mineral processing, however, advanced applications of computational chemistry are increasingly gaining ground and demonstrating merit in addressing these challenges. Accordingly, this contribution aims to encourage mineral scientists, especially those interested in rational reagent design, to become familiarized with the necessary concepts of molecular modeling and to apply similar strategies when studying and tailoring properties at the molecular level. This review also strives to deliver the state-of-the-art integration and application of molecular modeling in froth flotation studies to assist either active researchers in this field to disclose new directions for future research or newcomers to the field to initiate innovative works.

Predicting surfactant phase behavior with a molecularly informed field theory

HYPOTHESIS

The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations.

SIMULATION WORK

We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements.

FINDINGS

The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.

Free-energy differences of OPC-Water and SPC/HW-Heavy-Water Models using the Bennett Acceptance Ratio

Surface tension, vapor density of OPC-water and SPC/HW-heavy-water models have been estimated at low temperatures using the scaled model. The free-energy difference, -ΔF, of n-molecules and (n-1)-molecules plus a free probe has been calculated using the Bennett acceptance ratio with the aid of Monte-Carlo simulations. Our results show that the relation between the free-energy difference divided by kBT and the number of molecules to the power minus one-third is linear for n>6. Consequently, the surface tension can be extracted from the straight line slope, whereas the vapor density can be extracted from the intercept, which is proportional to the logarithmic ratio of liquid density to that of vapor density. By scaling the free-energy differences, for at least three different temperatures, to TCT−1, we estimated the critical temperature and hence the surface tension and the vapor density at a wide range of temperatures. The free-energy differences have been calculated at 240K, 260K, and 280K for OPC-water, and at 260K, 280K, and 300K for the SPC/HW-heavy water model.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows forrepulsiveand/orattractivecontributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

High-sensitivity magnetic sensor based on the evanescent scattering by a magnetorheological film

We present a simple concept to implement a magnetic sensor that uses evanescent scattering by a suspended magnetorheological (MR) film above a planar waveguide. The soft MR film embedded with ferromagnetic particles is to induce scattering on the evanescent field of a planar waveguide at a proximity distance. This distance can be controlled precisely by a magnetic field. Consequently, the waveguide output power changes in response to the magnetic intensity. Two sensor prototypes of different film thicknesses were designed and tested showing a trade-off between the sensitivity and dynamic sensing range. A maximum sensitivity of ∼2.62dB/mT was obtained. Compared to optical micro-electromechanical systems, the presented sensors feature a simple design, easy fabrication, low cost, and the potential for large-scale production and miniaturization to be integrated into portable devices.

The pair distribution function in the planar gas-liquid interface: Application to the calculation of the surface tension

A Monte Carlo simulation is used to calculate the pair distribution function g⁽²⁾r₁,r₂ for a planar gas-liquid interface. Due to the cylindrical symmetry of the system, g⁽²⁾ can be stored as a three-dimensional array that can be readily manipulated and used to calculate the surface tension and the single atom density profile directly. The consistency and accuracy of our calculation of g⁽²⁾(r₁, r₂) is demonstrated by a calculation of the single atom density through the first Born-Green-Yvon equation. We show that the surface tension calculated directly from the pair distribution function and from other well-established routes is completely consistent. In the case of the gas-liquid interface for argon modeled with an explicit inclusion of the three-body forces, an accurate pair distribution can be used to estimate the long-range contribution to the three-body part of the surface tension. A detailed analysis of this correction, its dependence on the three-body cutoff, and its overall contribution to the surface tension are presented.

Unexpected finite size effects in interfacial systems: Why bigger is not always better-Increase in uncertainty of surface tension with bulk phase width

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase L_l/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Vapour–liquid interfacial properties of square-well chains from density functional theory and Monte Carlo simulation

Vapour–liquid surface tension for tangent (open symbols) and vibrating (filled symbols) square-well chains.

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.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

The distribution of homogeneously grafted nanoparticles in polymer thin films and blends

Polymer nanocomposites are an important and growing class of materials where nanoparticles are mixed in a polymer matrix. Much of the interest in polymer nanocomposites is derived from the nanoparticles' ability to impart properties to the polymer not commonly found in polymer materials, such as tunable optical, electrical, and mechanical properties. Grafting polymer chains to the surface of a nanoparticle is one of the most common routes towards promoting dispersion of nanoparticles in a polymer matrix. However, we only understand the thermodynamics of grafted nanoparticles in a polymer matrix in the simplest of cases, and this problem is exacerbated by the lack of theoretical and computational tools capable of efficiently predicting the structure of phase separated grafted nanoparticle/polymer blends. In this work, we extend a recently developed field theoretic framework to study the distribution of homogeneously grafted nanoparticles in homopolymer thin films and blends. We demonstrate that our method reproduces trends observed experimentally in homopolymer thin films, and then we examine how the nanoparticle size, grafting density, and the length of the grafted chains relative to the matrix chains affects the distribution of the grafted nanoparticles in phase separated polymer blends. We find that position of the nanoparticles relative to the interface in the blends is sensitive to the brush conformation, even when the nanoparticles are miscible in one of the two homopolymer phases.

Quantitative Predictions of the Interfacial Tensions of Liquid-Liquid Interfaces through Atomistic and Coarse Grained Models

We report molecular simulations of oil-water liquid-liquid interfaces by using atomistic and coarse grained (CG) MARTINI force fields. We also apply the electronic continuum (EC) model to the MARTINI force field for the calculation of the interfacial tension of oil/water-salt systems. In a first step, we propose to calculate the interfacial tensions using thermodynamic and mechanical definitions of hydrocarbon-water interfacial systems modified by the addition of salts and alcohol. We also establish here the order of magnitude of the long-range corrections to the interfacial tension in fluid-fluid interfaces. Whereas the atomistic models are able to reproduce quantitatively the interfacial tension and the coexisting densities of oil-water systems, the coarse-description shows some deviations in the prediction of the interfacial tensions. Nevertheless, the physical features of these liquid-liquid interfaces are well-captured by this CG description. The CG force field offers then a very challenging alternative that will require however a more developed calibration of the parameters on the basis of liquid-liquid properties.

Constant-force approach to discontinuous potentials

Aiming to approach the thermodynamical properties of hard-core systems by standard molecular dynamics simulation, we propose setting a repulsive constant-force for overlapping particles. That is, the discontinuity of the pair potential is replaced by a linear function with a large negative slope. Hence, the core-core repulsion, usually modeled with a power function of distance, yields a large force as soon as the cores slightly overlap. This leads to a quasi-hardcore behavior. The idea is tested for a triangle potential of short range. The results obtained by replica exchange molecular dynamics for several repulsive forces are contrasted with the ones obtained for the discontinuous potential and by means of replica exchange Monte Carlo. We found remarkable agreements for the vapor-liquid coexistence densities as well as for the surface tension.