A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges.

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

DFT Analysis of Organotin Catalytic Mechanisms in Dehydration Esterification Reactions for Terephthalic Acid and 2,2,4,4-Tetramethyl-1,3-cyclobutanediol.

Polyesters synthesized from 2,2,4,4-tetramethyl-1,3-cyclobutanediol (TMCD) and terephthalic acid (TPA) are improved alternatives to toxic polycarbonates based on bisphenol A. In this work, we use ωB97X-D/LANL2DZdp calculations, in the presence of a benzaldehyde polarizable continuum model solvent, to show that esterification of TMCD and TPA will reduce and subsequently dehydrate a dimethyl tin oxide catalyst, becoming ligands on the now four-coordinate complex. This reaction then proceeds most plausibly by an intramolecular acyl-transfer mechanism from the tin complex, aided by a coordinated proton donor such as hydronium. These findings are a key first step in understanding polyester synthesis and avoiding undesirable side reactions during production.

Can we define a unique microscopic pressure in inhomogeneous fluids?

The estimation of a microscopic pressure tensor in an adsorbed thin film on a planar surface remains a challenge in both experiment and theory. While the normal pressure is well-defined for a planar surface, the tangential pressure at a point is not uniquely defined at the nanoscale. We report a new method that allows us to calculate the local pressure tensor and its spatial integral using an arbitrary contour definition of the "virial-route" local pressure tensor. We show that by integrating the local tangential pressure over a small region of space, roughly the range of the intermolecular forces, it is possible to define a coarse-grained tangential pressure that appears to be unique and free from ambiguities in the definition of the local pressure tensor. We support our argument by presenting the results for more than ten types of contour definitions of the local pressure tensor. By defining the coarse-grained tangential pressure, we can also find the effective thickness of the adsorbed layer and, in the case of a porous material, the statistical pore width. The coarse-grained in-layer and in-pore tangential pressures are determined for Lennard-Jones argon adsorbed in realistic carbon slit pores, providing a better understanding of the pressure enhancement for strongly wetting systems.

Conformal Sites Theory for Adsorbed Films on Energetically Heterogeneous Surfaces.

We present a conformal sites theory for a solid substrate whose surface is both geometrically and energetically heterogeneous and that interacts with an adsorbed film. The theory is based on a perturbation expansion for the grand potential of a real system with a rough surface about that of a reference system with an ideal reference surface, thus mapping the real system onto a much simpler interfacial system. The expansion is in powers of the intermolecular potential parameters, and leads to mixing rules for the potential parameters of the reference system. Grand canonical Monte Carlo simulations for the adsorption of argon at 87.3 K, carbon dioxide at 273 K, and water vapor at 298 K on heterogeneous carbon surfaces are investigated to explore the limits of applicability of the theory. Simulation results indicate that the theory works well with typical asymmetry of the potential parameters in the force field. However, care should be taken when applying the theory to strongly associating fluids and in the low-pressure region where the active surface sites play an important role. The conformal sites theory can be used to predict the adsorption properties and to characterize the solid substrate by taking advantage of the corresponding states principle. Other possible applications are also discussed.

Extending the fused-sphere SAFT-γ Mie force field parameterization approach to poly(vinyl butyral) copolymers.

SAFT-γ Mie, a molecular group-contribution equation of state with foundations in the statistical associating fluid theory framework, is a promising means for developing accurate and transferable coarse-grained force fields for complex polymer systems. We recently presented a new approach for incorporating bonded potentials derived from all-atom molecular dynamics simulations into fused-sphere SAFT-γ Mie homopolymer chains by means of a shape factor parameter, which allows for bond distances less than the tangent-sphere value required in conventional SAFT-γ Mie force fields. In this study, we explore the application of the fused-sphere SAFT-γ Mie approach to copolymers. In particular, we demonstrate its capabilities at modeling poly(vinyl alcohol-co-vinyl butyral) (PVB), an important commercial copolymer widely used as an interlayer in laminated safety glass applications. We found that shape factors determined from poly(vinyl alcohol) and poly(vinyl butyral) homopolymers do not in general correctly reproduce random copolymer densities when standard SAFT-γ Mie mixing rules are applied. However, shape factors optimized to reproduce the density of a random copolymer of intermediate composition resulted in a model that accurately represents density across a wide range of chemical compositions. Our PVB model reproduced copolymer glass transition temperature in agreement with experimental data, but heat capacity was underpredicted. Finally, we demonstrate that atomistic details may be inserted into equilibrated fused-sphere SAFT-γ Mie copolymer melts through a geometric reverse-mapping algorithm.

A CGenFF-based force field for simulations of peptoids with both cis and trans peptide bonds.

Peptoids, or poly-n-substituted glycines, are peptide-like polymers composed of a flexible backbone decorated with diverse chemical side chains. Peptoids can form a variety of self-assembling structures based on the type and sequence of the side chains attached to their backbones. All-atom molecular dynamics simulations have been useful in predicting the conformational structures of proteins and will be valuable tools for identifying combinations of peptoid side chains that may form interesting folded structures. However, peptoid models must address a major degree of freedom not common in proteins - the cis/trans isomerization of the peptide bond. This work presents CHARMM general force field (CGenFF) parameters developed to accurately represent peptoid conformational behavior, with an emphasis on a correct representation of both the cis and trans isomers of the peptoid backbone. These parameters are validated against experimental and quantum mechanics data and used to simulate three peptoid side chains in explicitly solvated systems. © 2019 Wiley Periodicals, Inc.

Bottom-Up Approach to the Coarse-Grained Surface Model: Effective Solid-Fluid Potentials for Adsorption on Heterogeneous Surfaces.

Coarse-grained surface models with a low-dimension positional dependence have great advantages in simplifying the theoretical adsorption model and speeding up molecular simulations. In this work, we present a bottom-up strategy, developing a new two-dimensional (2D) coarse-grained surface model from the "bottom-level" atomistic model, for adsorption on highly heterogeneous surfaces with various types of defects. The corresponding effective solid-fluid potential consists of a 2D hard wall potential representing the structure of the surface and a one-dimensional (1D) effective area-weighted free-energy-averaged (AW-FEA) potential representing the energetic strength of the substrate-adsorbate interaction. Within the conventional free-energy-averaged (FEA) framework, an accessible-area-related parameter is introduced into the equation of the 1D effective solid-fluid potential, which allows us not only to obtain the energy information from the fully atomistic system but also to get the structural dependence of the potential on any geometric defect on the surface. Grand canonical Monte Carlo simulations are carried out for argon adsorption at 87.3 K to test the validity of the new 2D surface model against the fully atomistic system. We test four graphitic substrates with different levels of geometric roughness for the top layer, including the widely used reference solid substrate Cabot BP-280. The simulation results show that adding one more dimension to the traditional 1D surface model is essential for adsorption on the geometrically heterogeneous surfaces. In particular, the 2D surface model with the AW-FEA solid-fluid potential significantly improves the adsorption isotherm and density profile over the 1D surface model with the FEA solid-fluid potential over a wide range of pressure. The method to construct an effective solid-fluid potential for an energetically heterogeneous surface is also discussed.

Development of a fused-sphere SAFT-γ Mie force field for poly(vinyl alcohol) and poly(ethylene).

SAFT-γ Mie, a group-contribution equation of state rooted in Statistical Associating Fluid Theory, provides an efficient framework for developing accurate, transferable coarse-grained force fields for molecular simulation. Building on the success of SAFT-γ Mie force fields for small molecules, we address two key issues in extending the SAFT-γ Mie coarse-graining methodology to polymers: (1) the treatment of polymer chain rigidity and (2) the disparity between the structure of linear chains of tangent spheres and the structure of the real polymers. We use Boltzmann inversion to derive effective bond-stretching and angle-bending potentials mapped from all-atom oligomer molecular dynamics (MD) simulations to the coarse-grained sites and a fused-sphere version of SAFT-γ Mie as the basis for non-bonded interactions. The introduction of an overlap parameter between Mie spheres leads to a degeneracy when fitting to monomer vapor-liquid equilibria (VLE) data, which we resolve by matching polymer density from coarse-grained MD simulation with that from all-atom simulation. The result is a chain of monomers rigorously parameterized to experimental VLE data and with structural detail consistent with all-atom simulations. We test our approach on atactic poly(vinyl alcohol) and polyethylene and compare the results for SAFT-γ Mie models with structural detail mapped from the Optimized Potentials for Liquid Simulations (OPLS) and Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) all-atom force fields.

Morphology and proton diffusion in a coarse-grained model of sulfonated poly(phenylenes).

A coarse-grained model previously used to simulate Nafion using dissipative particle dynamics (DPD) is modified to describe sulfonated Diels-Alder poly(phenylene) (SDAPP) polymers. The model includes a proton-hopping mechanism similar to the Grotthuss mechanism. The intramolecular parameters for SDAPP are derived from atomistic molecular dynamics (MD) simulation using the iterative Boltzmann inversion. The polymer radii of gyration, domain morphologies, and cluster distributions obtained from our DPD model are in good agreement with previous atomistic MD simulations. As found in the atomistic simulations, the DPD simulations predict that the SDAPP nanophase separates into hydrophobic polymer domains and hydrophilic domains that percolate through the system at sufficiently high sulfonation and hydration levels. Increasing sulfonation and/or hydration leads to larger proton and water diffusion constants, in agreement with experimental measurements in SDAPP. In the DPD simulations, the proton hopping (Grotthuss) mechanism becomes important as sulfonation and hydration increase, in qualitative agreement with experiment. The turning on of the hopping mechanism also roughly correlates with the point at which the DPD simulations exhibit clear percolated, hydrophilic domains, demonstrating the important effects of morphology on proton transport.

High-density equation of state for a two-dimensional Lennard-Jones solid.

We present a new equation of state for a two-dimensional Lennard-Jones (2D LJ-EOS) solid at high densities, ρ2D*≥0.9. The new 2D LJ-EOS is of analytic form, consisting of a zero-temperature contribution and vibrational contributions up to and including the second anharmonic term. A detailed analysis of all contributing terms is performed. Comparisons between the 2D LJ-EOS and Monte Carlo simulation results show that the 2D LJ-EOS is very accurate over a wide range of temperatures in the high-density region. A criterion to find the temperature range over which the 2D LJ-EOS is applicable at a certain density is derived. We also demonstrate an application of the equation of state to predict an effective tangential pressure for the adsorbed contact layer near the wall in a slit-pore system. Tangential pressures predicted by this "2D-route" are found to be in qualitative agreement with those found by the more traditional virial route of Irving and Kirkwood.

Computationally Mapping pKa Shifts Due to the Presence of a Polyelectrolyte Chain around Whey Proteins.

Experimental studies have shown the formation of soluble complexes in the pure repulsive Coulombic regime even when the net charges of the protein and the polyelectrolyte have the same sign ( De Kruif et al. Curr. Opin. Colloid Interface Sci. 2004 , 9 , 340 ; De Vries et al. J. Chem. Phys. 2003 , 118 , 4649 ; Grymonpre et al. Biomacromolecules 2001 , 2 , 422 ; Hattori et al. Langmuir 2000 , 16 , 9738 ). This attractive phenomenon has often been described as "complexation on the wrong side of pI". While one theory assumes the existence of "charged patches" on the protein surface from ion-dipole interactions, thus allowing a polyelectrolyte to bind to an oppositely heterogeneous charged protein region, another theoretical view considers the induced-charge interactions to be the dominant factor in these complexations. This charge regulation mechanism can be described by proton fluctuations resulting from mutual rearrangements of the distributions of the charged groups, due to perturbations of the acid-base equilibrium. Using constant-pH Monte Carlo simulations and several quantitative and visual analysis tools, we investigate the significance of each of these interactions for two whey proteins, α-lactalbumin (α-LA) and lysozyme (LYZ). Through physical chemistry parameters, free energies of interactions, and the mapping of amino acid pKa shifts and polyelectrolyte trajectories, we show the charge regulation mechanism to be the most important contributor in protein-polyelectrolyte complexation regardless of pH, dipole moment, and protein capacitance in a low salt regime.

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

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

Heterogeneous nucleation from a supercooled ionic liquid on a carbon surface.

Classical molecular dynamics simulations were used to study the nucleation of the crystal phase of the ionic liquid [dmim+][Cl-] from its supercooled liquid phase, both in the bulk and in contact with a graphitic surface of D = 3 nm. By combining the string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)], with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [Santiso and Trout, J. Chem. Phys. 134, 064109 (2011)], we computed minimum free energy paths, the approximate size of the critical nucleus, the free energy barrier, and the rates involved in these nucleation processes. For homogeneous nucleation, the subcooled liquid phase has to overcome a free energy barrier of ∼85 kcal/mol to form a critical nucleus of size ∼3.6 nm, which then grows into the monoclinic crystal phase. This free energy barrier becomes about 42% smaller (∼49 kcal/mol) when the subcooled liquid phase is in contact with a graphitic disk, and the critical nucleus formed is about 17% smaller (∼3.0 nm) than the one observed for homogeneous nucleation. The crystal formed in the heterogeneous nucleation scenario has a structure that is similar to that of the bulk crystal, with the exception of the layers of ions next to the graphene surface, which have larger local density and the cations lie with their imidazolium rings parallel to the graphitic surface. The critical nucleus forms near the graphene surface separated only by these layers of ions. The heterogeneous nucleation rate (∼4.8 × 1011 cm-3 s-1) is about one order of magnitude faster than the homogeneous rate (∼6.6 × 1010 cm-3 s-1). The computed free energy barriers and nucleation rates are in reasonable agreement with experimental and simulation values obtained for the homogeneous and heterogeneous nucleation of other systems (ice, urea, Lennard-Jones spheres, and oxide glasses).

A general method for molecular modeling of nucleation from the melt.

Crystallization is one of the fundamental phase transition processes, and it is also important practically, for example, in the chemical, food, and pharmaceutical industries. Despite its importance, however, our basic understanding of crystallization, and especially crystal nucleation, at the molecular level is still incomplete. In this work, we present a general molecular simulation approach that can be used to investigate the nucleation of crystals from a subcooled liquid. Our method combines a previously proposed general method to construct structure-based order parameters [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] with the string method in collective variables [L. Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] to obtain a minimum free energy path connecting the liquid and solid basins. We then use Markovian milestoning with Voronoi tessellations [E. Vanden-Eijnden and M. Venturoli, J. Chem. Phys. 130, 194101 (2009); L. Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] to obtain the free energy profile along the path and the nucleation kinetics. We illustrate the application of this method to the nucleation of Benzene-I crystals from the melt, and compare the results to those previously found using transition path sampling [M. Shah et al., J. Phys. Chem. B 115, 10400-10412 (2011)].

Molecular simulation of homogeneous nucleation of crystals of an ionic liquid from the melt.

The homogeneous nucleation of crystals of the ionic liquid [dmim(+)][Cl(-)] from its supercooled liquid phase in the bulk (P = 1 bar, T = 340 K, representing a supercooling of 58 K) was studied using molecular simulations. The string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] was used in combination with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] to sketch a minimum free energy path connecting the supercooled liquid and the monoclinic crystal phases, and to determine the free energy and the rates involved in the homogeneous nucleation process. The physical significance of the configurations found along this minimum free energy path is discussed with the help of calculations based on classical nucleation theory and with additional simulation results obtained for a larger system. Our results indicate that, at a supercooling of 58 K, the liquid has to overcome a free energy barrier of the order of 60 kcal/mol and to form a critical nucleus with an average size of about 3.6 nm, before it reaches the thermodynamically stable crystal phase. A simulated homogeneous nucleation rate of 5.0 × 10(10) cm(-3) s(-1) was obtained for our system, which is in reasonable agreement with experimental and simulation rates for homogeneous nucleation of ice at similar degrees of supercooling. This study represents our first step in a series of studies aimed at understanding the nucleation and growth of crystals of organic salts near surfaces and inside nanopores.

On the connection between nonmonotonic taste behavior and molecular conformation in solution: The case of rebaudioside-A.

The diterpene steviol glycoside, rebaudioside A, is a natural high potency non-caloric sweetener extracted from the leaves of Stevia rebaudiana. This compound shows a parabolic change in sweet taste intensity with temperature which contrasts with the general finding for other synthetic or natural sweeteners whose sweet taste increases with temperature. The nonmonotonic taste behavior was determined by sensory analysis using large taste panels. The conformational landscape of rebaudioside A was established at a range of temperatures by means of nuclear magnetic resonance and molecular dynamics simulation. The relationship between various conformations and the observed sweetness of rebaudioside A is described.

In Silico Structural Comparison of Aromatic and Aliphatic Chiral Peptoid Oligomers.

Atomistic simulations of peptoids have the capability to predict structure-property relationships, depending on the accuracy of the associated force field. This work presents an addendum to the CGenFF-NTOID peptoid force field for aliphatic side chains. We develop parameters for two aliphatic side chains, RN1-tertiary butylethyl glycine (r1tbe) and SN1-tertiary butylethyl glycine (s1tbe). Enhanced sampled (well-tempered metadynamics) atomistic simulations are performed using CGenFF-NTOID to determine the monomer structural preferences for these side chains. The free energy minima attained through these simulations are compared with structural observations obtained from experiments. We also compare the structural preferences of aliphatic s1tbe and aromatic SN1-naphthylethyl glycine (s1ne). This is done through parallel bias metadynamics on monomers and pentamers of s1tbe and s1ne. The structural observations through simulations are also compared with available experimental metrics of the dihedral angles and pitch. The pentamer minima structures are also compared with ab initio optimized structures, which show excellent agreement. This comparison illustrates alternatives to aromatic side chains that can be used to stabilize peptoid secondary structures. The developed parameters help to increase the diversity of peptoid side chains available for materials discovery through computational studies.

Design of linear ligands for selective separation using a genetic algorithm applied to molecular architecture.

Continuous purification of chemical reaction products through adsorption-based operations during workup may present advantages over batch chromatography or crystallization. In pharmaceutical syntheses, however, the desired product is often structurally similar to byproducts or unconverted reactant, so that identifying a suitable adsorption medium is challenging. We developed an in silico screening process to design organic ligands which, when chemically bound to a solid surface, would constitute an effective adsorption for a pharmaceutically relevant mixture of reaction products. This procedure employs automated molecular dynamics simulations to evaluate potential ligands, by measuring the difference in adsorption energy of two solutes which differed by one functional group. Then, a genetic algorithm was used to iteratively improve a population of such ligands through selection and reproduction steps. This procedure identified chemical designs of the surface-bound ligands that were outside the set we considered using chemical intuition. The ligand designs achieved selectivity by exploiting phenyl-phenyl stacking which was sterically hindered in the case of one solution component. The ligand designs had selectivity energies of 0.8-1.6 kcal/mol in single-ligand, solvent-free simulations, if entropic contributions to the relative selectivity are neglected. We believe this molecular evolution technique presents a useful method for the directed exploration of chemical space or for molecular design, when the chemical properties of interest can be efficiently evaluated through simulations.

Using Enhanced Sampling Simulations to Study the Conformational Space of Chiral Aromatic Peptoid Monomers.

Peptoids, or N-substituted glycines, are peptide-like materials that form a wide variety of secondary structures owing to their enhanced flexibility and a diverse collection of possible side chains. Compared to that of peptides, peptoids have a substantially more complex conformational landscape. This is mainly due to the ability of the peptoid amide bond to exist in both cis- and trans-conformations. This makes conventional molecular dynamics simulations and even some enhanced sampling approaches unable to sample the complete energy landscapes. In this article, we present an extension to the CGenFF-NTOID peptoid atomistic forcefield by adding parameters for four side chains to the previously available collection. We employ explicit solvent well-tempered metadynamics simulations to optimize our forcefield parameters and parallel bias metadynamics to study the cis-trans isomerism for SN1-phenylethyl (s1pe) and SN1-naphthylethyl (s1ne) peptoid monomers, the free energy minima generated from which are validated with available experimental data. In the absence of experimental data, we supported our atomistic simulations with ab initio calculations. This work represents an important step toward the computational design of peptoid-based materials.

An atomically smooth container: Can the native oxide promote supercooling of liquid gallium?

Metals tend to supercool-that is, they freeze at temperatures below their melting points. In general, supercooling is less favorable when liquids are in contact with nucleation sites such as rough surfaces. Interestingly, bulk gallium (Ga) can significantly supercool, even when it is in contact with heterogeneous surfaces that could provide nucleation sites. We hypothesized that the native oxide on Ga provides an atomically smooth interface that prevents Ga from directly contacting surfaces, and thereby promotes supercooling. Although many metals form surface oxides, Ga is a convenient metal for studying supercooling because its melting point of 29.8°C is near room temperature. Using differential scanning calorimetry (DSC), we show that freezing of Ga with the oxide occurs at a lower temperature (-15.6 ± 3.5°C) than without the oxide (6.9 ± 2.0°C when the oxide is removed by HCl). We also demonstrate that the oxide enhances supercooling via macroscopic observations of freezing. These findings explain why Ga supercools and have implications for emerging applications of Ga that rely on it staying in the liquid state.