Autohesion Mechanisms at Interfaces Between Random Copolymer Melts: Mesoscopic Simulations with Realistic Coarse-Grained Models.

The increase in welding time during the interdiffusion of a pair of non reacting random copolymer melts favors the strength rate of healing at the interface. Furthermore, the diffusion kinetic during the interpenetration of copolymer chains across the interface is strongly dependent on molecular weight. In this paper we perform mesoscopic simulations with realistic coarse grain models to study the autohesion mechanism across the interface between slightly entangled styrene-butadiene random copolymer melts.

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.

Anisotropic surface stresses of a solid/fluid interface: Molecular dynamics calculations for the copper/methane interface.

The full tensorial surface stress of an interface between a face-centered cubic crystal (copper) and an isotropic liquid (methane) is computed for two crystal orientations {100} and {110} using molecular dynamics simulations. The bulk crystal orientation {100} is symmetric, whereas the {110} orientation is not. Finite size effects, which can be important in the case of an interface between an isotropic solid and a liquid, are studied in detail for the two crystal orientations. We first show that the symmetry of the surface stress tensor is that of the bulk crystal orientation. In the case of the asymmetric crystal orientation {110}, the relative difference between the components of the surface stress is substantial (∼50%). Finally, we show that finite size effects persist to much larger sizes in the case of the {100} orientation compared to the case of the {110} interface, for instance, through an artificial breakdown of the symmetry of the surface stress tensor.

Calculation of a solid/liquid surface tension: A methodological study.

The surface tension of a model solid/liquid interface constituted of a graphene sheet surrounded by liquid methane has been computed using molecular dynamics in the Kirkwood-Buff formalism. We show that contrary to the fluid/fluid case, the solid/liquid case can lead to different structurations of the first fluid layer, leading to significantly different values of surface tension. Therefore we present a statistical approach that consists in running a series of molecular simulations of similar systems with different initial conditions, leading to a distribution of surface tensions from which an average value and uncertainty can be extracted. Our results suggest that these distributions converge as the system size increases. Besides we show that surface tension is not particularly sensitive to the choice of the potential energy cutoff and that long-range corrections can be neglected contrary to what we observed in the liquid/vapour interfaces. We have not observed the previously reported commensurability effect.

Test-area surface tension calculation of the graphene-methane interface: Fluctuations and commensurability.

The surface tension (γ) of methane on a graphene monolayer is calculated by using the test-area approach. By using a united atom model to describe methane molecules, strong fluctuations of surface tension as a function of the surface area of the graphene are evidenced. In contrast with the liquid-vapor interfaces, the use of a larger cutoff does not fully erase the fluctuations in the surface tension. Counterintuitively, the description of methane and graphene from the Optimized Potentials for Liquid Simulations all-atom model and a flexible model, respectively, led to a lessening in the surface tension fluctuations. This result suggests that the origin of fluctuations in γ is due to a model-effect rather than size-effects. We show that the molecular origin of these fluctuations is the result of a commensurable organization between both graphene and methane. This commensurable structure can be avoided by describing methane and graphene from a flexible force field. Although differences in γ with respect to the model have been often reported, it is the first time that the model drastically affects the physics of a system.

Surface tension and long range corrections of cylindrical interfaces.

The calculation of the surface tension of curved interfaces has been deeply investigated from molecular simulation during this last past decade. Recently, the thermodynamic Test-Area (TA) approach has been extended to the calculation of surface tension of curved interfaces. In the case of the cylindrical vapour-liquid interfaces of water and Lennard-Jones fluids, it was shown that the surface tension was independent of the curvature of the interface. In addition, the surface tension of the cylindrical interface is higher than that of the planar interface. Molecular simulations of cylindrical interfaces have been so far performed (i) by using a shifted potential, (ii) by means of large cutoff without periodic boundary conditions, or (iii) by ignoring the long range corrections to the surface tension due to the difficulty to estimate them. Indeed, unlike the planar interfaces there are no available operational expressions to consider the tail corrections to the surface tension of cylindrical interfaces. We propose here to develop the long range corrections of the surface tension for cylindrical interfaces by using the non-exponential TA (TA2) method. We also extend the formulation of the Mecke-Winkelmann corrections initially developed for planar surfaces to cylindrical interfaces. We complete this study by the calculation of the surface tension of cylindrical surfaces of liquid tin and copper using the embedded atom model potentials.

How does the dehydration change the host-guest association under homogeneous and heterogeneous conditions?

In this study, the thermodynamic properties of association of some inorganic ions (ClO4(-) and SO4(2-)) with ß-cyclodextrins (ß-CD) in aqueous solution are determined under both free ß-CD and surface confined ß-CD conditions using atomistic simulations. The potential of mean force (PMF) is calculated as a function of the environment and the thermodynamic properties of association are deduced by integrating the free energy profiles. No inclusion complex between SO4(2-) and ß-CD is detected. Nevertheless, the PMF curve obtained for gold-confined CD seems to evidence a small minimum at a larger separation distance that shows specific interactions such as hydrogen bonding outside the cavity. As concerns ClO4(-), our simulations reveal the formation of an inclusion complex with free ß-CD in perfect agreement with the available experimental results. Nevertheless, we do not detect any formation of the host-guest inclusion complex under heterogeneous conditions. Finally, the differences observed as a function of the anions are interpreted through an atomistic description. The general trend of weaker complex stabilities with the increasing free energy of hydration of the anions is found in homogeneous systems.

Communication: Slab thickness dependence of the surface tension: toward a criterion of liquid sheets stability.

Microscopic Monte Carlo simulations of liquid sheets of copper and tin have been performed in order to study the dependence of the surface tension on the thickness of the sheet. It results that the surface tension is constant with the thickness as long as the sheet remains in one piece. When the sheet is getting thinner, holes start to appear, and the calculated surface tension rapidly decreases with thickness until the sheet becomes totally unstable and forms a cylinder. We assume here that this decrease is not due to a confinement effect as proposed by Werth et al. [Physica A 392, 2359 (2013)] on Lennard-Jones systems, but to the appearance of holes that reduces the energy cost of the surface modification. We also show in this work that a link can be established between the stability of the sheet and the local fluctuations of the surface position, which directly depends on the value of the surface tension. Finally, we complete this study by investigating systems interacting through different forms of Lennard-Jones potentials to check if similar conclusions can be drawn.

Surface tension of spherical drops from surface of tension.

The determination of surface tension of curved interfaces is a topic that raised many controversies during the last century. Explicit liquid-vapor interface modelling (ELVI) was unable up to now to reproduce interfacial behaviors in drops due to ambiguities in the mechanical definition of the surface tension. In this work, we propose a thermodynamic approach based on the location of surface of tension and its use in the Laplace equation to extract the surface tension of spherical interfaces from ELVI modelling.

Molecular modeling of the liquid-vapor interfaces of a multi-component mixture: Prediction of the coexisting densities and surface tensions at different pressures and gas compositions.

Two-phase molecular simulations are performed in order to report the interfacial tensions and the coexisting densities of a multicomponent mixture (nitrogen + methane) + water for five gas compositions in the pressure range of 1-30 MPa at 298 K. The interfacial tensions are calculated using different definitions and the long range corrections of the surface tensions are considered using expressions designed for multicomponent mixtures and each definitions. We can conclude that the agreement with experiments is quantitative with deviations smaller than 5% for the interfacial tensions and 2% for the densities. The interfacial region is described in terms of specific arrangements of the gas components at the water surface.

Calculation of the surface tension and pressure components from a non-exponential perturbation method of the thermodynamic route.

Surface tension is probably the most important interfacial property and a large number of techniques have been devoted to its calculation. Usually, this calculation is carried out using mechanical or thermodynamic definitions. The mechanical route uses an arbitrary choice to affect the contribution of the pairwise force. To overcome this arbitrariness, a thermodynamic route based on the area perturbation (test-area (TA) method) has been developed for the calculation of surface tension. The volume perturbation (VP) method provides an original route to compute the components of the pressure tensor. These two routes are developed from the perturbation theory leading to working expressions using exponential averages of energy. The use of exponential averages makes the calculation strongly dependent on the occurrence of low values of ΔU. Additionally, the decomposition of the energy to obtain local surface tension is nontrivial. From the explicit derivation of the partition function the exponential average is avoided providing an interesting alternative to TA, VP, and mechanical methods. To make a consistent comparison, we study the profiles of the surface tension along the direction normal to the surface for the different definitions and techniques in the cases of liquid-vapor interfaces of acids gases, binary, and apolar systems.

Consistent and Transferable Force Fields for Statistical Copolymer Systems at the Mesoscale.

The statistical trajectory matching (STM) method was applied successfully to derive coarse grain (CG) models for bulk properties of homopolymers. The extension of the methodology for building CG models for statistical copolymer systems is much more challenging. We present here the strategy for developing CG models for styrene-butadiene-rubber, and we compare the quality of the resulting CG force fields on the structure and thermodynamics at different chemical compositions. The CG models are used through the use of a genuine mesoscopic method called the dissipative particle dynamics method and compared to high-resolution molecular dynamics simulations. We conclude that the STM method is able to produce coarse-grained potentials that are transferable in composition by using only a few reference systems. Additionally, this methodology can be applied on any copolymer system.

Surface tension of water-alcohol mixtures from Monte Carlo simulations.

Monte Carlo simulations are reported to predict the dependence of the surface tension of water-alcohol mixtures on the alcohol concentration. Alcohols are modeled using the anisotropic united atom model recently extended to alcohol molecules. The molecular simulations show a good agreement between the experimental and calculated surface tensions for the water-methanol and water-propanol mixtures. This good agreement with experiments is also established through the comparison of the excess surface tensions. A molecular description of the mixture in terms of density profiles and hydrogen bond profiles is used to interpret the decrease of the surface tension with the alcohol concentration and alcohol chain length.

Monte Carlo calculation of the methane-water interfacial tension at high pressures.

Monte Carlo simulations have been performed in the Np(N)AT statistical ensemble to study the methane-water mixture as a function of pressure. The interfacial tensions are calculated with different definitions and are reported for pressures from 1 to 50 MPa. The interfacial tensions, coexisting densities, and composition of the methane and water phases are shown to be in good agreement with the corresponding experimental properties. The interfacial region has been described through the profiles of the number of hydrogen bonds, the coordination number of each species, and the different energy contributions. We complete this study by a theoretical investigation of the thermal and mechanical equilibria in the binary mixture. We have also examined the profile of the intrinsic and long range correction parts of the interfacial tension along the normal to the water surface.

Calculation of the surface tension from Monte Carlo simulations: does the model impact on the finite-size effects?

We report two-phase Monte Carlo simulations of the liquid-vapor interface of the Lennard-Jones (LJ) fluids in order to study the impact of the methodology used for the energy calculation on the oscillatory behavior of the surface tension with the system sizes. The surface tension values are illustrated through the LJ parameters of methane. The first methodology uses a standard truncated LJ potential, the second one adds a long range correction (LRC) contribution to the energy into the Metropolis scheme, and the third one uses a LJ potential modified by a polynomial function in order to remove the discontinuities at the cutoff distance. The surface tension is calculated from the mechanical and thermodynamic routes and the LRCs to the surface tension are systematically calculated from appropriate expressions within these definitions. The oscillatory behavior has been studied as a function of the size of the interfacial area and of the length of the dimension perpendicular to the surface. We show that the methodology has an important effect on the oscillatory variation in the surface tension with the system size. This oscillatory variation in the surface tension with the system size is investigated through its intrinsic and LRC contributions. We complete this work by studying the dependence of the surface tension with respect to the cutoff distance when the LRC part to the energy is considered into the Metropolis scheme.

Molecular dynamics description of grafted monolayers: effect of the surface coverage.

Molecular dynamics simulations of monolayers of metal-chelating ligands grafted onto a graphite surface in water are carried out to calculate structural (density profiles, radius of gyration, and asphericity coefficients), dynamical (diffusion coefficients), and energetical properties as a function of the surface coverage. The purpose is to provide a better understanding of the dependence of various properties of these monolayers on the surface coverage. A critical value of the surface coverage from which all structural properties derive a limiting value has been established. It also appears that the chains rather adopt an elongated conformation along the direction normal to the surface from this critical surface coverage. The hydrogen-bonding structure and dynamics of water molecules are reported. An ordered structure of water in the region close to the terminal groups of the grafted molecules is shown at a relatively high surface coverage. This ordering is similar to that observed in the case of water in interaction with a solid surface.

Surface tensions of linear and branched alkanes from Monte Carlo simulations using the anisotropic united atom model.

The anisotropic united atoms (AUA4) model has been used for linear and branched alkanes to predict the surface tension as a function of temperature by Monte Carlo simulations. Simulations are carried out for n-alkanes ( n-C5, n-C6, n-C7, and n-C10) and for two branched C7 isomers (2,3-dimethylpentane and 2,4-dimethylpentane). Different operational expressions of the surface tension using both the thermodynamic and the mechanical definitions have been applied. The simulated surface tensions with the AUA4 model are found to be consistent within both definitions and in good agreement with experiments.

Molecular modeling of the structure and dynamics of the interlayer species of ZnAlCl layered double hydroxide.

Molecular dynamics simulations of the ZnAl layered double hydroxide containing interlayer chloride anions have been performed in the NpT and Np(zz)T statistical ensembles for metal Zn/Al ratios of 2 and 3. We have monitored the interlayer spacing as a function of the number of intercalated water molecules for each statistical ensemble. We have studied how these profiles are affected by the method of calculation of the charges of the hydroxide layer atoms. Diffusion coefficients of the interlayer water molecules have been calculated for different Zn/Al ratios. The calculation of the chemical potential of the interlayer water molecules has been carried out for three amounts of interlayer water molecules. The calculation showed a qualitative agreement with the bulk water chemical potential within a range of interlayer water molecule contents.

Expressions for local contributions to the surface tension from the virial route.

The expression of the surface tension using the virial route has been reinvestigated in order to establish a local version of the surface tension and of its long-range corrections. In fact, giving a local surface tension is very important for the simulation from a methodological viewpoint. It is also of basic interest to associate the profile of the intrinsic part of the surface tension with that of the long-range corrections to make the surface tension calculation consistent between the different approaches that can be used. Working expressions for two-phase systems interacting through dispersion-repulsion (Lennard-Jones) and Coulombic (Ewald summation) interactions are proposed. Different operational expressions of the surface tension are compared in the cases of n -pentane, carbon dioxide, and water liquid-vapor equilibria for which the orders of magnitude between the electrostatic and dispersion forces are different.

Computational and experimental investigations of supramolecular assemblies of p-sulfonatocalix[4]arene organized by weak forces.

We report the study of the supramolecular assemblies formed by the incorporation of quaternary ammonium cations such as Me4N+ or Et4N+ into host-guest assemblies with p-sulfonatocalix[4]arene in the presence of a lanthanide(III) cation in water. We use microcalorimetry to characterize the formation of these supramolecular assemblies. We obtain a molecular description of these assemblies by performing molecular dynamics simulations over a very large period of time. The structures of these supramolecular complexes have been determined and discussed through specific interaction energy contributions. By combining MD simulations and 1NMR spectroscopy, we highlight a specific behavior of the supramolecular assembly with the Me4N+.