Investigation of finite system-size effects in molecular dynamics simulations of lipid bilayers

In the absence of external stress, the surface tension of a lipid membrane vanishes at equilibrium, and the membrane exhibits long wavelength undulations that can be described as elastic (as opposed to tension-dominated) deformations. These long wavelength fluctuations are generally suppressed in molecular dynamics simulations of membranes, which have typically been carried out on membrane patches with areas <100 nm2 that are replicated by periodic boundary conditions. As a result, finite system-size effects in molecular dynamics simulations of lipid bilayers have been subject to much discussion in the membrane simulation community for several years, and it has been argued that it is necessary to simulate small membrane patches under tension to properly model the tension-free state of macroscopic membranes. Recent hardware and software advances have made it possible to simulate larger, all-atom systems allowing us to directly address the question of whether the relatively small size of current membrane simulations affects their physical characteristics compared to real macroscopic bilayer systems. In this work, system-size effects on the structure of a DOPC bilayer at 5.4 H2O/lipid are investigated by performing molecular dynamics simulations at constant temperature and isotropic pressure (i.e., vanishing surface tension) of small and large single bilayer patches (72 and 288 lipids, respectively), as well as an explicitly multilamellar system consisting of a stack of five 72-lipid bilayers, all replicated in three dimensions by using periodic boundary conditions. The simulation results are compared to X-ray and neutron diffraction data by using a model-free, reciprocal space approach developed recently in our laboratories. Our analysis demonstrates that finite-size effects are negligible in simulations of DOPC bilayers at low hydration, and suggests that refinements are needed in the simulation force fields.     

Oscillatory surface tension due to finite-size effects

The simulation results of surface tension at the liquid-vapor interface are presented for fluids interacting with Lennard Jones and square-well potentials. From the simulation of liquids we have reported [M. González-Melchor et al., J. Chem. Phys. 122, 4503 (2005)] that the components of pressure tensor in parallelepiped boxes are not the same when periodic boundary conditions and small transversal areas are used. This fact creates an artificial oscillatory stress anisotropy in the system with even negative values. By doing direct simulations of interfaces we show in this work that surface tension has also an oscillatory decay at small surface areas; this behavior is opposite to the monotonic decay reported previously for the Lennard Jones fluid. It is shown that for small surface areas, the surface tension of the square-well potential artificially takes negative values and even increases with temperature. The calculated surface tension using a direct simulation of interfaces might have two contributions: one from finite-size effects of interfacial areas due to box geometry and another from the interface. Thus, it is difficult to evaluate the true surface tension of an interface when small surface areas are used. Care has to be taken to use the direct simulation method of interfaces to evaluate the predicted surface tension as a function of interfacial area from capillary-wave theory. The oscillations of surface tension decay faster at temperatures close to the critical point. It is also discussed that a surface area does not show any important effect on coexisting densities, making this method reliable to calculate bulk coexisting properties using small systems.     

On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface

The long-range corrections (LRCs) to the configurational energy have been taken into consideration in the Monte Carlo simulation of the vapor-liquid interface for a pure Lennard-Jones (LJ) fluid. The simulated bulk densities agree satisfactorily with those obtained from the Gibbs ensemble method, and the simulated surface tension values agree reasonably well with those reported in the literature for a larger number of molecules and a larger cut-off distance. To compare the influence of the potential forms on the simulation results, a truncated LJ potential, and a shifted and truncated LJ potential have been examined. Although the bulk densities and surface tensions calculated for different model fluids are strongly affected by the LRC, the different potentials essentially lead to similar density values and similar surface tension values when the respective calculated values are compared on the basis of a reduced temperature scale.     

Effect of Temperature and Composition on the Surface Tension and Thermodynamic Properties of Binary Mixtures of Boltorn U3000 with Alcohols and Ether

The surface tension of the pure hyperbranched polymer, Boltorn U3000, and binary mixtures of Boltorn U3000 with alcohols (1-butanol, 1-hexanol) have been measured at atmospheric pressure in the range of temperatures from 298.15 K to 328.15 K, or of Boltorn U3000 with methyl-tert-butylether (MTBE) in the range of temperatures from 298.15 K to 318.15 K. These measurements have been provided to complete information of the influence of temperature on surface tension for the selected polymer, which was chosen as a possible new entrainer in extraction processes. The surface thermodynamic functions such as surface entropy and enthalpy have been derived from the temperature dependence of the surface tension, as well as the critical temperature, parachor and speed of sound for the pure polymer. The influences investigated here include the effects of the alkyl chain length of an alcohol and solvent polarity on the surface tension.     

Simulated surface tensions of common water models

Initial simulated values of the surface tension for the SPC/E water model have indicated excellent agreement with experiment. More recently, differing values have been obtained which are significantly lower than previous estimates. Here, we attempt to explain the differences between the previous studies and show that a variety of simulation conditions can affect the final surface tension values. Consistent values for the surface tensions of six common fixed charge water models (TIP3P, SPC, SPC/E, TIP4P, TIP5P, and TIP6P) are then determined for four temperatures between 275 and 350 K. The SPC/E and TIP6P models provide the best agreement with experiment.     

Stress anisotropy induced by periodic boundary conditions

Finite size effects due to periodic boundary conditions are investigated using computer simulations in the canonical ensemble. We study liquids with densities corresponding to typical liquid coexistence densities, and temperatures between the triple and critical points. The components of the pressure tensor are computed in order to analyze the finite size effects arising from the size and geometry of the simulation box. Two different box geometries are considered: cubic and parallelepiped. As expected the pressure tensor is isotropic in cubic boxes, but it becomes anisotropic for small noncubic boxes. We argue this is the origin of the anomalous behavior observed recently in the computation of the surface tension of liquid-vapor interfaces. Otherwise, we find that the bulk pressure is sensitive to the box geometry when small simulation boxes are considered. These observations are general and independent of the model liquid considered. We report results for liquids interacting through short range forces, square well and Lennard-Jones, and also long range Coulombic interactions. The effect that small surface areas have on the surface tension is discussed, and some preliminary results at the liquid vapor-interface for the square well potential are given.     

石墨烯/聚乙烯复合材料及其拉伸性能的分子动力学模拟

利用分子动力学方法,模拟石墨烯/聚乙烯复合材料的微观结构和性能,并采用单轴拉伸模拟方法研究石墨烯/聚乙烯复合材料的拉伸性能.结果表明,在石墨烯/聚乙烯复合材料平衡构型中,聚乙烯基体分子在石墨烯表面处形成多层吸附层,吸附层处于动态稳定状态,层内分子可以发生扩散迁移.吸附层内聚乙烯分子发生"吸附固化"现象,分子弯曲程度减弱,发生有序排列,且在垂直于石墨烯方向的运动性能受到抑制.拉伸模拟结果表明,石墨烯能够提高聚乙烯材料的拉伸性能.在弹性区和屈服区,石墨烯阻碍了复合材料在垂直于拉伸方向的压缩变形,聚乙烯分子"吸附固化"结构保持稳定,引起体系整体应力的迅速升高.在软化区,由于石墨烯发生剧烈弯曲,"吸附固化"结构发生破坏,最终引起体系应力迅速减小.在弹性区和屈服区,体系应变主要引起了非键相互作用的改变.在软化区之后,应变主要导致了体系内分子成键相互作用的改变.应变速率能够提高复合材料的屈服应力,而不改变复合材料应力应变的整体趋势.     

The Surface Tension and Density of Liquid Ag–Bi, Ag–Sn, and Bi–Sn Alloys

Summary. The sessile drop method has been used to measure density and surface tension for pure Ag, Bi, Sn, and their mixtures. For pure metals and Bi–Sn alloys negative temperature coefficients of surface tension have been obtained. In case of Ag–Bi and Ag–Sn alloys the temperature coefficients of surface tension take negative or positive values depending on composition. Experimental values of the surface tension for Ag–Bi, Ag–Sn, and Bi–Sn are compared with those computed from Butler’s model. A relatively good agreement is observed.     

Understanding the role of ion interactions in soluble salt flotation with alkylammonium and alkylsulfate collectors

There is anecdotal evidence for the significant effects of salt ions on the flotation separation of minerals using process water of high salt content. Examples include flotation of soluble salt minerals such as potash, trona and borax in brine solutions using alkylammonium and alkylsulfate collectors such as dodecylamine hydrochloride and sodium dodecylsulfate. Although some of the effects are expected, some do not seem to be encompassed by classical theories of colloid science. Several experimental and modeling techniques for determining solution viscosity, surface tension, bubble-particle attachment time, contact angle, and molecular dynamics simulation have been used to provide further information on air–solution and solid–solution interfacial phenomena, especially with respect to the interfacial water structure due to the presence of dissolved ions. In addition atomic force microscopy, and sum frequency generation vibrational spectroscopy have been used to provide further information on surface states. These studies indicate that the ion specificity effect is the most significant factor influencing flotation in brine solutions.     

Molecular simulation study of the effect of pressure on the vapor-liquid interface of the square-well fluid

We examine a model system to study the effect of pressure on the surface tension of a vapor-liquid interface. The system is a two-component mixture of spheres interacting with the square-well (A-A) and hard-sphere (B-B) potentials and with unlike (A-B) interactions ranging (for different cases) from hard sphere to strongly attractive square well. The bulk-phase and interfacial properties are measured by molecular dynamics simulation for coexisting vapor-liquid phases for various mixture compositions, pressures, and temperatures. The variation of the surface tension with pressure compares well to values given by surface-excess formulas derived from thermodynamic considerations. We find that surface tension increases with pressure only for the case of an inert solute (hard-sphere A-B interactions) and that the presence of A-B attractions strongly promotes a decrease of surface tension with pressure. An examination of density and composition profiles is made to explain these effects in terms of surface-adsorption arguments.     

Parameters ruling capillary forces at the submillimetric scale

This paper reviews the way to compute capillary forces between two solids by numerically integrating the Laplace equation describing the shape of an axially symmetric meniscus at equilibrium. The numerical results of the proposed model have been experimentally validated with a test bed able to measure forces of about 1 mN with an accuracy of about 1 microN. Thanks to the simulation tool and the test bed, the influence of the following parameters has been studied: surface tension, solid geometry, volume of liquid, materials, separation distance between both solids, and surrounding environment. The way to compute the force from a given meniscus geometry has been clarified as far as the "Laplace" and "tension" contributions are concerned.     

Thermodynamic and spectroscopic studies on cationic surfactant tetradecyltrimethylammonium bromide in aqueous solution of trisubstituted ionic liquid 1, 2-dimethyl-3-octylimidazolium chloride at different temperatures

In this work, the effects on micellar behavior of long chain cationic surfactant tetradecyltrimethylammonium bromide (TTAB) upon the addition of trisubstituted ionic liquid (IL), 1, 2-dimethyl-3-octylimidazolium chloride [odmim][Cl] at temperatures, 298.15–318.15 K has been studied. Different techniques such as conductance, surface tension, fluorescence and ¹H NMR have been employed to understand the interactional mechanisms. The values of critical micelle concentration (cmc) and various thermodynamic parameters have been calculated from conductivity measurements. The surface parameters like effectiveness of decrease in surface tension (Π_cmc), minimum surface area occupied per surfactant monomer (A_min), maximum surface excess concentration (Γ_max), and adsorption efficiency (pC₂₀) have been evaluated by surface tension measurements. Micellar aggregation number (N_agg) has been determined by quenching of pyrene. Further to understand interactions in post micellar region, ¹H NMR measurements have been performed. It has been observed that the lipophilicity of interacting ion modified the thermodynamic and aggregation properties of TTAB.     

Sulfur hexafluoride's liquid-vapor coexistence curve, interfacial properties, and diffusion coefficients as predicted by a simple rigid model

We present here molecular-dynamics simulation results of the vapor-liquid coexistence curve, surface tension, and self-diffusion coefficients of sulfur hexafluoride. Sulfur hexafluoride is modeled as a rigid molecule, following the model proposed by Pawley [Mol. Phys. 43, 1321 (1981)]. Vapor-liquid coexistence curve and surface tension are obtained through direct molecular-dynamic simulations in the NVT ensemble. Simulation results are able to reproduce the qualitative shape of the vapor-liquid envelope. However, lower densities, a higher critical temperature, and an overestimated surface tension are obtained here. Those deviations are explained on the basis of the rigidity of the molecular model used. Self-diffusion coefficients are calculated from simulations in the NVE ensemble for different gas states at atmospheric pressure. The rigid model performs better for dynamical properties since simulation results provide very good agreement with available experimental data in this case.     

Many-body and quantum effects in the surface tension and surface energy of liquid neon and argon using the Fowler’s approximation

The Fowler’s expression for calculation of the reduced surface tension and surface energy has been used with Lennard-Jones (LJ) and two-body Hartree-Fock dispersion (HFD)-like potentials for neon and argon, respectively. The required radial distribution functions (RDFs) have been used from two recently determined expressions in the literature and a new equation proposed in this work. Quantum corrections for neon system have been considered using the Feynman-Hibbs (FH) and Wigner-Kirkwood (WK) approaches. To take many-body forces into account for argon system, the simple three-body potentials of Wang and Sadus (2006) [33] and Hauschild and Prausnitz (1993) [30] used with the HFD-like potential without requiring an expensive three-body calculation. The results show that the quantum and three-body effects improve the prediction of the surface tension of liquid neon and argon using the Fowler’s expression.     

Nonequilibrium surface tension for mixed adsorption kinetics

Experimental nonequilibrium surface tension measurements of 1–9 nonanediol solutions obtained by the oscillating-jet method have been interpreted in terms of our theoretical predictions derived for a mixed-controlled adsorption kinetics of the surfactant. The surface tension values have been calculated from the Szyszkowski equation using the Langmuir model of surfactant adsorption. Our theoretical results, obtained by a numerical solution of the adsorption equations, agree well with experimental data giving a value of the kinetics Szyszkowski constant very similar to the thermodynamic equilibrium value determined from experimental measurements of the static surface tension of 1–9 nonanediol solutions of various concentration. The approximate kinetic equation derived by P. Joos, G. Bleys, and G. Petre (J. Chim. Phys.79, 387 (1982)) for purely barrier-controlled adsorption proved to be less accurate.     

Excess densities and equimolar surfaces for spherical cavities in water

For hard spheres with a radius up to 10 A in TIP4P water under ambient conditions, the author studies how the excess number of molecules at the accessible surface depends on the radius of the cavity. Simulation results derived from excess volumes are discussed in terms of radial distribution functions (rdfs), which compare well with extended simple point charge and theoretical rdfs from the literature. The excess number of molecules at the accessible surface inserted in the expression which refers to an arbitrary dividing surface enables one to find the position of the equimolar surface. The surface tension corresponding to this dividing surface was obtained from values of the free energy of cavity formation. For radii in the range of the simulation data, its behavior with curvature is quite different from that usually shown in the literature. A model, which describes how the excess number of molecules at the accessible surface changes with the radius, is discussed in the large length limit by examining consistent rdfs described by a simple analytical form. The inclusion in the model of a logarithmic term has also been considered. Comparison with theoretical results from the literature shows a good agreement for a cavity with a radius of 20 A. For a radius of 100 A and beyond, the model predicts instead sharper density profiles. Such differences have a poor effect on the surface tension at the equimolar surface.     

Effects of electrolyte and nonelectrolyte additives on adsorption and surface rheological characteristics of humic acid salt solutions

The du Noüy and oscillating droplet shape methods are employed to study the effects of the ionic strength and pH of a medium, as well as the addition of nonelectrolytes (lower alcohols and acetone), on the adsorption and surface rheological characteristics of aqueous solutions of humic acid salts (sodium humates) at the liquid-air interface. When added in concentrations at which the aggregation of humic substances is not yet observed, strong electrolytes (NaCl and HCl) decrease the equilibrium surface tension and increase the dilatational viscoelastic modulus of aqueous sodium humate solutions. The aggregation of humic substances enhances the surface tension and reduces the viscoelastic modulus of surface layers. Nonelectrolyte additives decrease the surface tension and dilatational modulus of aqueous humic acid salt solutions. The equilibrium surface tension of sodium humate-nonelectrolyte mixed solutions is described in terms of two different models, namely, a relatively exact model of polyelectrolyte-nonionic surfactant adsorption and a simple additive model. It is shown that the additive model may be used to predict the equilibrium surface tension for the mixtures of high- and low-molecular-mass surfactants.     

Wetting Study of Hydrophobic Membranes via Liquid Entry Pressure Measurements with Aqueous Alcohol Solutions

A new concept of liquid entry pressure measurements is applied to study the hydrophobicity of microporous membranes for aqueous alcohol solutions. The effects of alcohol concentration, type of alcohol, and temperature on liquid entry pressure of the membrane have been studied. Two theoretical equations for the determination of membrane pore size have been proposed. The former equation was developed taking into account the deviation from the Laplace–Young equation due to the membrane structure by means of the structure angle. The latter equation was established considering only the range of alcohol concentration in which the dispersion component of liquid surface tension remains practically constant. Hydrophobicity has been expressed in terms of wetting surface tension, γ_L^w. Based on these measurements, the maximum concentration before the spontaneous wetting occurs would be predicted.