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.     

Effect of softness of the potential on the stress anisotropy in liquids

We have performed molecular dynamics simulations of dense liquids using nonconformal and Gaussian potential models. We investigate the effect of the softness of the potential on the pressure tensor of liquids and dense fluids when the simulations are carried out using parallelepiped cells. The combination of periodic boundary conditions and small cross sectional areas induces an anisotropy in the diagonal components of the pressure tensor. This anisotropy results in an artificial stress in the system that has to be taken into account in simulations of explicit interfaces, where the artificial stress introduces errors in the computation of the surface tension. At high liquid densities the stress anisotropy exhibits an oscillatory dependence with the cross sectional area of the simulation box. We find that the softness of the potential has a dramatic effect on the amplitude of the oscillations, which can be significantly reduced in soft potentials, such as those used in the modeling of hydrocarbon liquids or polymers.     

Influence of drop volume on surface tension evaluated using the pendant drop method

The pendant drop technique is one of the most accurate methods to measure surface tension of liquids. Recently, it has been found that the value of the surface/interfacial tension found using the pendant drop method might be drop-volume dependent. In this work, the surface tension of glycerol at a 25 °C and the surface tension of polypropylene at 240 °C were measured using the pendant drop method for different drop volumes. It was shown that the values of the surface tension depend on the drop size if no calibration to take into account the anisotropy in the optical enlargement is performed. However, when a calibration procedure for optical anisotropy correction is performed, the values of the surface tension obtained do not depend on the volume drop size and they corroborate the values in the literature.     

Effect of flexibility on surface tension and coexisting densities of water

Molecular dynamics simulations of pure water at the liquid-vapor interface are performed using direct simulation of interfaces in a liquid slab geometry. The effect of intramolecular flexibility on coexisting densities and surface tension is analyzed. The dipole moment profile across the liquid-vapor interface shows different values for the liquid and vapor phases. The flexible model is a polarizable model. This effect is minor for liquid densities and is large for surface tension. The liquid densities increase from 2% at 300 K to 9% at 550 K when the force field is changed from a fully rigid simple point charge extended (SPCE) model to that of a fully flexible model with the same intermolecular interaction parameters. The increases in surface tension at both temperatures are around 11% and 36%, respectively. The calculated properties of the flexible models are closer to the experimental data than those of the rigid SPCE. The effect of the maximum number of reciprocal vectors (h(z) (max)) and the surface area on the calculated properties at 300 K is also analyzed. The coexiting densities are not sensitive to those variables. The surface tension fluctuates with h(z) (max) with an amplitude larger than 10 mN m(-1). The effect of using small interfacial areas is slightly larger than the error in the simulations.     

Dissipative particle dynamics simulations of polymersomes

A DPD model of PEO-based block copolymer vesicles in water is developed by introducing a new density based coarse graining and by using experimental data for interfacial tension. Simulated as a membrane patch, the DPD model is in excellent agreement with experimental data for both the area expansion modulus and the scaling of hydrophobic core thickness with molecular weight. Rupture simulations of polymer vesicles, or "polymersomes", are presented to illustrate the system sizes feasible with DPD. The results should provide guidance for theoretical derivations of scaling laws and also illustrate how spherical polymer vesicles might be studied in simulation.     

Determination of surface tension in binary mixtures using transition-matrix Monte Carlo

We present a methodology based on grand-canonical transition-matrix Monte Carlo and finite-size scaling analysis to calculate surface tensions in binary mixtures. In particular, mixture transition-matrix Monte Carlo is first used to calculate apparent, system-size-dependent free-energy barriers separating coexisting fluid phases. Finite-size scaling is then used to extrapolate these values to the infinitely large system limit to determine the true thermodynamic surface tension. A key distinction of the methodology is that it yields the entire isothermal surface-tension curve for a binary mixture in a relatively small number of simulations. We demonstrate the utility of the method by calculating surface-tension curves for three binary Lennard-Jones mixtures. While we have only examined the surface tension of simple fluids in this work, the method is general and can be extended to molecular fluids as well as to determine interfacial tensions of liquid-liquid interfaces.     

Forces between polyethylene surfaces in oxyethylene dodecyl ether solutions as influenced by the number of oxyethylene groups

The atomic force microscopy (AFM) colloidal probe technique was used to study the effect of oxyethylene dodecyl ethers, C12En (n = 1-7), on interactions between hydrophobic polyethylene (PE) surfaces in aqueous solutions. Long-range (colloidal) and contact (pull-off) forces were measured between 10 to 20 microm PE spheres and a flat PE surface at concentrations of surfactant of 1 x 10(-6) and 1 x 10(-4) M. The surface tension of the surfactant solutions and contact angles at PE surfaces were also studied. The influence of the number of oxyethylene groups in the surfactant molecule was examined. Initially, long-range attractive (hydrophobic) forces between the PE surfaces were observed that decreased in range and magnitude with an increase in the number of oxyethylene groups in 1 x 10(-4) M solutions. Above four oxyethylene groups per molecule, repulsive forces were observed. The measured pull-off force between PE surfaces decreased monotonically from approximately 500 mJ/m2 for C12E1 to 150 mJ/m2 for C12E7. The interfacial energy was calculated on the basis of the JKR model, taking into account long-range forces operating outside the contact area. The interfacial energies decreased from 43-47 mJ/m2 for PE-water and PE-C12E1 (1 x 10(-4) M) interfaces to approximately 18 mJ/m2 for PE-C12E7 (1 x 10(-4) M). The interfacial energy was also calculated from measured contact angles and surface tensions using Neumann's equation of state and Young's equation. A similar relationship between interfacial energy and the number of oxyethylene groups was observed on the basis of contact and surface tension measurements. However, interfacial energy values were smaller, within 15-20 mJ/m2, than those calculated from AFM pull-off force measurements.     

The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations

Results of Monte Carlo simulations are reported for the interfacial tension between two fluid phases in a binary mixture of penetrable spheres in which molecular pairs of like species do not interact, while those of unlike species interact as hard spheres. Semigrand canonical ensemble Monte Carlo simulations in a cubic cell with periodic boundary conditions are used to obtain histograms for various system sizes at various densities. At a given density, the interfacial tension and compositions of coexisting phases for an infinite system are evaluated via histogram analysis combined with finite-size scaling. The density dependence of the interfacial tension and phase diagram for an infinite system are thus obtained. The simulated behavior of the interfacial tension close to the critical density corroborates previous suggestions that the model belongs to the three-dimensional Ising universality class.     

Interfacial activity of polymer-coated gold nanoparticles

A systematic study of the interfacial activity of polymer-coated gold nanoparticles was performed with the use of a computer-controlled four-roll mill. The nanoparticle locality within the polymeric domains (bulk or interface) was controlled by means of a mixture of polymeric ligands grafted to the gold nanoparticle core. The bulk polymers were polybutadiene (PBd) and polydimethylsiloxane (PDMS). Monoterminated PDMS and PBd ligands were synthesized on the basis of the esterification of reactive groups (such as hydroxyl or amino groups) with lipoic acid anhydride. The formation of polymer-coated nanoparticles using these lipoic acid-functionalized polymers was confirmed via transmission electron microscopy (TEM), and their interfacial activity was manifested as a reduction of the interfacial tension and in the enhanced stability of thin films (as seen via the inhibition of coalescence). The nanoparticles showed an equal, if not superior, ability to reduce the interfacial tension when compared to previous studies on the effect of insoluble surfactants; however, these particles proved not to be as effective at inhibiting coalescence as their surfactant counterpart. We suggest that this effect may be caused by an increase in the attractive van der Waals forces created by the presence of metal-core nanoparticles. Experimental measurements using the four-roll mill allow us to explore the relationship between nanoparticle concentration at the interface and interfacial tension. In particular, we have found evidence that the interface concentration can be increased relative to the equilibrium value achieved by diffusion alone, and thus the interfacial tension can be systematically reduced if the interfacial area is increased temporarily via drop deformation or breakup followed by recoalescence.     

Origin of repulsive force and structure/dynamics of interfacial water in OEG-protein interactions: a molecular simulation study

Molecular simulations were performed to investigate the origin of the strong repulsive force acting on a protein as the protein approaches an oligo (ethylene glycol) self-assembled monolayer (OEG-SAM) surface. Since the repulsive force is mainly generated from water molecules, the force from the water molecules near the surface was calculated layer by layer to further identify the molecular origin of the repulsive force. Results show that the strong repulsive force acting on the protein near the OEG-SAM surface is dominantly generated by the interfacial water molecules located between the OEG-SAM surface and lysozyme. A hydroxyl-terminated SAM (OH-SAM) surface was used for comparison. No significant repulsive force was observed from the water molecules between the protein and OH-SAM surface. Further studies show that the dipole distribution of the interfacial water molecules is significantly affected by the OEG-SAM surface, as opposed to the negligible impact from the OH-SAM surface. The interfacial water molecules above the OEG-SAM surface stay longer and reorient more slowly than those above the OH-SAM surface. These results from this work support the hypothesis that the OEG-SAM surface interacts strongly with interfacial water molecules and creates a stable hydration layer that prevents proteins from adsorbing to the surface.     

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.     

Molecular dynamics simulations of the surface tension of ionic liquids

We report molecular dynamics computer simulations of the surface tension and interfacial thickness of ionic liquid-vapor interfaces modeled with a soft core primitive model potential. We find that the surface tension shows an anomalous oscillatory behavior with interfacial area. This observation is discussed in terms of finite size effects introduced by the periodic boundary conditions employed in computer simulations. Otherwise we show that the thickness of the liquid-vapor interface increases with surface area as predicted by the capillary wave theory. Data on the surface tension of size-asymmetric ionic liquids are reported and compared with experimental data of molten salts. Our data suggest that the surface tensions of size-asymmetric ionic liquids do not follow a corresponding states law.     

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.     

Self-assembly in two-dimensions of colloidal particles at liquid mixtures

The aim of this work is to simulate the formation of colloidal rings, circular clusters, and voids induced by oily lenses at the air-water interface. The presence of two liquids with different surface tension leads to the formation of a nonhomogeneous interface. In this case, the total interaction potential is assumed to be composed of only two terms; the first one is due to the (repulsive) pairwise dipolar force between partly immersed charged microspheres, whereas the second depends on the position of the particle at the interface and is connected to the interfacial stress caused by the difference of surface tension between both liquids. This simple potential is able to reproduce the experimental rings, circular clusters and voids found by different authors.     

Structure of the liquid-vacuum interface of room-temperature ionic liquids: a molecular dynamics study

Molecular dynamics simulations for the liquid-vacuum interface of the ionic liquid 1-ethyl-3-methylimidazolium nitrate (EMIM+/NO3-) were performed for both electronically polarizable and nonpolarizable potential energy surfaces. The interfacial structural properties, such as the oscillation in the number density profile, the orientational ordering, and the local clustering in the interfacial region, were calculated. The simulations with both the polarizable and nonpolarizable model demonstrate the existence of an inhomogeneous interfacial structure normal to the surface layer. It was found for both models that the ethyl tail group on EMIM+ is likely to protrude outward from the surface. In the outmost surface layer, the cation is likely to lie on the surface with the imidazolium ring parallel to the interface, while there is a second region with enhanced density from that in the bulk where the cation preferably slants with the imidazolium ring tending to be perpendicular to the surface. The results also reveal that the electronic polarization effect is important for the ionic liquid interface. It is found that the cation is likely to be segregated at the ionic liquid surface for the polarizable model, while for the nonpolarizable model, the anion is found to be more likely to exhibit such behavior. The surface tension of the polarizable model (58.5 +/- 0.5 mN/m) is much smaller than that of the nonpolarizable model (82.7 +/- 0.6 mN/m), in better agreement with extrapolated experimental measurements on similar ionic liquid systems.     

Bead-bead interaction parameters in dissipative particle dynamics: relation to bead-size, solubility parameter, and surface tension

Dissipative particle dynamics (DPD) is a mesoscale modeling method for simulating equilibrium and dynamical properties of polymers in solution. The basic idea has been around for several decades in the form of bead-spring models. A few years ago, Groot and Warren established an important link between DPD and the Flory-Huggins chi-parameter theory for polymer solutions. We revisit the Groot-Warren theory and investigate the DPD interaction parameters as a function of bead size. In particular, we show a consistent scheme of computing the interfacial tension in a segregated binary mixture. Results for three systems chosen for illustration are in excellent agreement with experimental results. This opens the door for determining DPD interactions using interfacial tension as a fitting parameter.     

Mechanisms of single-walled carbon nanotube probe-sample multistability in tapping mode AFM imaging

When using single-walled carbon nanotube (SWNT) probes to create AFM images of SWNT samples in tapping mode, elastic deformations of the probe and sample result in a decrease in the apparent width of the sample. Here we show that there are two major mechanisms for this effect, smooth gliding and snapping, and compare their dynamics to the case when a conventional silicon tip is used to image a bare silicon surface. Using atomistic and continuum simulations, we analyze in detail the shape of the tip-sample interaction potential for three model cases and show that in the absence of adhesion and friction forces, more than two discrete, physically meaningful solutions of the oscillation amplitude are possible when snapping occurs (in contrast to the existence of one attractive and one repulsive solution for conventional silicon AFM tips). We present experimental results indicating that a continuum of amplitude solutions is possible when using SWNT tips and explain this phenomenon with dynamic simulations that explicitly include tip-sample adhesion and friction forces. We also provide simulation results of SWNT tips imaging Si(111)-CH3 surface step edges and Au nanocrystals, which indicate that SWNT probe multistability may be a general phenomenon, not limited to SWNT samples.     

Budding dynamics of individual domains in multicomponent membranes simulated by N-varied dissipative particle dynamics

We study the budding dynamics of individual domains in flat, multicomponent membranes using dissipative particle dynamics (DPD) simulations with varied bead number N, in which addition and deletion of beads based on their density at the membrane boundary is introduced. The budding process of a tubular bud, accompanied by a dynamical transition reflected in the energy and morphology evolutions, is investigated. The simulations show that budding duration is shortened with increasing line tension and depends on the domain size quadratically. At low line tension, increasing bending modulus accelerates budding at first, but suppresses the process as it increases further. In addition, the controlling role of the surface tension in the budding process is also explored. Finally, we use the N-varied DPD to simulate the experimentally observed multicomponent tubular vesicles, and the three bud growth modes are confirmed.     

Grand canonical Monte Carlo simulation of a model colloid-polymer mixture: coexistence line, critical behavior, and interfacial tension

Grand canonical Monte Carlo simulations are used to study phase separation in a simple colloid-polymer model, the so-called Asakura-Oosawa model. To overcome the problem of small acceptance rates of the grand-canonical moves, cluster moves are introduced. Successive umbrella sampling, recently introduced by Virnau and Muller [J. Chem. Phys. 120, 10925 (2004)], is used to access the phase-separated regime. The unmixing binodal and the interfacial tension are measured and compared to theoretical predictions. By means of finite-size scaling, the behavior close to the critical point is also investigated. Close to criticality, we observe substantial deviations from mean-field behavior.     

Propensity for the air/water interface and ion pairing in magnesium acetate vs magnesium nitrate solutions: molecular dynamics simulations and surface tension measurements

Molecular dynamics simulations in slab geometry and surface tension measurements were performed for aqueous solutions of magnesium acetate and magnesium nitrate at various concentrations. The simulations reveal a strong affinity of acetate anions for the surface, while nitrate exhibits only a very weak surface propensity, and magnesium is per se strongly repelled from the air/water interface. CH3COO- also exhibits a much stronger tendency than NO3- for ion pairing with Mg2+ in the bulk and particularly in the interfacial layer. The different interfacial behavior of the two anions is reflected by the opposite concentration dependence (beyond 0.5 M) of surface tension of the corresponding magnesium salts. Measurements, supported by simulations, show that the surface tension of Mg(NO3)2(aq) increases with concentration as for other inorganic salts. However, in the case of Mg(OAc)2(aq) the surface tension isotherm exhibits a turnover around 0.5 M, after which it starts to decrease, indicating a positive net solute excess in the interfacial layer at higher concentrations.