Structure of the interface between two polar liquids: nitrobenzene and water

Synchrotron X-ray reflectivity is used to study the electron density as a function of depth through the bulk nitrobenzene-water interface at four different temperatures. The measured interfacial width differs from the predictions of capillary wave theory with a progressively smaller deviation as the temperature is raised. Computer simulations suggest the presence of both molecular layering and dipole ordering parallel to the interface. Either layering or a bending rigidity, that can result from dipole ordering, can explain these measurements.     

Capillary waves at the liquid-vapor interface and the surface tension of water

Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.     

Fluctuating Interfaces in Liquid Crystals

Summary: We review and compare recent work on the properties of fluctuating interfaces between isotropic and nematic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.     

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.     

Capillary waves in a colloid-polymer interface

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L x L x D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector-dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed.     

Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces

The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.     

Calculation of the crystal-melt interfacial free energy of succinonitrile from molecular simulation

The crystal-metal interfacial free energy for a six-site model of succinonitrile [N triple bond C-(CH(2))(2)-C triple bond N] has been calculated using molecular-dynamics simulation from the power spectrum of capillary fluctuations in interface position. The orientationally averaged magnitude of the interfacial free energy is determined to be (7.0+/-0.4)x10(-3) J m(-2). This value is in agreement (within the error bars) with the experimental value [(7.9+/-0.8)x10(-3) J m(-2)] of Marasli et al. [J. Cryst. Growth 247, 613 (2003)], but is about 20% lower than the earlier experimental value [(8.9+/-0.5)x10(-3) J m(-2)] obtained by Schaefer et al. [Philos. Mag. 32, 725 (1975)]. In agreement with the experiment, the calculated anisotropy of the interfacial free energy of this body-centered-cubic material is small. In addition, the Turnbull coefficient from our simulation is also in agreement with the experiment. This work demonstrates that the capillary fluctuation method of Hoyt et al. [Phys. Rev. Lett. 86, 5530 (2001)] can be successfully applied to determine the crystal-melt interfacial free energy of molecular materials.     

Comparison of the capillary wave method and pressure tensor route for calculation of interfacial tension in molecular dynamics simulations

We have studied the calculation of surface and interfacial tension for a variety of liquid–vapor and liquid–liquid interfaces using molecular dynamics (MD) simulations. Because of the inherently small scale of MD systems, large pressure fluctuations can cause imprecise calculations of surface tension using the pressure tensor route. The capillary wave method exhibited improved precision and stability throughout all of the simulated systems in this study. In order to implement this method, the interface was defined by fitting an error function to the density profile. However, full mapping of the interface from coordinate files produced enhanced accuracy. Upon increasing the system size, both methods exhibited higher precision, although the capillary wave method was still more reliable. © 2013 Wiley Periodicals, Inc.     

Molecular dynamics study of the interface between water and 2-nitrophenyl octyl ether

We present results of molecular dynamics simulations of the interface between water and 2-nitrophenyl octyl ether (NPOE). This system is analyzed in detail using a procedure to calculate intrinsic profiles of several important properties (density, radial distribution functions, hydrogen bonds, molecular orientation, self-diffusion). The interface was found to be molecularly sharp but corrugated by thermal fluctuations. Using a method based on capillary wave theory, we have estimated the interfacial tension and obtained good agreement with values calculated from the virial route. The results were compared to simulations of the water/nitrobenzene interface. The presence of an alkyl chain in NPOE introduces an added degree of hydrophobicity, which causes an increase in the interfacial tension. Furthermore, interfacial NPOE molecules are less organized than nitrobenzene and show a distinct dynamic response. These results shed light on the observed differences between these two organic liquids in electrochemical studies.     

Nematic-isotropic interfaces under shear: a molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.     

Interfaces between coexisting phases of polymer mixtures: Comparison between Monte Carlo simulations and theoretical predictions

Large scale Monte Carlo investigations of the interface between A-rich and B-rich phases of symmetric binary (AB) polymer mixtures are presented, using the bond fluctuation model of flexible chains with N_A=N_B=N=32 effective monomers. The temperature range studied, 0.144<T/T_c0.759, includes both the strong and the weak segregation limit. Interfacial free energy and interfacial structure are studied, and compared to predictions based on the selfconsistent field theory. Also the broadening of the interfacial width due to capillary waves is considered, and finite size effects due to the confinement of interfaces in thin films of polymer blends are discussed.     

On the fluctuation theory for the liquid—vapor interface

Using the statistical mechanical formulation of Triezenberg and Zwanzig, we argue that the “intrinsic” or “bare” width of the liquid—vapor interface in the Buff—Lovett—Stillinger capillary model may be identified as the interfacial width described by the “van der Waals-like” theories.     

On the Calculation of Surface Tensions of <Emphasis Type="Italic">n</Emphasis>-Alkanes Using the Modified SAFT-BACK-DFT Approach

Density functional theory is combined with the modified SAFT-BACK EOS to investigate liquid–vapor interfaces of n-alkanes. We evaluate the temperature dependence of the interfacial width and the surface tension. Differences in chain length of the alkanes lead to differences in the thermodynamic properties of the fluids. A single curve for the reduced width of the interface as a function of reduced temperature serves to correlate interfacial properties of a wide variety of linear chain fluids (excluding methane and ethane) with sufficient accuracy for our purposes.     

Quasi-elastic laser light scattering from thermally excited capillary waves on the polarised water/1,2-dichloroethane interface

Quasi-elastic laser light scattering (QELS) from thermally excited capillary waves on the polarised water/1,2-dichloroethane interface was measured using optical heterodyne mixing technique. Interfacial potential difference was controlled by equilibrium partition of tetraethylammonium, tetrapropylammonium, tetrabutylammonium or tetrapentylammonium bromide. Frequency of the capillary wave of a selected wavelength was shown to decrease with the increasing electrolyte concentration. Frequency decrease was related to the decreasing interfacial tension being caused by the increasing relative surface excess of the electrolyte. No significant effect of the electrolyte concentration on the capillary wave damping was observed. Adsorption data obtained from these measurements are consistent with the results of the double layer capacity studies.     

Anisotropic interfacial free energies of the hard-sphere crystal-melt interfaces

We present a reliable method to define the interfacial particles for determining the crystal-melt interface position, which is the key step for the crystal-melt interfacial free energy calculations using capillary wave approach. Using this method, we have calculated the free energies gamma of the fcc crystal-melt interfaces for the hard-sphere system as a function of crystal orientations by examining the height fluctuations of the interface using Monte Carlo simulations. We find that the average interfacial free energy gamma(0) = 0.62 +/- 0.02k(B)T/sigma(2) and the anisotropy of the interfacial free energies are weak, gamma(100) = 0.64 +/- 0.02, gamma(110) = 0.62 +/- 0.02, gamma(111) = 0.61 +/- 0.02k(B)T/sigma(2). The results are in good agreement with previous simulation results based on the calculations of the reversible work required to create the interfaces (Davidchack and Laird, Phys. Rev. Lett. 2000, 85, 4571). In addition, our results indicate gamma(100) > gamma(110) > gamma(111) for the hard-sphere system, similar to the results of the Lennard-Jones system.     

Effective surface tension for capillary fluctuations at the vapor-liquid interface

Thermal fluctuations of the surface of argon-like cluster are considered. Data obtained by molecular dynamics method are used to find effective surface tension for the capillary component of fluctuations, which characterizes the deviation of Fourier spectrum observed in numerical experiment from the spectrum of macroscopic capillary waves. The variational method was used to solve the problem. It is revealed that effective surface tension is close to constant value within a rather wide wavelength range. At the boundary of this range in the region of large wave numbers, the obtained value quickly tends to infinity, while spectral amplitudes decay thus corresponding to the theory proposed previously. The width of damping region is estimated for different temperatures and cluster sizes.     

Ions at the water-oil interface: interfacial tension of electrolyte solutions

A theory, based on a modified Poisson-Boltzmann equation, is presented that allows us to calculate the excess interfacial tension of an electrolyte-oil interface accurately. The chaotropic (structure-breaking) ions are found to adsorb to the water-oil interface as the result of large polarizability, weak hydration, and hydrophobic and dispersion interactions. However, kosmotropic (structure-making) anions as well as potassium and sodium ions are found to be repelled from the interface. The adsorption of I(-) and ClO(4)(-) is found to be so strong as to lower the interfacial tension of the water-oil interface, in agreement with the experimental data. The agreement between the calculated interfacial tensions and the available experimental data is very good. The theory is used to predict the interfacial tensions of six other potassium salts, for which no experimental data is available at the moment.     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Dynamics of liquid interfaces under various types of external perturbations

Dynamic interfacial parameters are the key properties of interfaces in many modern technologies and can be studied in various ways. For applications like foams and emulsions, the dynamics of adsorption and the dilational and shear rheology of liquid–fluid interfaces are investigated most frequently. This work gives an insight into recently developed new experimental approaches, such as fast capillary pressure tensiometry for growing and oscillating drops. These experiments are presented in comparison to more classical techniques like drop profile tensiometry and capillary wave damping. Progress in these experiments based on generated interfacial perturbations can be expected only by a close link to respective CFD simulations. We also present the state of the art of CFD simulations, which have reached a high level during the last decade and provide a substantial basis for dynamic interfacial experiments.     

Dendritic PtCo alloy nanoparticles as high performance oxygen reduction catalysts

We studied the physical properties and the concentration profile of benzene+water+caprolactam mixtures near the fluid-fluid interface using self-consistent field (SCF) theory. This yields the interfacial tension which plays an important role in describing the stability of transient liquid droplets of one phase in the other. The studies were performed at a fixed temperature of 313K. Flory-Huggins binary interaction parameters and the compound lattice segment numbers are input parameters for the applied SCF theory. These parameters were derived from activity coefficient relations, which are used to describe experimental liquid-liquid and vapor-liquid phase equilibrium measurements. Using first principles, the benzene-water interface was studied and the resulting interfacial tension was found to be in agreement with experimental values. This study illustrates that caprolactam accumulates at the benzene-water interface, acting as a weak surfactant. The interfacial tension is also demonstrated to be affected by the caprolactam concentration and the SCF results are in fair agreement with the experimental observations.