Spectra of the liquid cluster surface thermal fluctuations

Classification of cluster particles is proposed that introduces three particle types: the internal particles, surface particles, and virtual chains of particles. Thermal fluctuations of a surface passing through the surface particles of a Lennard-Jones liquid cluster are studied using a molecular dynamics simulation. It is shown that for large clusters, the Fourier spectral amplitude of these fluctuations decays faster than 1q, where q is the wave number. The frequency Fourier spectrum shows an overdamped system behavior, which is the evidence for the absence of thermal capillary waves for clusters comprising less than 10(5) particles. The time-averaged cluster density profile is given by an error function with the width parameter diverging as the logarithm of the cluster size.     

Microscopic theory for interface fluctuations in binary liquid mixtures

Thermally excited capillary waves at fluid interfaces in binary liquid mixtures exhibit simultaneously both density and composition fluctuations. Based on a density functional theory for inhomogeneous binary liquid mixtures we derive an effective wavelength dependent Hamiltonian for fluid interfaces in these systems beyond the standard capillary-wave model. Explicit expressions are obtained for the surface tension, the bending rigidities, and the coupling constants of compositional capillary waves in terms of the profiles of the two number densities characterizing the mixture. These results lead to predictions for grazing-incidence x-ray scattering experiments at such interfaces.     

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.     

Nucleation-fluctuation approach to determining the temperature dependence of the surface tension of metals

An analysis of nucleation processes that occur during a vapor-liquid phase transition and temperature fluctuations that take place in clusters of stable phases is employed to derive a semiempirical relation between the capillary and thermophysical characteristics of substances. The relation enables one to calculate the surface tension of elementary substances based on their thermophysical characteristics in a wide temperature range from melting to boiling points. The surface tension of metals is calculated within this temperature range. In most cases, the calculated results agree with available experimental data.     

Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.     

The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension

The capillary method of surface tension measurement has been used to measure the surface tension of oxygen–nitrogen solutions in the temperature range from 80 to 132 K. At temperatures below the nitrogen critical temperature (T_c = 126.2 K) the capillary constant and the surface tension of solutions are smaller than their additive values and vary linearly with the temperature. Experimental data are compared with the results of calculating the surface tension by the theories of Pinnes and Rowlinson.     

Capillary constant and surface tension of methane-nitrogen solutions: 1. Experiment

The differential version of the method of capillary rise has been used to measure the capillary constant and calculate the surface tension of methane-nitrogen solutions. Experiments have been conducted in the temperature range from 95 to 170 K at pressures up to 4 MPa. Experimental data on surface tension have been compared with the results of calculations by thermodynamic models. Equations are given which describe the dependence of the capillary constant of a solution on its temperature and composition.     

Laser excitation of high-frequency capillary waves

The laser-induced surface deformation (LISD) technique was applied to generate high-frequency capillary waves on liquid surfaces up to several tens of kHz in a noncontact manner. The dynamic response of the fluid near the surface was theoretically derived under the condition of periodical radiation pressure. The result of the numerical calculation predicts the propagation of induced capillary waves out from the excitation region. The efficiency of the wave generation was experimentally examined by changing the width of the excitation laser beam at the surface. The observed LISD spectra were well reproduced by the theory, showing that the effective frequency band can be extended up to over 100 kHz. The propagation of the optically generated wave was measured with a laser probe sweeping the position of the observation. The spatial profile gives the surface tension and the shear viscosity of the sample liquid. The frequency domain measurement was also carried out and the spectrum obtained at a fixed point agrees with the theory, demonstrating the rapid measurement of frequency-dependent phenomena.     

Surface tension measurements of imidazolium-based ionic liquids at liquid–vapor equilibrium

A series of high quality 1-alkyl-3-methylimidazolium-based ionic liquids are synthesized and used for studying their surface tension. The capillary rise method is used for measuring the surface tension of I⁻, Cl⁻, PF₆⁻, and BF₄⁻ salts in the temperature range 298–393 K. The capillary apparatus is evacuated and sealed under vacuum. The experimental results show that surface tension of these compounds depend systematically on temperature.     

Theoretical consideration of the anomalous temperature dependence of the surface tension of pure liquid gallium

The surface tension of pure liquid gallium in the temperature range 303–503 K (303 K is the melting point) was previously measured using the noninvasive method of capillary wave spectroscopy (CWS). The result of this experiment showed that the value of surface tension increases from 303 to 345 K indicating a negative surface excess entropy (S ^σ), and decreases linearly from ~345 to 503 K confirming a negative slope, and thus a positive S ^σ. This unusual behavior of Ga is not known for other liquid metals such as Bi, Pb, Hg, Sn and Al. The reported experimental behavior is modeled here. A theoretical equation for calculating the surface tension of liquid Ga, based upon formulating a proper partition function that includes the rotational part, is derived and described. The theory predicted no maximum in the temperature-dependence of the surface tension, as seen in the experiment, where the analysis was done over a large temperature range (325–503 K). The value obtained from this mathematical expression indicates that the temperature variation of surface tension has no positive slope within the temperature range 303–345 K. At T > 345 K, the surface tension shows the usual linear temperature-dependence with a negative slope. Therefore, the equation is only applicable for the latter temperature range. A comparison between the theoretical and experimental values of surface tension of liquid Ga is discussed.     

Measurement of the surface tension of liquid marbles

The capillary rise and Wilhelmy plate methods have been used to study the "surface tension" of water marbles encapsulated with polytetrafluoroethylene (PTFE) powders of 1-, 35-, and 100-μm particle size. With the capillary rise technique, a glass capillary tube was inserted into a water marble to measure the capillary rise of the water. The Laplace pressure exerted by the water marble was directly measured by comparing the heights of the capillary rise from the marble and from a flat water surface in a beaker. An equation based on Marmur's model was proposed to calculate the water marble surface tension. This method does not require the water contact angle with the supporting solid surface to be considered; it is therefore a simple but efficient method for determining liquid marble surface tension. The Wilhelmy method was used to measure the surface tension of a flat water surface covered by PTFE powder. This method offers a new angle for investigating liquid marble shell properties. A discussion on the nature and the realistic magnitude of liquid marble surface tension is offered.     

Thermal fluctuations of clusters with the long-range interaction

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.     

Parachors of liquid/vapor systems: A set of critical amplitudes

In light of the available experimental data and of our current understanding of liquid–vapor critical phenomena, we examine the values of the parachors and of the parachor exponent, which are commonly used to estimate surface tension from the density difference between coexisting liquid and vapor phases. This is a controversial issue, as values for the parachor exponent ranging from 3.5 to 4 have been proposed in the literature. The parachor exponent and parachors can be viewed as a critical exponent and critical amplitudes, respectively. The Ising value, equal to 3.88, should be observed for the exponent “close enough” to the liquid/vapor critical point, i.e., for “low enough” tensions and densities. However, a review of experimental data for several fluids suggests an effective value in the range of 3.6, in line with the effective values observed for the exponents that describe the vanishing of the density difference and capillary length with the distance to the critical temperature. In fact, the asymptotic Ising regime is not reached experimentally, as confirmed by an estimation of the parachors very near the critical point. Those (Ising) parachors can be inferred from other critical amplitudes corresponding to bulk properties by using two-scale factor universality. Their values exceed those deduced from off-critical tension and density data by more than 10%, corresponding to surface tension differences larger than 50%. We argue that effective parachors (i.e., corresponding to an exponent in the range of 3.6) can be utilized in combination with two-scale-factor universality for determining the critical behavior of fluid systems in an extended range around their liquid/vapor critical point.     

Solution/air interfaces I. An oscillating jet relative method for determining dynamic surface tensions

The oscillating jet method has been investigated for the determination of the surface tension of water using horizontal jets from elliptical orifices in bell-shaped and uniform-channel tubes. Improved techniques have been developed for measuring the wave parameters, the flow rate and for extending the range of investigations to include the initial 80–90 msec of jet surface age.The surface tension values, calculated using the Bohr equation from measurements on successive waves of the water jets, were dependent on the characteristics of the orifice, its position, the flow rate and the wave serial number, but were within ±2 mN/m of the equilibrium value if the initial wave values were disregarded. An extension of the Bohr equation developed for vertical jets was found to be invalid for horizontal jets.Calculated surface tension versus surface age relationships for surfactant solutions also varied with the experimental conditions, but by fixing the position of the orifice tube, and standardizing with water, a relative method was developed for determining dynamic tensions that were independent of the tube used and of the flow rate. The validity of the method was illustrated by results obtained with two surfactant solutions using seven tubes (bell-shaped and uniform-channel) over an age range from 0.6 to 75 msec. The surface tensions of deionized water samples have been determined by the relative method and compared with those obtained by a static method.The true surface age along the jet surface is concluded to be close to the value derived from the mean axial velocity.Evidence is given indicating that, within the millisecond age range, water does not have a dynamic tension above the equilibrium value.     

Surface tension and scaling of critical nuclei in diatomic and triatomic fluids

Density functional theory has been used to investigate surface tension and scaling of critical clusters in fluids consisting of diatomic and rigid triatomic molecules. The atomic sites are hard spheres with attractive interactions obtained from the tail part of the Lennard-Jones potential. Asymmetry in attractive interactions between the atomic sites has been introduced to cause molecular orientation and oscillatory density profiles at liquid-vapor interfaces. The radial dependence of cluster surface tension in fluids showing modest orientation in unimolecular layer at the interface or no orientation at all resembles the surface tension behavior of clusters in simple monoatomic fluids, although the surface tension maximum becomes more pronounced with increasing chain length of the molecule. Surface tension of clusters having multiple oscillatory layers at the interface shows a prominent maximum at small cluster sizes; however, the surface tension of large clusters is lower than the planar value. The scaling relation for the number of molecules in the critical cluster and the nucleation barrier height developed by McGraw and Laaksonen [Phys. Rev. Lett. 76, 2754 (1996)] are well obeyed for fluids with little structure at liquid-vapor interface. However, fluids having enhanced interfacial structure show some deviation from the particle number scaling, and the barrier height scaling breaks up seriously.     

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.     

Adsorption of cetyltrimethylammonium bromide and propanol mixtures with regard to wettability of polytetrafluoroethylene. I. Adsorption at aqueous solution-air interface

Measurements of surface tension of aqueous solutions of cetyltrimethylammonium bromide (CTAB) and propanol mixtures (gamma(L)) for 1 x1 0(-5), 1 x 10(-4), 6 x 10(-4), and 1 x 10(-3) M concentrations of CTAB as a function of propanol concentration in the range from 0 to 6.67 M at 293 K were carried out. The obtained results indicate that there is first-order exponential relationship between the surface tension and propanol concentration in the solution at constant CTAB concentration. These results were compared with those calculated from the equations derived by von Szyszkowski, Joos, Miller et al. From the comparison it resulted that the values of gamma(L) determined by the Szyszkowski equation are correlated with those measured only in a limited propanol concentration range because of changes of the constant related to the specific capillary activity in this equation as a function of propanol concentration, particularly in the range of its high concentration. In the case of the modified Joos equation there is a correlation between the calculated and measured values of gamma(L) only at a very low concentration of propanol. The values of the surface tension of aqueous solutions of CTAB and propanol mixtures determined by the relationships of Miller et al. at CTAB concentration, corresponding to unsaturated surface layer in the absence of propanol, are close to those measured, but there are bigger differences between the calculated and measured values of the surface tension for solutions at a constant value of CTAB concentration close to CMC. However, the values of the surface tension of aqueous solution of CTAB and propanol mixtures calculated from the modified Miller et al. equation, in which the aggregation process of alcohol molecules at water-air interface was taken into account, are in excellent agreement with those measured. The measured values of the surface tension and the Gibbs equations were used for determination of the surface excess of CTAB and propanol concentration at solution-air interface. The obtained results indicate that at the constant concentration of CTAB equal to 1 x 10(-5) and 1 x 10(-4) M there is a maximum of excess concentration of propanol in the surface region at its bulk concentration close to 1 M. Using the calculated values of the surface excess concentration of propanol and CTAB at solution-air interface and assuming the proper thickness of the interface region, the total values of their concentration in this region were evaluated. Next, the standard surface free energy of CTAB and propanol mixtures adsorption was calculated. The calculated values of this energy indicate that the tendency to adsorb molecules of CTAB and propanol decreases with increasing propanol concentration probably because of entropy of adsorption decrease resulting from water structure destruction by propanol molecules.     

Surface Tension of the Vapor–Liquid Interface with Finite Curvature

Based on the division of particles into internal and surface particles, the expression is derived closing the system of equations of classical thermodynamics for curvature-dependent surface tension, equimolar radius, and radius of tension surface. A solution to this system allows one to find the surface tension of new phase nucleus of any size (including minimal) and any sign of surface curvature. The obtained results indicate the weak size dependence of thermodynamic parameters that are the functions of surface tension; it is shown that Tolman's length cannot be determined using experimental determination of these parameters. It is shown that the work of nucleus formation strongly depends on its size and is the function of effective rather than true surface tension. Numerical simulation of clusters by the molecular dynamics method indicates that the pressure inside a fairly small cluster is described by Laplace's formula with the coefficient of surface tension for the plane surface of a liquid that agrees with the proposed theory.     

Using wavelets to analyze AFM images of thin films: surface micelles and supported lipid bilayers

This paper presents micro- and nanoanalysis of thin films based on images obtained by atomic force microscopy (AFM). The analysis exploits the discrete wavelet transform and the resulting wavelet spectrum to study surface features. It is demonstrated that the wavelet technique can characterize micro- and nanosurface features and distinguish between similar surface structures. The use of a feature extraction method is shown. The method involves the separation of certain frequency content from the original AFM images and analyzing the data independently to gain quantitative information about the images. By using the feature extraction method, soft surfaces in water are analyzed and nanofeatures are measured. The packing of surface micelles of sodium dodecyl sulfate on a self-assembled monolayer is analyzed. The characteristics of pore formation, due to penetration of the antibacterial peptide protegrin, into a solid-supported lipid bilayer are quantified. The sizes of the pores are obtained, and it is observed that the line tension of the pores reduces the fluctuations of the lipid bilayer.