Effect of temperature and pressure on surface tension of polystyrene in supercritical carbon dioxide

The surface tension of polymers in a supercritical fluid is one of the most important physicochemical parameters in many engineering processes, such as microcellular foaming where the surface tension between a polymer melt and a fluid is a principal factor in determining cell nucleation and growth. This paper presents experimental results of the surface tension of polystyrene in supercritical carbon dioxide, together with theoretical calculations for a corresponding system. The surface tension is determined by Axisymmetric Drop Shape Analysis-Profile (ADSA-P), where a high pressure and temperature cell is designed and constructed to facilitate the formation of a pendent drop of polystyrene melt. Self-consistent field theory (SCFT) calculations are applied to simulate the surface tension of a corresponding system, and good qualitative agreement with experiment is obtained. The physical mechanisms for three main experimental trends are explained by using SCFT, and none of the explanations quantitatively depend on the configurational entropy of the polymer constituents. These calculations therefore rationalize the use of simple liquid models for the quantitative prediction of surface tensions of polymers. As pressure and temperature increase, the surface tension of polystyrene decreases. A linear relationship is found between surface tension and temperature, and between surface tension and pressure; the slope of surface tension change with temperature is dependent on pressure.     

Development of a new methodology to study drop shape and surface tension in electric fields

Development of a new methodology for the study of both shape and surface tension of conducting drops in an electric field is presented. This methodology, called axisymmetric drop shape analysis-electric fields (ADSA-EF), generates numerical drop profiles in an electrostatic field, for a given surface tension. Then, it calculates the true value of the surface tension by matching theoretical profiles to the shape of experimental drops, using the surface tension as an adjustable parameter. ADSA-EF can be employed to simulate and study drop shapes in the electric field and to determine its effect on liquid surface tension. The method can also be used to measure surface tension in microgravity, where current drop-shape techniques are not applicable. The axisymmetric shape of the drop is the only assumption made in the development of ADSA-EF. The new scheme is applicable when both gravity and electrostatic forces are present. Preliminary measurements using ADSA-EF suggest that the surface tension of water increases by about 2% when an electric field with the magnitude of 10(6) V/m is applied.     

Contact angle interpretation in terms of solid surface tension

Recent experimental (low-rate) dynamic contact angles for 14 solid surfaces are interpreted in terms of their solid surface tensions. Universality of these experimental contact angle patterns is illustrated; other reasons that can cause data to deviate from the patterns are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming solid surface tension is constant for one and the same solid surface, experimental contact angle patterns are employed to deduce a functional relationship to be used in conjunction with the Young equation to determine solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelot’s rule together with experimental data; essentially constant solid surface tension values are obtained, independent of liquid surface tension and molecular structure. A new combining rule is also derived based on an expression similar to one used in molecular theory; such a combining rule should allow a better understanding of the molecular interactions between unlike solid–liquid pairs.     

Temperature Dependence of the Surface Tension of Alkali Metals: A Unified Correlation

Abstract

In this work, new definitions of the normalized temperature and surface tension are proposed which result in a single plot for the surface tension of molten alkali metals. The functional dependence of the reduced surface tension on the reduced temperature can be adequately described by a straight line; the intercept and slope have been obtained using the linear regression approach. The method proposed herein predicts the values of surface tension at various temperatures with an average error of about 5%.     

Comparative study of the effect of tail corrections on surface tension determined by molecular simulation

We report results from a comparative study of the influence of tail corrections on the surface tension of the Lennard-Jones fluid. We find that cutoff-independent surface tensions can be obtained by applying a set of tail corrections recently introduced by Janecek at each step of an interfacial Monte Carlo (MC) or molecular dynamics (MD) simulation. The effect of tail corrections on an alternative methodology for calculating surface tension, the combination of finite-size scaling and grand-canonical transition-matrix Monte Carlo (FSS/GC-TMMC), was also investigated. Using this indirect method, surface tensions were calculated with standard (bulk-fluid) tail corrections and lattice sums, the latter usually considered more accurate but computationally more intensive than the former. With standard tail corrections, we find that the surface tension decreases with increasing cutoff distance, reaching a limiting value corresponding to the maximum cutoff possible, namely half the simulation box length. In contrast, surface tension values obtained with the lattice summation were cutoff-independent. More importantly, these values were equivalent to those surface tension values obtained using standard tail corrections and a cutoff distance of half the box length. We also find that the surface tension values obtained here are in agreement with those found in the literature. Last, we find that surface tension values obtained by MD and FSS/GC-TMMC are in decent agreement so long as the appropriate tail correction schemes are used, and that the relative uncertainties in the surface tensions calculated by MD are generally an order of magnitude greater than those calculated by FSS/GC-TMMC. However, the time required by MD on a single central processing unit is less than that required by FSS/GC-TMMC.     

Studies on the application of dynamic surface tensiometry of serum and cerebrospinal liquid for diagnostics and monitoring of treatment in patients who have rheumatic, neurological or oncological diseases

Human biological liquids comprise various surfactants, which adsorb at liquid interfaces and lead to a variation in surface tension. The adsorption processes involving low molecular weight surfactants, proteins and phospholipids play a vital role in the physiological functions of the human organism, especially if large surfaces are involved (e.g., gas exchange in lungs, metabolism of kidneys, liver and brain). Dynamic surface tensiometric studies of biological liquids like serum and cerebrospinal fluid provide surrogate parameters that reflect surface tension phenomena. We provide dynamic surface tension data of serum and cerebrospinal fluid that were collected from healthy volunteers and patients with rheumatic, neurological or oncological diseases. Our studies indicate that dynamic surface tension data are helpful for diagnostic purposes and for monitoring of therapeutic interventions.     

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.     

Molecular dynamics study of structural and thermodynamic characteristics of nanodroplets of simple fluid

Equilibrium configurations of Lennard-Jones nanodroplets composed of 10–15000 spherically symmetric molecules placed in the center of a spherical container are studied at constant temperature by the molecular dynamics method. The distribution of local density is found and size dependences of density in the center of droplet, first coordination number, and energy surface tension coinciding for equimolecular dividing surface with specific excess free energy of droplet are studied. Radial distribution function is also determined. It is established that the passage of structural characteristics to their macroscopic values is observed for droplets containing as little as about 300 molecules, while, for energy surface tension, analogous passage for energy surface tension occurs for droplets containing 700–6000 molecules.     

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.     

Surface tension and vapor-liquid phase coexistence of confined square-well fluid

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envelope is in agreement with that given in literature. The surface tension of the vapor-liquid interface is calculated via molecular dynamics simulations. GC-TMMC with finite size scaling is also used to calculate the surface tension. The results from molecular dynamics and GC-TMMC methods are in very good mutual agreement. The vapor-liquid surface tension, under confinement, was found to be lower than the bulk surface tension. However, with the increase of the slit width the surface tension increases. For the case of a square-well fluid in an attractive planar slit pore, the vapor-liquid surface tension exhibits a maximum with respect to wall-fluid interaction energy. We also report estimates of critical properties of confined fluids via the rectilinear diameter approach.     

Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Surface tension of different sized single-component droplets,according to macroscopic data obtained using the lattice gas model and the critical droplet size during phase formation

Size dependences of the surface tension of spherical single-component droplets are calculated using equations of the lattice gas model for 19 compounds. Parameters of the model are found from experimental data on the surface tension of these compounds for a macroscopic planar surface. The chosen low-molecular compounds satisfy the law of corresponding states. To improve agreement with the experimental data, Lennard-Jones potential parameters are varied within 10% deviations. The surface tensions of different sized equilibrium droplets are calculated at elevated and lowered temperatures. It is found that the surface tension of droplets grows monotonically as the droplet size increases from zero to its bulk value. The droplet size R ₀ corresponding to zero surface tension corresponds to the critical size of the emergence of a new phase. The critical droplet sizes in the new phase of the considered compounds are estimated for the first time.     

Thermodynamic quantities of surface formation of aqueous electrolyte solutions X. Aqueous solution of 2:1 valence-type salts

The behaviors of a series of calcium halides and of alkali earth metal chlorides in the air/water surface region were studied in comparison with those of alkali metal halides by measuring the surface tension increments of solutions. The effect of salts with divalent cations on the surface tension increments is more pronounced than that of uni-univalent salts, but there are some similarities between these two types. It seems that the anions cause a marked effect on surface tension which is proportional to the magnitude of hydration in the bulk water. We also observed a decrease in the entropy change of surface formation with increasing concentration. The importance of an electrical double layer at the surface is discussed in relation to these surface tension increments.     

pH sensitive adsorption of polypeptide/sodium dodecyl sulfate mixtures

Neutron reflectivity and surface tension have been used to investigate the pH sensitivity of the adsorption of poly-L-lysine hydrobromide and sodium dodecyl sulfate mixtures at the air-solution interface. The surface tension variation with surfactant concentration is complex, and between the critical aggregation concentration and critical micellar concentration there is a marked increase in the surface tension. The neutron reflectivity results show that this is associated with a depletion of the surface of polypeptide/surfactant complexes. The variations in the adsorption and surface tension with pH are attributed to changes in the polypeptide conformation at the interface and in solution.     

Surface properties of aqueous amino acid solutions. I. Surface tension of hydrochloric acid-glycine and glycine-sodium hydroxide systems

The surface tensions of aqueous solutions of four mixtures (hydrochloric acid-glycine hydrochloride, glycine hydrochloride-glycine, glycine-sodium glycinate, and sodium glycinate-sodium hydroxide) were measured as a function of total molality and mole fraction. The measurements correspond to the change in surface tension with variation of pH. The contribution of glycine hydrochloride to the increments in surface tension is equivalent to that observed for the aqueous solution of glycine, while the contribution of sodium glycinate is much larger than that of glycine. The variations in surface tension on mixing in the surface region are discussed using comparisons with mixtures of simple salts.     

Which surfactants reduce surface tension faster? A scaling argument for diffusion-controlled adsorption

Consider the example of surfactant adsorbing from an infinite solution to a freshly formed planar interface. There is an implicit length scale in this problem, the adsorption depth h, which is the depth depleted to supply the interface with the absorbed surfactant. From a mass balance, h can be shown to be the ratio of the equilibrium surface concentration gamma eq to the bulk concentration C infinity. The characteristic time scale for diffusion to the interface is tau D = h2/D, where D is the diffusivity of the surfactant in solution. The significance of this time scale is demonstrated by numerically integrating the equations governing diffusion-controlled adsorption to a planar interface. The surface tension equilibrates within 1-10 times tau D regardless of bulk concentration, even for surfactants with strong interactions. Dynamic surface tension data obtained by pendant bubble method are rescaled using tau D to scale time. For high enough bulk concentrations, the re-normalized surface tension evolutions nearly superpose, demonstrating that tau D is indeed the relevant time scale for this process. Surface tension evolutions for a variety of surfactants are compared. Those with the smallest values for tau D equilibrate fastest. Since diffusion coefficients vary only weakly for surfactants of similar size, the differences in the equilibration times for various surfactant solutions can be attributed to their differing adsorption depths. These depth are determined by the equilibrium adsorption isotherms, allowing tau D to be calculated a priori from equilibrium surface tension data, and surfactant solutions to be sorted in terms of which will reduce the surface tension more rapidly. Finally, trends predicted by tau D to gauge what surfactant properties are required for rapid surface tension reduction are discussed. These trends are shown to be in agreement with guiding principles that have been suggested from prior structure-property studies.     

THE MECHANICAL VIEW OF THE SURFACE TENSION IS FALSE

The concept of surface tension is usually introduced as a force per unit length originated from the “stress tensor” at the liquid surface (and vaguely extended to solids). This mechanical model of the surface tension, a paradigm for many workers in the field, is wrong. The inferences from the model, however, are correct in the more common uses. Some contradictions may appear but not sufficient to abandon such a simple and intuitive concept. The origin of the surface tension, of a liquid or solid surface, is in the molecular interactions, when some other phase is put in contact with such a surface. Recent developments using the surface tension components allow to predict interfacial surface tensions and to measure surface tension of solids. Although the power of this approach is evident, its use is only incipient because some results, particularly the presence of negative interfacial tensions, are difficult to interpret using the erroneous vision of surface tension as a consequence of a “stress tensor” at the liquid (or solid) surface. We present here some properties of liquids useful to fundament the concept of surface tension and briefly refer to Laplace's equation, Young's equation and capillarity, attempting to correct some misinterpretations.     

A study of the refractive index and surface tension synergy of the binary water/ethanol: influence of concentration

Pure alcohols or alcohols mixed with water are the most widely used solvents in a great variety of industrial applications, including the formulation of pharmaceutical and cosmetic products. As a result of water/alcohol molecular associations, variations result in the physico-chemical characteristics of the system, such as density, viscosity, refractive index and surface tension.

The present study investigates the refractive index and the surface tension of ethanol and water mixtures at a temperature of 25°C, for different molar fractions. The data obtained allow us to study the corresponding refractive index and the surface tension synergies; in this sense, an absolute maximum refractive index is recorded for a molar fraction of 0.667, while maximum synergy (both absolute and relative) is observed for a molar fraction 0.333.

As regards surface tension, minimum absolute and relative synergy is recorded for molar fraction 0.2, since synergy is negative for the surface tensions of the mixtures.

Determinations are also made of the molar refraction of the mixtures and of the variation in refractive indices with temperature.     

Studies of dynamic surface tension of polyoxyethylene alkylphenols at the air–water interface

This paper presents the study of dynamic surface tension of polyoxyethylene alkylphenol surfactants (Igepals) at the air–solution interface. The experimental investigation of the surface tension dynamics are carried out using a pendant drop method for two of the representative alkylphenols (Igepal-630 and Igepal-720) nonionic surfactants. The general trend of the dynamic surface tension for the two surfactants appears to be similar. However, the absolute surface activities are different. Between the two poloxyethylene alkylphenol surfactants, it was found that Igepal-C0-630 has a higher surface activity and a lower critical micelle concentration (CMC) value. This agreed well with their reported hydrophile–lipophile balance (HLB). The equilibrium adsorption parameters for these surfactant systems have been estimation using two different methods and are in good agreement. The theoretical model developed for the surface tension dynamics based on the Statistical Rate Theory (SRT) in our earlier (J. Colloid Interface Sci., 286, 2005, 14–27) work satisfactorily predicted the experimental results for the present systems.