Vapor Interfacial Tension Research Articles

Measuring line tension: Thermodynamic integration during detachment of a molecular dynamics droplet

The contact line (CL) is where solid, liquid, and vapor phases meet, and Young’s equation describes the macroscopic force balance of the interfacial tensions between these three phases. These interfacial tensions are related to the nanoscale stress inhomogeneity appearing around the interface, and for curved CLs, e.g., a three-dimensional droplet, another force known as the line tension must be included in Young’s equation. The line tension has units of force, acting parallel to the CL, and is required to incorporate the extra stress inhomogeneity around the CL into the force balance. Considering this feature, Bey et al. [J. Chem. Phys. 152, 094707 (2020)] reported a mechanical approach to extract the value of line tension τℓ from molecular dynamics (MD) simulations. In this study, we show a novel thermodynamics interpretation of the line tension as the free energy per CL length, and based on this interpretation, through MD simulations of a quasi-static detachment process of a quasi-two-dimensional droplet from a solid surface, we obtained the value τℓ as a function of the contact angle. The simulation scheme is considered to be an extension of a thermodynamic integration method, previously used to calculate the solid–liquid and solid–vapor interfacial tensions through a detachment process, extended here to the three-phase system. The obtained value agreed well with the result by Bey et al. and showed the validity of thermodynamic integration at the three-phase interface.

Quantitative Predictions and Experimental Validation of Liquid-Vapor Interfacial Tension in Binary and Ternary Mixtures of Alkanes Using Molecular Dynamics Simulations.

Liquid-vapor interfacial properties of alkane mixtures present a challenge for experimental determination, especially under conditions relevant to the energy industry processes. Molecular dynamics (MD) simulations can accurately predict interfacial tensions (IFTs) for complex alkane mixtures under virtually any conditions, thereby alleviating the need for difficult and costly experiments. MD simulations with the CHARMM force field and empirical corrections for the IFT and pressure were used to obtain the IFT for three binary mixtures of ethane (with n-pentane, n-hexane, and n-nonane) and a ternary system (ethane/n-butane/n-decane) under a variety of conditions. The results were thoroughly validated against experimental data from the literature, and new original IFT data were collected using the pendant drop method. The simulations are able to reproduce the experimental IFT to better than 0.5 mN/m or 5% on average and within 1 mN/m or 10% in the worst case. IFTs for the studied three binary and ternary alkane mixtures were predicted for wide ranges of conditions with no known experimental data. Finally, using the MD simulation data, the reliability of the widely used empirical parachor model for predicting IFT was reaffirmed, and the significance of the empirical parameters examined to establish an optimal balance between the accuracy and broad applicability of the model.

Droplet depinning on superhydrophobic surfaces: from simple rigid wetting to complex soft wetting

Droplet depinning on superhydrophobic surfaces is pervasive in nature and critical to many applications and hence has been studied extensively over the past few decades. A consensus has been reached that the droplet depinning force mainly stems from the synergistic dynamics of the three-phase contact line and the liquid–vapor interface. Nevertheless, the aforementioned conclusions were made using simple (pure water) droplets depinning on rigid superhydrophobic surfaces, denoted as simple rigid wetting, where the main influencing factors are liquid–vapor interfacial tension, surface texture geometry and material wettability. In recent years, an increasing amount of attention has been paid to complex soft wetting, where liquid physiochemical properties (e.g. viscoelasticity) and solid surface rigidity play an important role. To encourage the investigation of complex soft wetting, in this perspective, depinning of simple droplets on soft surfaces and depinning of viscoelastic droplets on rigid surfaces are briefly introduced. Then, possible factors that affect viscoelastic droplet depinning on soft superhydrophobic surfaces are discussed. Moreover, applications that are highly relevant to complex soft wetting are introduced.

Statics and dynamics of nanodroplet electrowetting on an isothermally heated nanostructured surface

The statics and dynamics of electrowetting of a water nanodroplet on an isothermally heated nanostructured surface subjected to a vertical electric field are investigated via molecular dynamics (MD) simulations. The simulation results reveal that when imposing a constant electric field on the water nanodroplet, the static and dynamic contact angles of the water nanodroplet are always decreased with increasing the substrate temperature. At the same time, the spreading becomes faster at higher substrate temperatures. In the no-temperature-difference scenario, the statics and dynamics of electrowetting are found to strongly depend on the field strength and direction owing to small droplet sizes. Intriguingly, this dependence weakens with increasing the substrate temperature even completely disappears at high enough substrate temperatures. The result in the finite-temperature-difference scenario can be attributed to the weakened pining effect caused by vigorous evaporation in the vicinity of the contact line as well as the decreased liquid–vapor interfacial tension (or increased spreading coefficient) arising from the elevated interface temperature.

Dependency of Contact Angles on Three-Phase Contact Line: A Review

The wetted area of a sessile droplet on a practical substrate is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, contact angles of droplets have been studied for more than two hundred years, there are still some unanswered questions. In the last two decades, it was experimentally proven that the advancing and receding contact angles, and the contact angle hysteresis of rough and chemically heterogeneous surfaces, are determined by interactions of the liquid and the solid at the three-phase contact line alone, and the interfacial area within the contact perimeter is irrelevant. However, confusion and misunderstanding still exist in this field regarding the relationship between contact angle and surface roughness and chemical heterogeneity. An extensive review was published on the debate for the dependence of apparent contact angles on drop contact area or the three-phase contact line in 2014. Following this old review, several new articles were published on the same subject. This article presents a review of the novel articles (mostly published after 2014 to present) on the dependency of contact angles on the three-phase contact line, after a short summary is given for this long-lasting debate. Recently, some improvements have been made; for example, a relationship of the apparent contact angle with the properties of the three-phase line was obtained by replacing the solid–vapor interfacial tension term, γSV, with a string tension term containing the edge energy, γSLV, and curvature of the triple contact line, km, terms. In addition, a novel Gibbsian thermodynamics composite system was developed for a liquid drop resting on a heterogeneous multiphase and also on a homogeneous rough solid substrate at equilibrium conditions, and this approach led to the same conclusions given above. Moreover, some publications on the line energy concept along the three-phase contact line, and on the “modified” Cassie equations were also examined in this review.

Wilhelmy equation revisited: A lightweight method to measure liquid–vapor, solid–liquid, and solid–vapor interfacial tensions from a single molecular dynamics simulation

We have given theoretical expressions for the forces exerted on a so-called Wilhelmy plate, which we modeled as a quasi-2D flat and smooth solid plate immersed in a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line, and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. The force expressions were derived by a purely mechanical approach, which is exact and ensures the force balance on the control volumes arbitrarily set in the system, and are valid as long as the solid-liquid (SL) and solid-vapor (SV) interactions can be described by mean-fields. In addition, we revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γSL and γSV, and this was verified through the comparison with the SL and SV works of adhesion obtained by the thermodynamic integration (TI). From these results, it has been confirmed that γSL and γSV as well as the liquid-vapor interfacial tension γLV can be extracted from a single equilibrium MD simulation without the computationally demanding calculation of the local stress distributions and the TI.

Determination of the Solid–Vapor Interfacial Tension of Nitric Acid Dihydrate Crystals via Experiments on the Freezing of Aqueous Nitric Acid Droplets

We propose a method for determining the solid–vapor interfacial tension σsv of nitric acid dihydrate/trihydrate (NAD/NAT) crystals using experiments on crystal nucleation in aqueous nitric acid (NA) droplets. It exploits the dominance of the surface-stimulated mode of crystal nucleation in small droplets (of radii R ≲ 5 μm) and its negligibility in large ones (of radii R ≳ 20 μm). We show that, experimentally measuring the crystal nucleation rates in such large and small (but otherwise identical) droplets, one can determine the solid–vapor interfacial tension of that crystal facet which forms at the droplet surface in a surface-stimulated mode. A modified expression for the work of formation of NAD/NAT crystal nuclei in nonstoichiometric solutions is proposed; it more adequately takes account of the effects of NA vapors. Applying our method to existing experimental data, we estimate the σsv of NAD to be about 90 dyn/cm (in the temperature range from 190 to 204 K), weakly depending on temperature.

Circular plate deformed by a sessile droplet

Deformation of circular plates including clamped circular plate and simply supported circular plate induced by a sessile droplet is studied using linear, elastic, small-deflection theory for plate bending. In the theoretical analysis, it is assumed that the liquid–vapor interface has a thickness of 16 nm and liquid–vapor interfacial tension is uniformly distributed over a narrow area. Using superposition method, the theoretical solutions of the deflections of both plates are derived and agree well with the numeric solutions. Numerical simulation results show that when there is a sessile center-aligning droplet on the upper surface of the plates, the plates will bend downward and there are maximum deflections at the center of the wetted area, which are nearly proportional to . Moreover, 3D numerical simulations are made to discuss the effect of plate thickness on surface deformation and found that the surface deformation, decreases with increasing plate thickness. When the plate thickness exceeds the saturated value, it can be regarded as a plate with infinite thickness.

Semi-empirical description of the constant β in the equation of state for interfacial tension

A semi-empirical expression for the constant, β, in the Equation of State (EOS) for interfacial tension is proposed that exhibits a dependence on the surface area, heat capacity and thermal expansion coefficient of each of the materials involved in the three phase equilibrium (at constant temperature and pressure). The “wetting function”, which yields values between zero and unity as the contact angle, θ, varies from 0° to 180°, is also employed in the description of β. Empirical data is used to support that equation as well as the initially proposed relationship leading to its derivation that is based entirely on Classical Nucleation theory (CNT) outcomes and a “difference of the squares” correction term for the liquid–vapor and solid–vapor interfacial tensions.

Corresponding-States Analysis of the Surface Tension of Simple, Polar, and Ionic Fluids

The liquid–vapor interfacial tension of various simple, polar, and ionic fluids is studied in a corresponding-states analysis that was originally suggested by Guggenheim. Data for real fluids are compared to results of simulations and theoretical predictions for model fluids of each of the three types (namely, the Yukawa fluid, the square-well fluid, a fluid consisting of dipolar hard spheres, and the restricted primitive model of ionic fluids). As already demonstrated by Guggenheim, the data for simple and weakly polar fluids map onto a master curve. Strongly dipolar, associating fluids, which may also exhibit hydrogen-bonding (e.g., water), show deviations from this master curve at low temperatures. In addition, the surface tension of these fluids shows a characteristic sigmoid behavior as a function of temperature. A similar behavior is found from simulations of the ionic model fluid, but not from the electrolyte theories available up to now, for which we present new results here. Exceptionally low values of the reduced surface tension are obtained for hydrogen fluoride and for the Onsager model of dipolar fluids, which, however, agree remarkably well with each other in a corresponding-states plot.

Catalytic Nanomotors: Autonomous Movement of Striped Nanorods.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Liquid–vapor interfacial tension of blood plasma, serum and purified protein constituents thereof

A systematic study of water–air (liquid–vapor, LV) interfacial tension γ lv of blood plasma and serum derived from four different mammalian species (human, bovine, ovine and equine) reveals nearly identical concentration-dependence ( d γ lv d ln C B ; where C B is plasma/serum dilution expressed in v/v concentration units). Comparison of results to a previously-published survey of purified human-blood proteins further reveals that d γ lv d ln C B of plasma and serum is surprisingly similar to that of purified protein constituents. It is thus concluded that any combination of blood-protein constituents will be substantially similar because d γ lv d ln C B of individual proteins are very similar. Experimental results are further interpreted in terms of a recently-developed theory emphasizing the controlling role of water in protein adsorption. Accordingly, the LV interphase saturates with protein adsorbed from bulk solution at a fixed weight-volume concentration (∼436 mg/mL) independent of protein identity or mixture. As a direct consequence, d γ lv d ln C B of purified proteins closely resembles that of mixed solutions and does not depend on the relative proportions of individual proteins comprising a mixture. Thus variations in the plasma proteome between species are not reflected in d γ lv d ln C B nor is serum different from plasma in this regard, despite being depleted of coagulation proteins (e.g. fibrinogen). A comparison of pendant-drop and Wilhelmy-balance tensiometry as tools for assessing protein γ lv shows that measurement conditions employed in the typical Wilhelmy plate approach fails to achieve the steady-state adsorption state that is accessible to pendant-drop tensiometry.

Calculation of Solid−Liquid Work of Adhesion Patterns from Combining Rules for Intermolecular Potentials

The thermodynamic work of solid−liquid adhesion is a well-defined property. Their phenomenological patterns relating to surface tensions, however, have not been well-characterized. We employed a hard sphere model to determine the solid−liquid work of adhesion patterns from a mean-field theory through calculations of the liquid−vapor, solid−vapor, and solid−liquid interfacial tensions. By plotting the work of adhesion with the liquid−vapor interfacial tension, we constructed curves that appear to behave in a very regular manner for a variety of combining rules; the curves shift regularly when we increase the strength of solid−solid interaction and hence the solid−vapor surface tension. Contact angle patterns were also constructed via Young's equation. We found that, except Berthelot's rule, the (9:3), Steele, and (12:6) combining rules yield essentially similar adhesion patterns. The regularity of the patterns is remarkable and in reasonable agreement with recent experimental findings. We have shown that m...

Spreading of Surfactant Solutions over Hydrophobic Substrates

The spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid–vapor interfacial tension and hydrophilize the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by our experimental observations.

Thermodynamics of adsorption and gibbsian distance parameters: II. The pressure coefficient of interfacial tension in ternary two- and three-phase systems

The rigorous thermodynamic theory of the pressure coefficient of interfacial tension, for systems containing a surfactant film at a liquid—vapor interface or a liquid—liquid interface, is developed. It is shown that a thickness parameter, λ 21, can be obtained from this measurement. λ 21 is the thickness of the region from which the major components of the respective bulk phases are excluded. In Gibbsian terms, it is the distance between the Γ 1 = 0 and Γ 2 = 0 dividing surfaces, when substance 3 is surface-active. Experiments in which the theory may be applied are discussed, particularly the measurement of liquid—vapor interfacial tension in the presence of a lipid film at its equilibrium spreading pressure. The physical interpretation of Γ 21, on a microscopic scale, is discussed.

On the surface thermodynamics of a two—component liquid-vapor-ideal solid system

The surface thermodynamics of a two—component three—phase solid—liquid—vapor system is considered. Under the assumption that the solid is ideal, i.e., smooth, homogeneous, rigid, and has no appreciable vapor pressure, it is shown that an equation-of-state type of relation exists between the solid—vapor, the solid—liquid, and the liquid—vapor interfacial tensions. The existence of this relation in conjunction with Young's equation makes it, in principle, possible to determine the solid-vapor and the solid—liquid interfacial tensions from contact angles. A test is described which, on the basis of contact angle data for a solid in contact with several liquids, allows one to decide whether or not adsorption of the vapor of the liquids on the solid is appreciable.