Solid-vapor Interfacial Tensions 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.

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.

Free energy of formation of a crystal nucleus in incongruent solidification: Implication for modeling the crystallization of aqueous nitric acid droplets in polar stratospheric clouds.

Using the formalism of classical thermodynamics in the framework of the classical nucleation theory, we derive an expression for the reversible work W* of formation of a binary crystal nucleus in a liquid binary solution of non-stoichiometric composition (incongruent crystallization). Applied to the crystallization of aqueous nitric acid droplets, the new expression more adequately takes account of the effects of nitric acid vapor compared to the conventional expression of MacKenzie, Kulmala, Laaksonen, and Vesala (MKLV) [J. Geophys. Res.: Atmos. 102, 19729 (1997)]. The predictions of both MKLV and modified expressions for the average liquid-solid interfacial tension σls of nitric acid dihydrate (NAD) crystals are compared by using existing experimental data on the incongruent crystallization of aqueous nitric acid droplets of composition relevant to polar stratospheric clouds (PSCs). The predictions for σls based on the MKLV expression are higher by about 5% compared to predictions based on our modified expression. This results in similar differences between the predictions of both expressions for the solid-vapor interfacial tension σsv of NAD crystal nuclei. The latter can be obtained by using the method based on the analysis of experimental data on crystal nucleation rates in aqueous nitric acid droplets; it exploits the dominance of the surface-stimulated mode of crystal nucleation in small droplets and its negligibility in large ones. Applying that method to existing experimental data, our expression for the free energy of formation provides an estimate for σsv of NAD in the range ≈92 dyn/cm to ≈100 dyn/cm, while the MKLV expression predicts it in the range ≈95 dyn/cm to ≈105 dyn/cm. The predictions of both expressions for W* become identical for the case of congruent crystallization; this was also demonstrated by applying our method for determining σsv to the nucleation of nitric acid trihydrate crystals in PSC droplets of stoichiometric composition.

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.

Molecular dynamics analysis on wetting and interfacial properties of water-alcohol mixture droplets on a solid surface.

Molecular dynamics simulations of single water, water-methanol, or water-IPA (isopropyl-alcohol) mixture droplets on a solid surface were performed with various mixture ratios. An increase in alcohol fraction generally gave an increase in droplet wettability. Both methanol and IPA molecules showed a strong preference to gather at various interfaces, with methanol molecules also showing a tendency to diffuse into the droplet bulk. Specific interfacial tensions were investigated using quasi-one-dimensional simulation systems, and liquid-vapor and solid-liquid interfacial tensions were found to decrease greatly due to the presence of interfacial alcohol, while solid-vapor interfacial tensions were proved to have little influence on wettability. Young's relation was found to hold quantitatively well for both water-methanol and water-IPA droplets. The validity of using Bakker's equation on solid-liquid interfaces was also investigated, and it was shown that for tightly spaced crystal surfaces, the introduced uncertainly is small.

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.

ADSA-TRIS: a new method to study interfacial phenomena at polymer–aqueous solution interfaces

Axisymmetric drop shape analysis-profile (ADSA-P) was combined with total reflectometric interference spectroscopy (TRIS) in one experimental setup to study the interfacial phenomena at solid-liquid and liquid-vapor interfaces caused by adsorption/desorption (dissolution) of surface-active substances. Using sessile liquid droplets on polymer film/chromium-coated glass substrates that were optically matched with an immersion oil to a TRIS reflection prism, the optical thickness (product of physical thickness d and refractive index n) of the polymer film can be estimated by evaluating the wavelength-dependent intensity of reflected light. The sessile droplet is analyzed simultaneously by an ADSA setup arranged in a transverse direction to the path of the white-light beam of TRIS. From this analysis, the solid-vapor interfacial tension gamma (lv)(t), contact angle theta(t), contact radius r(t), drop volume V(t), and solid-liquid interfacial tension gamma (sl)(t) can be monitored as a function of time. The new method was applied to study polystyrene and poly(4-hydroxystyrene) surfaces in contact with aqueous buffer solutions and with protein solutions. The time-dependent changes in the optical film thickness caused by the adsorption of human serum albumin (HSA) and lysozyme (LSZ) were accompanied by changes in the solid-liquid interfacial tension. From the detailed study of both parameters, conclusions can be drawn with regard to the adsorption kinetics of the proteins on the hydrophobic polystyrene surfaces and to conformational changes occurring within the adsorbed protein layers.

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.