Surface tension of spherical drops from surface of tension

Probing the Free Energy of Small Water Clusters: Revisiting Classical Nucleation Theory

By addressing the defects in classical nucleation theory (CNT), we develop an approach for extracting the free energy of small water clusters from nucleation rate experiments without any assumptions about the form of the cluster free energy. For temperatures higher than ∼250 K, the extracted free energies from experimental data points indicate that their ratio to the free energies predicted by CNT exhibits nonmonotonic behavior as the cluster size changes. We show that this ratio increases from almost zero for monomers and passes through (at least) one maximum before approaching one for large clusters. For temperatures lower than ∼250 K, the behavior of the ratio between extracted energies and CNT's prediction changes; it increases with cluster size, but it remains below one for almost all of the experimental data points. We also applied a state-of-the-art quantum mechanics model to calculate free energies of water clusters (2-14 molecules); the results support the observed change in behavior based on temperature, albeit for temperatures above and below ∼298 K. We compared two different model chemistries, DLPNO-CCSD(T)/CBS//ωB97xD/6-31++G** and G3, against each other and the experimental value for formation of the water dimer.

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

Liquid-vapor surface tension (ST) in nanopores attracts great attention in many industries because of the prosperity of nanoscience and nanotechnology. Here, considering the important emerging new physical phenomena induced by nanoconfinement effects, including curvature-dependent and shift-critical temperature (T_c)-dependent effects, the anomalous variation of ST in nanopores is captured from the molecular potential perspective. Furthermore, a simple analytical model is proposed to determine the ST in nanopores by correlating these two effects with an easily accessible parameter, that is, normalized pore dimension, which is the ratio of the pore radius to Lennard-Jones size parameter. The model is validated to be reliable for determining the STs of different substances both in the bulk phase as well as nanopores through comparison with the experimental results and molecular simulations. Our results show that the reduction of ST induced by the nanoconfinement effects is visible when the pore diameter is within tens of nanometers, and the reduction is more sensitive as the pore size decreases. In detail, the curvature-dependent effect is remarkable in the pores with diameters ranging from a few nanometers to tens of nanometers. Moreover, a simply generalized formula is obtained to determine the curvature-dependent effect and the Tolman length for different substances. The shift-T_c-dependent effect is not only related to the pore dimension but also depends on the temperature. As the pore size decreases, the critical temperature of confined fluids diverges significantly from the bulk values. While at high temperatures, the range of pore size impacted by the shift-Tc-dependent effect is enlarged. Additionally, the nanoconfined STs of different substances are calculated and compared. Overall, the new model captures the underlying physics behind the variation of STs in nanopores and can determine the nanoconfined STs reasonably. Moreover, the simple formulation of the model is beneficial to the practical applications in many chemical engineering processes, such as chemical separation, nucleation phenomenon, and capillary condensation.

Importance of the tail corrections on surface tension of curved liquid-vapor interfaces

We report molecular simulations of the liquid-vapor cylindrical interface of methane. We apply the truncated Lennard-Jones potential and specific long-range corrections for the surface tension developed especially for cylindrical interfaces. We investigate the impact of the cutoff on the radial density profile, the intrinsic and long-range correction parts to the surface tension, and Tolman length. We also study the curvature dependence of the surface tension as a function of the cutoff used. In this work we shed light that both density and Tolman length are cutoff-dependent whereas the total surface tension is slightly curvature and cutoff dependent.

Effectiveness of the Young-Laplace equation at nanoscale

Using molecular dynamics (MD) simulations, a new approach based on the behavior of pressurized water out of a nanopore (1.3–2.7 nm) in a flat plate is developed to calculate the relationship between the water surface curvature and the pressure difference across water surface. It is found that the water surface curvature is inversely proportional to the pressure difference across surface at nanoscale, and this relationship will be effective for different pore size, temperature, and even for electrolyte solutions. Based on the present results, we cannot only effectively determine the surface tension of water and the effects of temperature or electrolyte ions on the surface tension, but also show that the Young-Laplace (Y-L) equation is valid at nanoscale. In addition, the contact angle of water with the hydrophilic material can be further calculated by the relationship between the critical instable pressure of water surface (burst pressure) and nanopore size. Combining with the infiltration behavior of water into hydrophobic microchannels, the contact angle of water at nanoscale can be more accurately determined by measuring the critical pressure causing the instability of water surface, based on which the uncertainty of measuring the contact angle of water at nanoscale is highly reduced.

Confinement Correction to Mercury Intrusion Capillary Pressure of Shale Nanopores

We optimized potential parameters in a molecular dynamics model to reproduce the experimental contact angle of a macroscopic mercury droplet on graphite. With the tuned potential, we studied the effects of pore size, geometry, and temperature on the wetting of mercury droplets confined in organic-rich shale nanopores. The contact angle of mercury in a circular pore increases exponentially as pore size decreases. In conjunction with the curvature-dependent surface tension of liquid droplets predicted from a theoretical model, we proposed a technique to correct the common interpretation procedure of mercury intrusion capillary pressure (MICP) measurement for nanoporous material such as shale. Considering the variation of contact angle and surface tension with pore size improves the agreement between MICP and adsorption-derived pore size distribution, especially for pores having a radius smaller than 5 nm. The relative error produced in ignoring these effects could be as high as 44%--samples that contain smaller pores deviate more. We also explored the impacts of pore size and temperature on the surface tension and contact angle of water/vapor and oil/gas systems, by which the capillary pressure of water/oil/gas in shale can be obtained from MICP. This information is fundamental to understanding multiphase flow behavior in shale systems.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.