A perspective on the interfacial properties of nanoscopic liquid drops

Abstract

The structural and interfacial properties of nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the macroscopic level and the microscopic level of density functional theory (DFT). With a novel analysis we show that a purely macroscopic (static) mechanical treatment can lead to a qualitatively reasonable description of the surface tension and the Tolman length of a liquid drop; the latter parameter, which characterizes the curvature dependence of the tension, is found to be negative and has a magnitude of about a half of the molecular dimension. A mechanical slant cannot, however, be considered satisfactory for small finite-size systems where fluctuation effects are significant. From the opposite perspective, a curvature expansion of the macroscopic thermodynamic properties (density and chemical potential) is then used to demonstrate that a purely thermodynamic approach of this type cannot in itself correctly account for the curvature correction of the surface tension of liquid drops. We emphasize that any approach, e.g., classical nucleation theory, which is based on a purely macroscopic viewpoint, does not lead to a reliable representation when the radius of the drop becomes microscopic. The description of the enhanced inhomogeneity exhibited by small drops (particularly in the dense interior) necessitates a treatment at the molecular level to account for finite-size and surface effects correctly. The so-called mechanical route, which corresponds to a molecular-level extension of the macroscopic theory of elasticity and is particularly popular in molecular dynamics simulation, also appears to be unreliable due to the inherent ambiguity in the definition of the microscopic pressure tensor, an observation which has been known for decades but is frequently ignored. The union of the theory of capillarity (developed in the nineteenth century by Gibbs and then promoted by Tolman) with a microscopic DFT treatment allows for a direct and unambiguous description of the interfacial properties of drops of arbitrary size; DFT provides all of the bulk and surface characteristics of the system that are required to uniquely define its thermodynamic properties. In this vein, we propose a non-local mean-field DFT for Lennard-Jones (LJ) fluids to examine drops of varying size. A comparison of the predictions of our DFT with recent simulation data based on a second-order fluctuation analysis (Sampayo et al 2010 J. Chem. Phys. 132 141101) reveals the consistency of the two treatments. This observation highlights the significance of fluctuation effects in small drops, which give rise to additional entropic (thermal non-mechanical) contributions, in contrast to what one observes in the case of planar interfaces which are governed by the laws of mechanical equilibrium. A small negative Tolman length (which is found to be about a tenth of the molecular diameter) and a non-monotonic behaviour of the surf...

Communication: Slab thickness dependence of the surface tension: Toward a criterion of liquid sheets stability

“…The behavior of the surface tension with the slab thickness seems analogous to that observed for liquid drops with increasing the surface curvature. [29][30][31][32][33] Simulations of drops and cylinders are currently under progress to investigate this point.…”

On the Calculation of Solid-Fluid Contact Angles from Molecular Dynamics

“…Furthermore, for very small nanoclusters, the fluid interfacial tension is a function of the curvature, and the planar limit is, in some cases, not recovered even after drop radii of 14 times the molecular diameter [10,11]. The change in the line tension with curvature (discussed in the latter part of this manuscript) is also an important factor affecting the result.…”

Pressure Tensor of Nanoscopic Liquid Drops

“…On the other hand, the results for systems of one or several components are self-consistent because the prediction for the mixture is reduced to the case of a single component when you take t = 1, and the results with multiple Gibbs dividing surfaces are reduced to the case of a single dividing surface when the choice is made on R i = R j = R. Finally, we emphasize that in this study, we have not only obtained consistent results with those in the literature, but we have gone beyond, considering the fluid mixture with an arbitrary number of components. However, the description of the behavior of the spherical interface in systems of one or several components is far from being a closed issue, because the numerical determination of its properties is not free of ambiguities [4,5,12,22]. We will address this task in the near future.…”

“…The relevance of this issue lies in the different situations in which the phenomenon occurs, for example in the nucleation of nanoscale drops or bubbles, wetting and drying, technology design for environmental pollution, and problems with recovering oil from porous rock [1][2][3][4][5].…”

“…The calculation of the microscopic expressions of the coefficients introduced in this model is a difficult task in the statistical physics of inhomogeneous fluids; although it has been made from different routes, it is still a subject of analysis and discussion [5,12,22]. We emphasize in this study calculating the microscopic expressions of the pressure difference between the two phases of a single and multicomponent system using the stress tensor in the mean field derived by Romero-Percus [23,24].…”