On the interfacial thermodynamics of nanoscale droplets and bubbles

An investigation of the kinetics and thermodynamics of NaCl nucleation through composite clusters

Having a good understanding of nucleation is critical for the control of many important processes, such as polymorph selection during crystallization. However, a complete picture of the molecular-level mechanisms of nucleation remains elusive. In this work, we take an in-depth look at the NaCl homogeneous nucleation mechanism through thermodynamics. Distinguished from the classical nucleation theory, we calculate the free energy of nucleation as a function of two nucleus size coordinates: crystalline and amorphous cluster sizes. The free energy surface reveals a thermodynamic preference for a nonclassical mechanism of nucleation through a composite cluster, where the crystalline nucleus is surrounded by an amorphous layer. The thickness of the amorphous layer increases with an increase in supersaturation. The computed free energy landscape agrees well with the composite cluster-free energy model, through which phase specific thermodynamic properties are evaluated. As the supersaturation increases, there is a change in stability of the amorphous phase relative to the solution phase, resulting in a change from one-step to two-step mechanism, seen clearly from the free energy profile along the minimum free energy path crossing the transition curve. By obtaining phase-specific diffusion coefficients, we construct the full mesoscopic model and present a clear roadmap for NaCl nucleation.

Formation free energy of an i-mer at spinodal

In statistical mechanics, the formation free energy of an i-mer can be understood as the Gibbs free energy change in a system consisting of pure monomers after and prior to the formation of the i-mer. For molecules interacting via Lennard-Jones potential, we have computed the formation free energy of a Stillinger i-mer [F. H. Stillinger, J. Chem. Phys. 38, 1486 (1963)] and a ten Wolde-Frenkel (tWF) [P. R. ten Wolde and D. Frenkel, J. Chem. Phys. 109, 9901 (1998)] i-mer at spinodal at reduced temperatures from 0.7 to 1.2. It turns out that the size of a critical Stillinger i-mer remains finite and its formation free energy is on the order of k_BT, and the size of a critical tWF i-mer remains finite and its formation free energy is even higher. This can be explained by Binder's theory [K. Binder, Phys. Rev. A 29, 341 (1984)] that for a system, when approaching spinodal, if the Ginzburg criterion is not satisfied, a gradual transition will take place from nucleation to spinodal decomposition, where the free-energy barrier height is on the order of k_BT.

What experiments on pinned nanobubbles can tell about the critical nucleus for bubble nucleation

The process of homogeneous bubble nucleation is almost impossible to probe experimentally, except near the critical point or for liquids under large negative tension. Elsewhere in the phase diagram, the bubble nucleation barrier is so high as to be effectively insurmountable. Consequently, there is a severe lack of experimental studies of homogenous bubble nucleation under conditions of practical importance (e.g., cavitation). Here we use a simple geometric relation to show that we can obtain information about the homogeneous nucleation process from Molecular Dynamics studies of bubble formation in solvophobic nanopores on a solid surface. The free energy of pinned nanobubbles has two extrema as a function of volume: one state corresponds to a free-energy maximum ("the critical nucleus"), the other corresponds to a free-energy minimum (the metastable, pinned nanobubble). Provided that the surface tension does not depend on nanobubble curvature, the radius of the curvature of the metastable surface nanobubble is independent of the radius of the pore and is equal to the radius of the critical nucleus in homogenous bubble nucleation. This observation opens the way to probe the parameters that determine homogeneous bubble nucleation under experimentally accessible conditions, e.g. with AFM studies of metastable nanobubbles. Our theoretical analysis also indicates that a surface with pores of different sizes can be used to determine the curvature corrections to the surface tension. Our conclusions are not limited to bubble nucleation but suggest that a similar approach could be used to probe the structure of critical nuclei in crystal nucleation.

Communication: superstabilization of fluids in nanocontainers

One of the main challenges of thermodynamics is to predict and measure accurately the properties of metastable fluids. Investigation of these fluids is hindered by their spontaneous transformation by nucleation into a more stable phase. We show how small closed containers can be used to completely prevent nucleation, achieving infinitely long-lived metastable states. Using a general thermodynamic framework, we derive simple formulas to predict accurately the conditions (container sizes) at which this superstabilization takes place and it becomes impossible to form a new stable phase. This phenomenon opens the door to control nucleation of deeply metastable fluids at experimentally feasible conditions, having important implications in a wide variety of fields.

Size-Dependent Surface Free Energy and Tolman-Corrected Droplet Nucleation of TIP4P/2005 Water

Classical nucleation theory is notoriously inaccurate when using the macroscopic surface free energy for a planar interface. We examine the size dependence of the surface free energy for TIP4P/2005 water nanodroplets (radii ranging from 0.7 to 1.6 nm) at 300 K with the mitosis method, that is, by reversibly splitting the droplets into two subclusters. We calculate the Tolman length to be -0.56 ± 0.09 Å, which indicates that the surface free energy of water droplets that we investigated is 5-11 mJ/m(2) greater than the planar surface free energy. We incorporate the computed Tolman length into a modified classical nucleation theory (δ-CNT) and obtain modified expressions for the critical nucleus size and barrier height. δ-CNT leads to excellent agreement with independently measured nucleation kinetics.

Toward a molecular theory of homogeneous bubble nucleation: II. Calculation of the number density of critical nuclei and the rate of nucleation

In the present paper, we develop a method to calculate the rate of homogeneous bubble nucleation within a superheated L-J liquid based on the (n,v) equilibrium embryo free energy surface introduced in the first paper (DOI: 10.1021/jp404149n). We express the nucleation rate as the product of the concentration of critical nuclei within the metastable liquid phase and the relevant forward rate coefficient. We calculate the forward rate coefficient of the critical nuclei from their average lifetime as determined from MD simulations of a large number of embryo trajectories initiated from the transitional region of the metastable liquid configuration space. Therefore, the proposed rate coefficient does not rely on any predefined reaction coordinate. In our model, the critical nuclei belong to the region of the configuration space where the committor probability is about one-half, guaranteeing the dynamical relevance of the proposed embryos. One novel characteristic of our approach is that we define a limit for the configuration space of the equilibrium metastable phase and do not include the configurations that have zero committor probability in the nucleation free energy surface. Furthermore, in order to take into account the transitional degrees of freedom of the critical nuclei, we develop a simulation-based approach for rigorously mapping the free energy of the (n,v) equilibrium embryos to the concentration of the critical nuclei within the bulk metastable liquid phase.

A perspective on the interfacial properties of nanoscopic liquid drops

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 surface tension with the drop radius are predicted for the LJ fluid. Finally, the limits of the validity of the Tolman approach, the effect of the range of the intermolecular potential, and the behaviour of bubbles are briefly discussed.