Interfacial Free Energy and Tolman Length of Curved Liquid–Solid Interfaces from Equilibrium Studies

Abstract

In this work, we study by means of simulations of hard spheres the equilibrium between a spherical solid cluster and the fluid. In the NVT ensemble we observe stable/metastable clusters of the solid phase in equilibrium with the fluid, representing configurations that are global/local minima of the Helmholtz free energy. Then, we run NpT simulations of the equilibrated system at the average pressure of the NVT run and observe that the clusters are critical because they grow/shrink with a probability of 1/2. Therefore, a crystal cluster equilibrated in the NVT ensemble corresponds to a Gibbs free energy maximum where the nucleus is in unstable equilibrium with the surrounding fluid, in accordance with what has been recently shown for vapor bubbles in equilibrium with the liquid. Then, within the Seeding framework, we use Classical Nucleation Theory to obtain both the interfacial free energy γ and the nucleation rate. The latter is in very good agreement with independent estimates using techniques that do not rely on Classical Nucleation Theory when the mislabeling criterion is used to identify the molecules of the solid cluster. We therefore argue that the radius obtained from the mislabeling criterion provides a good approximation for the radius of tension, R s . We obtain an estimate of the Tolman length by extrapolating the difference between R e (the Gibbs dividing surface) and R s to infinite radius. We show that such definition of the Tolman length coincides with that obtained by fitting γ versus 1/R s to a straight line as recently applied to hard spheres.

Parasitic crystallization of colloidal electrolytes: growing a metastable crystal from the nucleus of a stable phase

“…Consistent with our previous observations for CsCl and disordered fcc clusters, the kinetic pre-factor of HS fcc clusters (see In Fig. 10, we compare the interfacial free energy of HS fcc clusters 20,97 as a function of f l (black symbols) with our results of g for CsCl and disordered fcc clusters. For the three systems, we find very similar values of g versus f l .…”

“…Our results reveal that the interfacial free energy of both solids increases with f l . Assuming a linear dependence of g versus f l , as our data suggest, and as has been successfully proposed for hard-sphere colloids, 20,97 we find that g(f l ) for both crystals is roughly similar. Therefore, we cannot ascribe the differences in the free energy barrier to significant variations in the liquid-crystal interfacial free energy among these two polymorphs.…”

Fcc vs. hcp competition in colloidal hard-sphere nucleation: on their relative stability, interfacial free energy and nucleation rate

“…To model hard-sphere (HS) colloids, we employ the Pseudo-hard-sphere (PHS) continuous potential proposed by Jover et al [118] which quantitatively reproduces many properties of the HS phase behaviour such as the melting pressure [119], equation of state [118], diffusion coefficient [120], surface tension [121] and nucleation rate among many others [86]. The expression for the PHS potential is given by:…”

“…For instance, the validity of the Classical Nucleation Theory (CNT) [77,78] to successfully describe nucleation in widely diverse scenarios is still a matter of debate [76,[79][80][81]. While a considerable body of literature supports its applicability to provide fair predictions on the nucleation behaviour of many substances [82][83][84][85], as for the case of hard-spheres [29,55,86], other substantial studies have pointed out its limitations when describing certain specific systems [87][88][89][90] (even for hard-spheres [81]), or when assuming different approximations (i.e., the capillary approximation: the fact that the surface tension of a planar interface is roughly the same as that of the clusters) [91]. In that respect, the nucleation mechanisms of certain 'so-called' simple fluids such as hard-sphere colloidal particles [36,74,81,92], water [44,[93][94][95], or Lennard-Jones fluids [96,97] remain yet hotly debated.…”

Strong Coupling and Nonextensive Thermodynamics

“…In 1949, Tolman used elaborate classical theory and proposed a law (see in [ 28 ] eq. 4.3) whose applicability at the nanoscale has just been established [ 29 ]. As shown below, this law, and its applicability to small, strongly coupled systems, becomes a straightforward result in the framework of TSC.…”