The surface energy of the nucleus of a stable phase growing in the presence of several amorphous metastable phases of character intermediate between the initial and the final phases may depend non-trivially on the size of the nucleus. This size dependence is being increasingly used to explain diverse non-equilibrium phase selection, and relaxation, as in the random first-order transition (RFOT) theory of glasses. Here we develop an order parameter based Ginzburg-Landau approach that explicitly includes the rugged free energy landscape due to the metastable phases. The fractional dependence of total surface energy between melt and stable solid phase on the number of metastable phases($N_{MS}$) has been interrogated in this study. We have also analyzed how this fractional dependence gets modified with temperature. We find that the fractional size dependence of surface energy is omnipresent, arises from the minimization of free energy and demands certain ordering of metastable phases in the interface. Our results could recover the celebrated result of Villain that forms the basis of RFOT theory of glasses. We find the additional result that the surface tension saturates to a finite size independent value.
We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated anal…
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach we derive close formulas for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-monotonous dependence of the surface tension on the peak of the density of the suspended phase. Our results also predict the local value of the surface tension in the case in which the density of the suspended phase is not homogeneous along the interface…
We present a new finite deformation, dynamic finite element model that incorporates surface tension to capture elastocapillary effects on the electromechanical deformation of dielectric elastomers. We demonstrate the significant effect that surface tension can have on the deformation of dielectric elastomers through three numerical examples: (1) surface tension effects on the deformation of single finite elements with homogeneous and inhomogeneous boundary conditions; (2) surface tension effects on instabilities in constrained dielectric elastomer films, and (3) surface tension effects on burs…
Condensation and boiling are phase transitions highly relevant to industry, geology or atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult …
Molecular anatomy of the pressure anisotropy in the interface of one and two component fluids: local thermodynamic description of the interfacial tension
We present a microscopic theory for the nonequilibrium interfacial tension $γ_{\rm gl}$ of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find $γ_{\rm gl}\geq 0$, which opposes claims by Bialké et al. [Phys. Rev. Lett. $\bf{115}$, 098301 (2015)] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simul…
The long-range contribution to dispersion forces is known to have a major impact on the properties of inhomogeneous fluids, and its correct treatment is increasingly recognized as being a necessary requirement to avoid cutoff-related artefacts. Although analytical corrections for quantities like the surface tension are known, these can not take into account the structural changes induced by the long-range contributions. Here, we analyze the interfacial properties of seven popular water models, comparing the results with the cut-off version of the dispersion potential. The differences in surfac…
Surface tension plays a ubiquitous role in phase transitions including condensation or evaporation of atmospheric liquid droplets. Especially, understanding of interfacial thermodynamics of the critical nucleus of 1 nm scale is important for molecular characterization of the activation energy barrier of nucleation. Here, we investigate surface tension of spherical nanodroplets with both molecular dynamics and density functional theory, and find that surface tension decreases appreciably below 1 nm radius, whose analytic expression is consistently derived from the classic Tolman's equation. In …
In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard-Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory (FMT), di…
This paper considers the stress-induced phase transitions of shape memory alloy slender cylinder, and analytically studies the phase transition process and the associated instability. A three-dimensional (3D) phenomenological model with an internal variable is adopted, which is simplified to a 1D system of two strains in three regions (austenite, martensite and phase transition regions). Suitable boundary conditions and interface conditions are proposed. Theoretically, it is a free boundary problem, as the position and shape of phase interfaces are unknown. We then focus on planar interfaces (…
The preferential formation of one solid over the other, as it precipitates out from the melt at specific temperatures, is often explained by invoking a competition between thermodynamic and kinetic control. A quantitative theory, however, could not be developed because of the lack of accurate values of relevant surface tension terms. Motivated by the observations that wetting of the interface between two stable phases by multiple metastable phases of intermediate order can reduce the surface tension significantly (Kirkpatrick-Thirumalai-Wolynes (KTW), Phys. Rev. A 1989, 40 (2), 1045; Santra et…
