Dependence of Surface Tension of a Droplet Formed on the Molecular Condensation Nucleus or Ion on the Droplet Radius
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ndence of Surface Tension of a Droplet Formed on the Molecular Condensation Nucleus or Ion on the Droplet Radius T. S. Lebedevaa, D. Suhb, and A. K. Shchekina,* aSt.
Petersburg University, St. Petersburg, 199034 Russia University of Tokyo, Bunkyo-ku, Tokyo 113-8656 Japan *e-mail: [email protected]
b
Received September 5, 2019; revised September 18, 2019; accepted September 18, 2019
Abstract—The dependence of the thermodynamic surface tension of a small droplet formed on a molecular-size condensation nucleus on the droplet size, nucleus size, molecular field parameters, and nuclear charge in the case of an ion is investigated. Calculations have been performed for molecules of supersaturated argon vapor at different values of the chemical potential of the molecules in the framework of the gradient density functional theory (DFT) and the Carnahan–Starling model to take into account the contribution of hard spheres. The interaction of argon molecules with an uncharged condensation nucleus has been described by the Lennard–Jones potential. In the case of an ion, the long-range Coulomb potential of electric forces is additionally taken into account. The dielectric constant is defined as a function of the local density of the number of argon molecules. As a variable describing the size of the droplet, the radius of the equimolecular surface of the droplet is chosen. The obtained dependences of the surface tension of the droplets have been compared with the dependence of the surface tension on the size of droplet without a condensation nucleus. When the effect of the solvation layer is discarded, the dependence of the surface tension on the radius of the equimolecular surface of a small droplet with a condensation nucleus exhibits similar behavior as in the absence of the nucleus with almost the same negative Tolman correction. The effect of the rigidity constant, however, is clearly influenced by the existence of a condensation nucleus. It is shown that when the first solvation layer is divided around the condensation nucleus, the dependence of surface tension on the radius of the equimolecular surface of a small droplet with a condensation nucleus exhibits similar behavior with almost the same negative Tolman correction as in the absence of a nucleus, but with a different correction, namely, with effective rigidity constant for the surface layer. Keywords: heterogeneous nucleation, droplet, condensation nucleus, surface tension, statistical thermodynamics and mechanics, density functional theory DOI: 10.3103/S0025654420010161
1. INTRODUCTION There are a lot of studies dealing with analyzing the effect of a small droplet size on its surface tension. In [1–4], within the framework of the density functional theory, it was first shown that taking into account only the Tolman correction (proportional to the droplet curvature) is insufficient to describe this dependence, and some contribution to the surface tension that is proportional to the squared curvature and related to the effective rigidity constant of surface layer, mu
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