{
  "id": "2106.08604",
  "version": "v1",
  "published": "2021-06-16T08:03:26.000Z",
  "updated": "2021-06-16T08:03:26.000Z",
  "title": "Droplet condensation in the lattice gas with density functional theory",
  "authors": [
    "Manuel Maeritz",
    "Martin Oettel"
  ],
  "comment": "14 pages, 8 figures, to be published in Phys. Rev. E",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "A density functional for the lattice gas (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density $\\bar\\rho$ in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential $\\mu(\\bar\\rho)$ are seen upon lowering the temperature away from the critical temperature (oscillations in $\\mu(\\bar\\rho)$ in the slab portion and spiky undulations in $\\mu(\\bar\\rho)$ in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension $R_s$ in the droplet region). This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension $\\gamma(R_s)$ gave a dominant contribution $\\propto 1/R_s^2$, although the consistency of $\\gamma(R_s)$ with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution $\\propto \\ln R_s/R_s^2$ in $\\gamma(R_s)$. The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-16T08:03:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density functional theory",
      "lattice gas",
      "droplet condensation",
      "droplet region",
      "fundamental measure theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}