{
  "id": "1805.03408",
  "version": "v1",
  "published": "2018-05-09T08:23:41.000Z",
  "updated": "2018-05-09T08:23:41.000Z",
  "title": "Continuous condensation in nanogrooves",
  "authors": [
    "Alexandr Malijevský"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider condensation in a capillary groove of width $L$ and depth $D$, formed by walls that are completely wet (contact angle $\\theta=0$), which is in a contact with a gas reservoir of the chemical potential $\\mu$. On a mesoscopic level, the condensation process can be described in terms of the midpoint height $\\ell$ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves ($D\\to\\infty$), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second order phase transition, such that $\\ell\\sim (\\mu_{cc}-\\mu)^{-1/4}$ as $\\mu\\to\\mu_{cc}^-$ where $\\mu_{cc}$ is the chemical potential pertinent to capillary condensation in a slit pore of width $L$. For finite values of $D$, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than $\\mu_{cc}$ with a difference of the order of $D^{-3}$. For sufficiently deep grooves, the meniscus growth initially follows the power-law $\\ell\\sim (\\mu_{cc}-\\mu)^{-1/4}$ but this behaviour eventually crosses over to $\\ell\\sim D-(\\mu-\\mu_{cc})^{-1/3}$ above $\\mu_{cc}$, with a gap between the two regimes shown to be $\\bar{\\delta}\\mu\\sim D^{-3}$. Right at $\\mu=\\mu_{cc}$, when the groove is only partially filled with liquid, the height of the meniscus scales as $\\ell^*\\sim (D^3L)^{1/4}$. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a non-monotonic dependence on $D$ with a maximum at $D\\approx 3L/2$ and coincides with $\\mu_{cc}$ when $L\\approx D$. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance $D$ apart with potential strengths depending on $L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-09T08:23:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chemical potential",
      "continuous condensation",
      "nanogrooves",
      "second order phase transition",
      "non-monotonic dependence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}