The CassieWenzel transition of fluids on nanostructured substrates: Macroscopic force balance versus microscopic densityfunctional theory
Abstract
Classical density functional theory is applied to investigate the validity of a phenomenological forcebalance description of the stability of the Cassie state of liquids on substrates with nanoscale corrugation. A bulk freeenergy functional of third order in local density is combined with a squaregradient term, describing the liquidvapor interface. The bulk free energy is parameterized to reproduce the liquid density and the compressibility of water. The squaregradient term is adjusted to model the width of the watervapor interface. The substrate is modeled by an external potential, based upon the LennardJones interactions. The threedimensional calculation focuses on substrates patterned with nanostripes and squareshaped nanopillars. Using both the forcebalance relation and densityfunctional theory, we locate the CassietoWenzel transition as a function of the corrugation parameters. We demonstrate that the forcebalance relation gives a qualitatively reasonable description of the transition even on the nanoscale. The force balance utilizes an effective contact angle between the fluid and the vertical wall of the corrugation to parameterize the impalement pressure. This effective angle is found to have values smaller than the Young contact angle. This observation corresponds to an impalement pressure that is smaller than the value predicted by macroscopic theory. Therefore, this effective angle embodies effects specific to nanoscopically corrugated surfaces, including the finite range of the liquidsolid potential (which has both repulsive and attractive parts), line tension, and the finite interface thickness. Consistently with this picture, both patterns (stripes and pillars) yield the same effective contact angles for large periods of corrugation.
 Publication:

Journal of Chemical Physics
 Pub Date:
 October 2016
 DOI:
 10.1063/1.4963792
 arXiv:
 arXiv:1607.01636
 Bibcode:
 2016JChPh.145m4703T
 Keywords:

 Physics  Chemical Physics
 EPrint:
 13 pages 9 figures