Analyzing the Molecular Kinetics of Water Spreading on Hydrophobic Surfaces via Molecular Dynamics Simulation

In this paper, we report molecular kinetic analyses of water spreading on hydrophobic surfaces via molecular dynamics simulation. The hydrophobic surfaces are composed of amorphous polytetrafluoroethylene (PTFE) with a static contact angle of ~112.4° for water. On the basis of the molecular kinetic theory (MKT), the influences of both viscous damping and solid-liquid retarding were analyzed in evaluating contact line friction, which characterizes the frictional force on the contact line. The unit displacement length on PTFE was estimated to be ~0.621 nm and is ~4 times as long as the bond length of C-C backbone. The static friction coefficient was found to be ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-3}$$\end{document}10−3 Pa·s, which is on the same order of magnitude as the dynamic viscosity of water, and increases with the droplet size. A nondimensional number defined by the ratio of the standard deviation of wetting velocity to the characteristic wetting velocity was put forward to signify the strength of the inherent contact line fluctuation and unveil the mechanism of enhanced energy dissipation in nanoscale, whereas such effect would become insignificant in macroscale. Moreover, regarding a liquid droplet on hydrophobic or superhydrophobic surfaces, an approximate solution to the base radius development was derived by an asymptotic expansion approach.

where rij is the distance between two atoms, θijk is the angle of bond, and is the dihedral angle.
The detailed parameters are excerpted from the OPLSAA force field 1,2 and listed in Supplementary   Table S1.
To validate the PTFE model, an initial structure with a low density of 800 kg/m 3 was constructed by placing 10 chains of PTFE molecules into a cubic unit cell with dimensions of 3.1724 nm for each edge. As listed in Table 1, the bond length of C-C, which makes up the backbone of polymer chains, is 0.1529 nm, indicative of at least 21 C atoms in each direction of the box. After an energy minimization procedure, the system was brought into an NVT ensemble with temperature of 300 K. Then the system was maintained at temperature of 300 K and pressure of 1 bar to reach a steady density. Then an artificial melting process was applied to the system by increasing the temperature from 300 K to 600 K stepwise at an interval of 50 K in every 40 ps.
The PTFE showed two distinct states corresponding to the rubbery state and glassy state respectively. The specific volume versus temperature profile in rubbery state and glassy state was fitted into two straight lines using linear regression with 95% confidence interval. The detailed fitted parameters for the rubbery state and glassy state are shown in Supplementary Table S2. The intersection between these two straight lines defines the glass transition temperature Tg.
Supplementary Table S1. Force field parameters for PTFE structure 2,3 Lennard-Jones Potential C F Dihedral Potential C-C-C-F C-C-C-C F-C-C-F 0 (kJ/mol) 1.46440 2.92880 -5.23000 1 (kJ/mol) 1.88280 -1.46440 5.23000 The cubic thermal expansion coefficient is defined as The confined layer method was used to construct the smooth PTFE surface. Firstly, 6 PTFE chains were placed into a cubic box periodic only in x and y direction. Two simple cubic lattice structures with lattice constant of 0.2 nm were placed on the top of and at the bottom of the confined PTFE layer to comprise a sandwiched structure. The Lennard-Jones potential of gold atoms 4 was adopted for the virtual lattice structure. Besides, the sandwiched system was made periodic in the x, y and z directions; and the length of the system in z direction was tripled to eliminate the possible imaging effects 1 . Thus-formed system was firstly energy-minimized and then was brought into an NVT ensemble with a temperature of 300 K, during which the forces of the virtual atoms acting on the PTFE molecules were able to smooth out the interface. At last, by removing the top and bottom lattice structures, the PTFE structure with smoothened surfaces was ready to be used in the following wetting simulations. More detailed information on the preparation of smooth PTFE surface can be found in a previous study by Hirvi and Pakkanen 5 .