Accurate determination of the vapor-liquid-solid contact line tension and the viability of Young equation

In this work, we present a theoretical method to determine the line tension of nanodroplets on homogeneous substrates via decomposing the grand free energy into volume, interface and line contributions. With the obtained line tension, we check the viability of Young equation and find that the chemical potential dependence (or equivalently, droplet curvature dependence) of the interface tensions is crucial for the viability of modified Young equation at the nanometer scale. In particular, the linear relationship between the cosine of contact angle and the curvature of the contact line, which is often used to determine the line tension, is found to be incorrect at the nanometer scale.

[1]  A. Laio,et al.  Systematic improvement of classical nucleation theory. , 2012, Physical review letters.

[2]  G. Tarjus,et al.  Capillary Condensation in Disordered Porous Materials , 2001 .

[3]  J. Drelich.  The significance and magnitude of the line tension in three-phase (solid-liquid-fluid) systems , 1996 .

[4]  K. Binder,et al.  Simulation of vapor-liquid coexistence in finite volumes: a method to compute the surface free energy of droplets. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Hans-Jürgen Butt,et al.  On the derivation of Young's equation for sessile drops: nonequilibrium effects due to evaporation. , 2007, The journal of physical chemistry. B.

[6]  C. A. Ward,et al.  Effect of contact line curvature on solid-fluid surface tensions without line tension. , 2008, Physical review letters.

[7]  P. Attard,et al.  Curvature-dependent surface tension of a growing droplet. , 2003, Physical review letters.

[8]  A. Méndez-Vilas,et al.  Ultrasmall liquid droplets on solid surfaces: production, imaging, and relevance for current wetting research. , 2009, Small.

[9]  S. Herminghaus,et al.  Three-phase contact line energetics from nanoscale liquid surface topographies , 2000, Physical review letters.

[10]  Nucleation in hydrophobic cylindrical pores: a lattice model. , 2004, The journal of physical chemistry. B.

[11]  Paul F. Nealey,et al.  Wetting Behavior of Block Copolymers on Self-Assembled Films of Alkylchlorosiloxanes: Effect of Grafting Density , 2000 .

[12]  Conceptual aspects of line tensions. , 2007, The Journal of chemical physics.

[13]  A. Dillmann,et al.  A refined droplet approach to the problem of homogeneous nucleation from the vapor phase , 1991 .

[14]  M. Anisimov.  Divergence of Tolman's length for a droplet near the critical point. , 2007, Physical review letters.

[15]  Haiping Fang,et al.  Critical Dipole Length for the Wetting Transition Due to Collective Water-dipoles Interactions , 2012, Scientific Reports.

[16]  M. Ratner,et al.  Capillary force in atomic force microscopy. , 2004, The Journal of chemical physics.

[17]  Heinrich M. Jaeger,et al.  Hierarchical self-assembly of metal nanostructures on diblock copolymer scaffolds , 2001, Nature.

[18]  Xianren Zhang,et al.  Physical basis for constrained lattice density functional theory. , 2012, The Journal of chemical physics.

[19]  K. Binder,et al.  Monte Carlo test of the classical theory for heterogeneous nucleation barriers. , 2009, Physical review letters.

[20]  P. A. Monson.  Mean field kinetic theory for a lattice gas model of fluids confined in porous materials. , 2008, Journal of Chemical Physics.

[21]  M. Fisher,et al.  Curvature corrections to the surface tension of fluid drops: Landau theory and a scaling hypothesis , 1984 .

[22]  A. Amirfazli,et al.  Status of the three-phase line tension: a review. , 2004, Advances in colloid and interface science.

[23]  Histogram analysis as a method for determining the line tension of a three-phase contact region by Monte Carlo simulations. , 2004, The Journal of chemical physics.

[24]  D. Frenkel,et al.  Line tension controls wall-induced crystal nucleation in hard-sphere colloids. , 2003, Physical review letters.

[25]  A. Checco,et al.  Nonlinear dependence of the contact angle of nanodroplets on contact line curvature. , 2003, Physical review letters.

[26]  Wenchuan Wang,et al.  Nucleation and hysteresis of vapor-liquid phase transitions in confined spaces: effects of fluid-wall interaction. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  D. Lohse,et al.  Origin of line tension for a Lennard-Jones nanodroplet , 2010, 1010.0517.

[28]  G. Whitesides,et al.  Flexible Methods for Microfluidics , 2001 .

[29]  H. Schulze,et al.  Some new observations on line tension of microscopic droplets , 1999 .