Histogram analysis as a method for determining the line tension of a three-phase contact region by Monte Carlo simulations

Abstract

A method is proposed for determining the line tension, which is the main physical characteristic of a three-phase contact region, by Monte Carlo (MC) simulations. The key idea of the proposed method is that if a three-phase equilibrium involves a three-phase contact region, the probability distribution of states of a system as a function of two order parameters depends not only on the surface tension, but also on the line tension. This probability distribution can be obtained as a normalized histogram by appropriate MC simulations, so one can use the combination of histogram analysis and finite-size scaling to study the properties of a three phase contact region. Every histogram and results extracted therefrom will depend on the size of the simulated system. Carrying out MC simulations for a series of system sizes and extrapolating the results, obtained from the corresponding series of histograms, to infinite size, one can determine the line tension of the three phase contact region and the interfacial tensions of all three interfaces (and hence the contact angles) in an infinite system. To illustrate the proposed method, it is applied to the three-dimensional ternary fluid mixture, in which molecular pairs of like species do not interact whereas those of unlike species interact as hard spheres. The simulated results are in agreement with expectations.

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

“…4f as a function of the fluid-solid interaction. The figure shows that the line tension is always negative26, and reaches a minimal value at ε sf = 0.50. Taking σ = 0.37  nm and ε ff = 7.9226 × 10 −21   J 27, the values of the line tension obtained in this work is about 10 −11   J/m .…”

Line tension of a two dimensional gas-liquid interface

“…In this paper we have studied purely gasliquid line tension in 2D system whereas in 3D system there are studies on boundary tension relevant along a prewetting saturation line 25 and a line tension relevant for a droplet with nonzero contact angle on a solid surface. 26 It would be interesting to study the later problems in 2D system.…”

Adsorption of polymers on a brush: Tuning the order of the wetting phase transition

“…At a fixed adsorption the system will adopt the configuration that minimizes the free energy-be it a uniform film, two coexisting films of different thickness, or a droplet. 44,47 Importantly, states that correspond to the minima of the interface potential ͑i.e., the configurations that are pertinent to the equilibrium wetting behavior͒ will correspond to laterally uniform configurations and free energy differences between these states have the usual meaning. The configurations that a system adopts at fixed excess number of particles and their dependence on the system size have been discussed both for thin films on substrates 44 as well as for the periodic simulation cells ͑i.e., bulk simulations͒.…”