Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?

Abstract

Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle [Formula: see text] on the droplet radius [Formula: see text] of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on 'thermodynamic' observables, e.g. chemical potential, excess density due to the droplet, etc, is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation [Formula: see text], [Formula: see text] being the contact angle in the thermodynamic limit ([Formula: see text]). The possibility to use such results to estimate the excess free energy related to the contact line of the droplet, namely the line tension, at the wall, is discussed. Various problems that hamper this approach and were not fully recognized in previous attempts to extract the line tension are identified. It is also found that the dependence of wall tensions on the difference of chemical potential of the droplet from that at the bulk coexistence provides effectively a change of the contact angle of similar magnitude. The simulation approach yields precise estimates for the excess density due to wall-attached droplets and the corresponding free energy excess, relative to a system without a droplet at the same chemical potential. It is shown that this information suffices to estimate nucleation barriers, not affected by ambiguities on droplet shape, contact angle and line tension.

Probing the concept of line tension down to the nanoscale

“…5). Line tensions are sometimes assumed to correspond to the curvature dependence of the liquid-vapor surface tension described through the Tolman length 33,34 . Yet, a major difference between effects arising from the stress anisotropy close to the contact line and curvature effects lies in the the spatial distribution of the excess free energy.…”

Entropy Contribution to the Line Tension: Insights from Polymer Physics, Water String Theory and the Three-Phase Tension

“…In spite of the fact that the concept of line tension is intuitively clear, it remains one of the most obscure and disputable notions of the surface science [6][7][8].…”

“…Experimental values of a line tension  in the range of N were reported [6][7][8][9][10][11]. Very few methods allowing experimental measurement of line tension were developed [9][10][11][12][13][14] -9 N, and that it is positive for acute and negative for obtuse Young angles [15][16].…”

Entropy Contribution to the Line Tension: Insights from Polymer Physics, Water String Theory, and the Three-Phase Tension

“…Even though the concept of line tension is intuitively clear, it remains one of the most obscure and disputable notions in surface science [ 6 , 7 , 8 ]. Researchers disagree not only on the value of line tension, but even on its sign.…”

“…Researchers disagree not only on the value of line tension, but even on its sign. Experimental values of line tension in the range of 10 −5 –10 −12 N were reported [ 6 , 7 , 8 , 9 , 10 , 11 ]. Very few methods allowing experimental measurement of line tension were developed [ 9 , 10 , 11 , 12 , 13 , 14 ].…”