# Colloquium 7/18/2011

Kurt Binder, Institut für Physik, Universität Mainz

## Monte Carlo Methods for estimating interfacial free energies and line tensions

The surface free energy of (spherical) droplets (or bubbles,respectively) is obtained by a thermodynamic method for three models: Ising model, binary symmetric Lennard Jones mixture, simple Lennard-Jones fluid.It is shown that for the symmetric models the surface free energy depends on the droplet radius to leading order via a correction of order one over the droplet radius square.The coefficient of this correction is of the order of the molecular diameter. For the Lennard-Jones fluid, an additional small correction of order one over the droplet radius is found,the coefficient(Tolman length) being only a tenth of the molecular diameter. A corresponding analysis of wall-attached droplets, where one uses the above results and information on the contact angle (independently obtained) as an input, estimates of barriers against heterogeneous nucleation are inferred, as well as estimates for the line tension as function of the contact angle. For the binary Lennard-Jones mixture, which undergoes a first order wetting transition, it is found that the line tension changes sign (it is negative at large contact angles) at an angle of about 30 degrees, in good agreement with density functional predictions.

Work done in collaboration with B.J. Block, S.K. Das, P. Virnau and D.Winter, see

- B.J. Block et al., JCP 133, 154702 (2010)
- S.K. Das and K.B., Mol.Phys. 109, 1043 (2011)
- D.Winter et.al., PRL 103, 225703 (2009)