The influence of droplet size on line tension

Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with hemicylindrical droplets of volatile liquid sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension-which includes the inhomogeneity finite width effects-are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature TW1: for TTW1 the decay is algebraic in the heterogeneity width. In addition, a geometric construction of the corresponding contact angle is carried out and its implications are discussed