On interfacial free energy versus interfacial stress of fluids adsorbed on chemically patterned surfaces: lessons from the special case of striped substrates

The statistical mechanics of fluids adsorbed on chemically patterned surfaces is far from straightforward when attempting to develop virial theorems for the interfacial free energy. This is because in general one would have to devise new procedures to distinguish surface tension from surface stress, even for wall-fluid models where the substrate atoms are replaced by an effective external field. However, the distinction may be made explicit for the special case of striped walls. This paper makes use of striped wall-fluid models to discuss the significance of fluid interfacial stress to patterned inhomogeneous fluids. In particular, it considers the adsorption of hemicylindrical drops on an array of high energy stripes. For the planar stripe geometry it is also possible to make effective use of the pressure tensor formalism. Beyond the special case of striped patterns it is not possible to use standard procedures based on virial theorems to directly evaluate interfacial free energy. The lessons learnt from these exercises apply especially to computer simulation studies of patterned inhomogeneous fluids.