Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width 2L placed on an otherwise homogeneous, planar, solid surface. The excess point free energy eta(L,T) associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way eta(L,T) varies with L depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of L in the limit L-->infinity for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case eta(L,T) converges for large L to 2eta0, where eta0 is the corresponding point tension, and the dominant L-dependent correction to 2eta0 decays exponentially. The interaction between the liquid layer inhomogeneities at -L and L for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.