On the statistical mechanics of fluids adsorbed in chemically non-symmetric linear wedges

Recent work has seen models of fluids adsorbed in a wedge, or at an edge, emerge as a useful addition to our knowledge of inhomogeneous fluid phenomena, directly relevant to current interest on adsorption at structured substrates (so-called intelligent surfaces). The statistical mechanics of wedge/edge models has led to the identication of wall-fluid virial theorems, linking the thermodynamic properties of adsorbed fluids (surface tensions, line tensions, solvation torques) to integrals over moments of an exact representation of Derjaguin's disjoining pressure. These sum rules have proved particularly interesting for the consideration of capillarity (two-phase coexistence) within wedge geometry. This paper considers, instead, the geometric detail needed to fully de. ne and utilise a wedge/ edge model. Subtle issues arise concerning the choice of coordinate system and the choice of boundary condition far from the apex. Surprisingly, a signicant body of useful results follow from analytic evaluation of the sum rules in the limit of low density (an ideal gas in a wedge). The lessons learnt are particularly relevant to computer simulators wishing to make use of these one-body sum rules and related statistical mechanics. In particular, how to evaluate the sum rule integrals for specific classes of models and what consequences to expect for generalizations to models possessing atomic detail.