Elastic theory of surface deformation in molecular physisorption

In molecular physisorption, beyond attractive and repulsive forces, a third contribution arises from the elastic deformation of the surface. In the present work the dimple appearing on a deformable surface upon physisorption of a foreign molecule is studied and its effect on the adsorption energy is calculated. The depth and shape of the physisorption dimple are studied on the basis of the theory of elasticity. The problem of the deformation of a semi-infinite elastic medium, subject to central body forces, is solved, with the centre (i.e., the molecule) placed outside the medium. A vectorial Poisson equation for the displacement field is solved with the boundary condition that no surface forces act. For a centrosymmetrical molecule the solution is obtained in two steps, whose results are then superposed: (1) the deformation field in an infinite elastic medium subject to a central body force field, whose centre coincides with the centre of the molecule, is evaluated (the solution generates mismatch of the boundary conditions); (2) a complementary homogeneous problem is solved with boundary conditions compensating the spurious contributions generated in step (1). Specific attention is given to methane adsorption both on a metal surface (Au) and on a molecular crystal surface (solid Ar). The shape function zeta(R) is always positive (indicating a bulging surface) if the distance z of the molecule (i.e., of the carbon atom) from the surface is large, but becomes largely negative for z smaller, showing a definite dimple. The minimum energy (adsorption equilibrium) corresponds to the latter case. The dimple depth turns out to be 10.0 pm in the case of Au, while for Ar we find a depth of 30.5 pm at 80 K and 25.6 pm at 0 K. A discussion of the asymptotic behaviour (proportional, off equilibrium, to R-1) of the deformation at long distances R from the adsorbed molecule is also given. (c) 2005 Elsevier B.V. All rights reserved.