Particle on or near an Infinite Surface

A more efficient approach is to base the boundary-integral formulation on a fundamental solution (or more accurately a Green s function) that incorporates the relevant boundary conditions at one or more of the surfaces. In the case of a particle or drop moving near an infinite plane wall, this means finding a solution for a point force that exactly satisfies the no-slip and kinematic boundary conditions at the wall. If we were to consider the motion of a particle or drop in a tube, it would be useful to have the solution for a point force satisfying the same conditions on the tube walls. 

The valence band structure of very small metal crystallites is expected to differ from that of an infinite crystal for a number of reasons (a) with a ratio of surface to bulk atoms approaching unity (ca. 2 nm diameter), the potential seen by the nearly free valence electrons will be very different from the periodic potential of an infinite crystal (b) surface states, if they exist, would be expected to dominate the electronic density of states (DOS) (c) the electronic DOS of very small metal crystallites on a support surface will be affected by the metal-support interactions. It is essential to determine at what crystallite size (or number of atoms per crystallite) the electronic density of sates begins to depart from that of the infinite crystal, as the material state of the catalyst particle can affect changes in the surface thermodynamics which may control the catalysis and electro-catalysis of heterogeneous reactions as well as the physical properties of the catalyst particle [26]. 

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