Potential, surface corrugation

Even a molecularly smooth single-crystal face represents a potential energy surface that depends on the lateral position x, y) of the water molecule in addition to the dependence on the normal distance z. One simple way to introduce this surface corrugation is by adding the lattice periodicity. An example of this approach is given by Berkowitz and co-workers for the interaction between water and the 100 and 111 faces of the Pt crystal. In this case, the full (x, y, z) dependent potential was determined by a fit to the full atomistic model of Heinzinger and co-workers (see later discussion). 

Much more detailed information about the microscopic structure of water at interfaces is provided by the pair correlation function which gives the joint probability of finding an atom of type/r at a position ri, and an atom of type v at a position T2, relative to the probability one would expect from a uniform (ideal gas) distribution. In a bulk homogeneous liquid, gfn, is a function of the radial distance ri2 = Iri - T2I only, but at the interface one must also specify the location zi, zj of the two atoms relative to the surface. We expect the water pair correlation function to give us information about the water structure near the metal, as influenced both by the interaction potential and the surface corrugation, and to reduce to the bulk correlation Inunction when both zi and Z2 are far enough from the surface. 

Beardmore etal. [Ill] have presented a realistic empirical potential function to model the head-group interaction for SAMs of alkanethiols on Au(lll). The main result of these calculations is that the barriers within the surface corrugation potential are too small to pin S atoms at any particular site. 

The bimolecular reaction rate for particles constrained on a planar surface has been studied using continuum diffusion theory " and lattice models. In this section it will be shown how two features which are not taken account of in those studies are incorporated in the encounter theory of this chapter. These are the influence of the potential K(R) and the inclusion of the dependence on mean free path. In most instances it is expected that surface corrugation and strong coupling of the reactants to the surface will give the diffusive limit for the steady-state rate. Nevertheless, as stressed above, the initial rate is the kinetic theory, or low-friction limit, and transient exp)eriments may probe this rate. It is noted that an adaptation of low-density gas-phase chemical kinetic theory for reactions on surfaces has been made. The theory of this section shows how this rate is related to the rate of diffusion theory. 

A systematic study of physical effects that influence the water structure at the water/metal interface has been made. Water structure, as characterized by the atom density proflles, depends most strongly on the adsorption energy and on the curvature of the water-metal interaction potential. Structural differences between liquid/liquid and liquid/solid interfaces, investigated in the water/mercury two-phase system, are small if the the surface inhomogeneity is taken into account. The properties of a polarizable water model near the interface are almost identical to those of unpolarizable models, at least for uncharged metals. The water structure also does not depend much on the surface corrugation. 

As a result of thermodynamic fluctuations or outer disturbances, the surfaces of a thinning liquid film are corrugated (see Fig. 33d). When the derivative of the disjoining pressure, dU/dh, is positive, the amplitude of the film surface corrugations spontaneously grows with the decrease of the film thickness [5,6,420,492]. The appearance of unstable fluctuations is possible even in the relatively thick primary equilibrium films as a result of fluctuations in the electric potential [6,493]. The evaporation dr condensation of solvent... 

If surface corrugation is neglected, the potential in the equations of motion depends only on z, and the tangential motion is free at each brandi of the trajectory. The classical trajectory R t),z(t) is then found from the equations of motion involving the only potential Vq with boundaiy conditions mgi( 0) = 0, H( 0) = JZo fngi" -> Pf,i at t -> oo ... 

Figure 12.6 Surface corrugation. Potential energy contours, schematic, as a function of the distance of the molecule from the surface and the lateral position along the surface. The thicker line is the location of the barrier to dissociation. Its height and its location along the surface normal are seen to depend on the lateral position. Such a picture helps in understanding why different surface sites may be important for inelastic collisions and for dissociation and why also momentum along the surface can help overcome the barrier to dissociation.

---