What difference does it make if the molecules are aimed not straight down onto the surface, but at an angle ? This is the question we'll look at in this section. When the molecules are aimed straight down we term this normal incidence, otherwise it's just off-normal incidence.

We're really asking what effect does each of the two components of momentum have, i.e. the momentum perpendicular to the surface, and the momentum parallel to the surface. In order to answer this, we need to introduce some terminology: It is customary in gas-surface dynamics to discuss angular dependence in terms of "energies" and energy scaling. So instead of normal momentum, we would say normal energy. In fact the normal energy is just the energy associated with the normal component of momentum.

Using Ep (note should be epsilon but the browser can't support this) for the normal energy, it is easy to see from the figure that where M is the mass of the molecule.

By energy scaling we mean what is the value of n such that

      where      

What these equations mean is that if you take the dissociation probability at off-normal incidence and plot it not as a function of E, but as a function of E⁽ⁿ⁾ instead, then it will lie exactly on top of the normal incidence data, for which E⁽ⁿ⁾ = E anyway since the angle of incidence is zero.

Normal Energy Scaling

As an example, let's take n = 2 known as normal energy scaling, perhaps the most common example.

So, in other words, graphing dissociation/sticking probability versus normal energy will cause all the points at whatever angles of incidence to collapse on to one line, as shown in the example below.

This example shows what happens when the molecules are internally cold (unexcited) or hot (excited - in this case vibrationally), before they strike the surface.

Since normal energy scaling (NES) is so common, let's consider it in more detail:

What does normal energy scaling imply ?

It implies that only the momentum normal to the surface helps the molecule to dissociate - no matter how fast it moves parallel to the surface.

How can this come about ?

The simplest possibility is that the potential energy surface is flat, i.e. the barrier is perpendicular to the surface normal. In this case motion across the surface is at right angles to the barrier and doesn't help the molecule over it.

But surely surfaces aren't really flat ?

In fact it seems that even for the simplest dissociation reactions, the potential energy surface is very bumpy. To see what this means and to understand how normal energy scaling can occur on a rough surface is the subject of the following pages.

Dissociation on a corrugated PES.

©G.R. Darling