Editing Physisorption (section)

==Modeling by image charge==
[[File:physisorption 1.jpg|thumbnail|200px|Fig. 1. Schematic illustration of an adsorbed hydrogen atom near a perfect [[electrical conductor|conductor]] interacting with its [[image charge]]s.]]

To give a simple illustration of physisorption, we can first consider an adsorbed hydrogen atom in front of a perfect conductor, as shown in Fig. 1.  A nucleus with positive charge is located at '''R'''&nbsp;=&nbsp;(0,&nbsp;0,&nbsp;''Z''), and the position coordinate of its electron, '''r'''&nbsp;=&nbsp;(''x'',&nbsp;''y'',&nbsp;''z'') is given with respect to the nucleus.  The adsorption process can be viewed as the interaction between this hydrogen atom and its image charges of both the nucleus and electron in the conductor.  As a result, the total electrostatic energy is the sum of attraction and repulsion terms:

:<math>V = {e^2\over 4\pi\varepsilon_0}\left(\frac{-1}{|2\mathbf R|}+\frac{-1}{|2\mathbf R+\mathbf r-\mathbf r'|}+\frac{1}{|2\mathbf R-\mathbf r'|}+\frac{1}{|2\mathbf R+\mathbf r|}\right).</math>

The first term is the attractive interaction of the nucleus and its image charge, and the second term is due to the interaction of the electron and its image charge.  The repulsive interaction is shown in the third and fourth terms arising from the interaction between the nucleus and the image electron, and, the interaction between the electron and the image nucleus, respectively.

By [[Taylor expansion]] in powers of |'''r'''|&nbsp;/&nbsp;|'''R'''|, this interaction energy can be further expressed as:

:<math>V = {-e^2\over 16\pi\varepsilon_0 Z^3}\left(\frac{x^2+y^2}{2}+z^2\right)+ {3e^2\over 32\pi\varepsilon_0 Z^4}\left(\frac{x^2+y^2}{2}{z}+z^3\right)+O\left(\frac{1}{Z^5}\right).</math>

One can find from the first non-vanishing term that the physisorption potential depends on the distance ''Z'' between adsorbed atom and surface as ''Z''<sup>&minus;3</sup>, in contrast with the ''r''<sup>&minus;6</sup> dependence of the molecular [[Van der Waals force|van der Waals]] potential, where ''r'' is the distance between two [[dipoles]].