This project has two roots. Jeremy Piwowarczyk is a Physics undergraduate at ASU, experienced in computing, who wants to learn more physics, and to learn about the ways of research. John Venables is developing various models of surface processes, including physical adsorption, based on research already published and in progress. He is aiming to illustrate, primarily to graduate students in surface science and related fields, how such models work. The end point of these projects may be webpages, new programs, results or textbook material: our approach is experimental, in that the end product is not decided in advance, but is progressing as we get to know each other's needs and capabilities.
Physical adsorption is discussed in John's Surface Science lecture notes, section C, which can be accessed from the list of lectures. These project notes assume that the reader is familiar with the ideas of mono- and multi-layers and that these layers can exist on the surface of a solid substrate in various phases. The domain of existence of these different two-dimensional (2D) phases can be displayed on various types of phase diagrams, which are described in section C3 and section C4.
The project concentrates on understanding the phases formed when a a specific rare gas is adsorbed on graphite. This topic has been much studied over the years, as can be seen from some selected references. A set of models was developed as part of this project, starting from those in use in John's group in the early '80's. These statistical mechanical models have two types of input. First, they depend on the interatomic potentials between the graphite and the rare gas, and between the rare gas atoms themselves; second, they depend on models for the vibrations of the rare gas atoms in these potential wells. The virtue of these models for educative purposes is that one can 'turn on' a particular potential term, or change the model of the vibrations, and see the effect directly in the output. This output is readily plotted in graphical form.
The project has been conceived generally, and open-endedly: we will stop when we get fed up with it. However, in order to a be sure that the models produce good results, one gas, neon, was chosen to set up the model.The programs are written using subroutines so that the gas can be changed with a minimum of effort. Our intent is to create a model that can be used to show how any of the heavier rare gases (Ne,Ar,Kr,Xe) behaves when it is adsorbed on graphite.
In the initial study of neon on graphite four quantities are modelled. These are set out in the following section 2, namely 2.1 Free Energy, 2.2 Entropy, 2.3 Specific Heat, and 2.4 Pressure.
Each of these results is based on evaluating a free energy at a given temperature (K), with other thermodynamic quantities appearing as derivatives. The model computes these quantities for three lattice parameters. In order to avoid unnecessary complications, the neon lattice parameters were set at evenly spaced intervals, 3.09 A, 3.19 A, and 3.29 A. These conditions can be changed at a later date if required.
Each part of section 2 contains the formulae used, as well as a brief explanation of the physical process being modelled. A limited data table and a graphical plot is given. Detailed derivations of some formulae used may be presented as appendices. A listing is given of the curent program.
The further development of this model may become the subject of Section 3. Go forward now to 2.1 Free Energy, or backwards to the REU index page.