Nanotechnology

Molecular Dynamics

A useful simplified method of modeling is called “Molecular Dynamics” (abbreviated “M-D”); it is based on the concepts of “statistical mechanics”. In statistical mechanics, one tries to understand the interactions between some representative atoms or molecules and then extrapolates by averaging over ensembles of very large numbers of such molecules. For strict success one needs to know all of the interactions of a chosen molecule with its multitudinous neighbors; practical calculations look for realistic simplifications in the forms of these interactions.

M-D is a useful subset of statistical mechanics^[1]; Newton’s law of motion is retained but highly simplified interaction models, often just a picture of binary interactions, is enough to make considerable progress.

Rieth^[2] has used M-D methods with some success in the field of nanotechnology. While the details of these calculations are too abstract in the present context, one or two of the results can be easily appreciated quite easily. The attached Figure 1 is a composite from Rieth; to make this picture the coupled dynamical equations for 1660 aluminum atoms had to be solved simultaneously as a function of time. What was assumed is the initial shape “F” and a simple force law between the Al atoms. At 0 K the calculations are stable such as for frame 1; then the model is heated to 270K and the motions allowed to evolve over time. After some time, the “F” sags a little (frame 2) eventually reaching the distorted condition in frame 3. If the calculation is taken nearer to the melting point of aluminum, 933K, (as in frame 4 at 750K) the “F” is much the worse for wear; a noticeable fraction of the aluminum atoms have in fact sublimated (vaporized without ever becoming liquid).

There are macro thermodynamic and transport models of the effects of heating aluminum from 0K to 750K as in this example; however, the macro methods are incapable of the resolution of local effects as illustrated in Figure 1. The macroscopic methods will break down when we wish to ask questions about small clusters or about the fate of individual atoms. Indeed in quantum mechanics, the latter question itself is not deterministic and M-D will also break down.