Lately I've been studying the forces between "atoms" and the configurations or assemblies they can form. A simple model for an atom that mimics the short range repulsive force and a longer range attractive force employs inverse first and second power potentials. So for two atoms we can determine the equilibrium distance between them. The potentials can be simplified using a scaling factor, κ, which represents a distance determined by the ratio of the two potential field strengths. For two atoms only one pair of links can be formed between them.
The relative distance between the two atoms can be represented by a single parameter ρ and we can use Newton's method to find the distance where the forces balance. It turns out the equilibrium distance between the atoms is κ.
The case for three atoms is nearly identical since we can define a plane by their three positions and symmetry suggests that the equilibrium distances will all be the same and can be again represented by the single parameter ρ.
The equilibrium distance is again κ.
The actual forces between atoms is more complicated but the model appears to give qualitatively correct results.
No comments:
Post a Comment