Original article: http://www.sciencedirect.com/science/article/pii/S2405844022001876
This study explores the positions and stability of C₇₀ fullerenes (a type of carbon molecule) at the nanoscale. Using MATHEMATICA software, we performed numerical simulations to analyze how different parameters affect the behavior of these molecules.
We focused on the total molecular energy, which represents the combined interaction forces between two C₇₀ fullerenes. This was calculated using a simplified, continuous model. The forces involved are mainly van der Waals attractions, which act between individual molecules and help create centripetal forces when three fullerenes interact.
In this research, we:
- Calculated the overall potential energy, mutual interaction forces, and angular velocity of the system.
- Found that stationary points (positions where forces balance out) lie along the ξ-axis and are symmetrical about the η-axis. This symmetry reflects the even distribution of carbon atoms in each fullerene.
- Discovered that for every set of parameters tested, there is at least one complex root with a positive real part—indicating that these stationary points are unstable according to Lyapunov’s stability theory.
In summary, although balanced configurations can exist, they are not stable and will likely change if disturbed.