Determination of the Maximal Lyapunov Exponent through the Effective Potential Energy: Exact Phase Transition Temperature of Few Particle System CF4

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We calculate the maximal Lyapunov exponent of carbon tetra fluoride using the classical molecular dynamics (MD) simulation for different temperatures. The system is composed of 108 particles interacting either through an effective intermolecular potential energy in the vicinity of its liquid–gas phase transition point. As a main result, we find that at the transition temperature $T_{\text{c}}$, the Lyapunov exponent exhibits a power-law behavior with a functional form $\lambda = |T - T_{\text{c}}|^{-\omega}$, where the exponent $\omega$ is 0.155. This confirms that the maximal Lyapunov exponent behaves as an exact order parameter to signal the phase transition point for a system even with the infinite particles if the effective potential energy has been used in simulation. The applied effective intermolecular potential-energy function for carbon tetra fluoride has been obtained directly from the extended law of corresponding states for viscosity data using the inversion method. Then results were used to obtain a best Morse-Split-van der Waals (MSV) potential model.
2009-12-15