JAMP> Vol.8 No.9, September 2020

Author(s)

Kostas Parisis¹, Fei Shuang², Bo Wang², Pu Hu², Andreas Giannakoudakis¹, Avraam Konstantinidis^1*

¹Aristotle University of Thessaloniki, Thessaloniki, Greece.
²University of Florida, Gainesville, FL, USA.

Motivated by the special theory of gradient elasticity (GradEla), a proposal is advanced for extending it to construct gradient models for interatomic potentials, commonly used in atomistic simulations. Our focus is on London’s quantum mechanical potential which is an analytical expression valid until a certain characteristic distance where “attractive” molecular interactions change character and become “repulsive” and cannot be described by the classical form of London’s potential. It turns out that the suggested internal length gradient (ILG) generalization of London’s potential generates both an “attractive” and a “repulsive” branch, and by adjusting the corresponding gradient parameters, the behavior of the empirical Lennard-Jones potentials is theoretically captured.

Gradient Elasticity, London’s Potential, Gradient Interatomic Potentials

Parisis, K. , Shuang, F. , Wang, B. , Hu, P. , Giannakoudakis, A. and Konstantinidis, A. (2020) From Gradient Elasticity to Gradient Interatomic Potentials: The Case-Study of Gradient London Potential. Journal of Applied Mathematics and Physics, 8, 1826-1837. doi: 10.4236/jamp.2020.89137.