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Interactions between nanoparticles is one of the key factors governing their assembly for ordered structures. Understanding such interactions between non-spherical nanoparticles and developing a quantitative force model are critical to achieving the ordered structures for various applications. In the present study, the non-contact interactions of two identical gold nanorods (AuNRs) with different aspect ratios have been studied by molecular dynamics simulation. A new interaction potential and force model for two nanorods approaching side-by-side has been proposed as a function of particle surface separation and their relative orientation. In addition, the interaction potentials of two nanorods approaching in other typical orientation configurations (i.e., crossed, head-to-head and head-to-side) have also been investigated.