Vol. 7, 2022-14 Cite as: Hernandez, H. (2022). A General Multiscale Pair Interaction Potential Model. ForsChem Research Reports, 7, 2022-14, 1 - 25. doi: 10.13140/RG.2.2.18525.90088. Publication Date: 13/09/2022. A General Multiscale Pair Interaction Potential Model Hugo Hernandez ForsChem Research, 050030 Medellin, Colombia hugo.hernandez@forschem.org doi: 10.13140/RG.2.2.18525.90088 Abstract A general empirical model for describing interaction potential energies between two bodies at different scales is presented. The model considers a general non-linear model as a function of the ratio between the distance of the centers of mass of the bodies and the distance of close contact of the bodies in the axis of interaction. If such distance ratio is large, the interaction potential becomes negligible. If the distance ratio is close to 1, a repulsive potential becomes dominant. One or more mechanical equilibrium points can be observed depending on the different types and ranges of interaction forces considered in the model. The model is not intended to provide a mechanistic interpretation of interaction forces and potential energy, but rather a simple mathematical representation of the multiscale complexity of the interaction between two composite bodies (necessarily involving all individual pair interactions between their components). It is also shown that the most commonly used pair interaction models are particular cases of the general model presented in this report. Keywords Attraction, Empirical Model, Equilibrium, Interaction Forces, Inverse-square Law, Laurent Series, Multi-scale, Pair Interaction, Potential Energy, Repulsion 1. Introduction Physical systems are characterized by motion and interaction of the different composing elements. Motion simply consists in the relative change in the position of the elements over time. The relative change in the position of an element can be considered in general to be nonlinear with respect to time. However, it is possible to approximate such nonlinear behavior using a series expansion approximation as follows [1]: