# Composition and Resolution Dependence of Effective Coarse-Graining Potentials in Multi-Resolution Simulations

## TL;DR

This paper develops a formal approach to derive effective coarse-grained potentials for multi-resolution polymer simulations, ensuring consistency of physical properties across different resolutions and simplifying complex simulations.

## Contribution

It introduces Mixed Resolution Potentials (MRPs) that depend on composition, temperature, and density, enabling accurate multi-resolution modeling of polymeric liquids.

## Key findings

- MRPs ensure structural and thermodynamic property consistency.
- Analytical solutions for long-chain polymers reveal decay scaling exponents.
- MRPs simplify multi-resolution simulations while maintaining accuracy.

## Abstract

Given that the physical properties of polymeric liquids extend on a wide range of lengthscales, it is computationally convenient to represent them by coarse-grained (CG) descriptions at various granularities to investigate local and global properties simultaneously. This paper addresses how modeling the same system with mixed resolutions affects the consistency of the structural and thermodynamic properties, and shows that it is possible to formally derive interacting potentials that ensure consistency of the relevant physical properties in the mixed resolution region with the corresponding atomistic resolution simulations. The composition, temperature, and density dependences of such Mixed Resolution Potentials (MRPs) are investigated. In the limit of long polymer chains, where Markovian statistics is obeyed, the MRPs are analytically solved and decay with characteristic scaling exponents that depend on the mixture composition and CG resolution of the two components. Adopting MRPs simplifies the structure of multi-resolution simulations while quantitatively producing the structural and thermodynamical properties of the related atomistic systems such as radial distribution function and pressure.