Numerical methods for unraveling inter-particle potentials in colloidal suspensions: A comparative study for two-dimensional suspensions

Rees-Zimmerman, Clare R; Martín-Roca, José; Evans, David; Miller, Mark A; Aarts, Dirk G A L; Valeriani, Chantal

Abstract

We compare three model-free numerical methods for inverting structural data to obtain interaction potentials, namely, iterative Boltzmann inversion (IBI), test-particle insertion (TPI), and a machine-learning (ML) approach called ActiveNet. Three archetypal models of two-dimensional colloidal systems are used as test cases: Weeks-Chandler-Anderson short-ranged repulsion, the Lennard-Jones potential, and a repulsive shoulder interaction with two length scales. Additionally, data on an experimental suspension of colloidal spheres are acquired by optical microscopy and used to test the inversion methods. The methods have different merits. IBI is the only choice when the radial distribution function is known but particle coordinates are unavailable. TPI requires snapshots with particle positions and can extract both pair- and higher-body potentials without the need for simulation. The ML approach can only be used when particles can be tracked in time and it returns the force rather than the potential. However, it can unravel pair interactions from any one-body forces (such as drag or propulsion) and does not rely on equilibrium distributions for its derivation. Our results may serve as a guide when a numerical method is needed for application to experimental data and as a reference for further development of the methodology itself.

Citation

Rees-Zimmerman, C. R., Martín-Roca, J., Evans, D., Miller, M. A., Aarts, D. G. A. L., & Valeriani, C. (2025). Numerical methods for unraveling inter-particle potentials in colloidal suspensions: A comparative study for two-dimensional suspensions. The Journal of Chemical Physics, 162(7), Article 074103. https://doi.org/10.1063/5.0246890

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2025
• Online Publication Date: Feb 18, 2025
• Publication Date: Feb 21, 2025
• Deposit Date: Mar 14, 2025
• Publicly Available Date: Feb 19, 2026
• Journal: The Journal of chemical physics
• Print ISSN: 0021-9606
• Electronic ISSN: 1089-7690
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 162
• Issue: 7
• Article Number: 074103
• DOI: https://doi.org/10.1063/5.0246890
• Public URL: https://durham-repository.worktribe.com/output/3699854