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Determination of interaction potentials of colloidal monolayers from the inversion of pair correlation functions: A two-dimensional predictor-corrector method

Buzza, D. M. A.; Buzza, Martin; Law, A. D.; Buzza, D. M. A.

Authors

D. M. A. Buzza

A. D. Law

Abstract

The structure and stability of colloidal monolayers depend crucially on the effective pair potential u (r) between colloidal particles. In this paper, we develop a two-dimensional (2D) predictor-corrector method for extracting u (r) from the pair correlation function g (r) of dense colloidal monolayers. The method is based on an extension of the three-dimensional scheme of Rajagopalan and Rao [Phys. Rev. E 55, 4423 (1997)] to 2D by replacing the unknown bridge function B (r) with the hard-disk bridge function B d (r); the unknown hard-disk diameter d is then determined using an iterative scheme. We compare the accuracy of our predictor-corrector method to the conventional one-step inversion schemes of hypernetted chain closure (HNC) and Percus-Yevick (PY) closure. Specifically we benchmark all three schemes against g (r) data generated from Monte Carlo simulation for a range of 2D potentials: exponential decay, Stillinger-Hurd, Lennard-Jones, and Derjaguin-Landau-Verwey-Overbeek. We find that for all these potentials, the predictor-corrector method is at least as good as the most accurate one-step method for any given potential, and in most cases it is significantly better. In contrast the accuracy of the HNC and PY methods relative to each other depends on the potential studied. The proposed predictor-corrector scheme is therefore a robust and more accurate alternative to these conventional one-step inversion schemes. © 2009 American Institute of Physics.

Journal Article Type Article
Publication Date 2009-09
Journal JOURNAL OF CHEMICAL PHYSICS
Print ISSN 0021-9606
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 131
Issue 9
Article Number ARTN 094704
Pages 094704 - 094704
Institution Citation Law, A. D., & Buzza, D. M. A. (2009). Determination of interaction potentials of colloidal monolayers from the inversion of pair correlation functions: A two-dimensional predictor-corrector method. The Journal of chemical physics, 131(9), 094704 - 094704. doi:10.1063/1.3216568
DOI https://doi.org/10.1063/1.3216568
Keywords Physical and Theoretical Chemistry; General Physics and Astronomy
Publisher URL https://aip.scitation.org/doi/full/10.1063/1.3216568