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Density functional theory for the crystallization of two-dimensional dipolar colloidal alloys

Somerville, W. R.C.; Stokes, J. L.; Adawi, A. M.; Horozov, T. S.; Archer, A. J.; Buzza, D. M.A.

Authors

W. R.C. Somerville

J. L. Stokes

A. J. Archer

Abstract

Two-dimensional mixtures of dipolar colloidal particles with different dipole moments exhibit extremely rich self-assembly behaviour and are relevant to a wide range of experimental systems, including charged and super-paramagnetic colloids at liquid interfaces. However, there is a gap in our understanding of the crystallization of these systems because existing theories such as integral equation theory and lattice sum methods can only be used to study the high temperature fluid phase and the zero-temperature crystal phase, respectively. In this paper we bridge this gap by developing a density functional theory (DFT), valid at intermediate temperatures, in order to study the crystallization of one and two-component dipolar colloidal monolayers. The theory employs a series expansion of the excess Helmholtz free energy functional, truncated at second order in the density, and taking as input highly accurate bulk fluid direct correlation functions from simulation. Although truncating the free energy at second order means that we cannot determine the freezing point accurately, our approach allows us to calculate \emph{ab initio} both the density profiles of the different species and the symmetry of the final crystal structures. Our DFT predicts hexagonal crystal structures for one-component systems, and a variety of superlattice structures for two-component systems, including those with hexagonal and square symmetry, in excellent agreement with known results for these systems. The theory also provides new insights into the structure of two-component systems in the intermediate temperature regime where the small particles remain molten but the large particles are frozen on a regular lattice.

Journal Article Type Article
Publication Date Sep 13, 2018
Journal Journal of Physics: Condensed Matter
Print ISSN 0953-8984
Electronic ISSN 1361-648X
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 30
Issue 40
Institution Citation Somerville, W. R., Stokes, J. L., Adawi, A. M., Horozov, T. S., Archer, A. J., & Buzza, D. M. (2018). Density functional theory for the crystallization of two-dimensional dipolar colloidal alloys. Journal of physics. an Institute of Physics journal. Condensed matter, 30(40), doi:10.1088/1361-648X/aaddc9
DOI https://doi.org/10.1088/1361-648X/aaddc9
Keywords General Materials Science; Condensed Matter Physics
Publisher URL http://iopscience.iop.org/article/10.1088/1361-648X/aaddc9
Copyright Statement © 2018 IOP Publishing Ltd

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