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Issue 7, 2017
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Phase diagram of elastic spheres

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Abstract

Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant–Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.

Graphical abstract: Phase diagram of elastic spheres

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Publication details

The article was received on 02 Nov 2016, accepted on 28 Dec 2016 and first published on 03 Jan 2017


Article type: Paper
DOI: 10.1039/C6SM02474B
Citation: Soft Matter, 2017,13, 1463-1471
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    Phase diagram of elastic spheres

    L. Athanasopoulou and P. Ziherl, Soft Matter, 2017, 13, 1463
    DOI: 10.1039/C6SM02474B

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