Purely entropic self-assembly of the bicontinuous Ia
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            d gyroid phase in equilibrium hard-pear systems

Schönhöfer, Philipp W. A.; Ellison, Laurence; Maréchal, Matthieu; Cleaver, Douglas J.; Schröder‐Turk, Gerd E.

doi:10.1098/rsfs.2016.0161

Cited by 18 publications

(40 citation statements)

References 73 publications

(89 reference statements)

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“…While the phase behavior of spherical ABPs can be explained solely by effective attractions [10,15,16] and that of active nematic rods by an effective (longer) aspect ratio [33], an appropriate effective potential for SPRs should account for their characteristic broken updown symmetry. The most simplistic passive model system with this property consists of hard pear-shaped objects, for which it has been detailed recently that the nematic phase destabilizes with increasing deviation from ellipsoidal shape [56]. This observation suggests an intuitive mapping to describe the IN transition in qualitative agreement with our simulations, which is yet to be quantified.…”

Section: Discussionsupporting

confidence: 77%

Isotropic-nematic transition of self-propelled rods in three dimensions

et al. 2018

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Using overdamped Brownian dynamics simulations we investigate the isotropic-nematic (IN) transition of self-propelled rods in three spatial dimensions. For two well-known model systems (Gay-Berne potential and hard spherocylinders) we find that turning on activity moves to higher densities the phase boundary separating an isotropic phase from a (nonpolar) nematic phase. This active IN phase boundary is distinct from the boundary between isotropic and polar-cluster states previously reported in two-dimensional simulation studies and, unlike the latter, is not sensitive to the system size. We thus identify a generic feature of anisotropic active particles in three dimensions.

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Section: Discussionsupporting

confidence: 77%

Isotropic-nematic transition of self-propelled rods in three dimensions

et al. 2018

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“…2). The simulations are carried out using the same methodology as in [61], adjusted to include the hard-sphere solvent. The system is set up within a cubic box with three-dimensional periodic boundary conditions, with an overall particle packing fraction ρ = 0.56 and a 1:9 volume ratio of solvent particles to pear-shaped particles (v= .…”

Section: Molecular Dynamics Of Mixtures Of Sphere and Pear-shaped Parmentioning

confidence: 99%

“…The implementation of spheres to create curvature might be also an explanation for the stabilisation and preference of the double Diamond phase over the double Gyroid in general. In our earlier studies [61] we determined a correlation between the interdigitation depth and the local Gauss curvature of the system. The further pears reach into the realm of the opposite channel system, the more curvature is contributed to the interface between both pear particle clusters.…”

Section: Self-assembly Of Bicontinuous Phases In Pear Sphere Systemsmentioning

confidence: 99%

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Double diamond phase in pear-shaped nanoparticle systems with hard sphere solvent

Schönhöfer¹,

Cleaver²,

Schröder‐Turk³

2018

J. Phys. D: Appl. Phys.

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The mechanisms behind the formation of bicontinuous nanogeometries, in particular in vivo, remain intriguing. Of particular interest are the many systems where more than one type or symmetry occurs, such as the Schwarz' Diamond surface and Schoen's Gyroid surface; a current example are the butterfly nanostructures often based on the Gyroid, and the beetle nanostructures often based on the Diamond surface. Here, we present a computational study of self-assembly of the bicontinuous Pn3m Diamond phase in an equilibrium ensemble of pear-shaped particles when a small amount of a hard-sphere 'solvent' is added. Our results are based on previous work that showed the emergence of the Gyroid Ia3d phase in a pure system of pear-shaped particles [Interface Focus 7, 20160161 (2017)], in which the pear-shaped particles form an interdigitating bilayer reminiscent of a warped smectic structure. We here show that the addition of a small amount of hard spherical particles tends to drive the system towards the bicontinuous Pn3m double Diamond phase, based on Schwarz Diamond minimal surface. This result is consistent with the higher degree of spatial heterogeneity of the Diamond minimal surface as compared to the Gyroid minimal surface, with the hard-sphere 'solvent' acting as an agent to relieve packing frustration. However, the mechanism by which this relief is achieved is contrary to the corresponding mechanism in copolymeric systems; the spherical solvent tends to aggregate within the matrix phase, near the minimal surface, rather than within the labyrinthine channels. While it may relate to the specific form of the potential used to approximate the particle shape, this mechanism hints at an alternative way for particle systems to both release packing frustration and satisfy geometrical restrictions in double Diamond configurations. Interestingly, the lattice parameters of the Gyroid and the Diamond phase appear to be commensurate with those of the isometric Bonnet transform.

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“…While shape and form adapt through evolution, this process is mediated by the physical forces and principles that actually shape the material. Again, this collection offers some insights, both relating to the very same forces that Thompson was considering (surface tension, [16]), as well as more complex interfacial forces [17] and interactions [18], as well as entropic principles [19] and non-equilibrium effects in pattern formation [20]. In our view, science must ultimately reconcile the geometry and forces approaches, that remain largely divorced from each other.…”

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confidence: 92%