Packing and self-assembly of truncated triangular bipyramids

Haji-Akbari, Amir; Chen, Elizabeth R.; Engel, Michael; Glotzer, Sharon C.

doi:10.1103/physreve.88.012127

Cited by 24 publications

(33 citation statements)

References 70 publications

(120 reference statements)

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“…Second, hard particle systems often assemble into their densest packing structure, however some do not [16,18,39,41,44,53]. The present work helps to highlight two key differences between self-assembly and packing.…”

Section: A Pmft As An Effective Potential At Finite Densitymentioning

confidence: 80%

“…(iii) By computing quantities for DEFs that can be compared to intrinsic forces between particles, we determine when shape entropy is important in laboratory systems, and suggest how to measure DEFs in the lab. (iv) We explain two no-table features of the hard particle literature: the observed frequent discordance between self-assembled and densest packing structures, [16,18,39,41,44,53] and the high degree of correlation between particle coordination in dense fluids and crystals. [18] (v) As we illustrate in Fig.…”

Section: Introductionmentioning

confidence: 90%

See 1 more Smart Citation

Understanding shape entropy through local dense packing

Anders¹,

Klotsa²,

Ahmed³

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

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256

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Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy (k B T ) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.entropy | self-assembly | colloids | nanoparticles | shape N ature is replete with shapes. In biological systems, eukaryotic cells often adopt particular shapes, for example, polyhedral erythrocytes in blood clots (1) and dendritic neurons in the brain (2). Before the development of genetic techniques, prokaryotes were classified by shape, as bacteria of different shapes were implicated in different diseases (3). Virus capsids (4, 5) and the folded states of proteins (6) also take on well-recognized, distinct shapes. In nonliving systems, recent advances in synthesis make possible granules, colloids, and nanoparticles in nearly every imaginable shape (7-12). Even particles of nontrivial topology now are possible (13).The systematic study of families of idealized colloidal and nanoscale systems by computer simulation has produced overwhelming evidence that shape is implicated in the self-assembly* of model systems of particles (14-17). In these model systems, the only intrinsic forces between particles are steric, and the entropic effects of shape (which we term "shape entropy" † ) can be isolated. Those works show that shape entropy begins to be important when systems are at moderate density (21).In laboratory systems, however, it is not possible to isolate shape entropy effects with as much control, and so the role of shape entropy in experiment is less clear. However, intuition suggests that shape entropy becomes important when packing starts to dominate intrinsic interactions ...

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Section: A Pmft As An Effective Potential At Finite Densitymentioning

confidence: 80%

Section: Introductionmentioning

confidence: 90%

Understanding shape entropy through local dense packing

Anders¹,

Klotsa²,

Ahmed³

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

223

256

View full text Add to dashboard Cite

show abstract

“…The crystallization in this case may be problematic due to the kinetic trapping and complex ground state. Additionally, TBP was computationally predicted to yield quasi-crystals over a wide range of TBP vertex truncations 50 . Thus, it is quite possible that the observed amorphous organization of NP-TBP system is related to this aspect of TBP geometry.…”

Section: Enabling Lattice Types By Shaping Polyhedral Framesmentioning

confidence: 99%

Lattice engineering through nanoparticle–DNA frameworks

et al. 2016

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Advances in self-assembly over the last decade have demonstrated that nano-and microscale particles can be organized into a large diversity of ordered three-dimensional (3D) lattices. However, the ability to generate the desired lattice type from the same set of particles remains challenging. Here, we show that nanoparticles can be assembled into crystalline and open 3D frameworks by connecting them through designed DNA-based polyhedral frames. The welldefined geometrical shapes of the frames, combined with the DNA-assisted binding properties of their vertices, facilitate the well-defined topological connections between particles in accordance with frame geometry. With this strategy, different crystallographic lattices using the same particles can be assembled by introduction of the corresponding DNA polyhedral frames. This approach should facilitate the rational assembly of nanoscale lattices through the design of the unit cell.The progress in nano-material fabrication methods was for long time motivated by the idea that self-assembly will endow us with ability to organize nanoparticles in the designed arrays. In reality, the particle characteristics have a profound effect on the assembled structure, thus, a little room is remaining for a structure architecting. Yet, it would be far more powerful to have an ability generating the different desired types of 3D lattices from the same particles. Such freedom of lattice engineering will permit fabricating targeted materials, which properties can be enhanced and manipulated by precise organization of functional components [1][2][3][4][5] .Colloids, often presented as a model of atomic systems, have revealed a great insight about the fundamentals of crystal formation [6][7][8][9] and the role of a particle nature [10][11][12] . Although an Reprints and permissions information is available online at www.nature.com/reprints. Supplementary information is available in the online version of the paper. Competing financial interestsThe authors declare no competing financial interests. HHS Public AccessAuthor manuscript Nat Mater. Author manuscript; available in PMC 2017 January 31. Author Manuscript Author ManuscriptAuthor Manuscript Author Manuscript extremely rich variety of lattices have been demonstrated 12-15 , the particular particle characteristics-such as sizes 13,16,17 , interactions, entropic and many-body effects 18-21 , and shape 22-24 -dominate lattice formation. These dependencies are both natural and useful; numerous investigations have detailed how particle characteristics drive structure formation 12,[24][25][26][27][28] . While these studies uncovered a great depth of physical insight, the goal of lattice "engineering" remains elusive, due to the complex dependences between the structural and energetic parameters of particle and lattice, and the necessity to tailor particles for each target lattice.Anisotropic interparticle interactions, induced by precise arrangement of binding patches or by particle shaping, were considered as means to simplify ...

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“…ref. [1][2][3][4][5][6]. Several sub-problems have to be distinguished, among them is the question of the maximum density and other characteristics of a randomly packed arrangement, the so-called random close packing, or the quest for the maximum achievable packing density in regular structures.…”

Section: Introductionmentioning

confidence: 99%

Frustrated packing in a granular system under geometrical confinement

et al. 2018

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Optimal packings of uniform spheres are solved problems in two and three dimensions. The main difference between them is that the two-dimensional ground state can be easily achieved by simple dynamical processes while in three dimensions, this is impossible due to the difference in the local and global optimal packings. In this paper we show experimentally and numerically that in 2 + ε dimensions, realized by a container which is in one dimension slightly wider than the spheres, the particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. If these positions are denoted by up and down the packing problem can be mapped to a 1/2 spin system. At first it looks frustrated with spin-glass like configurations, but the system has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres.

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Packing and self-assembly of truncated triangular bipyramids

Cited by 24 publications

References 70 publications

Understanding shape entropy through local dense packing

Understanding shape entropy through local dense packing

Lattice engineering through nanoparticle–DNA frameworks

Frustrated packing in a granular system under geometrical confinement

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