Hydrophobically-Driven Self-Assembly:  A Geometric Packing Analysis

Tsonchev, Stefan; Schatz, George C.; Ratner, Mark A.

doi:10.1021/nl0340531

Cited by 65 publications

(80 citation statements)

References 4 publications

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“…The approximately spherical shape of these larger clusters is consistent with the theoretical prediction of Tsonchev et al (14) that spherical structures are preferred in the limit of large N. The absence of cylindrical clusters is likely due to the hard-core repulsive interactions between cones, which is equivalent to a cone-cone interaction of effectively high bending energy. According to continuum theory (28), spherical structures are energetically preferred for high ratios of bending energy to stretching energy.…”

Section: Self-assembly Of Cones and Spherical Particles (Moderate To supporting

confidence: 88%

A precise packing sequence for self-assembled convex structures

Chen¹,

Zhang²,

Glotzer

2007

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

117

111

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Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self-assemble into clusters and that clusters comprised of particular numbers of cones (e.g., 4 -17, 20, 27, 32, and 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes (a ''precise packing sequence'') that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to convexity constraints, including an initial spherical convexity constraint for moderate-and large-sized clusters. This sequence contains six of the most common virus capsid structures obtained in vivo, including large chiral clusters and a cluster that may correspond to several nonicosahedral, spherical virus capsids obtained in vivo. Our findings suggest that this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.colloids ͉ self-assembly ͉ simulation ͉ virus assembly T he recent fabrication by means of evaporation-driven selfassembly of colloidal clusters containing micrometer-sized plastic spheres arranged in perfect polyhedra (1) has generated much excitement in the materials community. Precise structures such as these are rare in materials self-assembly problems (2, 3), with some notable, recent exceptions (e.g., refs. 4-6). In biology, however, precise structures are commonplace. A classic example is that of viruses, in which protein subunits, or small groups of protein subunits called capsomers, self-organize into precisely structured shells with icosahedral and other symmetries (7). Although obtained via wholly different processes, the precise packing of colloidal clusters [often referred to as colloidal ''molecules'' (8)] and virus capsids motivates us to investigate, in this article, the minimum set of organizing principles required for the self-assembly of precise structures such as these.One interesting building block shape that self-organizes into precise structures is the cone. Certain amphiphilic nanoparticles (9), molecules (4, 10, 11), and some virus capsomers (12, 13) that self-assemble into precise structures can, to first approximation, be modeled as cone-shaped particles associating via weak attractive interactions. What are the rules that govern the selfassembly of finite numbers of cones into precise clusters? Tsonchev et al. (14) presented a geometric packing analysis to explain the spherical shape resulting from the self-assembly of N cone-shaped amphiphilic nanoparticles in the limit of very large N, in which local hexagonal packing of hard cones is assumed. For clusters of smaller numbers of particles, however, the f...

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Section: Self-assembly Of Cones and Spherical Particles (Moderate To supporting

confidence: 88%

A precise packing sequence for self-assembled convex structures

Chen¹,

Zhang²,

Glotzer

2007

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

117

111

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“…We will assume that the cones have flat bases with the opening angle ␣ at their apex and the slant height L. In micelles (20), the solvent induces a tip-to-tip attraction between the cones. Here, we consider the role of base-to-base stacking in facilitating planar packing.…”

Section: Resultsmentioning

confidence: 99%

“…For a cylindrical micelle, the number of cones in an elementary cell, defined as a cylinder section of thickness L sin(␣/2) ͌ 3 (20), is N c ϭ [2 /␣], and the volume of such an elementary cell is V cell cyl ϭ L 3 sin(␣/2) ͌ 3. The packing fraction of cylinders in a hexagonal arrangement is /(2 ͌ 3).…”

Section: [3]mentioning

confidence: 99%

Symmetry, shape, and order

Trovato

Hoang

Banavar

et al. 2007

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

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Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of /(3 ͌ 2) ϳ 0.7405. Much more recently, an unusually high-density packing of Ϸ0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of highdensity packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of /4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at c* ‫؍‬ ͌ 2 ؊ 1.biaxial order ͉ packing ͉ truncated cones M any natural forms (1), such as the DNA double helix (2, 3) and seed arrays on sunflowers (4), arise from simple geometrical principles rather than from complex interactions. Symmetry considerations often play a key role in determining the nature of order of a system (5, 6). ‡ ‡ The simplest model of matter, a collection of isotropic objects (spheres), exhibits both the isotropic fluid and the crystalline phases with a phase transition between them upon varying the packing fraction or density (7). Dense packing can result from either the maximization of the packing fraction (7) or the minimization of the area exposed (8, 9) to probe objects such as water molecules. Efficient packing of a system of rods (10) leads again to an isotropic fluid phase or to uniaxial order with the orientation of the axis of one of the rods dictating the preferred alignment of nearby rods. Liquid crystalline phases (5) exist between a liquid with no translational order and a crystal with translational order in all three directions. This is accomplished by employing constituent particles that are anisotropic-the molecules of liquid crystals are not spherical and can form phases with translational order in fewer than three dimensions and/or orientational order. Recent work has shown that an unusually high-density packing of Ϸ0.770732 is achieved for congruent ellipsoids (11). Packing studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, and ceramics (12-18).Here, we study the packing of truncated cones and show how the nature of order of a system composed of identical objects can depend not only on the symmetry of the object but also on its shape. The geometry of small self-assemb...

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“…The formation of b-sheets blocks the formation of alternative aggregates, such as spherical micelles or layered structures even when molecules vary greatly in their shapes. Tsonchev et al (2003Tsonchev et al ( , 2004 showed through calculations and Monte Carlo simulations that spherical micelles are preferred by tapered molecules. Israelachvili et al (1976) has postulated that surfactants will aggregate into spheres, cylinders or layered assemblies depending on how tapered is the shape of molecules.…”

Section: One-dimensional Assembliesmentioning

confidence: 99%

Supramolecular self-assembly codes for functional structures

Palmer

Velichko

Cruz

et al. 2007

Phil. Trans. R. Soc. A.

102

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Small-molecule self-assembly has proven to be a rich field for the controlled synthesis of supramolecular objects with the size scale of polymers and interesting properties. Using several recent examples from our laboratory, we discuss the development of chemical structure codes for supramolecular self-assembly objects with defined shapes. The resulting materials formed by these objects are promising for electronic functions and biological functions for regenerative medicine.

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Hydrophobically-Driven Self-Assembly: A Geometric Packing Analysis

Cited by 65 publications

References 4 publications

A precise packing sequence for self-assembled convex structures

A precise packing sequence for self-assembled convex structures

Symmetry, shape, and order

Supramolecular self-assembly codes for functional structures

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