Free-energy functional method for inverse problem of self assembly

Torikai, Masashi

doi:10.1063/1.4917175

Cited by 14 publications

(12 citation statements)

References 33 publications

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“…The other pair potentials known to stabilize this structure do so via incorporation of other features at specific separations (e.g., attractive wells, concave shoulders, etc.) 11,12,26,27 , which may be more challenging to realize in practice.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, assembly of the kagome lattice is of interest in magnetic materials due to its unusual properties arising from geometrical frustration 24,25 . Materials exhibiting a kagome lattice are known to be difficult to synthesize experimentally, and though there are now a few isotropic model potentials known to stabilize this structure 11,12,26,27 , none of them are of the simple convex repulsive type considered here. Additionally, the kagome lattice presents an attractive design target for an isotropic potential in one respect: the spatial distributions of particles in its coordination shells are symmetric.…”

Section: Introductionmentioning

confidence: 98%

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Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices

Piñeros

Bâldea

Truskett

2016

The Journal of Chemical Physics

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Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices

Piñeros

Bâldea

Truskett

2016

The Journal of Chemical Physics

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“…21–24 The assembly of similar purely repulsive binary mixtures have been studied extensively. 25–36 Consequently, it also known that subtle changes to such a pair potential’s form or shape can shift the relative stability of different crystal polymorphs.…”

Section: Introductionmentioning

confidence: 99%

Assembly of multi-flavored two-dimensional colloidal crystals

et al. 2017

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We systematically investigate the assembly of binary multi-flavored colloidal mixtures in two dimensions. In these mixtures all pairwise interactions between species may be tuned independently. This introduces an additional degree of freedom over more traditional binary mixtures with fixed mixing rules, which is anticipated to open new avenues for directed self-assembly. At present, colloidal self-assembly into non-trivial lattices tends to require either high pressures for isotropically interacting particles, or the introduction of directionally anisotropic interactions. Here we demonstrate tunable assembly into a plethora of structures which requires neither of these conditions. We develop a minimal model that defines a three-dimensional phase space containing one dimension for each pairwise interaction, then employ various computational techniques to map out regions of this phase space in which the system self-assembles into these different morphologies. We then present a mean-field model that is capable of reproducing these results for size-symmetric mixtures, which reveals how to target different structures by tuning pairwise interactions, solution stoichiometry, or both. Concerning particle size asymmetry, we find that domains in this model’s phase space, corresponding to different morphologies, tend to undergo a continuous “rotation” whose magnitude is proportional to the size asymmetry. Such continuity enables one to estimate the relative stability of different lattices for arbitrary size asymmetries. Owing to its simplicity and accuracy, we expect this model to serve as a valuable design tool for engineering binary colloidal crystals from multi-flavored components.

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“…Here, r is the distance between particle centers and θ are the parameters required for the pair potential. By minimizing either the ground state energy of the ideal configuration (relative to competing structures) or the free energy of an associated configurational ensemble at a higher temperature (relative to competing phases), researchers have successfully found isotropic interactions that stabilize a wide variety of structures and phases including, for example, two-dimensional honeycomb [40][41][42] and kagome [43][44][45] lattice assemblies as well as three-dimensional simple cubic 46 and diamond [46][47][48] crystals. Isotropic pair potentials that stabilize more exotic phases have also been discovered via recently introduced inverse design strategies [49][50][51] .…”

Section: Introductionmentioning

confidence: 99%

Inverse design of multicomponent assemblies

Piñeros

Lindquist

Jadrich

et al. 2018

The Journal of Chemical Physics

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Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology-relative entropy optimization-to determine isotropic interactions that promote assembly of targeted multicomponent phases, and we apply this extension to design interactions for a variety of binary crystals ranging from compact triangular and square architectures to highly open structures with dodecagonal and octadecagonal motifs. We compare the resulting optimized (self- and cross) interactions for the binary assemblies to those obtained from optimization of analogous single-component systems. This comparison reveals that self-interactions act as a "primer" to position particles at approximately correct coordination shell distances, while cross interactions act as the "binder" that refines and locks the system into the desired configuration. For simpler binary targets, it is possible to successfully design self-assembling systems while restricting one of these interaction types to be a hard-core-like potential. However, optimization of both self- and cross interaction types appears necessary to design for assembly of more complex or open structures.

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Free-energy functional method for inverse problem of self assembly

Cited by 14 publications

References 33 publications

Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices

Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices

Assembly of multi-flavored two-dimensional colloidal crystals

Inverse design of multicomponent assemblies

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