Competing nucleation pathways in a mixture of oppositely charged colloids: Out-of-equilibrium nucleation revisited

Peters, Baron

doi:10.1063/1.3271024

Cited by 67 publications

(98 citation statements)

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“…Instead, we need explicit information about the dynamics undergone by components, together with a predictive theory that works "far" from equilibrium. Despite much progress in this direction [13][14][15][16][17][18][19][20][21][22], such a theory does not exist. Here we present evidence suggesting that concepts of nonequilibrium statistical physics may provide a route to a predictive theory of far-from-equilibrium self-assembly.…”

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confidence: 99%

“…The result is a structure whose component types are distributed in a nonequilibrium manner [18][19][20][21][22][23]. Returning to the picture of evolution on a free-energy landscape, one must think of the direction of motion across this landscape as being biased strongly by the underlying microscopic dynamics [22].Predicting the outcome of such "far-from-equilibrium" self-assembly is not generally possible. For the reasons just described, we cannot do so within the framework of equilibrium statistical mechanics, i.e., by calculating and inspecting the appropriate free-energy landscape.…”

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confidence: 99%

“…Because the mobility of particles within solid structures is usually very low (red arrows on figure), such interchange can fail to happen on experimental time scales. The result is a structure whose component types are distributed in a nonequilibrium manner [18][19][20][21][22][23]. Returning to the picture of evolution on a free-energy landscape, one must think of the direction of motion across this landscape as being biased strongly by the underlying microscopic dynamics [22].…”

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confidence: 99%

“…The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in two and three dimensions. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature. DOI: 10.1103/PhysRevLett.112.155504 PACS numbers: 81.16.Dn, 05.20.-y, 81.16.Fg Nature builds its materials using multiple component types. The properties of these materials depend on the properties of their components, and on how components are distributed spatially: the exciton transfer properties of a light-harvesting complex, for instance, depend on the way that its constituent proteins cluster [1]. Achieving similar mesoscale spatial control with many synthetic selfassembled materials [2] is made difficult by the fact that the self-assembly of multicomponent systems generally happens "far" from equilibrium, where we possess few predictive theoretical tools. Although self-assembly is a nonequilibrium process, much of our understanding of it is based upon a physical picture that assumes dynamics to play no role except to convey a system along the "easiest" pathways on its free-energy landscape [3]. This "nearequilibrium" or "quasiequilibrium" assumption tends to hold, for instance, for simple one-component systems under mild nonequilibrium conditions [4][5][6][7][8]. It fails when there exist time scales within a given self-assembly process that exceed the time of the experiment or computer simulation. For one-component systems, long time scales can emerge if bonds between particles are strong, and so break infrequently, which can happen when subjected to "harsh" nonequilibrium conditions (e.g., conditions of deep supercooling). Binding errors made as components associate can then fail to anneal as structures grow, and the result is a kinetically trapped structure rather than an object corresponding to a favored position on the free-energy landscape [9][10][11][12].The self-assembly of multicomponent solid structures, however, is also affected by kinetic traps that emerge even under mild nonequilibrium conditions. The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig. 1(a), which shows in cartoon form a fluid of two types of mutually attractive particles (call them "red" and "blue"), present in equal number, self-assembling into a solid structure. The equilibrium pattern of red and blue within this structure-shown in the figure as demixed red and blue domains-is determined only by the particles' mutual interactions. But achieving this equilibrium pattern via self-assembly requires that particle types interchange their positio...

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“…The long time scale responsible for such trapping is the slow interchange of component types within solid structures [13][14][15][16][17][18][19][20][21][22][23]. Consider Fig.…”

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Self-Assembly at a Nonequilibrium Critical Point

2014

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“…Although we cannot rule out a thermodynamic origin for the 2:1 disordered regime, our findings suggest a possible nonequilibrium origin for MOF-2000s robust composition ratio. Previous work has demonstrated that kinetic trapping of multiple component types during self-assembly can occur in a variety of contexts (20,(24)(25)(26)(27)(28)(29). Our simulations also suggest a set of requirements for generating nontrivial magic number ratios of components within covalent frameworks generally.…”

Section: Growth Simulations Reveal That Magic Number Component Ratiosmentioning

confidence: 69%

Heterogeneity of functional groups in a metal–organic framework displays magic number ratios

Sue

Mannige

Deng

et al. 2015

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

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Multiple organic functionalities can now be apportioned into nanoscale domains within a metal-coordinated framework, posing the following question: how do we control the resulting combination of "heterogeneity and order"? Here, we report the creation of a metal-organic framework, MOF-2000, whose two component types are incorporated in a 2:1 ratio, even when the ratio of component types in the starting solution is varied by an order of magnitude. Statistical mechanical modeling suggests that this robust 2:1 ratio has a nonequilibrium origin, resulting from kinetic trapping of component types during framework growth. Our simulations show how other "magic number" ratios of components can be obtained by modulating the topology of a framework and the noncovalent interactions between component types, a finding that may aid the rational design of functional multicomponent materials.metal-organic framework | out of equilibrium | polycrystalline | Monte Carlo simulationT he assembly of multiple types of component offers a potential route to the precise control of component heterogeneity within ordered 3D frameworks. Metal-organic frameworks (MOFs) (1-5) possessing well-defined connectivities (6, 7) and tunable pore sizes (8-10) can assemble from a variety of building blocks (11)(12)(13)(14)(15)(16)(17). Recently, a MOF harboring two components distributed in a heterogeneous fashion on an ordered framework was demonstrated (1, 2). There exists no framework, however, whose component heterogeneity remains controlled in the face of changes of environment. Here, we report the creation of a material with exactly this property. MOF-2000 is assembled from two types of organic struts, called L r and L b (Fig. 1A). These struts have identical rigid backbones but bear either a crown ether (L r ) or [2] catenane (L b ) side chain attached at their center. X-ray diffraction of MOF-2000 single crystals revealed that struts form a twofold interpenetrated cubic framework of pcu-c topology (Fig. 1A, Right, and SI Appendix, section S1.3; structure available in Dataset S1). As a result of optical investigations, we confirmed that the two struts are distributed in the crystalline framework in an isotropic manner (Fig. 1B), suggesting that the two components are not distributed in a simple periodic way throughout the framework (because such arrangements would give rise to optical anisotropy; SI Appendix, section S1.5).Even though the arrangement of the two components in MOF-2000 is indiscernible by X-ray crystallography, presumably as a result of the positional disorder of the two strut types within the framework, and the rotational (11, 18) and conformational (11) disorder of the side chains, the presence of the two organic struts can be clearly determined by 1 H-NMR (SI Appendix, section S1.4). Strikingly, MOF-2000 displays a 2:1 ratio of L r and L b struts, even when the ratios of components in the parent solution are varied by over an order of magnitude (Fig. 1C). This feature makes MOF-2000 unique among multicomponent extended framework...

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