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In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can sense and select the finite size of assembly at length scales much larger than constituent building blocks or their interactions. At present, self-limitation is chiefly understood to derive from zero-temperature considerations, specifically the competition between cohesion and scale-dependent elastic costs of frustration. While effects of entropy and finite-temperature fluctuations are necessarily significant for self-assembling systems, their impact on the self-limiting states of frustrated assemblies is not known. We introduce a generic, minimal model of frustrated assembly and establish its finite-temperature and concentration-dependent thermodynamics by way of simulation and continuum theory. The phase diagram is marked by three distinct states of translation order: a dispersed vapor, a defect-riddled condensate, and the self-limiting aggregate state. We show that, at finite temperature, the self-limiting state is stable at intermediate frustration. Furthermore, in contrast to the prevailing picture, its thermodynamic boundaries with the macroscopic disperse and bulk states are temperature controlled, pointing to the essential importance of translational and conformational entropy in their formation.
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Building blocks of non-Euclidean ribbons: size-controlled self-assembly via discrete frustrated particles
Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current challenge is to understand the connection between microscopic physical properties of misfitting “building blocks” and emergent assembly behavior at the mesoscale. We present and analyze a particle-based description of what is arguably the best studied example for frustrated soft matter assembly, negative-curvature ribbon assembly, observed in both assemblies of chiral surfactants and shape-frustrated nanoparticles. Based on our particle model, known as saddle wedge monomers, we numerically test the connection between microscopic shape and interactions of the misfitting subunits and the emergent behavior at the supra-particle scale, specifically focussing on the propagation and relaxation of inter-particle strains, the emergent role of extrinsic shape on frustrated ribbons and the equilibrium regime of finite width selection. Beyond the intuitive role of shape misfit, we show that self-limitation is critically dependent on the finite range of cohesive interactions, with larger size finite assemblies requiring increasing short-range interparticle forces. Additionally, we demonstrate that non-linearities arising from discrete particle interactions alter self-limiting behavior due to both strain-softening in shape-flattened assembly and partial yielding of highly strained bonds, which in turn may give rise to states of hierarchical, multidomain assembly. Tracing the regimes of frustration-limited assembly to the specific microscopic features of misfitting particle shapes and interactions provides necessary guidance for translating the theory of size-programmable assembly into design of intentionally-frustrated colloidal particles.
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- Award ID(s):
- 2028885
- PAR ID:
- 10394988
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 19
- Issue:
- 5
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 858 to 881
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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