Coarsening of complex microstructures following spinodal decomposition

Park, C.-L.; Gibbs, John W.; Voorhees, Peter W.; Thornton, Katsuyo

doi:10.1016/j.actamat.2017.03.020

Cited by 16 publications

(22 citation statements)

References 43 publications

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“…To control the characteristics of the resulting porous bicontinuous microstructures, we fix the average fill fraction at 50% and tune the surface energy of the interface between the two phases to modify the resulting feature morphology. Drawing inspiration from nanoporous foams and block copolymers with morphology and directionality that can be controlled by properly choosing the alloying (40,41) or mixing ratios (42), we computed anisotropic shell architectures that mimic such directional tunability (43). Specifically, we prescribed an anisotropic surface energy γ(n) as a function of the surface normal n to penalize growth along a particular set of directions defined by {m1, .…”

Section: Parameter Space Explorationmentioning

confidence: 99%

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

Portela

Vidyasagar

Krödel

et al. 2020

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

109

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Low-density materials with tailorable properties have attracted attention for decades, yet stiff materials that can resiliently tolerate extreme forces and deformation while being manufactured at large scales have remained a rare find. Designs inspired by nature, such as hierarchical composites and atomic lattice-mimicking architectures, have achieved optimal combinations of mechanical properties but suffer from limited mechanical tunability, limited long-term stability, and low-throughput volumes that stem from limitations in additive manufacturing techniques. Based on natural self-assembly of polymeric emulsions via spinodal decomposition, here we demonstrate a concept for the scalable fabrication of nonperiodic, shell-based ceramic materials with ultralow densities, possessing features on the order of tens of nanometers and sample volumes on the order of cubic centimeters. Guided by simulations of separation processes, we numerically show that the curvature of self-assembled shells can produce close to optimal stiffness scaling with density, and we experimentally demonstrate that a carefully chosen combination of topology, geometry, and base material results in superior mechanical resilience in the architected product. Our approach provides a pathway to harnessing self-assembly methods in the design and scalable fabrication of beyond-periodic and nonbeam-based nano-architected materials with simultaneous directional tunability, high stiffness, and unsurpassed recoverability with marginal deterioration.

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Section: Parameter Space Explorationmentioning

confidence: 99%

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

Portela

Vidyasagar

Krödel

et al. 2020

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

109

View full text Add to dashboard Cite

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“…Since a full description of surface curvature is typically built on two variables, such as the pair of principal curvatures, we quantified the interface shape distributions (ISD) for different curvature measures. These types of 2D probability density maps have been used to characterize the morphological evolution of spinodal decomposition systems during coarsening [28,29].…”

Section: Curvature Distributionsmentioning

confidence: 99%

“…In case of the interface shape distributions (ISD), this implied that the ratio of the face areas with a certain combination of curvature to the total mesh area was considered. For example, in case of the ISD of the principal curvature, this means [28]:…”

Section: Curvature Probability Density Distributionsmentioning

confidence: 99%

The local and global geometry of trabecular bone

Callens

Tourolle

Müller

et al. 2020

Preprint

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The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and can serve as blueprints for biomaterial design. To devise fundamental structure-property relationships, it is essential to characterize trabecular bone from the perspective of geometry, the mathematical study of shape. Here, we used the micro-computed tomography images of 70 donors at five different sites to characterize the local and global geometry of human trabecular bone, respectively quantified by surface curvatures and Minkowski functionals. We find that curvature density maps provide sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of complex tissue engineering scaffolds.

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“…This mechanism is commonly observed in the growth of thin films [13] and quantum dots [12]. In the following, we numerically predict the formation of bi-continuous phase networks through anisotropic spinodal decomposition, and we analyse the resulting structures in terms of their morphology and topology [7,[14][15][16].…”

Section: Introductionmentioning

confidence: 95%

“…As a quantitative measure of the morphology of microstructures resulting from anisotropic spinodal decomposition, we derive the interfacial shape distribution (ISD) on contours of constant ϕ = 0.5 within the RVE. The ISD is used to investigate self-similarity of bi-continuous structures and is related to the genus or the topology of microstructures [14][15][16]. Representative interface contours are visualized in figure 5a-d.…”

Section: (D) Interface Morphologymentioning

confidence: 99%

Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition

2018

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The generation of mechanical metamaterials with tailored effective properties through carefully engineered microstructures requires avenues to predict optimal microstructural architectures. Phase separation in heterogeneous systems naturally produces complex microstructural patterns whose effective response depends on the underlying process of spinodal decomposition. During this process, anisotropy may arise due to advection, diffusive chemical gradients or crystallographic interface energy, leading to anisotropic patterns with strongly directional effective properties. We explore the link between anisotropic surface energies during spinodal decomposition, the resulting microstructures and, ultimately, the anisotropic elastic moduli of the resulting medium. We simulate the formation of anisotropic patterns within representative volume elements, using recently developed stabilized spectral techniques that circumvent further regularization, and present a powerful alternative to current numerical techniques. The interface morphology of representative phase-separated microstructures is shown to strongly depend on surface anisotropy. The effective elastic moduli of the thus-obtained porous media are identified by periodic homogenization, and directionality is demonstrated through elastic surfaces. Our approach not only improves upon numerical tools to simulate phase separation; it also offers an avenue to generate tailored microstructures with tunable resulting elastic anisotropy.

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Coarsening of complex microstructures following spinodal decomposition

Cited by 16 publications

References 43 publications

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

The local and global geometry of trabecular bone

Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition

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