Phase Separation in Binary Alloys - Modeling Approaches

Fratzl, Peter; Weinkamer, Richard

doi:10.1007/3-211-27404-9_2

Cited by 2 publications

(4 citation statements)

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“…Nature's biological diversity relies on multitier self1 assembly based on weak non1covalent interactions such as electrostatic, hydrogen (H)1bonding, and hydrophobic forces. 1 A classic example is provided by the interstrand H1bonds that stabilize the double helical structure of DNA, an essential el1 ement for genetics. 2 Furthermore, for polypeptides, the precise positioning of the H1bonding segments is of crucial im1 portance for the correct folding of polypeptide chains and thus the function of proteins.…”

Section: ! !mentioning

confidence: 99%

“…This can resemble the assembly of collagen fibrils to form the main scaffold in bone. 1 For example, a synthetic collagen mimic polypeptide has been shown to assemble into nanofibers, which can further hierarchically assemble to form hydrogels. 12 Similarly, Janus cylinders made from synthetic BCPs can ag1 gregate through well1defined solvophobic regions in selective solvents to form cylindrical bundles.…”

Section: ! !mentioning

confidence: 99%

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Hierarchical Assembly of Cylindrical Block Comicelles Mediated by Spatially Confined Hydrogen-Bonding Interactions

Gao

Harniman

et al. 2016

J. Am. Chem. Soc.

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Hydrogen bonds are among the most common interactions used by nature for the creation of hierarchical structures from smaller building blocks. Herein, we describe an in-depth study of the hierarchical assembly of cylindrical block comicelles with a crystallizable poly(ferrocenyldimethylsilane) (PFS) core via H-bonding interactions to form complex supermicellar structures. Well-defined block comicelles bearing H-bond donor (HD) segments (M(PFS-b-PMVSOH)), or H-bond acceptor (HA) segments (M(PFS-b-P2VP)), and non-interacting (N) segments (M(PFS-b-PtBA)) were created by the living crystallization-driven self-assembly (CDSA) method [PMVSOH = hydroxyl-functionalized poly(methylvinylsiloxane), P2VP = poly(2-vinylpyridine), PtBA = poly(tert-butyl acrylate), M = micelle segment]. Due to the control provided by the living CDSA approach, both the block comicelles and the individual segments were virtually monodisperse in length, which facilitated their predictable hierarchical assembly into higher-level structures. Two cases were investigated in detail: first, the interaction of N-HA-N triblock comicelles with the HD homopolymer PMVSOH, and second, the interaction of N-HD-N triblock comicelles with very short HA cylinders (seeds). By manipulation of several factors, namely coronal steric effects (via the PtBA corona chain) and attractive interaction strength (via the H-bonding interaction between P2VP and PMVSOH), the aggregation of the triblock comicelles could be controlled, and well-defined multi-micrometer-size structures such as “shish-kebab”-shaped supermicelles were prepared. The ability of the seeds adsorbed on the block comicelles to function as initiators for living CDSA to generate fence-like “shish-kebab” superstructures was also explored.

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Section: ! !mentioning

confidence: 99%

Section: ! !mentioning

confidence: 99%

Hierarchical Assembly of Cylindrical Block Comicelles Mediated by Spatially Confined Hydrogen-Bonding Interactions

Gao

Harniman

et al. 2016

J. Am. Chem. Soc.

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“…During various scientific investigations, we frequently come across phase segregation or separation phenomena in a range of materials, spanning from simple binary mixtures to complex systems [12,31]. To comprehensively understand these phenomena, one must adopt a versatile approach based on a diverse array of experiments, each underpinned by a unique set of statistical assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, the geometry of the system can also affect the flow of the binary components and the rate of segregation. Lattice gas models are simple models that can be used to model phase segregation in binary mixtures [12]. In a lattice gas model, the particles are located on a lattice of sites and the particle interactions are modelled by the operation H int through a potential between them.…”

Section: Introductionmentioning

confidence: 99%

Unified framework for the separation property in binary phase-segregation processes with singular entropy densities

Gal,

Poiatti

2024

Eur. J. Appl. Math

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This paper investigates the separation property in binary phase-segregation processes modelled by Cahn-Hilliard type equations with constant mobility, singular entropy densities and different particle interactions. Under general assumptions on the entropy potential, we prove the strict separation property in both two and three-space dimensions. Namely, in 2D, we notably extend the minimal assumptions on the potential adopted so far in the literature, by only requiring a mild growth condition of its first derivative near the singular points $\pm 1$ , without any pointwise additional assumption on its second derivative. For all cases, we provide a compact proof using De Giorgi’s iterations. In 3D, we also extend the validity of the asymptotic strict separation property to the case of fractional Cahn-Hilliard equation, as well as show the validity of the separation when the initial datum is close to an ‘energy minimizer’. Our framework offers insights into statistical factors like particle interactions, entropy choices and correlations governing separation, with broad applicability.

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Phase Separation in Binary Alloys - Modeling Approaches

Cited by 2 publications

References 100 publications

Hierarchical Assembly of Cylindrical Block Comicelles Mediated by Spatially Confined Hydrogen-Bonding Interactions

Hierarchical Assembly of Cylindrical Block Comicelles Mediated by Spatially Confined Hydrogen-Bonding Interactions

Unified framework for the separation property in binary phase-segregation processes with singular entropy densities

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