NDLI: Universal collapse of stress and wrinkle-to-scar transition in spherically confined crystalline sheets

Content Provider	PubMed Central
Author	Grason, Gregory M. Davidovitch, Benny
Abstract	Imposing curvature on crystalline sheets, such as 2D packings of colloids or proteins, or covalently bonded graphene leads to distinct types of structural instabilities. The first type involves the proliferation of localized defects that disrupt the crystalline order without affecting the imposed shape, whereas the second type consists of elastic modes, such as wrinkles and crumples, which deform the shape and also are common in amorphous polymer sheets. Here, we propose a profound link between these types of patterns, encapsulated in a universal, compression-free stress field, which is determined solely by the macroscale confining conditions. This “stress universality” principle and a few of its immediate consequences are borne out by studying a circular crystalline patch bound to a deformable spherical substrate, in which the two distinct patterns become, respectively, radial chains of dislocations (called “scars”) and radial wrinkles. The simplicity of this set-up allows us to characterize the morphologies and evaluate the energies of both patterns, from which we construct a phase diagram that predicts a wrinkle–scar transition in confined crystalline sheets at a critical value of the substrate stiffness. The construction of a unified theoretical framework that bridges inelastic crystalline defects and elastic deformations opens unique research directions. Beyond the potential use of this concept for finding energy-optimizing packings in curved topographies, the possibility of transforming defects into shape deformations that retain the crystalline structure may be valuable for a broad range of material applications, such as manipulations of graphene’s electronic structure.
Related Links	http://dx.doi.org/10.1073/pnas.1301695110
Ending Page	12898
Page Count	6
Starting Page	12893
File Format	PDF
ISSN	00278424
e-ISSN	10916490
Journal	Proceedings of the National Academy of Sciences of the United States of America
Issue Number	32
Volume Number	110
Language	English
Publisher	National Academy of Sciences
Publisher Date	2013-08-06
Access Restriction	Open
Rights Holder	National Academy of Sciences
Subject Keyword	General Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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