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

Proceedings of the National Academy of Sciences of the United States of America

Volumn 110, Issue 32, 2013, Pages 12893-12898

  Grason, Gregory M ^a   Davidovitch, Benny ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Curved crystals; Tension field theory; Topological defects

Indexed keywords

GRAPHENE; POLYMER;

ARTICLE; CELL SIZE; CHEMICAL STRUCTURE; COMPRESSION; CONCEPTUAL FRAMEWORK; CRYSTALLINE SHEETS; ELASTICITY; ENCAPSULATION; ENERGY; GEOMETRY; MATERIALS; MORPHOLOGY; PRIORITY JOURNAL; STATIC ELECTRICITY; STRESS; TENSION; THICKNESS; TOPOGRAPHY;

CURVED CRYSTALS; TENSION FIELD THEORY; TOPOLOGICAL DEFECTS;

ALGORITHMS; COLLOIDS; COMPUTER SIMULATION; CRYSTALLIZATION; ENERGY TRANSFER; GRAPHITE; KINETICS; MODELS, CHEMICAL; MODELS, MOLECULAR; PHASE TRANSITION; PROTEINS;

EID: 84881436679     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1301695110     Document Type: Article

References (30)

1. Sleytr UB, Sára M, Pum D, Schuster B (2001) Characterization and use of crystalline bacterial cell surface layers. Prog Surf Sci 68:231-278.
2. Pearse BMF, Crowther RA (1987) Structure and assembly of coated vesicles. Annu Rev Biophys Biophys Chem 16:49-68.
3. Korlach J, Schwille P, Webb WW, Feigenson GW (1999) Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. Proc Natl Acad Sci USA 96(15):8461-8466.
4. Schneider S, Gompper G (2005) Shapes of crystalline domains on spherical fluid vesicles. Europhys Lett 70:136-142.
5. VernizziG, Sknepnek R,Olvera de la Cruz M (2011) Platonic andArchimedean geometries in multicomponent elastic membranes. Proc Natl Acad Sci USA 108(11):4292-4296.
6. Bausch AR, et al. (2003) Grain boundary scars and spherical crystallography. Science 299(5613):1716-1718.
7. Irvine WTM, Vitelli V, Chaikin PM (2010) Pleats in crystals on curved surfaces. Nature 468(7326):947-951.
8. Seung HS, Nelson DR (1988) Defects in flexible membranes with crystalline order. Phys Rev A 38(2):1005-1018.
9. Saff EB, Kuijlaars ABJ (1997) Distributing many points on a sphere. Math Intelligencer 19:5-11.
10. Nelson DR, Peliti L (1987) Fluctuations in membranes with crystalline and hexatic order. J Phys 48:1085-1092.
11. Bowick MJ, Nelson DR, Travesset A (2000) Interacting topological defect on frozen topographies. Phys Rev B 62:8738-8751.
12. Vitelli V, Lucks JB, Nelson DR (2006) Crystallography on curved surfaces. Proc Natl Acad Sci USA 103(33):12323-12328.
13. Bowick MJ, Giomi L (2009) Two-dimensional matter: Order, curvature and defects. Adv Phys 58:449-563.
14. Azadi A, Grason GM (2012) Defects in crystalline packings of twisted filament bundles. II. Dislocations and grain boundaries. Phys Rev E Stat Nonlin Soft Matter Phys 85(3 Pt 1):031604.
15. Mansfield EH (1989) The Bending and Stretching of Plates (Cambridge Univ Press, Cambridge, UK).
16. Witten TA (2007) Stress focusing in elastic sheets. Rev Mod Phys 79:643-675.
17. King H, Schroll RD, Davidovitch B, Menon N (2012) Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities. Proc Natl Acad Sci USA 109(25):9716-9720.
18. Hure J, Roman B, Bico J (2012) Stamping and wrinkling of elastic plates. Phys Rev Lett 109(5):054302.
19. Hure J, Roman B, Bico J (2011) Wrapping an adhesive sphere with an elastic sheet. Phys Rev Lett 106(17):174301.
20. Stein M, Hedgpeth JM (1961) Analysis of Partly Wrinkled Membranes (Natl Aeronautics Space Admin, Washington), Technical Note D-813.
21. Pipkin AC (1986) The relaxed energy density for isotropic elastic membranes. IMA J Appl Math 36:85-99.
22. Davidovitch B, Schroll RD, Vella D, Adda-Bedia M, Cerda EA (2011) Prototypical model for tensional wrinkling in thin sheets. Proc Natl Acad Sci USA 108(45): 18227-18232.
23. Irvine WTM, Bowick MJ, Chaikin PM (2013) Fractionalization of interstitials in curved colloidal crystals. Nat Materials 11:948-951.
24. Hirth JP, Lothe J (1982) Theory of Dislocation (Wiley, New York).
25. Romanov AB, Vladimirov VI (1981) Straight disclinations near a free surface I. Stress fields. Phys Stat Sol (a) 63:109-118.
26. Romanov AB, Vladimirov VI (1981) Straight disclinations near a free surface II. The interactions between wedge disclinations and surface. Phys Stat Sol (a) 63: 383-388.
27. Cerda E, Mahadevan L (2003) Geometry and physics of wrinkling. Phys Rev Lett 90(7):074302.
28. Yao Z, Bowick M, Ma X, Sknepnek R (2013) Planar sheets meet negative-curvature interfaces. Eur Phys Lett 101:44007.
29. Davidovitch B, Schroll RD, Cerda E (2012) Nonperturbative model for wrinkling in highly bendable sheets. Phys Rev E Stat Nonlin Soft Matter Phys 85(6 Pt 2):066115.
30. Pereira VM, et al. (2009) Strain engineering of graphene's electronic structure. Phys Rev Lett 103:046801.