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A three-dimensional phase diagram of growth-induced surface instabilities.

Wang Q, Zhao X - Sci Rep (2015)

Bottom Line: However, a general model that accounts for the formation and evolution of these various surface-instability patterns still does not exist.The predicted wavelengths and amplitudes of various instability patterns match well with our experimental data.It is expected that the unified phase diagram will not only advance the understanding of biological morphogenesis, but also significantly facilitate the design of new materials and structures by rationally harnessing surface instabilities.

View Article: PubMed Central - PubMed

Affiliation: 1] Soft Active Materials Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA [2] Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA.

ABSTRACT
A variety of fascinating morphological patterns arise on surfaces of growing, developing or aging tissues, organs and microorganism colonies. These patterns can be classified into creases, wrinkles, folds, period-doubles, ridges and delaminated-buckles according to their distinctive topographical characteristics. One universal mechanism for the pattern formation has been long believed to be the mismatch strains between biological layers with different expanding or shrinking rates, which induce mechanical instabilities. However, a general model that accounts for the formation and evolution of these various surface-instability patterns still does not exist. Here, we take biological structures at their current states as thermodynamic systems, treat each instability pattern as a thermodynamic phase, and construct a unified phase diagram that can quantitatively predict various types of growth-induced surface instabilities. We further validate the phase diagram with our experiments on surface instabilities induced by mismatch strains as well as the reported data on growth-induced instabilities in various biological systems. The predicted wavelengths and amplitudes of various instability patterns match well with our experimental data. It is expected that the unified phase diagram will not only advance the understanding of biological morphogenesis, but also significantly facilitate the design of new materials and structures by rationally harnessing surface instabilities.

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Experimental validation of the phase diagram for instability patterns in film-substrate structures with moderate adhesion energies.Comparison between experimental data and the phase diagrams of surface instability patterns with delamination: (A) flat to delaminated-buckle, (B) crease to delaminated-buckle, (C) wrinkle to delaminated-buckle, (D) fold to delaminated-buckle, (E) period-double to delaminated-buckle, and (F) ridge to delaminated-buckle. The circle markers with different colors in each phase domain represent the observed instability patterns. The inset images in each phase diagram represent the corresponding delaminated-buckle patterns. The two-dimensional phase diagrams are achieved by sectioning the three-dimensional phase diagram at the normalized adhesion energies Γ/(μsHf) equal to (A) 0.13, (B) 0.28, (C) 0.46, (D) 0.81, (E) 3.99 and (F) 66.63, respectively.
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f4: Experimental validation of the phase diagram for instability patterns in film-substrate structures with moderate adhesion energies.Comparison between experimental data and the phase diagrams of surface instability patterns with delamination: (A) flat to delaminated-buckle, (B) crease to delaminated-buckle, (C) wrinkle to delaminated-buckle, (D) fold to delaminated-buckle, (E) period-double to delaminated-buckle, and (F) ridge to delaminated-buckle. The circle markers with different colors in each phase domain represent the observed instability patterns. The inset images in each phase diagram represent the corresponding delaminated-buckle patterns. The two-dimensional phase diagrams are achieved by sectioning the three-dimensional phase diagram at the normalized adhesion energies Γ/(μsHf) equal to (A) 0.13, (B) 0.28, (C) 0.46, (D) 0.81, (E) 3.99 and (F) 66.63, respectively.

Mentions: Next, we discuss the observed patterns in film-substrate structures with moderate adhesion energies, which allow delamination between films and substrates. To compare the experimental observations with the calculated phase diagram, we section the three-dimensional phase diagram at various values of normalized adhesion energy, i.e., Γ/(μsHf) = 0.13, 0.28, 0.46, 0.81, 3.99 and 66.63 (Fig. 4). The phase boundaries between delaminated-buckle and other patterns are highlighted as red curves in these sections. From Fig. 4, it can be seen that the observed transitions of phases with the increase of εM indeed follow the calculated phase diagram, for various values of Γ/(μsHf) and μf/μs. In particular, the delaminated-buckle can coexist with other instability patterns, and the phase boundaries between delaminated-buckle and other patterns can consistently predict whether delamination occurs in the film-substrate structures.


A three-dimensional phase diagram of growth-induced surface instabilities.

Wang Q, Zhao X - Sci Rep (2015)

Experimental validation of the phase diagram for instability patterns in film-substrate structures with moderate adhesion energies.Comparison between experimental data and the phase diagrams of surface instability patterns with delamination: (A) flat to delaminated-buckle, (B) crease to delaminated-buckle, (C) wrinkle to delaminated-buckle, (D) fold to delaminated-buckle, (E) period-double to delaminated-buckle, and (F) ridge to delaminated-buckle. The circle markers with different colors in each phase domain represent the observed instability patterns. The inset images in each phase diagram represent the corresponding delaminated-buckle patterns. The two-dimensional phase diagrams are achieved by sectioning the three-dimensional phase diagram at the normalized adhesion energies Γ/(μsHf) equal to (A) 0.13, (B) 0.28, (C) 0.46, (D) 0.81, (E) 3.99 and (F) 66.63, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4352857&req=5

f4: Experimental validation of the phase diagram for instability patterns in film-substrate structures with moderate adhesion energies.Comparison between experimental data and the phase diagrams of surface instability patterns with delamination: (A) flat to delaminated-buckle, (B) crease to delaminated-buckle, (C) wrinkle to delaminated-buckle, (D) fold to delaminated-buckle, (E) period-double to delaminated-buckle, and (F) ridge to delaminated-buckle. The circle markers with different colors in each phase domain represent the observed instability patterns. The inset images in each phase diagram represent the corresponding delaminated-buckle patterns. The two-dimensional phase diagrams are achieved by sectioning the three-dimensional phase diagram at the normalized adhesion energies Γ/(μsHf) equal to (A) 0.13, (B) 0.28, (C) 0.46, (D) 0.81, (E) 3.99 and (F) 66.63, respectively.
Mentions: Next, we discuss the observed patterns in film-substrate structures with moderate adhesion energies, which allow delamination between films and substrates. To compare the experimental observations with the calculated phase diagram, we section the three-dimensional phase diagram at various values of normalized adhesion energy, i.e., Γ/(μsHf) = 0.13, 0.28, 0.46, 0.81, 3.99 and 66.63 (Fig. 4). The phase boundaries between delaminated-buckle and other patterns are highlighted as red curves in these sections. From Fig. 4, it can be seen that the observed transitions of phases with the increase of εM indeed follow the calculated phase diagram, for various values of Γ/(μsHf) and μf/μs. In particular, the delaminated-buckle can coexist with other instability patterns, and the phase boundaries between delaminated-buckle and other patterns can consistently predict whether delamination occurs in the film-substrate structures.

Bottom Line: However, a general model that accounts for the formation and evolution of these various surface-instability patterns still does not exist.The predicted wavelengths and amplitudes of various instability patterns match well with our experimental data.It is expected that the unified phase diagram will not only advance the understanding of biological morphogenesis, but also significantly facilitate the design of new materials and structures by rationally harnessing surface instabilities.

View Article: PubMed Central - PubMed

Affiliation: 1] Soft Active Materials Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA [2] Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA.

ABSTRACT
A variety of fascinating morphological patterns arise on surfaces of growing, developing or aging tissues, organs and microorganism colonies. These patterns can be classified into creases, wrinkles, folds, period-doubles, ridges and delaminated-buckles according to their distinctive topographical characteristics. One universal mechanism for the pattern formation has been long believed to be the mismatch strains between biological layers with different expanding or shrinking rates, which induce mechanical instabilities. However, a general model that accounts for the formation and evolution of these various surface-instability patterns still does not exist. Here, we take biological structures at their current states as thermodynamic systems, treat each instability pattern as a thermodynamic phase, and construct a unified phase diagram that can quantitatively predict various types of growth-induced surface instabilities. We further validate the phase diagram with our experiments on surface instabilities induced by mismatch strains as well as the reported data on growth-induced instabilities in various biological systems. The predicted wavelengths and amplitudes of various instability patterns match well with our experimental data. It is expected that the unified phase diagram will not only advance the understanding of biological morphogenesis, but also significantly facilitate the design of new materials and structures by rationally harnessing surface instabilities.

Show MeSH
Related in: MedlinePlus