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Wrinkle motifs in thin films.

Budrikis Z, Sellerio AL, Bertalan Z, Zapperi S - Sci Rep (2015)

Bottom Line: Although these patterns are part of everyday experience and are important in industry, they are not completely understood.Here, we report simulation studies of a previously-overlooked phenomenon in which pairs of wrinkles form avoiding pairs, focusing on the case of graphene over patterned substrates.Our simulations uncover the generic behaviour of avoiding wrinkle pairs that should be valid at all scales.

View Article: PubMed Central - PubMed

Affiliation: ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy.

ABSTRACT
On length scales from nanometres to metres, partial adhesion of thin films with substrates generates a fascinating variety of patterns, such as 'telephone cord' buckles, wrinkles, and labyrinth domains. Although these patterns are part of everyday experience and are important in industry, they are not completely understood. Here, we report simulation studies of a previously-overlooked phenomenon in which pairs of wrinkles form avoiding pairs, focusing on the case of graphene over patterned substrates. By nucleating and growing wrinkles in a controlled way, we characterize how their morphology is determined by stress fields in the sheet and friction with the substrate. Our simulations uncover the generic behaviour of avoiding wrinkle pairs that should be valid at all scales.

No MeSH data available.


Related in: MedlinePlus

Wrinkle propagation is controlled by isotropic stresses.(a–d) Contour lines of the trace of the stress tensor outside the wrinkles during the evolution of an avoiding pair of wrinkles, with a field of view that excludes the sheet edges. The nucleus separations are X = Y = 56.6 nm. The line joining the wrinkle tips is a local maximum in the stress distribution and the tips propagate around the centre of this line, which is a saddle point. For clarity, the interiors of the wrinkles (defined by a height threshold of 2 Å) are not shown. All images have the same scale; the scale bar in panel (a) represents 100 nm.
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f4: Wrinkle propagation is controlled by isotropic stresses.(a–d) Contour lines of the trace of the stress tensor outside the wrinkles during the evolution of an avoiding pair of wrinkles, with a field of view that excludes the sheet edges. The nucleus separations are X = Y = 56.6 nm. The line joining the wrinkle tips is a local maximum in the stress distribution and the tips propagate around the centre of this line, which is a saddle point. For clarity, the interiors of the wrinkles (defined by a height threshold of 2 Å) are not shown. All images have the same scale; the scale bar in panel (a) represents 100 nm.

Mentions: When two wrinkles are grown in proximity, their behaviour is determined by the superposition of their stress fields. A video showing the evolution of stresses for a growing pair of wrinkles is provided as Supplementary Information. As shown in Fig. 4, wrinkles propagate along the steepest stress gradient in front of them. Pairs of wrinkles propagate in a spiral around the centre of the line joining their tips. As seen in Fig. 4(a,b), wrinkle tips initially propagate outwards slightly, and the high-stress central region expands. As the tips pass each other, their motion changes to an inwards propagation, as seen in Fig. 4(c), and the high-stress region contracts. The wrinkles continue to propagate around the centre of the line joining their tips, and come to a stop in the configuration seen in Fig. 4(d). This configuration is stabilized by the balance between applied forces and stresses in the sheet. The deformations required to merge two wrinkles are highly unfavourable and avoiding pairs are hard to remove. As seen in Fig. 2(d), when wrinkle nuclei are close, wrinkles are short because they are unable to grow far before blocking each other. On the other hand, for large nuclei distances, stresses due to interactions are reduced and wrinkle propagation is decreased accordingly. The existence of an optimal tip distance for wrinkle growth is due to the competition between these factors.


Wrinkle motifs in thin films.

Budrikis Z, Sellerio AL, Bertalan Z, Zapperi S - Sci Rep (2015)

Wrinkle propagation is controlled by isotropic stresses.(a–d) Contour lines of the trace of the stress tensor outside the wrinkles during the evolution of an avoiding pair of wrinkles, with a field of view that excludes the sheet edges. The nucleus separations are X = Y = 56.6 nm. The line joining the wrinkle tips is a local maximum in the stress distribution and the tips propagate around the centre of this line, which is a saddle point. For clarity, the interiors of the wrinkles (defined by a height threshold of 2 Å) are not shown. All images have the same scale; the scale bar in panel (a) represents 100 nm.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4355740&req=5

f4: Wrinkle propagation is controlled by isotropic stresses.(a–d) Contour lines of the trace of the stress tensor outside the wrinkles during the evolution of an avoiding pair of wrinkles, with a field of view that excludes the sheet edges. The nucleus separations are X = Y = 56.6 nm. The line joining the wrinkle tips is a local maximum in the stress distribution and the tips propagate around the centre of this line, which is a saddle point. For clarity, the interiors of the wrinkles (defined by a height threshold of 2 Å) are not shown. All images have the same scale; the scale bar in panel (a) represents 100 nm.
Mentions: When two wrinkles are grown in proximity, their behaviour is determined by the superposition of their stress fields. A video showing the evolution of stresses for a growing pair of wrinkles is provided as Supplementary Information. As shown in Fig. 4, wrinkles propagate along the steepest stress gradient in front of them. Pairs of wrinkles propagate in a spiral around the centre of the line joining their tips. As seen in Fig. 4(a,b), wrinkle tips initially propagate outwards slightly, and the high-stress central region expands. As the tips pass each other, their motion changes to an inwards propagation, as seen in Fig. 4(c), and the high-stress region contracts. The wrinkles continue to propagate around the centre of the line joining their tips, and come to a stop in the configuration seen in Fig. 4(d). This configuration is stabilized by the balance between applied forces and stresses in the sheet. The deformations required to merge two wrinkles are highly unfavourable and avoiding pairs are hard to remove. As seen in Fig. 2(d), when wrinkle nuclei are close, wrinkles are short because they are unable to grow far before blocking each other. On the other hand, for large nuclei distances, stresses due to interactions are reduced and wrinkle propagation is decreased accordingly. The existence of an optimal tip distance for wrinkle growth is due to the competition between these factors.

Bottom Line: Although these patterns are part of everyday experience and are important in industry, they are not completely understood.Here, we report simulation studies of a previously-overlooked phenomenon in which pairs of wrinkles form avoiding pairs, focusing on the case of graphene over patterned substrates.Our simulations uncover the generic behaviour of avoiding wrinkle pairs that should be valid at all scales.

View Article: PubMed Central - PubMed

Affiliation: ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy.

ABSTRACT
On length scales from nanometres to metres, partial adhesion of thin films with substrates generates a fascinating variety of patterns, such as 'telephone cord' buckles, wrinkles, and labyrinth domains. Although these patterns are part of everyday experience and are important in industry, they are not completely understood. Here, we report simulation studies of a previously-overlooked phenomenon in which pairs of wrinkles form avoiding pairs, focusing on the case of graphene over patterned substrates. By nucleating and growing wrinkles in a controlled way, we characterize how their morphology is determined by stress fields in the sheet and friction with the substrate. Our simulations uncover the generic behaviour of avoiding wrinkle pairs that should be valid at all scales.

No MeSH data available.


Related in: MedlinePlus