Determinative scrolling and folding of membranes through shrinking channels

Area of Science:

• Materials Science
• Mechanical Engineering
• Physics

Background:

• Flat membranes naturally adopt complex shapes, a phenomenon observed in both natural and artificial systems.
• Understanding the underlying deformation modes is crucial for controlling these transformations and developing new applications.
• Existing models for membrane deformation lack comprehensive rules applicable across various scales.

Purpose of the Study:

• To identify and characterize the fundamental deformation modes of thin membranes.
• To establish quantitative relationships between deformation modes and material properties.
• To provide a mechanical framework for designing foldable 2D structures and microrobots.

Main Methods:

• Investigated membrane deformation through spontaneous scrolling and folding as they pass through shrinking channels.
• Validated the identified modes across a wide range of membrane thicknesses, from micrometers to the atomic scale.
• Correlated the occurrence and fold number of deformations with the Föppl-von Kármán number and shrinkage ratio.

Main Results:

• Deciphered two elemental deformation modes: spontaneous scrolling and folding.
• Confirmed these modes are applicable to membranes across a broad thickness spectrum.
• Established quantitative correlations between deformation behavior, Föppl-von Kármán number, and shrinkage ratio.

Conclusions:

• The study unveils two deterministic deformation modes governing thin membrane transformations.
• These findings offer a new mechanical principle for designing advanced 2D sheet structures and microrobots.
• The results provide fundamental insights into shape determination beyond biological morphogens.