Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping

Area of Science:

• Materials Science
• Nanotechnology
• Solid Mechanics

Background:

• Two-dimensional (2D) materials such as molybdenum disulfide (MoS2), tungsten diselenide (WSe2), and graphene exhibit significant application potential.
• Understanding the fundamental mechanical properties of these 2D membranes is crucial for their technological advancement.
• Out-of-plane bending rigidity is a critical parameter influencing the morphology and behavior of 2D membranes under external stimuli.

Purpose of the Study:

• To develop an accessible experimental method for determining the bending rigidity of 2D membranes.
• To validate the applicability of continuum mechanics models for describing the bending behavior of atomic-thick 2D materials.
• To provide an alternative to purely theoretical approaches for measuring mechanical properties of flexible 2D membranes.

Main Methods:

• Utilizing high-resolution scanning/transmission electron microscopy (S/TEM) images to reconstruct the 3D atomic-scale structures of folded 2D membrane edges.
• Employing a quantitative comparison between experimental reconstructions and a continuum mechanics shell model.
• Fitting experimental data to the linear elastic shell model to derive bending rigidity values.

Main Results:

• An easy and effective method for reconstructing the 3D structures of folded 2D membrane edges at the atomic scale was established.
• The bending behavior of studied 2D materials (MoS2, WSe2, graphene) was accurately described by the linear elastic shell model.
• Experimental bending rigidities were successfully derived by fitting the model to the obtained results.

Conclusions:

• The proposed experimental technique offers a novel approach to measure the bending rigidity of flexible, atomically thin 2D membranes.
• This method bridges the gap between theoretical predictions and experimental validation of mechanical properties for 2D materials.
• The findings confirm the suitability of the linear elastic shell model for characterizing the bending response of various 2D membranes.