Reviewed by Frances BriggsJul 25 2025
Scientists at the Institute of Science Tokyo have developed a new simulation-based method to measure how graphene bends, even with defects, helping design stronger, flexible 2D materials.
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A research team at the Institute of Science Tokyo has developed a new computational approach to assess the mechanical behaviour of graphene nanosheets. The technique enables direct measurement of bending rigidity in sheets with structural defects, without the need for laboratory experiments.
The research, published in Nanoscale, combines molecular dynamics simulations with the Helfrich theory of membrane bending. The researchers say the method offers a practical way to model how graphene bends at the atomic level, including in sheets containing imperfections.
Graphene nanosheets are a type of two-dimensional (2D) nano-carbon material, known for their exceptional strength, flexibility, and ability to adapt to curved shapes. These properties can be altered by introducing five- or seven-membered rings into the regular hexagonal carbon lattice.
These irregular ring structures, known as disclinations, change the local geometry of the sheet. Removing a triangle from the hexagonal structure forms a five-membered ring, producing a cone-like shape; adding a triangle results in a seven-membered ring, leading to a saddle-shaped surface.
Such disclinations are already used in practical applications. For example, "egg-tray" graphene, which features a wave-like structure formed by periodic disclinations, is noted for its impact resistance. Graphene nanosheets with seven-membered rings also show potential for use as nanoscale springs.
While the bending rigidity of flat graphene sheets has been extensively studied, the mechanical properties of those with disclinations remain poorly understood. The presence of defects makes it difficult to obtain accurate experimental measurements.
To address this, the researchers developed a method that uses molecular simulations to estimate bending rigidity directly from atomic configurations. It is based on the Helfrich theory, which was originally developed to describe the curvature of biological membranes but is also applicable to graphene due to structural similarities.
We have developed a new hybrid approach, combining molecular dynamics simulations with Helfrich theory of membrane bending. This method allows for direct evaluation of bending rigidity of graphene sheets with lattice defects directly from atomic configurations without requiring experimental tests.
Xiao-Wen Lei, Associate Professor, School of Materials and Chemical Technology, Institute of Science Tokyo (Science Tokyo)
The researchers used their hybrid method to examine four different kinds of analytical models of graphene sheets (GSs) with disclinations: five-membered (positive) monopoles, seven-membered (negative) monopoles, and two types of dipoles, pairs of disclinations that were either connected or separated by varying distances.
The computed values of bending rigidity were in line with previous experimental findings, supporting the method's validity. More significantly, the findings showed that GSs with monopoles and dipoles have different patterns for the first time. After removing nonlinear influences, bending rigidity was comparable for disclination dipoles.
Combining conical and saddle-shaped surfaces caused a local shape change and a corresponding local bending rigidity change for dipoles. Additionally, bending rigidity converges to a stable value as the distance between disclinations increases. This suggests that the density and arrangement of lattice defects play a key role in determining mechanical properties.
Our findings not only offer a foundation for understanding mechanical properties of GSs with lattice defects but also insights for designing new GSs with specific bending rigidities and tailored mechanical properties.
Xiao-Wen Lei, Associate Professor, School of Materials and Chemical Technology, Institute of Science Tokyo (Science Tokyo)
This research may hasten the creation of innovative GS-based materials, including impact-resistant graphene structures and nano-springs, resulting in even more sophisticated 2D materials.
Journal Reference:
Kunihiro, Y., et al. (2025). A New Computational Approach for Evaluating Bending Rigidity of Graphene Sheets Incorporating Disclinations. Nanoscale. doi.org/10.1039/D5NR01102G.