🔬 mesoscale physics

Self-Folding and Self-Scrolling Mechanisms of Edge-Deformed Graphene Sheets: A Molecular Dynamics Study

This molecular dynamics study reveals that the self-folding and self-scrolling behaviors of edge-deformed graphene sheets into graphene-based nanofolds or nanoscrolls are critically determined by the initial edge twist angles and temperature, with specific configurations leading to single-folded, multi-folded, or dual-state morphologies.

Original authors: Marcelo Lopes Pereira Junior, Luiz Antonio Ribeiro Junior

Published 2026-09-09

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CC BY 4.0

Original authors: Marcelo Lopes Pereira Junior, Luiz Antonio Ribeiro Junior

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a sheet of material so thin it is essentially a single layer of atoms, yet strong enough to hold up a bicycle and flexible enough to be woven into fabric. This is graphene, a form of carbon that has captured the imagination of scientists for its unique ability to bend, twist, and roll without breaking. While we often think of such materials as flat and static, nature has a way of curling them up. Under the right conditions, these sheets can spontaneously twist themselves into tight spirals or fold over like a piece of paper, creating new shapes with different electrical and mechanical properties. Understanding exactly how and why these transformations happen is crucial for engineers who hope to build tiny machines or advanced batteries from carbon, but the process occurs too quickly and on a scale too small for even the most powerful microscopes to watch in real time.

To solve this puzzle, researchers Marcelo Lopes Pereira Junior and Luiz Antonio Ribeiro Junior turned to a powerful tool called molecular dynamics simulation. Instead of building physical models, they used a supercomputer to create a virtual version of a graphene sheet, allowing them to watch every single atom move as if they were observing a high-speed movie. They started with sheets that had their edges pre-twisted, mimicking a specific experimental setup where carbon layers are spun to form complex structures. By adjusting the angle of these twists and running the simulation at different temperatures, they could see exactly how the sheet reacted over time, tracking the energy changes that drive the material to change its shape.

The researchers discovered that the amount of twist at the edge acts as a switch that determines the final shape of the graphene. When the edges were twisted by a moderate amount, the sheet did not roll up; instead, it folded over onto itself, creating a neat, stacked structure. This folding happened incredibly fast, often within just a few trillionths of a second. However, when the twist angle was increased beyond a certain point, the behavior changed completely. The sheet began to curl into a spiral, resembling a scroll or a rolled-up newspaper. This transformation into a scroll was also rapid, but it required a stronger initial twist to overcome the natural stiffness of the carbon atoms. The team found that if the twist was too slight, the sheet simply relaxed back into a flat state, unable to overcome its own rigidity to form a new shape.

One of the most striking findings was how temperature influenced these changes. At lower temperatures, the sheet could form complex structures, such as a double-folded shape where the edges met and bonded together. But as the researchers heated the simulation, the intense jiggling of the atoms disrupted these delicate bonds. In some cases, a structure that would have folded into two layers at room temperature instead collapsed into a single layer when heated, because the thermal energy was too strong for the double-fold to hold. Yet, the scrolls proved to be more resilient; even at high temperatures, once the graphene formed a spiral, it tended to stay that way, maintaining its shape despite the heat.

Perhaps the most surprising result occurred when the researchers twisted the two edges of the sheet by different amounts. In this scenario, the graphene did not choose just one path. Instead, it created a hybrid structure where one side folded over while the other side rolled into a scroll. This dual state, combining both a folded section and a scrolled section in the same piece of material, had never been observed before. The simulation showed that this mixed shape was stable and could form regardless of the temperature, suggesting that the material has a natural tendency to find a balance between these two different forms when pushed in conflicting directions.

The study also revealed that the specific arrangement of atoms along the edge of the sheet did not change the outcome. Whether the edge was arranged in a straight line or a zigzag pattern, the sheet behaved the same way, folding or rolling based solely on the angle of the twist and the temperature. This suggests that the mechanism driving these changes is universal for this type of carbon material, depending more on the overall shape and energy than on the microscopic details of the edge. By mapping out these pathways, the researchers have provided a clear picture of how edge-deformed graphene behaves, offering a guide for future experiments. They showed that by carefully controlling the twist at the edges, it is possible to direct the material to become a specific type of folded or scrolled structure, opening the door to designing carbon-based materials with precise, custom-made shapes.

Technical Summary: Self-Folding and Self-Scrolling Mechanisms of Edge-Deformed Graphene Sheets

Problem Statement
Graphene-based nanofolds (GNFs) and nanoscrolls (GNSs) represent significant structural modifications to single-layer graphene (SLG) that induce changes in mechanical and optoelectronic properties. While experimental studies have observed self-folding and self-scrolling phenomena triggered by edge deformations, and theoretical works have utilized continuum mechanics or molecular dynamics (MD) to study these processes, the specific time scales, intermediate metastable states, and final morphologies resulting from edge-deformed SLG remain not fully understood. Previous theoretical investigations often relied on external agents (such as carbon nanotubes or nanoribbons) to trigger deformation, rather than focusing on the intrinsic self-deformation mechanisms driven solely by edge geometry.

Methodology
The authors employed fully atomistic reactive molecular dynamics (MD) simulations using the ReaxFF force field, implemented within the LAMMPS software package. The study utilized the C/H/O parameter set developed by Chenoweth et al.

Models: The initial configurations were armchair edge-scrolled graphene (AESG) sheets with dimensions of 100 Å × 200 Å (7,776 atoms). These models featured specific twist angles ( $\phi$ and $\theta$ ) applied to the edges to mimic experimental setups for forming biscrolled sheets. The twist angles investigated included values of $-3\pi, -2\pi, 0, 2\pi,$ and $3\pi$ .
Simulation Conditions: Simulations were conducted in the NVT ensemble using a Nosé-Hoover thermostat. The temperature was varied from 100 K to 1000 K in 100 K increments. The equations of motion were integrated using the velocity-Verlet algorithm with a 0.25 fs time step for a total duration of 250 ps.
Comparative Analysis: The study also included simulations of zigzag edge-scrolled graphene (ZESG) to determine if edge topology (armchair vs. zigzag) influenced the deformation mechanisms.

Key Results
The simulations revealed distinct morphological outcomes based on the initial twist angles and temperature:

Twist Angles $\leq \pi$ : Twist angles lower than $\pi$ were insufficient to trigger self-deformation. In these cases, the interlayer van der Waals interactions could not overcome the SLG bending rigidity, and the structures relaxed back into conventional single-layer graphene.
Twist Angles $> 2\pi$ (Folding):
- AESG(0, 2 $\pi$ ): Evolved into a single-folded, fully stacked morphology (GNF).
- AESG(2 $\pi$ , 2 $\pi$ ): Evolved into a two-folded, fully stacked morphology. However, this specific two-folded structure was only stable below a critical temperature of approximately 900 K. At 1000 K, thermal fluctuations overcame the potential energy well required for the two-folded state, resulting in a single-folded morphology instead.
- Kinetics: The transition from twisted edges to folded structures occurred within an ultrafast period (approx. 2 ps at 300 K, and <1 ps at 1000 K).
Twist Angles $> 2\pi$ (Scrolling):
- AESG(0, 3 $\pi$ ) and AESG(3 $\pi$ , 3 $\pi$ ): These configurations transitioned rapidly into stable GNSs after an initial relaxation period.
- AESG(3 $\pi$ , 3 $\pi$ ) Dynamics: A metastable "biscroll" state formed initially due to the interplay between left- and right-sided partial scrolling. This state eventually collapsed into a single GNS. The formation of the final GNS occurred within 76 ps.
- Stability: Unlike the folding cases, the formation of stable GNSs from these high-twist angles occurred even at high temperatures (up to 1000 K).
Dual State Formation:
- AESG(2 $\pi$ , 3 $\pi$ ): This system, with different twist angles on opposing edges, evolved into a unique dual state combining both folded and scrolled structures. This process was found to be temperature-independent.
Negative Twist Angles:
- AESG(-2 $\pi$ , 2 $\pi$ ): Evolved into a collapsed structure with two-folded edges, stabilized by the formation of carbon-carbon covalent bonds due to the extreme proximity of the edges.
- AESG(-3 $\pi$ , 3 $\pi$ ): Yields a dual state that combines folded and scrolled structures, similar to the results presented for the positive twist angle case.
Edge Topology Independence: Comparisons between armchair (AESG) and zigzag (ZESG) lattices demonstrated that the edge topology does not affect the fundamental folding and scrolling mechanisms; the time evolution of potential energy and final morphologies were similar for both lattice types.
Energetics: Potential energy analysis confirmed that scrolled and folded configurations are energetically favorable. The potential energy curves showed a downhill trend during the formation of GNSs, stabilizing after 40–100 ps depending on the system.

Significance and Claims
The authors claim that this study provides crucial insights into the self-deformation of curved graphene sheets, specifically addressing the time scales and intermediate states that are difficult to capture experimentally. The paper highlights several novel findings:

It reports the first observation of a collapsed structure with two-folded edges stabilized by covalent bond formation in the AESG(-2 $\pi$ , 2 $\pi$ ) case.
It identifies a dual state where folded and scrolled structures coexist in the final morphology (observed in AESG(2 $\pi$ , 3 $\pi$ ), AESG(-3 $\pi$ , 3 $\pi$ ), and other cases), a configuration not previously reported.
It establishes that the self-deformation process is temperature-independent for the dual state and high-twist angle scrolling, whereas the specific two-folded folding morphology is temperature-sensitive (stable only below ~900 K).
The study clarifies that edge topology (armchair vs. zigzag) is not a determining factor in the self-folding or self-scrolling mechanisms.

The work serves to bridge the gap between experimental observations of edge-deformed graphene and theoretical understanding, offering a detailed atomistic view of the formation of GNFs and GNSs without the need for external triggering agents.

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