Toroidal graphene represents a groundbreaking carbon nanostructure with a closed-loop topology of sp²-hybridized carbon atoms. Its unique toroidal geometry fosters a closed π-electron system, enabling extraordinary field amplification effects driven by quantum and curvature-induced phenomena. Unlike planar or cylindrical nanostructures, toroidal graphene exhibits unparalleled electromagnetic field localization, positioning toroidal graphene as a cornerstone for sustainable and high-performance technologies.

The toroidal graphene molecule is a nano-scientifically engineered zero-dimensional¹ sp2-hybridized carbon allotrope, consisting of 20-40 defect-free graphene layers without function-group content, geometrically fixed in a closed conjugated system with delocalized pi-electrons interacting freely in circular motion in the closed loop of the cyclic structure of the toroid instead of being occupied in pi-bonds with adjacent graphene layers. Thus, the toroidal graphene molecule exhibits delocalization of pi-electrons from the multiple layers in coherent oscillations across the entire molecule.

The coherent motion of delocalized pi-electrons arises from quantum mechanical principles, where neighboring pi-electrons exhibit wave-like constructive interference patterns, which occur when the wavefunctions of pi-electrons of the multiple layers align in phase, leading to an amplification of the oscillations that ultimately trigger a resonant response.

This resonance phenomenon, known as giant resonance, leads to a significant enhancement of the electromagnetic field of the molecule, amplifying its intensity by a factor of 30,000, as observed in Raman scattering experiments, where the amplification results in stronger Raman signals, providing direct evidence of the giant resonance phenomenon.

CNTs have been used as an additive in tens of thousands of attempts to modify materials and exits from this market include Bayer AG which described the potential applications of CNTs as ‘fragmented with comprehensive commercialization not likely in the foreseeable future’.

In the competitive landscape of nanomaterials, 2D graphene stands out as a key player, having been recognized by the Nobel Prize in Physics in 2010 for its remarkable properties. However, while the nanostructure of the graphene layer holds great promise, realizing its potential in real-world applications requires exploring alternative graphene solutions that offer defect-free graphene layers with greater structural and thermal integrity, such as the toroidal graphene molecule.

Discovery and Isolation of 2D graphene

• 2D Graphene, a single layer of carbon atoms arranged in a honeycomb lattice, was first isolated in 2004 by Andre Geim and Konstantin Novoselov using the Scotch tape method, a simple exfoliation technique that separates thin layers of graphite into monolayers.
• This groundbreaking discovery earned them the 2010 Nobel Prize in Physics for proving 2D Graphene’s existence and demonstrating its unique properties.
• Early enthusiasm surrounding 2D Graphene led to widespread misconceptions, particularly the belief that 2D Graphene sheets could directly replace existing materials in real-world components. However, practical challenges, such as the small size of 2D Graphene flakes and their inherent defects, limit 2D Graphene’s usability as standalone materials.

2D Graphene as Flakes

• In practical terms, 2D Graphene is usually available as 2D Graphene flakes—tiny fragments of monolayer or few-layer 2D Graphene, typically micrometers in size.
• These flakes are prone to various defects, which impact their performance:
  • Structural defects: Vacancies and dislocations in the atomic lattice that weaken mechanical properties.
  • Edge defects: Dangling carbon bonds at the edges of flakes, which are highly reactive.
  • Chemical defects: Functional groups, contaminants, or adsorbed molecules from processing.
  • Wrinkles and ripples: Out-of-plane distortions that affect 2D Graphene’s flat 2D nature.
• These defects reduce 2D Graphene’s strength, electrical conductivity, and thermal conductivity, causing its real-world performance to fall short of theoretical predictions.

Challenges of Using 2D Graphene Flakes

• The main focus of 2D Graphene projects involves developing methods to integrate 2D Graphene into composite materials (e.g., polymers, ceramics, or metals) to enhance properties such as strength, conductivity, and heat resistance. However, incorporating 2D Graphene flakes into host matrices poses significant challenges:
• Agglomeration: 2D Graphene flakes naturally clump together due to van der Waals forces and the reactivity of dangling bonds, reducing their surface area and usability.
• Dispersion Issues: Achieving uniform dispersion of 2D Graphene flakes in a composite is difficult but critical for consistent performance.
• Interfacial Bonding: 2D Graphene often interacts weakly with host materials, limiting the transfer of properties like mechanical reinforcement or electrical conductivity.

2D Graphene vs. Graphite: Defining the Transition

• A monolayer of 2D Graphene exhibits unique properties, such as high electrical conductivity, mechanical strength, and transparency, that are fundamentally different from graphite, the bulk material composed of stacked graphene layers.
• However, even a two-layer 2D Graphene flake begins to exhibit interlayer interactions, such as:
  • Van der Waals forces, which cause layers to stick together and mimic the behavior of graphite.
  • Electronic coupling, which disrupts the unique linear band structure of monolayer 2D Graphene, shifting it toward graphite-like parabolic or hybridized bands.
• Few-layer graphene (FLG): Materials with up to 10 layers are often classified as 2D Graphene for practical purposes, but their properties are closer to graphite as more layers are added.
• Scientifically, only monolayer 2D Graphene is true 2D Graphene, while bilayer and few-layer structures represent a transitional state toward graphite.

Functionalization of 2D Graphene

• To improve 2D Graphene’s usability, flakes are often functionalized by attaching chemical groups (e.g., hydroxyl, carboxyl, or alkyl groups). Functionalization helps prevent agglomeration and improves dispersion in host materials, but it degrades 2D Graphene’s intrinsic properties:
• Disruption of the sp² Lattice: Covalent functionalization converts sp²-hybridized carbons into sp³-hybridized ones, breaking the π-electron network that gives 2D Graphene its high electrical and thermal conductivity.
• Introduction of Defects: Functionalization processes, such as oxidation, create lattice imperfections that weaken mechanical strength and reduce carrier mobility.
• Increased Surface Roughness: Chemical groups attached to the surface alter 2D Graphene’s smoothness and reduce optical transparency.
• Despite these trade-offs, functionalization is essential for integrating 2D Graphene into composites, coatings, or biomedical applications.

High Cost and Fragility of Monolayer 2D Graphene

• Monolayer 2D Graphene, such as the 1 square inch sheets sold by Sigma-Aldrich for $334, is prohibitively expensive at an equivalent price of $661 billion per kilogram, reflecting the challenges of producing and handling it.
• Even if isolated from its copper substrate, freestanding monolayer 2D Graphene is extremely fragile and prone to:
  • Tearing: Due to its atomic thinness and lack of support.
  • Wrinkling or folding: Induced by mechanical stress or minor disturbances like a small gust of air.
  • Loss of Properties: Without a substrate, 2D Graphene’s mechanical, electrical, and thermal properties degrade quickly.

Funding Definitions of 2D Graphene

• Organizations like SIO Grafen, Sweden’s innovation agency for graphene, set practical definitions to classify materials with 10 or fewer layers as graphene to facilitate funding and industrial applications. They also include functionalized graphene derivatives such as graphene oxide, which have significantly lower carbon content, acknowledging their potential in real-world applications despite diverging from pristine graphene’s properties. While this approach broadens the scope of materials eligible for support, real-world commercialization of graphene-enhanced products remains challenging, as evidenced by pilot-stage projects evaluated during the agency’s activities.
• Two notable examples from startups illustrate these challenges. One developed a graphene-enhanced adhesive, achieving 30% faster drying times and reduced energy consumption in labs, but failed to replicate these effects in pilot production trials, likely due to scaling issues. Another created graphene oxide-enhanced lubricants with excellent tribological properties and good electrical conductivity, but these materials remain at the pilot stage, with ongoing efforts to improve dispersion and scale production.

Interlayer Interactions and Agglomeration

• Monolayer 2D Graphene has dangling bonds at its edges and π-electrons in its basal plane, which create strong tendencies for flakes to agglomerate:
  • Van der Waals forces: Pull flakes together into stacked structures.
  • π–π stacking: Interactions between the electron clouds of adjacent layers encourage restacking.
• Agglomeration diminishes 2D Graphene’s intrinsic properties, such as its large surface area and conductivity, making it behave more like graphite.

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