Fullerene Networks: Structures & Properties

Updated 10 July 2026

Fullerene networks are covalently linked architectures built from fullerene cages, exhibiting diverse structural motifs and emergent collective behaviors.
These networks enable anisotropic elasticity, tunable semiconducting gaps, and photocatalytic functionalities via controlled intermolecular bonding.
Graph-theoretical and simulation studies elucidate network stability, fracture mechanics, and quantum magnetic phenomena, guiding material design.

Searching arXiv for recent fullerene network papers to ground the article. Fullerene networks are extended architectures in which fullerene units are linked into larger frameworks, most prominently as two-dimensional monolayer polymeric fullerene phases formed by covalently connecting C $_{60}$ cages, but also as smaller-fullerene lattices such as C $_{24}$ , magnetic C $_{40}$ monolayers, endohedral derivatives, heterostructures, nanoribbons, and, in chemical graph theory, fullerene graphs. Across these realizations, the central theme is the conversion of molecular curvature and cage connectivity into emergent collective behavior: anisotropic elasticity and thermal response, direct and indirect semiconducting gaps, excitonic and photocatalytic functionality, flat bands, edge states, altermagnetism, and frustrated quantum magnetism (Peng et al., 30 Apr 2025, Paupitz et al., 2 Sep 2025, Wu et al., 28 Aug 2025).

1. Structural archetypes and routes to realization

Two-dimensional fullerene networks are monolayers formed by covalently linking fullerene molecules into extended frameworks. The experimentally emphasized C $_{60}$ families include rhombohedral, quasi-hexagonal phase (qHP), tetragonal, and quasi-tetragonal phase (qTP) networks. In the qHP monolayer, C $_{60}$ units form a quasi-hexagonal array; in the qTP form, they organize into a rectangular motif. Inter-cage bonding is primarily via covalent [2+2] cycloaddition, although qHP additionally contains intermolecular C $-$ C single bonds (Paupitz et al., 2 Sep 2025).

A more detailed structural partition of polymeric C $_{60}$ monolayers distinguishes qTP1, qTP2, and qHP. qTP1 forms nearly one-dimensional chains of C $_{60}$ cages linked along one direction by nearly in-plane [2+2] cycloaddition bonds, with weak or absent C $-$ C bonding perpendicular to the chains. qTP2 is a tightly bound 2D network linked in both directions by in-plane and vertical [2+2] cycloaddition bonds. qHP is a closely packed hexagonal network connected by planar [2+2] cycloaddition bonds and C $-$ C single bonds (Peng, 2022).

Newer fullerene-network chemistries expand the building-block set beyond C $_{24}$ 0. Monolayer C $_{24}$ 1 networks use the smallest stable [5,6]fullerene units as “superatomic” nodes connected by three non-coplanar covalent bonds; the qTP phase forms a square-like lattice, whereas the qHP phase is a buckled monolayer of misaligned chains with denser packing and stronger inter-chain connectivity (Wu et al., 2024). A distinct magnetic limit is realized in the C $_{24}$ 2 system: charge-neutral pure-carbon C $_{24}$ 3 molecules are rotated by $_{24}$ 4 with respect to each neighbor to form a 2D rutile-like lattice, and the distribution of effective spin clusters maps the network onto a 2D Shastry-Sutherland lattice (Wu et al., 28 Aug 2025).

Historical synthesis routes included photopolymerization, electron-beam and plasma treatments, and high-pressure/high-temperature methods, which often yielded mixtures of phases. More recent methods include organic cation slicing, in which Mg ions are used during initial synthesis and later chemically removed to exfoliate monolayers; mechanical exfoliation of graphullerene; electrochemical exfoliation with rates up to 5 g/day; and controlled heating or pyrolysis to create nanoporous membranes (Paupitz et al., 2 Sep 2025).

Class	Structural motif	Connectivity or status
qHP-C $_{24}$ 5	Quasi-hexagonal array	[2+2] cycloaddition + C $_{24}$ 6C single bonds; monolayer realized
qTP-C $_{24}$ 7	Rectangular motif	[2+2] cycloaddition; few-layer form synthesized
qTP1/qTP2-C $_{24}$ 8	1D-chain-like / tightly bound 2D net	Weak interchain bonding in qTP1; 2D [2+2] bonding in qTP2
qTP/qHP-C $_{24}$ 9	Square-like / buckled misaligned chains	Three non-coplanar covalent bonds
C $_{40}$ 0 monolayer	Rutile-like rotated network	Effective spin-1/2 clusters form Shastry-Sutherland lattice

2. Stability, elasticity, fracture, and thermal expansion

The stability problem in fullerene networks is multi-layered: thermodynamic, dynamic, and mechanical criteria do not collapse to a single ordering. For monolayer polymeric C $_{40}$ 1, qHP and qTP2 have no imaginary phonon frequencies and are dynamically stable, whereas qTP1 exhibits imaginary modes, especially along $_{40}$ 2-X, indicating dynamic instability toward separation into 1D chains under out-of-plane vibrations. Mechanical stability follows the same trend: only qTP2 and qHP satisfy the Born criteria, while qTP1 fails because its shear modulus is negative. At the same time, thermodynamic ordering is different: qTP2 is most stable at $_{40}$ 3 K, the isolated 0D C $_{40}$ 4 molecule is more stable than qTP1 and qTP2 between 150–380 K, qTP1 becomes thermodynamically favored above 380 K, and qHP is always least thermodynamically stable (Peng, 2022).

This distinction addresses a common simplification in the literature: experimental isolability is not equivalent to minimum Gibbs or Helmholtz free energy. Only qHP monolayers have been exfoliated as single layers, whereas qTP phases are observed in few-layer form, and the theoretical explanation emphasizes qHP’s high dynamic and mechanical robustness rather than thermodynamic preference (Peng, 2022).

Reactive molecular dynamics further quantifies thermal and fracture behavior in synthesized qHPC $_{40}$ 5 and qTPC $_{40}$ 6. Using ReaxFF in LAMMPS on $_{40}$ 7 \AA $_{40}$ 8 supercells containing 8,640 atoms, the reported sublimation points are 3898 K for qHPC $_{40}$ 9 and 3965 K for qTPC $_{60}$ 0. Both retain crystalline order up to approximately 3500 K, then undergo major morphology changes and eventual atomization. Under tension, both show a linear elastic regime followed by abrupt fracture. The estimated Young’s moduli are $_{60}$ 1 GPa and $_{60}$ 2 GPa for qHPC $_{60}$ 3, and $_{60}$ 4 GPa and $_{60}$ 5 GPa for qTPC $_{60}$ 6. Crack propagation is linear for qHPC $_{60}$ 7 along the x direction but non-linear for qTPC $_{60}$ 8, reflecting differences in the number and arrangement of inter-fullerene covalent bonds (Junior et al., 2022).

Thermal expansion is similarly topology-dependent. In 2D C $_{60}$ 9 networks, qTP shows nearly isotropic positive thermal expansion along both lattice axes because all neighboring cages are connected by [2+2] cycloaddition bonds, whereas qHP shows anisotropic expansion: positive along the double-bonded axis and negative along the single-bonded axis up to 500 K. The microscopic explanation combines geometric flexibility and phonon anharmonicity: flexible single bonds act as hinges, and low-frequency ZA and ZO branches carry large negative mode Grüneisen parameters in the negative-expansion direction (Shaikh et al., 2 Apr 2025). The corresponding tensor component is written as

$_{60}$ 0

3. Electronic structure, optics, and photocatalytic functionality

Monolayer fullerene networks are predominantly narrow-gap semiconductors, but the exact gap character depends strongly on topology and electronic-structure treatment. For C $_{60}$ 1 monolayers, hybrid-functional calculations with weak screening and TDHF excitonic corrections yield indirect gaps of 1.88 eV for qTP1 and 1.74 eV for qTP2, and a direct gap at $_{60}$ 2 of 1.67 eV for qHP, close to the experimental 1.6 eV optical gap. Exciton binding energies are reported as 5–50 meV. Band edges of all three phases straddle the water redox potentials at $_{60}$ 3, providing sufficient thermodynamic driving force for overall water splitting (2208.00015).

The phase dependence of optoelectronic response is pronounced. qTP1 and qTP2 exhibit low-energy anisotropic absorption and dark excitons at the gap edge, which suppress recombination and favor electron-acceptor behavior. qHP shows strong isotropic absorption in the visible range around 2 eV and bright excitons near the band edge, favoring electron-donor behavior in photocatalysis (2208.00015). A concise criterion used in this context is

$_{60}$ 4

with the redox alignment expressed as

$_{60}$ 5

and

$_{60}$ 6

A separate first-principles study of the experimentally realized $_{60}$ 7-C $_{60}$ 8-2D reports a direct HSE06 gap of 1.49 eV at the Y point, attributed to a flat conduction-band bottom. The same asymmetric bridge bonding arrangement produces strong optical linear dichroism, anisotropic in-plane elasticity, large hole mobility, an ultrahigh Seebeck coefficient at middle low temperatures, and facile Li migration along the X path (Yu et al., 2022).

The broader review literature places these results in a larger application space. qHP-C $_{60}$ 9 is described as having a direct band gap around 1.55 eV with anisotropic mechanical and optoelectronic responses traced to asymmetric interfullerene bridging, whereas qTP-C $-$ 0 has been identified as suitable as an electronic acceptor in photocatalysis. The same literature also reports high UV absorbance up to 5.5 eV, strong excitonic effects, field-tunable band gaps, and hydrogen-separation capability for qTP and qHP membranes (Paupitz et al., 2 Sep 2025).

4. Altermagnetism and frustrated quantum magnetism in C $-$ 1 networks

A qualitatively different limit of fullerene networking is realized in the altermagnetic C $-$ 2 monolayer on a Shastry-Sutherland lattice. In each C $-$ 3 unit, the central W-shaped chain of five carbon atoms has three possible resonance structures for the double bonds. This localizes an unpaired electron and produces an averaged magnetic moment of $-$ 4 per magnetic carbon site, or $-$ 5 per W-chain. Each group of three such magnetic carbons is then treated as a single effective spin-1/2 cluster, and the rotated molecular crystal forms an altermagnetic ground state with zero net magnetization but spin-resolved band splitting along selected symmetry directions (Wu et al., 28 Aug 2025).

The electronic and magnonic signatures are explicit. The spin-up and spin-down electronic states are degenerate along some high-symmetry directions and split along others; the iso-energy surface $-$ 6 below the VBM has a $-$ 7-wave-like shape reminiscent of RuO $-$ 8. In the magnon spectrum, linear magnon dispersion appears near the $-$ 9 point, degeneracy persists along $_{60}$ 0–X–M, and giant chiral band splitting occurs along M– $_{60}$ 1–M’. All magnon frequencies are non-negative, which confirms stability (Wu et al., 28 Aug 2025).

The effective-spin description maps the network onto a Shastry-Sutherland model with intramolecular coupling $_{60}$ 2 and intermolecular coupling $_{60}$ 3. The cluster coupling is defined as

$_{60}$ 4

The resulting phase diagram contains dimer, plaquette, quantum spin liquid, and altermagnetic phases. Specifically, the quantum spin liquid regime is reported for $_{60}$ 5, while bi-axial strain tunes $_{60}$ 6 and can drive transitions among all these phases. DFT and hybrid-functional calculations indicate that modest strains of 2–3\% can switch the system between ordered altermagnetic and quantum-disordered regimes (Wu et al., 28 Aug 2025).

This suggests that fullerene networks are not limited to conventional semiconducting or membrane roles. In the C $_{60}$ 7 realization, the fullerene cage acts as a molecularly engineered spin cluster, and the network topology directly encodes frustrated quantum magnetism and altermagnetic spin splitting in a fully carbon platform (Wu et al., 28 Aug 2025).

5. Derived architectures, chemical modification, and dimensional reduction

Changing the fullerene size from C $_{60}$ 8 to C $_{60}$ 9 strongly alters the network energy landscape. In monolayer C $_{60}$ 0, the qTP and qHP phases are exothermic relative to the isolated molecule, with cohesive energies of $_{60}$ 1 and $_{60}$ 2 eV per atom and formation energies of $_{60}$ 3 and $_{60}$ 4 eV, respectively. Both are dynamically stable, qHP is more stable than qTP at all temperatures, and the Young’s and layer moduli are approximately 1.5 times higher than in C $_{60}$ 5 networks. Their hybrid-functional band gaps are 3.74 eV for qTP and 3.10 eV for qHP, comparable to TiO $_{60}$ 6, with band edges that straddle the water-splitting potentials over the acidic and neutral pH range (Wu et al., 2024).

The photocatalytic consequence is a sharp increase in chemically active surface density. Each monolayer C $_{60}$ 7 possesses three times as many accessible surface sites as C $_{60}$ 8 under moderate and high pH, and under photoexcitation both Volmer–Tafel and Volmer–Heyrovsky pathways become thermodynamically spontaneous at all sites in both qTP and qHP (Wu et al., 2024). A plausible implication is that fullerene size functions as a design parameter for simultaneously tuning stability, band alignment, and catalytic site density.

Machine-learning molecular dynamics on C $_{60}$ 9 networks reinforces this size effect in the elastic and thermal sectors. qTP-C $-$ 0 shows nearly isotropic elastic properties and thermal conductivities along its principal axes because of four-fold symmetry, whereas qHP-C $-$ 1 is strongly anisotropic due to its chain-like misaligned topology. At 300 K, the thermal conductivities are $-$ 2 and $-$ 3 W m $-$ 4K $-$ 5 for qHP-C $-$ 6 along $-$ 7 and $-$ 8, and $-$ 9 W m $-$ 0K $-$ 1 for qTP-C $-$ 2, with heat transport dominated by low-frequency acoustic phonons below 5 THz and by strong inter-fullerene covalent bonds rather than van der Waals interactions (Li et al., 29 Nov 2025).

Chemical modification of fullerene networks produces further electronic diversity. In endohedral qHPC $-$ 3, encapsulated N preserves semiconducting character but creates a localized intragap N $-$ 4 state and reduces the gap to about 0.46 eV; Ce and Sr generate impurity-derived states near the conduction edge and can render the system metallic at moderate-to-high encapsulation. All encapsulated systems show a red shift of the absorption onset into the visible range and enhanced refractive and absorptive responses (Junior et al., 10 Mar 2026).

Beyond all-carbon systems, hexagonal boron-carbon fullerene heterostructures built from B $-$ 5 and C $-$ 6 cages are predicted to be thermally and dynamically stable semiconductors with topological flat bands, room-temperature lattice thermal conductivity in the 4–10 W/mK range, elastic modulus over 70 GPa, and tensile strength between 8 and 15 GPa. Their failure mode is described as ductile-like rather than brittle, with bond elongation, boron-cluster deflections, and boron-chain formation at high strain (Mortazavi et al., 2023). Dimensional reduction into quasi-1D nanoribbons derived from qTP and qHP monolayers produces width- and edge-dependent direct and indirect gaps, positive and negative effective masses, and robust in-gap edge states; in qHP-ZZ ribbons, the edge bands become nearly degenerate and flat as width increases (Peng et al., 10 Apr 2025).

6. Graph-theoretical and molecular-network viewpoints

In chemical graph theory, a fullerene is modeled as a cubic planar graph with exactly 12 pentagonal faces and $-$ 7 hexagons. This discrete notion of “fullerene network” underlies enumeration, matching theory, and structural generation. The buckygen algorithm introduced an isomorph-free generator for all non-isomorphic fullerenes and IPR fullerenes, using canonical construction paths and combinatorial invariants. It is reported to be over 3.5 times faster than fullgen, to scale beyond 100 vertices, and to enumerate fullerenes up to 400 vertices. The same work verified Barnette’s conjecture up to 316 vertices and confirmed that the smallest counterexample to the spiral conjecture has 380 vertices (Brinkmann et al., 2012).

A complementary invariant is the anti-forcing number. For a graph $-$ 8 with a perfect matching, the anti-forcing number is

$-$ 9

For fullerene graphs, $_{24}$ 00 for every fullerene. Moreover, for every even $_{24}$ 01 with $_{24}$ 02, there exists a fullerene on $_{24}$ 03 vertices with anti-forcing number 4, while the unique fullerene with 26 vertices has anti-forcing number 5 (Yang et al., 2015). In the graph-theoretic literature, this quantity is tied to the control of Kekulé structure uniqueness.

The term “fullerene network” also appears in bottom-up molecular-growth studies relevant to astrochemistry. Gas-phase fullerene/anthracene cluster cations such as $_{24}$ 04 form efficiently by ion-molecule reactions for $_{24}$ 05, and 355 nm irradiation induces sequential anthracene loss without dehydrogenation. Smaller fullerene cations such as C $_{24}$ 06 and C $_{24}$ 07 are more reactive than C $_{24}$ 08 and C $_{24}$ 09, which is attributed to curvature and lower reaction barriers (Zhen et al., 2019). Related experiments with oxygenated PAHs show efficient formation of fullerene/9-hydroxyfluorene cluster cations, with enhanced reactivity at defective 7-membered rings and binding energies up to about $_{24}$ 10 eV for C $_{24}$ 11-based adducts (Wu et al., 2024).

These molecular cluster results are not crystalline 2D fullerene networks, but they demonstrate another legitimate network limit: fullerene-centered covalent growth through sequential accretion. Taken together with the graph-theoretic and solid-state literatures, they show that “fullerene networks” denotes a family of connected fullerene-based architectures whose properties are controlled by topology, bond type, and dimensionality rather than by cage chemistry alone.