What happens when a carbon nanomaterial is pushed, stretched, and heated far beyond ordinary conditions? This study uses a machine-learned interatomic potential to test DHQ sheets and nanotubes at scales first-principles calculations cannot reach.

Nanomaterials are promising for electronics, energy storage, sensors, and biomaterials because of their unique properties and high surface-to-volume ratio. Atomic-level manipulation enables devices with specific functionalities, while dimensionality helps determine material properties and applications.

Two independent studies introduced a novel monolayer consisting of laterally bonded dehydrogenated naphthalene molecules. The system was named DHQ-Graphene, or DHQ, because it contains decagonal pores and hexagonal and quadrilateral carbon rings. The study built a data set from ab initio molecular dynamics based on density functional theory, capturing atomic arrangements and energies under different deformation and temperature conditions.

That data trained a machine learning interatomic potential using the Moment Tensor Potential framework. Classical molecular dynamics then applied the validated force field to larger two-dimensional and quasi-one-dimensional systems beyond feasible density functional theory scales.

Nanotubes are modeled by defining a chiral vector from the monolayer’s lattice vectors; this vector gives the rolling direction and determines the nanotube circumference and diameter. A translational vector, chosen perpendicular to the chiral vector, generates repetitions and defines the nanotube’s longitudinal length.

The study considers armchair and zigzag chiralities, with diameters from approximately 4 to 60 angstroms and systems containing 480 to 6400 atoms. A machine learning approach was used to derive a parametric force field specifically for DHQ because existing empirical potentials were found to be nonscalable for this nanomaterial.

The training used a database constructed from ab initio calculations. The data set was built through ab initio molecular dynamics using the Vienna Ab initio Simulation Package, the PBE functional, and the Projected Augmented Wave method. The DHQ calculations used two by two by one supercells containing 80 atoms, with a one-femtosecond time step and 500 simulation steps for each case.

Structural deformation ranged from 15 percent compression to 15 percent tension in five-percent increments, while temperatures ranged from 300 to 1000 kelvin. The first force-field evaluation calculated mean squared errors against the training and validation data sets to assess the field’s ability to describe the material’s intrinsic properties.

Fields with errors exceeding the expected range were discarded. Figure 2 compares the DHQ monolayer’s phonon dispersion along the same symmetry path, with DFT results in panel a and the MTP-trained interatomic potential in panel b. Both panels plot frequency in terahertz across Gamma, X, E, Y, and Gamma, showing closely similar band patterns.

This agreement supports the authors’ validation of the machine-learned potential for describing the monolayer’s dynamic properties. The phonon dispersions from first-principles calculations and the trained force field show very similar trends, especially within the acoustic vibrational modes.

The maximum optical vibrational modes are 51.6 terahertz for density functional theory and 51.9 terahertz for the Moment Tensor Potential model. The absence of imaginary frequencies confirms the system’s dynamic stability and highlights the accuracy of the machine-learned force field.

The DHQ monolayer’s elastic constants are 230.7, 299.4, 61.3, and 82.7 newtons per meter for C eleven, C twenty-two, C twelve, and C sixty-six, respectively. These values reflect anisotropy and are consistent with two-dimensional materials possessing rectangular symmetry.

The elastic constants also satisfy the Born–Huang criterion, further indicating DHQ stability. Figure three shows polar plots of Young’s modulus and Poisson’s ratio for DHQ monolayers as the in-plane deformation angle changes relative to the horizontal axis.

The modulus varies from 212.1 to 283.2 newtons per meter, with an average of 233.8 newtons per meter, while the changing shape of both curves reveals directional dependence, or mechanical anisotropy. This matters because it shows that the monolayer’s elastic response depends on loading direction.

Young’s modulus varies from 212.1 to 283.2 newtons per meter, with an average of 233.8 newtons per meter and a standard deviation of 24.4 newtons per meter, indicating moderate anisotropy. The minimum values occur at 30 degrees, while the maximum values occur at 90 degrees, the y-direction.

The extrema repeat every 90 degrees, consistent with the tetragonal symmetry associated with the C four v point group. Figure four shows the DHQ monolayer’s stress–strain response under separate uniaxial deformation along the x-direction in green and the y-direction in red.

Both curves rise from zero stress before dropping abruptly near failure, revealing a brittle-fracture response. The initial slopes quantify directional Young’s moduli, reported as two hundred two point two newtons per meter along x and two hundred forty-three point two newtons per meter along y, highlighting the monolayer’s anisotropic mechanical behavior.

The stress–strain response of the 3840-atom DHQ supercell shows brittle fracture under uniaxial deformation along both directions. The extracted Young’s modulus is 202.2 newtons per meter in the x-direction and 243.2 newtons per meter in the y-direction. These values are consistent with density functional theory predictions of 218.1 and 283.2 newtons per meter in the x- and y-directions.

Figure five shows DHQ monolayer snapshots approaching and passing fracture, with normalized von Mises stress mapped from blue, the minimum, to red, the maximum. The top row follows x-direction deformation at seventeen point four, seventeen point five, and eighteen percent, while the bottom row shows y-direction deformation at fourteen point eight, fourteen point nine, and fifteen point five percent.

The images make the brittle, crack-like failure process visible, including stress concentration and crack propagation through the lattice. Under x-direction strain, only 0.1 percent of additional strain is sufficient for the system to fracture almost entirely.

The fracture begins centrally at hexagonal rings, propagates diagonally, and primarily breaks the more rigid four-membered rings, which accumulate higher stress. Under y-direction strain, the process is also brittle but preserves more hexagonal rings; after fracture, small linear atomic chains form through atomic-bond reconfiguration.

The smallest armchair nanotube investigated has a diameter of 4.3 angstroms and a Young’s modulus of approximately 127 newtons per meter, nearly 38 percent lower than the monolayer. All nanotube systems examined show no significant differences in critical strain.

For the two-zero DHQ nanotube, critical strain is 17 percent compared with 17.4 percent for the two-dimensional system, occurring at approximately 19 newtons per meter of critical stress. Figure six plots stress against strain for DHQ nanotubes under longitudinal tension, separating armchair chirality in panel a from zigzag chirality in panel b, across several diameters.

The curves rise toward a peak stress and then drop sharply, while low-amplitude fluctuations appear after the critical strain. The authors use this comparison to show brittle fracture behavior and to examine how diameter and chirality affect the transition from quasi-one-dimensional to two-dimensional-like mechanical response.

Figure seven shows fracture snapshots for two DHQ nanotubes: the armchair case, panels a through c, and the zigzag case, panels d through f. The colored atoms indicate the von Mises stress distribution as each tube is stretched, from fourteen point four percent strain through twenty-five percent.

The snapshots capture localized necking, bond rearrangement, and eventual separation, making the figure useful for visualizing how these nanotube topologies fail under tensile deformation. Figure eight plots the energy of a DHQ monolayer against temperature from molecular-dynamics simulations using the MLIP force field.

The linear energy regime changes around the critical temperature of two thousand two hundred kelvin, marking the loss of the original four-, six-, and ten-membered ring topology as the structure becomes amorphous. The snapshots show the preserved arrangement at two thousand two hundred kelvin and the disordered ring network at two thousand three hundred kelvin, making the transition visually clear.

For the 3840-carbon-atom DHQ monolayer, the critical temperature is 2200 kelvin, determined with a temperature resolution of 100 kelvin. This is the highest temperature at which DHQ retains its topology with four-, six-, and ten-membered carbon rings. At 2200 kelvin the topology is preserved, whereas at 2300 kelvin numerous covalent-bond reconstructions result in an amorphous-like system.

Slight deviations in energy and force predictions were noted because the training data set lacked explicit high-temperature configurations. These deviations could influence the fine details of the amorphization process and related thermodynamic properties. A proposed improvement is to retrain the machine-learned interatomic potential with an expanded data set containing high-temperature configurations derived from density functional theory calculations.

The trained potential captures DHQ’s stability and predicts nanotube stiffness between 127 and 243 newtons per meter, fracture between 13.6 and 17.4 percent strain, and a transition toward an amorphous phase above 2200 kelvin.