Vibrational dynamics of TODD-graphene nanosheets via molecular dynamics simulations and machine-learning surrogate models: implications for adaptive nanomechanical devices

Abstract

Context

TODD-Graphene (TODD-G), a porous two-dimensional carbon allotrope composed of interconnected 3-8-10-12 carbon rings, has recently emerged as a promising candidate for nanoelectromechanical and adaptive nanodevice applications due to its metallic conductivity, mechanical compliance, and topologically engineered phonon structure. In this work, the vibrational dynamics of TODD-G nanosheets were systematically investigated to establish structure–property relationships governing resonant behavior under varying geometric, thermal, mechanical, and defect conditions. Fundamental frequencies were found to span 2.93–13.28 THz and follow the classical \(f\propto {L}^{-2}\) scaling relation. Increasing temperature from 1 to 1000 K reduced resonance frequencies by up to 22% because of thermal expansion and anharmonic phonon interactions, while tensile strain up to 10% enhanced frequencies by more than 50%, yielding gauge factors of 5.3–5.7 that exceed those of graphene. Vacancy defects significantly degraded quality factors and resonance stability, whereas multilayer stacking improved energy retention despite modest frequency reduction. Boundary conditions strongly altered modal spectra, with clamped–clamped configurations producing the highest frequencies and quality factors. Phonon density-of-states analysis revealed distinct acoustic, mixed, and optical vibrational regimes with a maximum phonon cutoff frequency of 56.5 THz. To accelerate device-level optimization, machine-learning surrogate models were developed for predicting resonance frequency and quality factor across the multidimensional design space. Gradient-boosting models achieved excellent predictive accuracy (\({R}^{2}=0.98\) for frequency and \({R}^{2}=0.972\) for quality factor), demonstrating that thermal activation and vacancy concentration dominate vibrational dissipation mechanisms. The combined molecular dynamics and machine-learning framework establishes TODD-G as a promising platform for tunable nanoresonators, strain sensors, RF filters, vibration energy harvesters, and cryogenic nanomechanical systems.

Methods

Atomic-scale simulations were performed using classical molecular dynamics within the large-scale atomic/molecular massively parallel simulator (LAMMPS) package. Interatomic interactions were described using the adaptive intermolecular reactive empirical bond order (AIREBO) potential with activated Lennard–Jones and torsional terms, while multilayer van der Waals interactions employed a 12–6 Lennard–Jones potential. Structural relaxation was conducted using conjugate-gradient energy minimization. Thermal equilibration employed the Nosé–Hoover thermostat within the canonical (NVT) ensemble, followed by microcanonical (NVE) simulations for vibrational analysis using a timestep of 0.5 fs. Vibrational properties were extracted using impulse-response analysis, velocity autocorrelation functions, harmonic forcing, fast Fourier transform (FFT) spectral analysis, and phonon density-of-states calculations. Simulations systematically examined the effects of nanosheet size, temperature (1–1000 K), tensile strain (0–10%), vacancy-defect concentration (0.5–5%), multilayer stacking (1–5 layers), and boundary conditions (free-free, clamped-free, simply supported, and clamped–clamped). Machine-learning surrogate models including linear regression, support-vector regression with radial-basis-function kernels, random forest regression, and gradient-boosting regression were trained using an 80/20 train-test split and five-fold cross-validation to predict resonance frequency and quality factor across the multidimensional parameter space.