Molecular dynamics (MD) simulations have become a cornerstone for investigating thermal transport in nanomaterials, offering atomic-scale insights that complement experimental measurements and theoretical models. Among the various approaches, the Green-Kubo method and direct nonequilibrium molecular dynamics (NEMD) are widely used to compute thermal conductivity. These techniques, combined with phonon scattering analysis, provide a detailed understanding of heat transfer mechanisms in nanostructures, particularly at grain boundaries and interfaces in nanocomposites. Additionally, MD simulations reveal size effects and anisotropic behavior in two-dimensional (2D) materials, offering unique perspectives that contrast with Boltzmann transport theory.

The Green-Kubo method derives thermal conductivity from fluctuations in the heat current within an equilibrium system. It relies on the fluctuation-dissipation theorem, which relates the decay of spontaneous heat current autocorrelations to the thermal conductivity tensor. The thermal conductivity is calculated by integrating the heat current autocorrelation function over time. This approach is advantageous for isotropic systems and does not require imposing a temperature gradient, making it suitable for studying bulk-like behavior in nanomaterials. However, the Green-Kubo method demands long simulation times to achieve converged results due to the slow decay of heat current correlations, particularly in systems with strong phonon scattering.

In contrast, NEMD simulations directly impose a temperature gradient across the nanomaterial and measure the resulting heat flux. By dividing the system into hot and cold regions and applying thermostats to maintain a steady-state temperature difference, the thermal conductivity is computed using Fourier's law. NEMD is particularly effective for studying finite-sized systems, such as nanowires or thin films, where boundary effects dominate thermal transport. However, the imposed temperature gradient can introduce nonlinear effects, especially at high temperature differences, requiring careful validation against linear response theory.

Phonon scattering at grain boundaries and interfaces plays a critical role in reducing thermal conductivity in nanocomposites. MD simulations reveal that atomic disorder, strain fields, and chemical heterogeneity at these interfaces scatter phonons, increasing thermal resistance. For instance, in silicon-germanium nanocomposites, the thermal conductivity can drop by an order of magnitude due to phonon scattering at interfaces. MD allows visualization of localized vibrational modes and energy trapping at boundaries, providing mechanistic insights into interfacial thermal resistance. The spectral decomposition of heat currents further identifies which phonon frequencies are most affected by scattering, linking atomic-scale defects to macroscopic thermal properties.

Size effects are another key focus of MD studies, particularly in low-dimensional materials. In nanowires and thin films, phonon-boundary scattering reduces thermal conductivity as the characteristic dimension decreases. For example, silicon nanowires with diameters below 100 nm exhibit significantly lower thermal conductivity than bulk silicon due to increased surface scattering. In 2D materials like graphene, thermal conductivity is highly anisotropic, with in-plane values reaching up to 3000 W/mK while out-of-plane conduction is orders of magnitude lower. MD simulations capture these effects by explicitly modeling atomic interactions and finite dimensions, revealing how phonon confinement and edge scattering dictate thermal transport.

Anisotropy in 2D materials is particularly pronounced due to their layered structures. MD studies show that in-plane thermal conductivity is dominated by strong covalent bonds, while weak van der Waals interactions between layers limit cross-plane heat transfer. For instance, in hexagonal boron nitride, the in-plane thermal conductivity is nearly 100 times higher than the cross-plane value. MD simulations also demonstrate that stacking order, layer thickness, and defects such as vacancies or substitutions further modulate anisotropic behavior. These findings are critical for designing thermal management materials with tailored directional heat transfer properties.

Comparing MD results with Boltzmann transport theory highlights the strengths and limitations of each approach. Boltzmann theory treats phonons as semiclassical particles and solves the transport equation under the relaxation time approximation. It efficiently captures phonon dispersion and scattering rates but often relies on empirical parameters for boundary scattering and anharmonic effects. In contrast, MD simulations inherently include all anharmonicities and atomic-scale defects without ad hoc assumptions, providing a more fundamental description of heat transfer. However, MD is computationally expensive and limited to smaller systems and shorter timescales than Boltzmann methods. The two approaches are complementary, with MD validating Boltzmann models in regimes where atomic details are critical, such as near interfaces or in highly disordered systems.

One unique advantage of MD is its ability to capture nonlinear thermal transport phenomena. At high temperatures or large temperature gradients, phonon-phonon interactions become strongly nonlinear, leading to phenomena like phonon hydrodynamic flow or second sound. MD simulations directly model these effects, revealing deviations from Fourier's law that are challenging to predict with linearized theories. For example, in carbon nanotubes, MD has shown that non-diffusive phonon transport dominates at room temperature, leading to length-dependent thermal conductivity that persists over micrometers.

In summary, molecular dynamics simulations provide indispensable insights into thermal conductivity in nanomaterials, leveraging the Green-Kubo and NEMD methods to explore equilibrium and nonequilibrium behavior. By analyzing phonon scattering at interfaces, size effects, and anisotropy, MD reveals atomic-scale mechanisms that govern heat transfer in nanocomposites and 2D materials. While Boltzmann transport theory offers efficient predictions for bulk-like systems, MD excels in capturing nonlinearities and atomic disorder, bridging the gap between microscopic interactions and macroscopic properties. These computational advances continue to drive the design of nanomaterials with tailored thermal performance for applications ranging from electronics cooling to energy conversion.