Multiscale modeling approaches have become essential for predicting thermal conductivity in nanocomposites, where phenomena at different length and time scales collectively determine macroscopic properties. These methods bridge atomic-level interactions with continuum-scale behavior, offering insights that purely experimental or single-scale computational methods cannot provide alone. In systems like boron nitride-epoxy composites, where high thermal conductivity fillers are dispersed in a polymer matrix, understanding phonon transport, interfacial effects, and filler distribution is critical for accurate predictions.

At the atomic scale, phonon transport governs thermal conductivity in crystalline fillers such as boron nitride. Molecular dynamics simulations and lattice dynamics calculations reveal how phonons scatter at defects, grain boundaries, and interfaces. For hexagonal boron nitride, in-plane thermal conductivity can exceed 300 W/mK due to strong sp2 bonding and low phonon scattering rates. However, out-of-plane conductivity is significantly lower, often below 10 W/mK, due to weak van der Waals interactions between layers. Phonon density of states calculations show that high-frequency optical phonons contribute minimally to heat transfer, while acoustic phonons dominate thermal transport. Atomic-scale modeling also captures interfacial thermal resistance, known as Kapitza resistance, between boron nitride and the epoxy matrix. This resistance arises from phonon mode mismatch and weak bonding, reducing effective thermal conductivity across the interface.

Transitioning to microscale modeling, effective medium theory provides a framework to homogenize the composite's thermal properties based on filler geometry, volume fraction, and interfacial effects. The Maxwell-Garnett model approximates thermal conductivity for dilute dispersions of spherical particles, while the Bruggeman model extends this to higher filler loadings. For anisotropic fillers like boron nitride platelets, modifications account for orientation and aspect ratio. A typical expression for a composite with aligned platelets is given by:

k_eff = k_m * (1 + (f * (k_f - k_m)) / (k_m + S * (1 - f) * (k_f - k_m)))

where k_eff is the effective thermal conductivity, k_m and k_f are matrix and filler conductivities, f is the volume fraction, and S is a shape factor dependent on platelet aspect ratio. For random orientations, averaging over all possible angles introduces additional terms. These models assume perfect interfaces; incorporating interfacial resistance requires additional parameters such as the Kapitza radius, which quantifies the thermal barrier's relative impact.

Multiscale integration combines these approaches by passing parameters between scales. Atomic-scale phonon properties inform interfacial resistance values used in microscale models. For example, non-equilibrium molecular dynamics simulations can quantify the thermal conductance of a boron nitride-epoxy interface in W/m2K, which is then incorporated into effective medium theory as a boundary condition. Conversely, microscale models identify critical filler arrangements that require more detailed atomic-scale analysis, such as regions with high interfacial density or percolation pathways. Hierarchical multiscale methods systematically link these scales, while concurrent methods couple them simultaneously in a single simulation framework.

Challenges persist in accurately capturing the stochastic nature of filler dispersion and its impact on thermal pathways. Monte Carlo methods or representative volume element approaches sample possible microstructures, with each realization evaluated through the multiscale pipeline. For boron nitride-epoxy composites, percolation thresholds typically occur around 10-15% volume fraction for randomly dispersed platelets, leading to a sharp increase in thermal conductivity as continuous heat transfer pathways form. Below this threshold, conductivity increases linearly with filler content, while above it, the enhancement becomes more pronounced due to interconnected networks.

Temperature dependence introduces additional complexity. At room temperature, epoxy matrices exhibit low thermal conductivity, often below 0.2 W/mK, due to their amorphous structure and weak phonon transport. Boron nitride's conductivity decreases with temperature due to increased phonon-phonon scattering, while interfacial resistance may also vary. Multiscale models must account for these trends by incorporating temperature-dependent phonon properties and matrix thermal expansion effects.

Validation against experimental data, though not the focus here, ensures model accuracy. Computational predictions for boron nitride-epoxy composites typically align with measured values when interfacial resistance and filler dispersion are properly accounted for. For instance, a composite with 30% volume fraction of boron nitride platelets may reach 2-4 W/mK, representing a tenfold increase over pure epoxy but still far below the filler's intrinsic conductivity due to interfacial losses.

Future directions include incorporating more detailed interfacial chemistry, such as functionalization effects on phonon coupling, and extending models to dynamic conditions like thermal cycling. Machine learning techniques are beginning to accelerate parameter space exploration, identifying optimal filler geometries and distributions without exhaustive simulations. These advances will further refine predictions and guide the design of nanocomposites with tailored thermal properties.

In summary, multiscale modeling of thermal conductivity in nanocomposites integrates atomic-scale phonon dynamics with microscale homogenization techniques, providing a comprehensive understanding of heat transfer mechanisms. For boron nitride-epoxy systems, this approach reveals the interplay between filler properties, interfacial resistance, and percolation effects, enabling rational design of materials for thermal management applications.