Carbon nanotubes (CNTs) and graphite nanoplatelets (GNPs) are carrying great promise as two important constituents of future multifunctional materials. Originating from their minimal defect confined nanostructure, exceptional thermal and electrical properties have been reported for these two allotropic forms of carbon. However, a brief survey of the literature reveals the fact that the incorporation of these species into a polymer matrix enhances its effective properties usually not to the degree predicted by the composite\textquoteright s upper bound rule. To exploit their full potential, a proper understanding of the physical laws characterizing their behavior is an essential step. With emphasis on the electrical and thermal properties, the following study is an attempt to provide more realistic physical and computational models for studying the transport properties of these nanomaterials.

Originated from quantum confinement effects, electron tunneling is believed to be an important phenomenon in determining the electrical properties of nanocomposites comprising CNTs and GNPs. To assess its importance, in this dissertation this phenomenon is incorporated into simulations by utilizing tools from statistical physics. A qualitative parametric study was carried out to demonstrate its dominating importance. Furthermore, a model is adopted from the literature and extended to quantify the electrical conductivity of these nanocomposite. To establish its validity, the model predictions were compared with relevant published findings in the literature. The applicability of the proposed model is confirmed for both CNTs and GNPs.

To predict the thermal properties, a statistical continuum based model, originally developed for two-phase composites, is adopted and extended to describe multiphase nanocomposites with high contrast between the transport properties of the constituents. The adopted model is a third order strong-contrast expansion which directly links the thermal properties of the composite to the thermal properties of its constituents by considering the microstructural effects. In this approach, a specimen of the composite is assumed to be confined into a reference medium with known properties subjected to a temperature field in the infinity to predict its effective thermal properties. It was noticed that such approach is highly sensitive to the properties of the reference medium. To overcome this shortcoming, a technique to properly select the reference medium properties was developed. For verification purpose the proposed model predictions were compared with the corresponding finite element calculations for nanocomposites comprising cylindrical and disk-shaped nanoparticles.

To shed more light on some conflicting reports about the performance of the hybrid CNT/GNP/polymer nanocomposites, an experimental study was conducted to study a hybrid ternary system. CNT/polymer, GNP/polymer and CNT/GNP/polymer nanocomposite specimens were processed and tested to evaluate their thermal and electrical conductivities. It was observed that the hybrid CNT/GNP/polymer composites outperform polymer composites loaded solely with CNTs or GNPs.

Finally, the experimental findings were utilized to serve as basis to validate the models developed in this dissertation. The experimental study was utilized to reduce the modeling uncertainties and the computational predictions of the proposed models were compared with the experimental measurements. Acceptable agreements between the model predictions and experimental data were observed and explained in light of the experimental observations.

The work proposed herein will enable significant advancement in understanding the physical phenomena behind the enhanced electrical and thermal conductivities of polymer nanocomposites specifically CNT/GNP/polymer nanocomposites. The dissertation results offer means to tune-up the electrical and thermal properties of the polymer nanocomposite materials to further enhance their performance.