## 4 Conclusions  
This study investigates the electromagnetic interference shielding properties of hybrid buckypaper/carbon fiber-reinforced composites. A novel quantum tunneling-based equivalent circuit approach combined with Monte Carlo simulations was introduced to predict the frequency-dependent electrical conductivity of unidirectional carbon fiber lamina. The model provides an accurate approach for estimating both longitudinal and transverse electrical conductivity of unidirectional plies of arbitrary size, morphology, and constituent electrical properties. Subsequently, effective electrical properties were employed to evaluate the shielding performance of buckypaper against external electromagnetic radiation in the 50 MHz-12 GHz frequency range. The findings demonstrate a significant improvement in the overall shielding effectiveness of carbon fiber-reinforced polymer composites with the inclusion of buckypaper interleaves at high frequencies. This enhancement is attributed to the consistent electrical conductivity of buckypaper, even as the conductivity of carbon fiber lamina declines beyond 1 GHz. The integration of buckypaper into fiber-reinforced composites leads to a comprehensive improvement in both the electrical and mechanical properties, making them an ideal choice for use in composite structures. Conceptualization, A.C., T.C.H., A.H. and M.A.M. ; methodology, K.T. ; software, K.T. ; validation, K.T. ; formal analysis, K.T. and M.H.H. ; investigation, K.T. ; resources, A.C.; data curation, K.T. ; writing--original draft preparation, K.T. ; writing--review and editing, A.C. and M.H.H. ; visualization, K.T. ; supervision, A.C.; project administration, T.C.H., A.H. and M.A.M. ; funding acquisition, A.C. All authors have read and agreed to the published version of the manuscript. This research was funded by Army Research Laboratory grant number W911 NF-17-2-0207. Not applicable. The raw data required to reproduce these findings will be made available upon request. This research was sponsored by the Army Research Laboratory (Cooperative Agreement W911 NF-17-2-0207). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes, notwithstanding any  
Figure 19: Comparison between the shielding effectiveness exhibited by composites with buckypaper (BP) and copper mesh interleaves [24]. copyright notation herein. This article is a revised and expanded version of a paper entitled \"Electrical Characterization and Electromagnetic Interference Shielding Properties of Hybrid Buckypaper-Reinforced Polymer Matrix Composites\" [41], which was presented at the Aerospace Structures, Structural Dynamics, and Materials Conference at Renton, Washington on 29 April 2024. **Conflicts of Interest**: The authors declare no conflicts of interest. **Nomenclature**  
\(\rho_{f}\) Fiber resistivity  
\(\rho_{m}\) Matrix resistivity  
\(\epsilon_{o}\) Vacuum permittivity  
\(\epsilon_{r}\) Relative permittivity of medium  
\(\mu_{o}\) Vacuum permeability  
\(\mu_{r}\) Relative permeability of medium  
\(n_{m}\) Refractive Index of matrix  
\(R_{f}\) Fiber resistance  
\(len_{f}\) Fiber length  
\(r_{f}\) Mean fiber radius  
\(X_{L}\) Fiber inductive reactance  
\(L_{f}\) Fiber inductance  
\(f\) Signal frequency  
\(T_{avg}\) Average fiber separation  
\(\left|Z_{long.