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Homogenization-based numerical modeling of MXene composites: effects of nanostructure, anisotropy, and structural disorder
Dissertation   Open access

Homogenization-based numerical modeling of MXene composites: effects of nanostructure, anisotropy, and structural disorder

Rituparna Ghosh
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2026
DOI:
https://doi.org/10.17918/00011412
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Abstract

Anisotropy Dielectric properties Homogenization Nanostructure Numerical modeling of MXene composites Structural disorder Computational Physics
MXenes are two-dimensional transition metal carbides and nitrides that exhibit strong interactions with electromagnetic waves and outstanding electromagnetic shielding efficiency. Their potential for electromagnetic interference (EMI) shielding, devices for communication technologies, sensing and energy-storage applications has attracted significant research interest. However, lack of predictive models capable of relating MXene nanostructure to effective electromagnetic properties limits the rational design and optimization of MXene-based materials and devices. In principle, several types of material models can be useful depending on how the model is to be employed in a particular application. Probably among the simplest types of models useful for layered materials with structures similar to MXene are those based on treating the material as consisting of infinitely large arrangement of parallel sheets. Such models can provide a good fit to measured reflection and transmission of electromagnetic waves. However, they are not particularly useful when attempting to predict electromagnetic field interactions with devices of more complex geometries such as those which are likely to be used in MXene based antennas, transmission lines and shields. A more useful type of model in such applications is a homogenization-based model. Classical linear homogenization approaches, such as Maxwell-Garnett-type models, are generally applicable to composites with relatively low inclusion volume fractions and weak dipolar interactions between the inclusions. These assumptions are not well suited for MXene systems, which consist of high-aspect-ratio conducting flakes arranged in layered or structurally disordered configurations with strong inter-flake electrostatic coupling. Consequently, a more physically representative homogenization modeling framework is required to capture the collective electromagnetic response of MXene nanostructures. In this work, a numerical homogenization framework based on a Surface Charge Boundary Integral Equation formulation is developed to estimate the effective dielectric response of MXene films by explicitly accounting for nanoscale flake arrangement and electrostatic interactions. MXene flakes are modeled as high-aspect-ratio two-dimensional conducting structures separated by nanoscale dielectric gaps. Under the quasi-static approximation, induced surface charge distributions are computed numerically on flake boundaries using surface integral equations. The effective relative permittivity of the system is then extracted by comparing the stored electrostatic energy in the presence and absence of the flakes within a representative observation region. Parametric studies over flake aspect ratios, interflake spacing, and stacking configurations demonstrate that the effective dielectric constant increases strongly with increasing aspect ratio and fill fraction. The dielectric response also shows strong sensitivity to vertical interlayer spacing and weaker, but non-negligible, dependence on horizontal spacing. Interleaved configurations consistently produce larger dielectric enhancement than aligned structures due to stronger interlayer electrostatic coupling and localized field concentration within dielectric gaps. The angular anisotropy and structural disorder of MXene assemblies are also investigated using misaligned multilayer configurations. By varying the orientation of the applied electric field and introducing rotational and positional misalignment between flakes, the model predicts effective dielectric constants on the order of 10⁴-10⁵ at relatively low MXene volume fractions (~ 7%-10%). The results demonstrate that structural disorder enhances localized field concentration and multidirectional dipolar interactions, partially compensating for reduced filling ratio. The numerical predictions are validated through comparison with finite element method (FEM) simulations and analytical estimates based on layered electrostatic coupling models. While periodic FEM models reproduce similar qualitative trends, the proposed Surface Charge Boundary Integral Equation framework more naturally accommodates non-periodic interactions and structural disorder characteristic of realistic MXene films. Overall, the findings provide a classical physics-based explanation for the large dielectric permittivity observed in MXene-based composites and establish the importance of nanoscale geometry, stacking configuration, anisotropy, and structural disorder in governing the effective electromagnetic response. The proposed framework offers physically transparent design insight for engineering high-dielectric MXene materials for applications including EMI shielding, antennas, communication systems, and advanced electronic devices.

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