Enhancing Strain Sensing: A Computational Analysis of Tunneling in Carbon Nanotube Polymer Composites


Carbon Nanotube (CNT) polymer composites are created by embedding carbon nanotubes, which are cylindrical nanostructures made entirely of carbon atoms, into a polymer matrix. This integration of CNTs with polymers yields materials with enhanced properties that are not found in either component alone. For instance, CNTs are renowned for their exceptional strength and stiffness. When incorporated into polymers, they significantly enhance the mechanical properties of the composite, such as tensile strength and durability. Moreover, CNTs are known for their excellent electrical conductivity. In a polymer matrix, they create pathways for electron flow, thereby imparting conductive properties to the otherwise insulating polymers. CNTs also have high thermal conductivity. In polymer composites, this leads to improved heat dissipation, which is beneficial in applications where thermal management is crucial.

Piezoresistivity refers to the change in electrical resistance of a material under mechanical strain. CNT polymer composites exhibit unique piezoresistive characteristics. Due to their unique properties, CNT polymer composites are used in various applications including as strain sensors, pressure sensors, and tactile sensors due to their high sensitivity to mechanical deformation. A new study published in the Journal of Intelligent Material Systems and Structures by Associate Professor Kawai Kwok and PhD candidate Wolfgang Klimm from the Department of Mechanical and Aerospace Engineering at the University of Central Florida, the researchers conducted computational analysis of tunneling in CNT polymer composites, and designed a detailed and innovative approach to understanding the piezoresistive properties of these materials. Their work focused on developing a model that could more accurately predict the behavior of CNT composites under strain, specifically addressing the tunneling conduction that plays a crucial role in their functionality.

The authors constructed three-dimensional cubic representative volume elements (RVEs) filled with randomly distributed carbon nanotubes. Each nanotube within these RVEs was modeled as a straight line, defined by its origin point and two orientation angles. This approach allowed for a realistic representation of the complex microstructure of CNT networks. They employed statistical methods to evaluate the tunneling conduction within these networks. This step was crucial for understanding how the individual CNTs interacted within the composite and how these interactions influenced the overall piezoresistive response. A key aspect of their study was the analysis of the effects of CNT extensibility. By considering both extensible and inextensible CNTs, they could explore how the mechanical properties of the nanotubes influenced the composite’s behavior.  The researchers also examined the impact of different assumptions about the tunneling cross-section conduction channels. This parameter was critical in determining the electrical conductivity and, therefore, the piezoresistivity of the composite. They implemented these two approaches to better model the quantum mechanical aspects of electron tunneling in the CNT junctions.

Klimm and Kwok found that assuming CNT inextensibility leads to a higher predicted piezoresistivity in the composites. This insight is crucial for understanding the mechanical-electrical coupling in these materials. Moreover, the choice of tunneling cross-section area was identified as a highly influential factor. Different assumptions about this parameter could significantly alter the predicted behavior of the composite. Furthermore, their model was able to avoid the need for fitting parameters to experimental data, a common limitation in previous studies. This advancement significantly enhances the predictive accuracy of the model, making it a valuable tool for the design and optimization of CNT-based composites.

The implications of the authors’ study are important for the field of sensor technology. Firstly, the findings provide a more comprehensive understanding of the piezoresistive behavior of CNT polymer composites. This understanding is crucial for the development of more accurate and efficient strain sensors, which are fundamental in applications such as structural health monitoring and motion sensing. Moreover, the researchers’ approach addresses the limitations of previous models by avoiding ad hoc assumptions and enhancing predictive accuracy. This advancement opens up new possibilities for the design and optimization of CNT-based composites, potentially leading to the development of materials with tailored properties for specific applications.

In conclusion, the authors analyzed the effects of CNT extensibility, tunneling cross-section conduction channels, and the implementation of the Simmons approximation and Landauer formula. The findings highlighted that CNT inextensibility leads to higher predicted piezoresistivity, and the choice of tunneling cross-section area is a highly influential parameter in determining the overall behavior of the composite material. Klimm and Kwok’s new study provided a more accurate understanding of the behavior of CNT polymer composites under strain. Their findings are essential for developing advanced strain sensors and could have broader implications for the design of nanocomposite materials across various technological applications.

Note: Associate Professor Kawai Kwok is currently affiliated with Purdue University and Wolfgang Klimm is now working for Apple Inc.

Enhancing Strain Sensing: A Computational Analysis of Tunneling in Carbon Nanotube Polymer Composites - Advances in Engineering

About the author

Dr. Kawai Kwok
Associate Professor in Aeronautics and Astronautics
Purdue University

Kawai Kwok is an Associate Professor in the School of Aeronautics and Astronautics at Purdue University. He received his M.S. and Ph.D. degrees in Aerospace Engineering from the California Institute of Technology. Prior to joining Purdue, he was a faculty in Mechanical and Aerospace Engineering at the University of Central Florida. His research interests are in the mechanics of thin-shells and membranes, design of deployable structures, in-space manufacturing of composite structures, nanocomposites, high-throughput material characterization at extreme and space environments. He is a recipient of the NSF CAREER award and the NASA Robert H. Goddard Exceptional Achievement for Engineering award.


Wolfgang Klimm and Kawai Kwok. Computational analysis of tunneling conduction in piezoresistive carbon nanotube polymer composites. Journal of Intelligent Material Systems and Structures 2023, Vol. 34(8) 928–943.

Go to Journal of Intelligent Material Systems and Structures

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