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Open Access Review

Review on Material Performance of Carbon Nanotube-Modified Polymeric Nanocomposites

Zhong Hu 1,*, Haiping Hong 2,*

  1. South Dakota State University, Brookings, South Dakota 57007, USA

  2. South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, USA

Correspondences: Zhong Hu and Haiping Hong

Academic Editor: Chih-Ching Huang

Received: March 21, 2023 | Accepted: August 11, 2023 | Published: August 16, 2023

Recent Progress in Materials 2023, Volume 5, Issue 3, doi:10.21926/rpm.2303031

Recommended citation: Hu Z, Hong H. Review on Material Performance of Carbon Nanotube-Modified Polymeric Nanocomposites. Recent Progress in Materials 2023; 5(3): 031; doi:10.21926/rpm.2303031.

© 2023 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.


The chemically functionalized carbon nanotubes (f-CNTs) and hydrogen bonding modified polymer composites (CPCs) exhibit unique chemical, mechanical, electrical, and thermal properties and are emerging as promising materials to achieve extraordinarily high electrical and thermal conductivity, lightweight and anticorrosion, superior strength and stiffness for potential applications in the aerospace and automotive industries, energy conversion, and optical and electronic devices, therefore, attracting considerable research efforts over the past decade. In this review, the fundamentals of the topics on f-CNTs, hydrogen bonding, and CNT directional alignment have been briefly introduced. The research on the electrical, thermal, and mechanical properties have been reviewed. The effects of the CNT morphology, hydrogen bonding, CNT alignment and aspect ratio, and the interactions between the constitutes on the CPC performance is critical to understand the fundamentals and challenges of designing such materials with desired properties and their potential applications. However, to gain a comprehensive and quantitative understanding of the effects of these factors on the performance of CPCs, further studies by computer modeling, especially MD simulations, will be highly needed for effective new/novel material design and development.


Material performance; carbon nanotubes (CNTs); functionalized CNTs (f-CNTs); hydrogen bonding; CNT modified polymeric composites (CPCs); CNT directional alignment

1. Introduction

Carbon nanotubes (CNTs) exhibit excellent electrical, thermal, and mechanical properties. CNTs are well-known nanofillers that can be used to produce high-performance CNT-modified polymer nanocomposites (CPCs) [1]. The chemically functionalized CNTs (f-CNTs), incorporating hydrogen bonding and appropriate solvents, facilitate the formation of well-dispersed CNT networks as electronic pathways in polymer nanocomposites [1,2,3,4,5,6,7]. Furthermore, it extends the CNT length to enhance the directional performance, together with proper design to create desired properties for desired applications [7]. It has shown promise in aerospace, electrical and automotive industries, energy conversion, ultra-high-strength nanocomposites and high-performance composites, surface engineering, and promising devices in the field of optics and electronics, including energy storage, energy harvesting, mobile phones, optical coatings and antistatic coatings, integrated circuit chips, flexible electrodes in displays, electronic paper, bullet-proof vests, protective clothing, etc. [1,2,3,4,5,6,7,8]. However, polymers are generally considered effective insulators due to their low thermal and electrical conductivity [9]. Research has been actively conducted to improve their electrical, mechanical, and thermal properties, and to develop new functionalities by adding nanoscale fillers to polymeric materials. The choice of nanofillers depends on the properties of the nanocomposite to be designed, the polymer matrix used, their composition, size and shape, their functional groups, their amount, their dispersion in the polymer matrix, and interfacial interactions. Examples of nanofillers include carbon-based nanofillers, layered nanoclays, porous and hollow nanoparticles, nanocellulose, and metallic alloy nanoparticles, to name a few [10,11]. Among various nanofillers, carbon-based fillers have attracted much attention due to their excellent physical properties.

Carbon materials are unique, and surprise s of the scientific community are constantly escalating their uniqueness, whether it is the structure of benzene, the complex behavior of polymers, or the popular materials such as graphene and its derivatives. The exceptional properties of carbon exist in every phase of matter, which is the most important reason why carbon materials dominate our daily lives. In the past 3-4 decades, carbon nanomaterials have flourished, and nearly 60% of research results in chemistry, physics, materials science engineering, and chemical engineering are directly or indirectly related to carbon nanomaterials. Among various materials, 2D and 3D carbon materials have been rigorously studied in the past 10 years. These materials have made great contributions to modern science, technologies, and industries. Nanomaterials composed of heteroatoms have been extensively explored worldwide, especially in the fields of electrochemical sensing, solar cells, batteries, and catalysis. For energy applications and catalysis, heteroatom-doped carbon nanostructures are considered as potential candidates due to their high surface area, low density, good electrical conductivity, thermomechanical stability, and densely dispersed tunable active sites. Several excellent reviews and books on key carbon materials such as graphite, carbon black, graphene oxide, graphene, porous carbon, and carbon nanotubes composed of nitrogen, sulfur, etc. have been published by renowned research groups around the world. For example, lanthanum aluminate was used for the first time as a thermal barrier coating material for internal combustion engines, transforming standard engines into low-heat-exhaust engines. The piston crowns, cylinder heads and valves of the engine are coated with lanthanum aluminate with a thickness of about 200 μm to reduce the emission of harmful nitrogen oxides [12]. Carbon-based multilayer films for electronic applications such as charge-trap flash memories, flexible organic resistive memory devices, photovoltaic devices, flexible and transparent electronics, heat sinks in electronic materials, liquid crystal displays (LCDs), thin-film solar cells, flexible touch-screen panels, electronic papers, micro-batteries, electrochemical micro-capacitors, humidity sensors, optoelectronic device, etc. [13]. Furthermore, the development of topological defects induced by heteroatoms doping and its impact on the intrinsic activity of carbon nanostructures has been extensively studied recently. Various active sites have been created in carbon nano-catalysts to enhance their activity [14,15,16,17].

Since their discovery, CNTs have been studied as fillers in polymer composites due to their one-dimensional geometry, outstanding mechanical properties, efficient thermal conductivity, and unique electrical properties. As promising materials, their poor solubility in aqueous and organic solvents hinders the application of CNTs. To date, controlled dispersion of CNTs in solutions or polymeric matrices has remained a challenge due to the strong van der Walls binding energy associated with the CNT aggregates. Altering the sidewalls of CNTs may affect the solubility characteristics. The solubility of CNTs can be significantly enhanced by radical grafting, as the large functional molecules facilitate the dispersion of CNTs in various solvents even at low functionalization [18,19]. Altering the sidewall of CNTs means functionalizing the nanotube. The good part is that it could increase the solubility and dispersion. But the functionalization may break the perfect conjugated structure of nanotube, then decrease physical properties such as thermal, electrical, and mechanical of nanotube. It is always challenging, need to be balanced. Several functionalization methods are chemical [20], electrochemical [21], mechano-chemical [22], and plasmonic [23] in nature. The most common chemical functionalization method is to use strong acid to remove the end caps and shorten the CNT length [6,24]. In addition, oxide groups were added at the ends and defect sites of CNTs to improve the surface characteristics [25,26,27,28,29,30,31,32].

According to these high expectations, the ultimate practical applications seek CPCs with physical properties closing to the theoretical maximum values of an individual CNT in a polymer matrix. The initial interest in CNT alignment in polymer matrices was described by Ajayan et al. [30], who demonstrated conceptually that the remarkable properties of CNTs could be transferred to a polymer matrix. The physicochemical properties of nanocomposites are mainly determined by the macro- and microstructures generated during the fabrication and processing of the composites. There are several identified factors that affect these properties and the subsequent performance of the resulting nanocomposites. The alignment of CNTs in polymer matrix composites yields more practical properties that fully meet the needs and expectations of innovative applications. Alignment has been recognized as a crucial structural parameter for one-dimensional materials such as CNTs with high aspect ratios. The mechanical properties of the final composite depend on the degree of CNT alignment, particularly when the composite is loaded parallel or perpendicular to the CNT orientation. Alignment can also provide effective conductive pathways for electrons and phonons, which can greatly improve electrical and thermal properties. For composites, highly aligned fillers typically represent dense packing and minimize the lateral degrees of freedom within the bulk matrix; thus, the material is more likely to exhibit similar anisotropic properties to the individual components. These findings pave the way for the development of various approaches for the incorporation and arrangement of CNTs into host matrices [30,31,32].

A comprehensive understanding of the impact of composition, hydrogen bonding, CNT orientation, and their interactions on the material system responses for the development of new materials is both scientifically appealing and technologically important. The co-existence of f-CNT structures and networks, matrices, and interfaces from nano- to macro-scales results in these heterogeneous and multifactorial anomalous responses. The broad interest of the scientific community in the development of advanced nanomaterials is evident in the numerous annual international conferences, dedicated journals, and publications on the topic. Examples of potential applications of nanomaterials include:

Hydrogen bonds formed between f-CNTs serve as electronic pathways in highly electrically and thermally conductive erosion-corrosion-resistive nanostructured composite coatings and greases [33,34]. The areas of applications are in hydro turbine blades, coal-fired boilers, cutting tools, nanofluids (in heat exchangers to increase the heat transfer rate of fluids), the automotive industry, rechargeable batteries, mechanical wear and tear prevention and many specialized applications such as the next generation electric vehicles, super electric motor bearing protection, and electrical contact improvement, to name a few [33,34]. Hydrogen bonding is believed to be attributed to the best performing samples. With further studies, this finding can be extended to other nanomaterials with functional groups such as OH, COOH, F and NH2 [8,33,34].

Due to their excellent mechanical properties and high aspect ratio, CNTs are envisioned as attractive nanofillers in polymer composites. However, detrimental CNT aggregation is often observed in polymer nanocomposites due to strong van der Waals interactions. Moreover, only limited reinforcement can be obtained due to the low stress transfer between the matrix polymer and the nanotube filler. The mechanical properties of CPCs are still far behind the theoretical predictions. A critical issue in solving this dilemma is to align CNTs in a polymer matrix. One such protocol is electrospinning followed by hot stretching. Another approach is to use functionalization strategy to obtain CNTs with pendant self-complementary hydrogen bonding groups [4,35,36,37,38,39,40].

As electronic devices tend to become thinner and more integrated, thermal management becomes a core task in device design and application. Using high thermal conductivity polymer-based composite materials instead of metallic materials as traditional heat dissipation materials has the advantages of lightweight, corrosion resistance, easy processing, and lower manufacturing cost. Hydrogen bonding is a special type of secondary bonding that is widely present/adopted in composites. The effect of hydrogen bonding on thermal transport is found at the electrode/electrolyte interface of solid-state lithium-ion batteries. The structure, orientation and bonding pattern can greatly affect thermal conductivity. As the size of electronic and mechanical devices decreases to the micro- and nanoscale, it becomes more important to predict the thermal transport properties of components [9,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55].

CNTs have excellent electrical conductivity and flexibility and are suitable for chemical delivery and touch screen devices for aerospace and defense applications. Understanding the pathways of charge transport within the networks is crucial for developing new functional materials and improving existing devices. The hydrogen-bonded CPCs offer have significantly lower electrical resistance. The hydrogen bonding formed between f-CNTs acts as electronic pathways and dramatically enhances the electrical conductivity of the CPCs [9,54,55,56,57,58,59,60,61].

Nevertheless, these findings show that very few of the nanocomposite architectures developed to date achieve their ideal performance, especially in mechanical, electrical, and thermal [31]. A vast portion of research is still struggling to meet target expectations. The challenges of transferring CNT properties to polymer matrix composites and the difficulties of the reproducibility of CNT properties with different preparation methods must be addressed. Incorporating an organized CNT architecture into a well-chosen polymer matrix and engineering the interface between the two constituents is crucial. When considering a CNT/polymer composite, the two critical issues related to CNTs and the CNT-polymer interfacial chemistry are the dispersion and alignment of CNTs in the polymer matrix. While the former is highly desirable to obtain a unform system and a higher CNT density for more capillary distribution in the polymer matrix [33], the latter is of particularly important for anisotropic thermal and electrical properties as well as mechanical strength and fluid transport characteristics. However, in order to enhance the anisotropy of CNTs and attain the optimal performance, it is essential to develop directionally aligned CNT structures and extend the length of CNTs, incorporate hydrogen bonding, in composites and obtain the highest possible to exploit the excellent intrinsic axial properties of CNTs in an actual material [30,31,33,34,36,38,39,56,62,63,64].

In this review, research conducted in the recent decades on the effects of the CPC composition, CNT morphology and aspect ratio, hydrogen bonding, CNT alignment, and interactions among the constitutions on CPC performance will be reviewed to understand how to design such CPCs with desired properties and their potential applications. The research reviews in the relative areas include highly electrically and thermally conductive erosion-corrosion-resistive nanostructured composites, alignment of CNTs in polymer matrix composites for enhanced mechanical, electrical, and thermal applications, thermal management as a core task of a device design and application, and the excellent electrical conductivity and flexibility for chemical transmission and touch screen devices for aerospace and defense applications. Further research method by computer modeling on these topics will be discussed.

2. Concepts of CNT Functionalization, Hydrogen Bonding, and CNT Alignment

The emergence of CNTs has created new opportunities for fabricating polymer composites with potential for a wide range of applications. Numerous significant advances have been attained to date, and more technological challenges await the optimization of the system to fill the gap between expectations and practical performance. Despite this tremendous progress, challenging issues related to CNT functionalization, CNT directional alignment, and assembly within a polymer matrix incorporating hydrogen bonding still remain. This section presents the concepts and fundamentals of these contemporary approaches.

2.1 CNT Functionalization

According to the various technologies are involved in fabricating CNTs/polymer nanocomposites, achieving reproducible, precise and economical nanocomposite remains challenging [65,66]. It has been reported that functionalization of CNTs can enhance the uniform dispersion of the conductive nanofiller in non-conductive polymers. Azizighannad and Mitra [67] fabricated f-CNTs/polydimethylsiloxane (PDMS) pressure sensors and reported that the functionalization of CNTs can enhance the piezo-resistive behavior of the nanocomposite due to the uniform distribution of the CNTs and the better interfacial interaction between CNTs and the polymer. This is because of the electrostatic repulsion of the functional groups on the CNTs, which in turn increases the adhesion at the interface between the polymers. This results in enhanced mechanical properties such as initial modulus and thermal degradation compared to the pristine CNTs. McClory et al. [68] analyzed the distribution behavior of f-CNTs through the rheological properties of CNTs/poly (methyl methacrylate) (PMMA) nanocomposites, showing its ability to form a highly rheologically percolated network in PMMA. Although an excellent dispersion with enhanced mechanical properties is achieved, the addition of functional groups degrades the electrical properties of the nanocomposites. This is due to the introduction of sp3 hybridization inside the nanotubes and the simultaneous loss of the pi-conjugated system of the graphene layer, thereby disturbing the graphitic structure of the nanotubes [69]. The sp3 hybridization can increase the electronic bandgap and act as defect sites in terms of electron transport through CNTs and lead to a decrease in the tunneling mechanism. It was also noticed that the high interfacial adhesion of the functionalization CNTs between the non-conductive polymers would impede the electron flow between CNTs, i.e., hopping mechanism. Chemical functionalization is based on the covalent linkage of functional entities on the CNT surfaces [67,70].

Functionalization is to generate functional groups on the surface of CNTs. These functional groups help reduce the long-range van der Waals attraction and increase the CNTs-matrix/solvent interaction and produce a uniform dispersion or lead to CNT solubilization. The effect of CNT functionalization on properties includes enhanced solubility and stability in aqueous and organic solvents. Further functionalized derivatives can be used as molecular linkers to interconnect CNTs, can be soluble in water and capable of trapping water-soluble metal ions and then enhance dispersion of CNTs in a wide variety of polar and non-polar solvents and polymer matrices, etc. [71,72,73,74,75,76,77].

There are many well-reported methods for the synthetic functionalization of f-CNTs, which is the primary prerequisite for applying CNTs to any area. Both covalent and non-covalent approaches for functionalization have been reported [76]. Broadly speaking, they can be classified as either exohedral or endohedral, depending on whether the modifications are made on the outer walls of the CNTs [77]. The exohedral functionalization is further subdivided into two categories: (a) covalent functionalization, and (b) non-covalent functionalization, which may be filled with tailored materials to meet specific needs, etc. [77].

In addition to the nanofiller functionalization, there are also many ways to functionalize polymer matrices. Many studies have reported the oxidation of organic synthetic alcohols using polymer-supported reagents. New functional materials have been developed through coordination of polymers, which have a wide range of applications. For the oxidation of alcohols, several oxidizing agents are used. Coordination of polymers via catalyst is more advantageous due to high stability and many active metals. Recently, many nanomaterials have been used as catalysts to increase the oxidation rate in the base matrices. The synthesis of base matrices can also be used to enhance alcohol oxidation [78].

2.2 Hydrogen Bonds

According to IUPAC journal Pure and Applied Chemistry, the hydrogen bonding definition specifies: The hydrogen bonding is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H in which X is more electronegative than H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation [79]. Such an interacting system is generally denoted as Dn-H···Ac, where Dn denotes a more electronegative “donor” atom or group, and Ac denotes another electronegative atom with a lone pair of electrons – hydrogen bond acceptor, the solid line denotes a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond. Hydrogen bonds can be intermolecular or intramolecular. The energy of a hydrogen bond depends on the geometry, environment, and the nature of the specific donor and acceptor atoms and can vary more than two orders of magnitude between about -0.2 to -40 kcal/mol [80]. This makes them somewhat stronger than van der Waals interactions, but weaker than fully covalent or ionic bonds. This type of bond can occur in inorganic molecues such as water and organic molecules such as DNA and proteins.

Hydrogen bonds are responsible for holding materials like paper and felted wool together and cause individual sheets of paper to stick together when they get wet and then dry. Hydrogen bonding is due in part to the high electronegativity difference between a hydrogen atom and an atom of one of the elements fluorine (F), oxygen (O), or nitrogen (N) [81,82]. Since the σ bond that causes this is linear and polar, a positive charge will be exerted through the hydrogen atoms in a direction parallel to the bond. A second vital requirement for hydrogen bonding to occur is the presence of a lone pair on the local species. The negative charge of a lone pair of electrons acts in a direction away from the atom with which it is associated. Combining these factors, it is easier to see that due to charge attraction, the strength of the hydrogen bond will be the strongest when the two forces act in as different directions as possible, which is the case when the original electronegative atom, the hydrogen atom, the atom with lone pair, and the lone pair itself, are all aligned with one another [72,83,84,85,86,87]. A schematic diagram of H-bond examples is shown in Figure 1.

Click to view original image

Figure 1 Examples of hydrogen bonds.

Compared with other similar structures, hydrogen bonding is responsible for many physical and chemical properties of compounds of N, O and F that seem unusual. It also plays an important role in the structure of both synthetic and natural polymers. It plays an important role in determining the three-dimensional structures and properties adopted by many synthetic and natural proteins. Compared to the C-C, C-O, and C-N bonds that make up most polymers, hydrogen bonding is much weaker, only about 5%. Thus, hydrogen bonding can be broken by chemical or mechanical means while retaining the basic structure of the polymer backbone. This hierarchy of bond strengths (covalent bonds, which are stronger than hydrogen bonds, are stronger than van de Waals forces) is key to understanding the properties of many materials [88].

2.3 CNT Directional Alignment

Materials with high electrical and thermal conductivity as well as lightweight are highly desired for applications in aerospace and electronics [56]. The most common materials used for these applications are metal-based and conductive polymer-based materials. However, metal-based materials are heavy, and polymer-based materials cannot be used in ultra-high temperature environments. Although some advanced ceramics have applications at high temperatures, they are still not ideal choices for aerospace applications due to their high specific weight. On the other hand, carbon materials such as CNTs, graphene, fullerene, graphite, carbon nanofibers and carbon/carbon composites are lightweight materials that can not only be used at high temperatures (non-oxidizing environments), but also have excellent conductive properties. Carbon materials have emerged as suitable candidates for lightweight and high conductive aerospace applications. The crystal-packed structure of CNT assemblies can limit contact resistance and facilitate charge transfer among individual nanotubes and bundles of CNT assemblies. For example, the electrical conductivity of the composite material reaches 7.70 × 102 S·m-1 through the vapor-phase infiltration of carbon to densify the aligned CNT films [87]. Recently, an electrical conductivity of ~1.3 × 106 S·m-1 for aligned CNT sheets was achieved by using mechanical stretching of CNT sheets and surface chemical iodine doping [51,87]. A schematic diagram of CNT aligning and assembling under electric field is shown in Figure 2 [88].

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Figure 2 Schematic model of CNT aligning and joining in liquid medium in the direction of electric field. (a) Initial state. (b) Schematic diagram of a polarized CNT in an electric field. (c) CNT aligning in the electric field direction. (d) The polarized CNTs align and assemble into a network.

The physicochemical properties of nanocomposites are primarily dictated by the macro- and microstructures generated during the fabrication and processing of the composites. There are many identified factors that affect these properties and the subsequent performance of the resulting nanocomposites. The alignment of CNTs in polymer-based composites yields more practical properties that perfectly meet the needs and expectations of innovative applications [31].

Since the CNT alignment has a significant impact on the properties of the resulting polymeric composites, tailoring the degree of CNT alignment to the composite is a fundamental issue, particularly during the synthesis stage of the material [31]. In general, CNTs can be aligned horizontally or vertically to the surface of the polymer composite films, which largely depends on the application of the resulting composite. It is generally accepted that vertically aligned configurations are more challenging and complex to achieve than horizontally aligned CNTs [31]. In most established methods, an external force such as a magnetic or electric field, mechanical stretching, or shear force is applied to orientate the CNTs [31].

Based on the predictability of the nonlinear stress-strain constitutive relationships, elastic hysteresis, hygro-thermo-mechanical properties, and elastic damping response of CNT-modified polymeric composites, there are many studies based on the stochastic nature of the constituent parameters, elastic energy release approach based on stick-slip analytical method, and multi-scale computational method based on finite element method for understanding the effects of the CNT alignment, constituent and process parameters on the performance of the CNT-modified polymeric matrix composites [89,90,91,92,93].

Through a fundamental understanding of the strongly dependent processing–structure–performance relationships, the creation of aligned CNT/polymer multi-functional nanocomposites with controlled hierarchical structures offers a wide range of applications [31]. Aligned CNT/polymer nanocomposites fabricated by various methods exhibit many outstanding properties that have been extensively explored for applications in electronic nanodevices, chemical and biological sensors, actuators, and energy sources [31].

The incorporation of CNTs into polymer matrices offers a viable route to extend the interesting properties of CNTs from the nanoscale to the macroscopic level. However, the most important limitation for practical applications in the fields of composite science and technology comes from the fact that randomly oriented CNTs embedded in bulk samples exhibit much lower performance (especially in mechanical, electrical, and thermal) than expected [31]. Therefore, it has been proposed to incorporate an organized CNT architecture (align CNTs) into a carefully selected polymer matrices and engineer the interfaces between the two constituents to extend the interesting properties of CNTs from the nanoscale to the macroscale [62,87,88,94,95,96,97,98,99].

3. Research Summary on f-CNTs, CNT Alignment, Hydrogen Bonding, CPCs

Understanding how the addition of CNTs to polymer composites and how to effectively transfer the unique properties of CNTs from the nanoscale to the macroscale into CPCs is vital which is related to the mechanical, thermal, and electrical performance of CPCs. The primary focus of our review on the relative topics is to understand why the thermal, electrical, and mechanical properties of polymers can be improved using nanofillers. The CPC material design involves manipulating the material system composition, including chemically f-CNTs, hydrogen bonding, various structures of CNTs (chirality, number of wall layers, aspect ratio, etc.), and interactions among the constitutes and matrices based on chemical physics and materials science.

3.1 Electrical Properties

Electrical resistivity and/or conductivity is an important property of materials. Conductivity and resistivity are inversely proportional to each other. Electrical conductivity is based on electrical transport properties. Polymers offer distinguished advantages as dielectrics over traditional inorganic materials. Suitable applications may vary, for example, polymers with a low dielectric constant are ideal for communication cable insulation. The electrical characteristics of CPCs have been receiving much attention. However, evaluating the electrical conductivity of CPCs by experiments for the development of CPCs with desired properties is an expensive and inefficient method. It is certainly more efficient and economical to preform computational evaluations by using mathematical models of the physics governing charge transport in CPCs. To obtain the electrical conductivity of the CPC, Figure 3 depicts the geometrical configuration of the computational modeling domain of a specimen, where the test voltage, Vtest, is applied throughout the cross-sectional area A of the entire specimen length L0 [100]. Therefore, the electrical conductivity can be calculated by

\[ \sigma=\frac{J}{E}=\frac{\left(\frac{I}{A}\right)}{\left(\frac{V}{L_{0}}\right)}=\frac{1}{\rho} \tag{1} \]

where σ and ρ are conductivity and resistivity, respectively. E and J are the electrical field and the current density, respectively.

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Figure 3 Schematic model of CPC electrical property test.

An interesting finding is that the voltage distribution on the CNTs belonging to the percolation network follows a nearly linear distribution from top to bottom. Since the uniformly distributed CNTs are interconnected by electron tunneling, it is likely to form a linear voltage distribution across the entire CNT/polymer composite region. Otherwise, more locations/points may need for higher accuracy to take the measurements along the length of the model. It was found that the electrical properties of the CPCs depended on the state, geometry, and processing of CNTs. Table 1 summarizes some electrical properties of CPCs with various polymer matrices, different morphological CNT fillers and aspect ratios, fabrication processes, and percolation thresholds [57].

Table 1 The electrical properties of some CPCs from literatures.

3.2 Thermal Properties

For the thermal property measurements, the schematic diagram is similar to Figure 3, where the heat (phonons) flows through the CNTs instead of electrons through the CNTs, with heat flux applied on one side (hot region) and heat sink applied on the other side (cold region). The heat flux J can be calculated by

\[ J=\frac{dq}{2Adt} \tag{2} \]

where dq is the heat added to the hot region duing the time incremental dt, and A is the cross-sectional area over which the heat is transferred. Then the thermal conductivity k can be calculated as

\[ k=\frac{J}{\partial T/\partial L}=\frac{dq}{2Adt(\partial T/\partial L)} \tag{3} \]

The coefficient of thermal expansion α(T) can be calculated as

\[ \alpha(T)=\frac{1}{L_{0}}\frac{dL}{dT} \tag{4} \]

where L0 is the original length of the specimen in the direction of heat transfer and T is the temperature in the specimen. Table 2 summarized some thermal properties of CPCs with various polymer matrices, different morphological CNT fillers and aspect ratios, fabrication processes and percolation thresholds.

Table 2 The thermal properties of some CPCs from literatures.

3.3 Mechanical Properties

For the mechanical property measurements, the schematic diagram is similar to Figure 3, where the stresses are transmitted through the CNTs instead of electrons through the CNTs. The model/specimen can be defined as a cubic shape whose dimensions can be defined by the initial length L0 and the cross-sectional aera A, and the tensile force F or tensile stress can be applied on the area, so that a uniaxial tensile test can be performed on the model. The Young’s modulus of the CPC specimen can be calculated by

\[ E=\frac{\Delta\sigma}{\Delta\varepsilon}=\frac{F}{A}\frac{L_{0}}{\Delta L} \tag{5} \]

where Δσ and Δε are the incremental stress and strain, respectively, in the elastic deformation region (the stress and strain data at the beginning part of the uni-axial tensile test). ΔL is the incremental length of the specimen in the tensile direction after the tensile force is applied. The Poisson’s ratio can be calculated by

\[ v_{ij}=-\frac{\varepsilon_{j}}{\varepsilon_{i}} \tag{6} \]

where εi and εj are the strains in the tensile force applied direction and the lateral direction, respectively.

Other mechanical properties can be determined accordingly according to American Society for Testing and Materials (ASTM) standards. Table 3 summarizes some mechanical properties of CPCs with various polymer matrices, different morphological CNT fillers and aspect ratios, fabrication processes, and percolation thresholds.

Table 3 The mechanical properties of some CPCs from literatures.

3.4 Other Properties

The review so far has focused on the general electrical, thermal, and mechanical properties of CPCs and factors influencing them. In this subsection, recent advances in various fields/topics, such as applications in flexible and stretchable CNTs/polymer films for realizing high-performance strain and pressure sensors, and transparency in tough screens, are precented. Table 4 summarizes some additional properties of CPCs with various polymer matrices, different morphological CNT fillers and aspect ratios, fabrication processes, and percolation thresholds.

Table 4 The other properties of some CPCs from literatures.

4. Discussion

As can be seen from the data in the tables above, the material properties of the CNT-modified nanocomposites depend on many factors, including the type of CNT filler (morphology and aspect ratio of CNTs), fabrication process, functionalization type, and percentage of the CNT addition, etc. For example, the electrical conductivity generally increases with increasing CNT length, diameter, or number of CNT wall layers. There are similar trends for other properties. The fabrication processes have been adopted/chosen according to the material synthesis requirements. However, there is still a lack of quantitative analysis and comparison. The effects of these factors are usually not in a monotonically changing pattern (monotonically increasing or monotonically decreasing). There is usually an inflection point (threshold value) where the material performance is at a maximum or minimum point that can be fully accounted for when we conduct effective new/novel material design.

However, it is not yet fully quantitively clear how the chemical f-CNTs incorporating hydrogen bonding can effectively transfer the unique attributes exhibited by CNTs at the nanoscale to the macroscale, and it is vital to comprehensively understand the ways in which CNTs are added to polymer composites correlates with the mechanical, thermal, and electrical performance of CPCs. CPC material design involves the accurate prediction of desired material properties by manipulating the material system composition including hydrogen bonded f-CNTs, CNT morphology (chirality, number of wall layers, aspect ratio, etc.), CNT hydrogen bonding forms (end-to-end alignment or overlapping connections, etc.), the interactions among the constitutions and matrices based on chemical physics and materials science.

Depending on the problem and spatial and time scales of interest, various approaches to materials design based on computer modeling exist, from quantum mechanics to continuum simulations. Molecular dynamics (MD) or first principles simulations are ideal for studying nanoscale material properties. MD is an atomistic scale simulation that describes the interactions between atoms through interatomic potentials. In the MD method, electronic effects are averaged, and the time evolution of atomic positions and velocities is calculated from Newton’s equations of motion. The electron-dependent approximation is based on the Born-Oppenheimer theory, and the MD time step used to describe atomic motion is long enough for electrons to achieve their ground stable state, as compared to nuclei due to mass differences. The interatomic potentials (force fields) are established from the first principles or experiment to describe the interactions between the atoms, including the effect of electrons, in terms of reproducible forces. The reliability of the interatomic potentials determines the accuracy of the MD simulations is furthermore related to the ability to bridge the effectiveness of mesoscale methods [40,42,192,193,194,195,196,197]. The polymer matrices and CNTs can interact through strong covalent or electrostatic interactions or hydrogen bonding. These chemical interactions lead to strong coupling at the interface. Alternatively, polymer matrices can interact with CNTs through weak electrostatic interactions, such as van der Waals forces [29,198,199,200,201]. These detailed considerations are very important when considering the design and optimization of the load/electron/phonon transferring/passing through across the interface.

Because there are too many factors involved in the preparation, fabrication, and post-processing of the matrix, the CNT reinforcement, and the composite material, too complex and too strongly coupled, it is difficult to quantitatively draw the summary research results of this topic as each individual factor changes. Fortunately, there are some specific examples or case studies that can demonstrate the effective applications of CNT-modified polymeric nanocomposites. Those findings were obtained by MD simulations, which outlines the effects of factors, such as CNT chirality, CNT length, CNT volume fraction, and CNT overlap length, individually on the thermal and electrical properties of CNTs and CNT-modified polymeric composites, respectively. Furthermore, those quantitative results provide tangible evidence for the potential of these materials and guidelines for material design [202].

5. Conclusions

CNTs are well-known nanofillers that can be used to produce high-performance polymer nanocomposites. The chemically f-CNTs, incorporating hydrogen bonding and appropriate solvents help to create well-dispersed CNT networks as electron pathways in polymer nanocomposites, in addition to extending the length of CNTs to enhance directional performance, and by proper design to create desired properties to fit desired applications and show promise in energy storage, energy harvesting, mobile phones, surface engineering, optical coatings, and integrated circuit chips. However, multiple factors and strong coupling among CNT nanofillers and matrix materials pose difficulties in designing and optimizing such CPCs using traditional experimental trial and error approaches. The lack of a comprehensive understanding the effects of the composition, f-CNTs nanofillers, hydrogen bonding, CNT alignment and morphology, and interactions between the constitutions, on the CPC performance limits both the knowledge of designing CPCs with desired properties and their potential applications. This paper presents research in recent two decades in the relative areas, including CNT-modified highly electrically and thermally conductive erosion-corrosion-resistive nanostructured composites, chemically f-NCTs, incorporating hydrogen bonding, and CNT directional alignment in a polymer matrix for reinforcement in mechanical, electrical, and thermal applications. However, to gain a comprehensive and quantitative understanding of the effects of these factors on the performance of CPCs, further studies by computer modeling, especially MD simulations, will be highly needed for effective new/novel material design and development.


This work was supported by the J. J. Lohr College of Engineering and Mechanical Engineering Department at South Dakota State University and are gratefully acknowledged.

Author Contributions

Conceptualization, Z.H. and H.H.; methodology, Z.H. and H.H.; investigation, Z.H. and H.H.; resources, Z.H. and H.H.; data curation, Z.H.; writing—original draft preparation, Z.H.; writing—review and editing, Z.H. and H.H.; visualization, Z.H.; project administration, Z.H. and H.H.; funding acquisition, H.H. All authors have read and agreed to the published version of the manuscript.


This research was fund through US Army Research Lab (Cooperative agreement W911NF15-2-0034-S).

Competing Interests

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.


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