# Modern Fiber Art Creation Based on Traditional Hakka Hand Tie-Dyeing Process Based on Carbon Nanotube Nanomaterials

Authors: Fuying Zhang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

With the change of the times, modern fiber art has greatly changed and developed in the traditional technology. This artistic expression brings people richness in form and artistic language and is a kind of performance art between art and decoration. Modern fiber art is a part of life. With the change of living environment, people's things will also change, so if we want to adapt, we have to change appropriately. Molecular dynamics and calculation of resistance values are used to study the relationship between the length, cross section, and temperature of materials in carbon nanotube composites. Modern fibers are mainly made of composite materials such as carbon nanotubes. This paper mainly uses the repeated expansion of polymer carbon nanotube materials, uses the interaction between electrons and phonons as well as the interaction between phonons and phonons to test the thermal conductivity value and the curing regime of different composite materials at different stages, and in order to study the thermal conductivity of carbon nanotube composites, the relevant data in the model are set to a unified packing density system and melting point, uses the temperature of 280 K and 320 K to normalize the composite materials, and explores the change law of the heat flow correlation function and the thermal conductivity. It can be seen from the experimental data that the heat flow correlation function changes with time and gradually becomes stable and finally fluctuates around 0, which means that the model is in a stable state and the scheme is feasible. With the development of the times, fiber art has various forms of expression, and this art is expected to shine in all walks of life.


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## Body

## 1. Introduction

The tie-dyeing process has a long history, and the times of the tie-dyeing process have also changed with it. The original foundation has been constantly changed and innovation has never disappeared. Humans have a long history of using fiber to make, and the expressions of modern fiber art are different in various fields, but most of them have the same goal. The carbon nanotube is a hollow fullerene tube, which is a special carbon fiber carbon nanotube. It is composed of some cylindrical carbon tubes coaxially sleeved, the width is only a few nanometers, but the length is 103–106 times the diameter, which can reach 1 micrometer or even 1 mm. Therefore, carbon nanotubes are standard Quantum Materials. Typically, carbon nanotubes are closed, but there are also incomplete openings. The unique molecular structure of carbon nanotubes directly causes them to exhibit unique properties, such as good ductility, good electrical conductivity, tensile strength, thermal conductivity, and chemical inertness. In addition, a potential project is the use of high-strength carbon cables for extraterrestrial elevators.The design and application of composite materials are mainly on load-bearing devices. During actual operation, composite materials are usually interfered by unfavorable factors such as high pressure, high temperature, strong corrosion, material aging, and high-altitude radiation, resulting in material fatigue and damage. Therefore, it is very necessary to establish a complete set of the structural health monitoring system for composite materials under continuous working conditions. In this way, it can monitor the local damage status and evaluate the damage situation in real-time, and then provide the basis for accurate data analysis, and avoid huge potential safety hazards and economic losses due to the damage of the internal structure of the material. By changing the material of fiber materials, the products created by fiber art can have new vitality, change the form of artistic expression, and convey different ideas.The material application range of modern fiber art is very wide. This is because different fiber material properties are made of different composite materials. In order to achieve the desired material effect, continuous innovation is required. Through the molecular dynamics analysis and resistance value calculation of the composite material, this paper uses the manufacturing process to compare and analyze the trajectory of the carbon nanotubes embedded in the composite material preform, gives the error analysis results, conducts basic experimental analysis and data analysis on the sensing characteristics of carbon nanotubes, and finds a suitable fabrication method. And through the experiment to test the curing of the composite material, the curing results of the three-stage test can reflect the effect of different times and temperatures on the curing of the material.


## 2. Related Work

Sequence-specific molecular interactions on carbon nanotube surfaces remain the subject of fundamental research in most cases. Nshimiyimana et al. investigated the effect of magnetic fields on the electrical resistance of single-walled carbon nanotube (SWNT) arrays. SWNT devices consist of a mixture of metallic and semiconducting SWNTs between palladium electrodes. The resistance increases as the external magnetic field becomes higher, indicating that the MR of SWNTs is positive [1]. Salem et al. observed and analyzed universal ionic strength-mediated phase transitions exhibited by more than 25 different oligonucleotides adsorbed onto single-walled carbon nanotubes (SWCNTs) in colloidal suspension. At high (low) ionic strength, the negatively charged phosphate backbone increases (decreases) DNA surface coverage and is well described by a two-state equilibrium model [2]. Zhiheng et al. used a simple hydrothermal method to synthesize nanoribbons and carbon nanotube composites and then incorporated CNTs to evaluate the electrochemical behavior of the composites [3]. Magnin et al. deduce the structure diagram and phase diagram of the composite material through the chemical properties of the catalyst through the thermodynamic model, so that the catalyst and growth parameters can be reasonably selected [4]. These studies are all studies on carbon nanotube materials, and lack of product application analysis.Molecular dynamics is a comprehensive technique with a wide range of applications. Boyd et al. used the coarse-grained Martini model for the atomic molecular dynamics analysis of bilayer materials, and the results showed that the mechanical properties of the surface bilayer vary greatly depending on the similarities and differences in the properties of the molecular and bulk bilayers [5]. Arcon et al. simulated each system in pure water to determine their structure and potential key interactions, and molecular dynamics simulations in the presence of different solvent probes have been increasingly used to analyze protein binding sites, revealing protein-ligand interaction hotspots [6]. Yuan et al. analyzed the interaction of CUR with model lipid bilayer mixtures and biomembrane mimics through all-atom explicit solvent molecular dynamics (MD) simulation studies [7]. The decomposition of low-rank matrices obtained by Hamm and Huang by choosing certain column and row submatrices of CUR gives perturbation estimates for each variant in terms of the size of the noise matrix in the broad norm, illustrating how the choice of columns and rows affects the quality of the approximation [8]. The scope of these studies is very broad, and there is a lack of focused research on carbon nanotube materials.


## 3. Fabrication Process of Carbon Nanotube Composites

Modern fiber art is influenced by modern art and modern design concepts. The artist reflects on the relationship between hand weaving and industrialized society. In order to create great artistry and find new ways of doing things, technicians must have a solid understanding of materials, seek to innovate, and showcase their creativity in the weaving process. The soft and hard appearance of different material properties gives people different feelings, which is the material basis for the artist to choose the materials needed to express the artistic conception.Carbon nanotubes are all composed of carbon atoms, and the central tube is made of a single-layer graphite hexagonal mesh surface that is curled 360° with a certain angle above it as the axis. Carbon nanotubes with high thermal conductivity have become more suitable additives for thermal conductors. Filling carbon nanotubes with polyethylene to form carbon nanotube polyethylene compounds is expected to produce new materials with better thermal conductivity [9]. Brugman’s formula for calculating the thermal conductivity of composite materials is:(1)1−f100=δc−δdδr−δdδrδc.After adding multi-walled carbon nanotubes (MWCNTs), the thermal conductivity of the nanocomposites was significantly improved [10]. The nanoscale thermal diffusion of carbon nanotubes to the polymer matrix can effectively reduce the heat storage of polyethylene in local areas, prevent the breakage of polymer molecular chains, and prolong the service life of tools and packaging materials [11]. The thermal conductivity of nanocomposites is the result of the combination of fillers and polymers. A suitable condition for maximizing the thermal conductivity of the polymer matrix compound is that in a given filler state, the filler is completely uniformly dispersed in the polymer mold, and the fillers are interconnected to form a thermally conductive network or thermoset [12]. The conductor chain structure is small enough to keep the thermal resistance of the interface constant for heat flux conduction. Heat treatment and acid treatment can enhance the diffusion of carbon nanotubes, so that the carbon nanotube polyethylene composites have the best properties to optimize the diffusion of carbon nanotubes [13]. In addition, longer carbon nanotubes are less prone to handling semi-one-dimensional structures and are easier to form and bend in polymers, making them a more feasible approach [14].


### 3.1. Molecular Dynamics

Molecular dynamics is a commonly used mechanical model. On the carbon nanotube structure, the equation of motion of the molecular system is solved numerically, and the thermal conductivity simulation calculation of the molecular system and properties of the carbon nanotube is studied [15]. Molecular dynamics has different mechanical models both macroscopically and microscopically and provides clear microscopic explanations for surface phenomena that are difficult to understand from theoretical and empirical observations [16]. This method mainly relies on Newtonian mechanics to simulate the motion of the molecular system to draw samples in the system composed of different states of the molecular system.Due to the development of modern software and the popularization of hardware technology, molecular dynamics modeling is widely used in the chemical industry and plays a crucial role in material and molecular modeling. When starting to calculate the dynamics of the system, it is first necessary to find the energy-reducing surface as a stable starting point. There are 3 general methods for reducing the potential energy of the system to find the global optimal structure: steep descent method, combined gradient method, and Newton–Raphson method. The steep descent method, while particularly safe, is not a particularly efficient method of calculation. By taking a step in the negative growth direction ofE, there is:(2)i2=i1−λ∇Ei1,Ei2≤Ei1.The potential function is a mathematical function whose value is a physical vector potential or a scalar potential, also known as a harmonic function, which is the research topic of the mathematical potential theory. The AIREBO potential function consists of three parts:(3)E=12∑x∑y≠xExyREBO+ExyLJ,ExyREBO=EWrxy+bxyEArxy.EW represents the repulsive part of the interaction, given by:(4)EWrxy=A1+Trxye−arxy.EA represents the attractive part of the interaction, given by:(5)EArxy=∑x=13Bk1+Trxye−brxy.The main elements in the molecular dynamics calculation process are time, velocity, acceleration, and force, which interact with each other. Although there is no informative description of temperature among these factors, the temperature can be measured by molecular average kinetic energy and applied energy [17]. The total kinetic energy Bk of the molecules in the system is calculated as:(6)Bk=12∑x=1NmxSx2,Bk=32,T=33NkB∑x=1NmxVx2.The heat flow vector can be defined as follows:(7)P=zzt∑xrxEx.For pairs of potentials, the expression can be changed to the following form:(8)W=∑xexvx+12∑xySxyvxrxy.Based on the observed normalized heat flow autocorrelation function, a double exponential curve can be applied:(9)G0•Gt3=A1exp−tε1+A2exp−t|ε2.The fitting formula of the double exponential decay curve is as follows:(10)Gν0•Gνt3=Ashexp−tεsh+A1gexp−t|ε1g.Carbon nanotubes are quasi-one-dimensional nanomaterials with excellent thermal conductivity. The thermal conductivity of carbon nanotubes strongly depends on the mean free path of phonons, and the thermal conductivity of carbon nanotubes is extremely sensitive to the arrangement of atomic defects. In fact, carbon nanotubes have many forms of defect types in the structure due to insufficient manufacturing levels. The essence of defects is the introduction of disorder into the complete lattice of carbon nanotubes, and the main defect types are shown in Figure1. Defects first break the original energy band symmetry of the system and destroy all aspects of the properties of carbon nanotubes. In some cases, a very small amount of defects may fundamentally change some aspects of its properties [18]. The number, arrangement, and interaction of defects can affect the thermal conductivity of carbon nanotubes. Studies have shown that the thermal conductivity of carbon nanotubes is generally contributed by two parts: the interaction between electrons and phonons and the interaction between phonons and phonons [19–21]. For carbon nanotubes, the interaction between phonons and phonons plays a major role in the entire heat conduction process; due to the large energy gap and low density of free carriers, the interaction between electrons and phonons makes little contribution to the thermal conduction process of carbon nanotubes [22].Figure 1
Schematic diagram of carbon nanotubes and their defects. (a) Intact carbon nanotubes. (b) diatomic defect. (c) shape defect. (d) cell vacancy defect.
(a)(b)(c)(d)The production skills of fiber art materials have grown with the development of the times, but in order to express the concepts and ideas of modern art, it still needs to be conveyed in the form of products [23, 24]. Only through works of art can the creative thoughts and emotions of the artist be conveyed, the breakthrough of materials and the evolution of the form of works are due to major changes in the design concept. Although the content and form of traditional fiber craft products are rich and diverse, they are inevitably limited in production. At this time, the material, color, form, and composition of the fiber product can have a style. Although centuries have passed and evolution has matured in all respects, design is very dependent on people’s culture and traditional concepts, or is completely dominated by so-called art, which is already a picture of pure art.Introducing defects on the sidewalls of carbon nanotubes can easily cause the bending of carbon nanotubes, and the longer the carbon nanotubes are, the more they tend to bend [25]. If defects are introduced into the tube wall, it is very difficult for long carbon nanotubes to maintain their quasi-one-dimensional structure. In order to eliminate the interference caused by large deformation and calculate the influence of the interaction of defect spacing on the thermal conductivity of carbon nanotubes, it is necessary to take necessary measures to avoid the interference of large deformation when establishing the model. After trial and error, it was found that the situation was largely improved when the optimization calculations were performed to minimize the carbon nanotubes by placing them in a lattice just covering their size. This is like placing it on a flat surface, which will generate a certain local depression and deformation around the defect, but will not cause a larger bending deformation [26].The thermal conductivity of carbon nanotubes depends on the atomic structure, diameter, type, defect, and degree of purification [27]. The structural types of carbon nanotubes were unified to study the effect of defect spacing of different defect types on the thermal conductivity of carbon nanotubes. The larger the number of defects in the carbon nanotube defect, the more complex the interaction between the defects, which is completely different from the case where the carbon nanotube contains only one defect. Carbon nanotubes are extremely sensitive to defects. The existence of defects greatly changes the properties of carbon nanotubes in various aspects. The type of defects, the number of defects, the distance between defects, and the symmetrical distribution of defects all affect the thermal conductivity of defects.So far, the research conclusions about the influence of carbon nanotubes and their defects on thermal conductivity are not completely consistent, and the exploration of the heat transport mechanism is far from enough. In this chapter, the equilibrium molecular dynamics method is used to calculate the thermal conductivity of different models, and the influence of the spacing of different defect types on the thermal conductivity is explored.


### 3.2. Calculation of Resistance Value

A heat flow sensor is a tool for measuring heat flow density or heat flux and is the most critical component of a heat flow meter. The performance and use of the heat flow sensor determine the performance and use of the heat flow meter. For carbon nanotube sensor, calculating its initial resistance value in three-dimensional braided composite material has important reference significance for the design and modeling of the structural health monitoring system. Designers can calculate the resistance value of a single carbon nanotube according to the length of the tube, and estimate the overall resistance of the prefabricated part, which can provide a basis for the design of signal acquisition, processing subsystems, and electronic components. The constraints of objective conditions bring certain difficulties to the calculation of the resistance value of carbon nanotubes:(11)SO=βOLORO.It can be seen from the formula that under the condition of stable temperature and magnetic field, the initial resistance value of carbon nanotubes is related to its initial resistivityβO, initial length LO, and initial cross-sectional areaRO. The change in the resistance of the carbon nanotubes can be calculated as:(12)ΔSS=Δββ+ΔTT−ΔBB.Since the load and relative resistivity increase are symmetrical, the carbon nanotube sensor still has good linearity within a certain load range. When studying the carbon nanotube sensor to monitor the curing behavior of composite materials, it was found that the resistance of the carbon nanopaper sensor gradually increased with the decrease of temperature in the cooling stage, and the corresponding changes of temperature and resistance in the cooling stage were extremely linear. To demonstrate the sensor stability, a graph of the temperature and resistance response data for the cooling phase at 70°C and 120°C was added, as shown in Figure2.Figure 2
Changes of temperature and resistance curves in cooling stages at (a) 70°C and (b) 120°C.The expression for the length change of carbon nanotubes is:(13)ΔTT=φ11−φ1122.According to the Poisson effect, the change of the cross section is transversely isotropic, then the second term is ignored and expressed as:(14)P′=P1−2V12φ11.In the formula, 1 represents the Poisson's ratio of the carbon nanotube, so(15)ΔPP=−2V12φ11.Then(16)ΔSS=Δββ+φ11+2v12φ11=Δββ+φ111+2v12.According to the algorithms for solving the length of carbon nanotubes, including the ideal mean estimation method, the pitch node connection method, the Bezier curve fitting method, the B-spline curve method, and the weaving angle algorithm, the length L of a single carbon nanotube can be calculated, and then use the resistivity formula to calculate the initial resistance valueR.For different curing regimes, the curing degree of the composite material is different, and the resins with different curing degrees also respond differently to temperature. For the experimental results, the temperature responses of the embedded carbon nanopaper sensors during the cooling phase of different curing cycles are not identical. The DSC method has been introduced to measure the curing degree. In the experiment, DSC was used to measure the curing degree of six groups of different curing systems. The curing degree and resistance temperature coefficient are sorted as shown in Table1:Table 1
Correlated changes in resistance for five curing regimes.
Temperature (°C)Degree of cure %12011150.981050.95850.81700.75The change of resistance is mainly caused by two reasons: the resistance change after the conductive structure is changed and the resistance change caused by the sensitive response of the sensor to temperature. The structure of the sensor’s solidification response to temperature is shown in Figure3.Figure 3
Sensor response to temperature system.Due to the negative temperature coefficient of the sensor itself, the resistance decreases as the temperature increases, and the response of the resistance to temperature changes is not particularly obvious. Compared with the resistance resulting from the temperature-sensitive behavior, the resistance changes in the two stages are of two orders of magnitude and have different growth trends. Therefore, the resistance change in the first stage of curing is mainly due to the resin flow changing the conductive structure. This also proves from another perspective that the contact resistance plays a major role. In the second stage of the curing experiment, the temperature in this stage remains unchanged, and the temperature-sensitive behavior does not produce resistance changes. The internal resin curing shrinkage and final stabilization is the main reason for the resistance change at this stage. Both the temperature and resistance during heating are shown in Figure4.Figure 4
Graph of temperature and resistance changes during heating.With the help of modern technology, real-time control of structures is possible based on information acquired by sensors. In the process of material production, use and maintenance, 3D woven composite materials are prone to internal damage such as degumming, air bubbles, and fiber breakage that are not visible on the surface due to external impact and strong collision, resulting in the reduction of the overall bearing strength and bearing capacity of the material, resulting in potential safety hazards. The main defect types of composite materials and their influence on material properties are shown in Table2. Therefore, it is of great practical significance to study the nondestructive testing (NDE, Nondestructive Evaluation) technology of 3D braided composites, especially the health monitoring of 3D braided composite parts based on carbon nanotube (CNT) wire.Table 2
Composite defect types and their impact on properties.
Defect typePerformance impact under defect correspondenceLayeredIt has a serious impact on the overall performance of the composite materialFractureThe strength in the direction of the broken fiber decreases by about 20%RippleThe bearing strength is lost by about 25%, and the lifespan is decreased by about 10%Pores are too largeThe strength loss is small, and the life is reduced by 50%Surface crackBearing strength decreased by 40%–50%The advancement of modern science and technology has provided modern fiber manufacturers with a wide variety of materials, and the creation of fiber art products is no longer limited by traditional fiber materials. Through modern craftsmanship, traditional fiber materials are changed to form new high-tech fiber materials, providing artists with more creative choices. Many new materials such as synthetic materials, metal fibers, and glass and ceramic fibers also provide artists with more modern Fiber Art Creation. Through special processing technology, these new materials will undergo different changes in texture, some become flexible, and some are rigid. At the same time, compared with traditional materials, the new materials have more morphological plasticity. Like perforated plastics and rubbers, they can exhibit very rich variations on demand, increasing the freedom of artistic conception. Fiber creation artists should be more advanced than traditional materials in the expression of creative concepts, which is the difference between modern new materials. Through fiber creation attempts to express and realize personal emotions. Both traditional fiber materials and modern new composite materials can express artistic information and ideas through artistic products, under the condition of desire and motivation expressed through works.


## 3.1. Molecular Dynamics

Molecular dynamics is a commonly used mechanical model. On the carbon nanotube structure, the equation of motion of the molecular system is solved numerically, and the thermal conductivity simulation calculation of the molecular system and properties of the carbon nanotube is studied [15]. Molecular dynamics has different mechanical models both macroscopically and microscopically and provides clear microscopic explanations for surface phenomena that are difficult to understand from theoretical and empirical observations [16]. This method mainly relies on Newtonian mechanics to simulate the motion of the molecular system to draw samples in the system composed of different states of the molecular system.Due to the development of modern software and the popularization of hardware technology, molecular dynamics modeling is widely used in the chemical industry and plays a crucial role in material and molecular modeling. When starting to calculate the dynamics of the system, it is first necessary to find the energy-reducing surface as a stable starting point. There are 3 general methods for reducing the potential energy of the system to find the global optimal structure: steep descent method, combined gradient method, and Newton–Raphson method. The steep descent method, while particularly safe, is not a particularly efficient method of calculation. By taking a step in the negative growth direction ofE, there is:(2)i2=i1−λ∇Ei1,Ei2≤Ei1.The potential function is a mathematical function whose value is a physical vector potential or a scalar potential, also known as a harmonic function, which is the research topic of the mathematical potential theory. The AIREBO potential function consists of three parts:(3)E=12∑x∑y≠xExyREBO+ExyLJ,ExyREBO=EWrxy+bxyEArxy.EW represents the repulsive part of the interaction, given by:(4)EWrxy=A1+Trxye−arxy.EA represents the attractive part of the interaction, given by:(5)EArxy=∑x=13Bk1+Trxye−brxy.The main elements in the molecular dynamics calculation process are time, velocity, acceleration, and force, which interact with each other. Although there is no informative description of temperature among these factors, the temperature can be measured by molecular average kinetic energy and applied energy [17]. The total kinetic energy Bk of the molecules in the system is calculated as:(6)Bk=12∑x=1NmxSx2,Bk=32,T=33NkB∑x=1NmxVx2.The heat flow vector can be defined as follows:(7)P=zzt∑xrxEx.For pairs of potentials, the expression can be changed to the following form:(8)W=∑xexvx+12∑xySxyvxrxy.Based on the observed normalized heat flow autocorrelation function, a double exponential curve can be applied:(9)G0•Gt3=A1exp−tε1+A2exp−t|ε2.The fitting formula of the double exponential decay curve is as follows:(10)Gν0•Gνt3=Ashexp−tεsh+A1gexp−t|ε1g.Carbon nanotubes are quasi-one-dimensional nanomaterials with excellent thermal conductivity. The thermal conductivity of carbon nanotubes strongly depends on the mean free path of phonons, and the thermal conductivity of carbon nanotubes is extremely sensitive to the arrangement of atomic defects. In fact, carbon nanotubes have many forms of defect types in the structure due to insufficient manufacturing levels. The essence of defects is the introduction of disorder into the complete lattice of carbon nanotubes, and the main defect types are shown in Figure1. Defects first break the original energy band symmetry of the system and destroy all aspects of the properties of carbon nanotubes. In some cases, a very small amount of defects may fundamentally change some aspects of its properties [18]. The number, arrangement, and interaction of defects can affect the thermal conductivity of carbon nanotubes. Studies have shown that the thermal conductivity of carbon nanotubes is generally contributed by two parts: the interaction between electrons and phonons and the interaction between phonons and phonons [19–21]. For carbon nanotubes, the interaction between phonons and phonons plays a major role in the entire heat conduction process; due to the large energy gap and low density of free carriers, the interaction between electrons and phonons makes little contribution to the thermal conduction process of carbon nanotubes [22].Figure 1
Schematic diagram of carbon nanotubes and their defects. (a) Intact carbon nanotubes. (b) diatomic defect. (c) shape defect. (d) cell vacancy defect.
(a)(b)(c)(d)The production skills of fiber art materials have grown with the development of the times, but in order to express the concepts and ideas of modern art, it still needs to be conveyed in the form of products [23, 24]. Only through works of art can the creative thoughts and emotions of the artist be conveyed, the breakthrough of materials and the evolution of the form of works are due to major changes in the design concept. Although the content and form of traditional fiber craft products are rich and diverse, they are inevitably limited in production. At this time, the material, color, form, and composition of the fiber product can have a style. Although centuries have passed and evolution has matured in all respects, design is very dependent on people’s culture and traditional concepts, or is completely dominated by so-called art, which is already a picture of pure art.Introducing defects on the sidewalls of carbon nanotubes can easily cause the bending of carbon nanotubes, and the longer the carbon nanotubes are, the more they tend to bend [25]. If defects are introduced into the tube wall, it is very difficult for long carbon nanotubes to maintain their quasi-one-dimensional structure. In order to eliminate the interference caused by large deformation and calculate the influence of the interaction of defect spacing on the thermal conductivity of carbon nanotubes, it is necessary to take necessary measures to avoid the interference of large deformation when establishing the model. After trial and error, it was found that the situation was largely improved when the optimization calculations were performed to minimize the carbon nanotubes by placing them in a lattice just covering their size. This is like placing it on a flat surface, which will generate a certain local depression and deformation around the defect, but will not cause a larger bending deformation [26].The thermal conductivity of carbon nanotubes depends on the atomic structure, diameter, type, defect, and degree of purification [27]. The structural types of carbon nanotubes were unified to study the effect of defect spacing of different defect types on the thermal conductivity of carbon nanotubes. The larger the number of defects in the carbon nanotube defect, the more complex the interaction between the defects, which is completely different from the case where the carbon nanotube contains only one defect. Carbon nanotubes are extremely sensitive to defects. The existence of defects greatly changes the properties of carbon nanotubes in various aspects. The type of defects, the number of defects, the distance between defects, and the symmetrical distribution of defects all affect the thermal conductivity of defects.So far, the research conclusions about the influence of carbon nanotubes and their defects on thermal conductivity are not completely consistent, and the exploration of the heat transport mechanism is far from enough. In this chapter, the equilibrium molecular dynamics method is used to calculate the thermal conductivity of different models, and the influence of the spacing of different defect types on the thermal conductivity is explored.


## 3.2. Calculation of Resistance Value

A heat flow sensor is a tool for measuring heat flow density or heat flux and is the most critical component of a heat flow meter. The performance and use of the heat flow sensor determine the performance and use of the heat flow meter. For carbon nanotube sensor, calculating its initial resistance value in three-dimensional braided composite material has important reference significance for the design and modeling of the structural health monitoring system. Designers can calculate the resistance value of a single carbon nanotube according to the length of the tube, and estimate the overall resistance of the prefabricated part, which can provide a basis for the design of signal acquisition, processing subsystems, and electronic components. The constraints of objective conditions bring certain difficulties to the calculation of the resistance value of carbon nanotubes:(11)SO=βOLORO.It can be seen from the formula that under the condition of stable temperature and magnetic field, the initial resistance value of carbon nanotubes is related to its initial resistivityβO, initial length LO, and initial cross-sectional areaRO. The change in the resistance of the carbon nanotubes can be calculated as:(12)ΔSS=Δββ+ΔTT−ΔBB.Since the load and relative resistivity increase are symmetrical, the carbon nanotube sensor still has good linearity within a certain load range. When studying the carbon nanotube sensor to monitor the curing behavior of composite materials, it was found that the resistance of the carbon nanopaper sensor gradually increased with the decrease of temperature in the cooling stage, and the corresponding changes of temperature and resistance in the cooling stage were extremely linear. To demonstrate the sensor stability, a graph of the temperature and resistance response data for the cooling phase at 70°C and 120°C was added, as shown in Figure2.Figure 2
Changes of temperature and resistance curves in cooling stages at (a) 70°C and (b) 120°C.The expression for the length change of carbon nanotubes is:(13)ΔTT=φ11−φ1122.According to the Poisson effect, the change of the cross section is transversely isotropic, then the second term is ignored and expressed as:(14)P′=P1−2V12φ11.In the formula, 1 represents the Poisson's ratio of the carbon nanotube, so(15)ΔPP=−2V12φ11.Then(16)ΔSS=Δββ+φ11+2v12φ11=Δββ+φ111+2v12.According to the algorithms for solving the length of carbon nanotubes, including the ideal mean estimation method, the pitch node connection method, the Bezier curve fitting method, the B-spline curve method, and the weaving angle algorithm, the length L of a single carbon nanotube can be calculated, and then use the resistivity formula to calculate the initial resistance valueR.For different curing regimes, the curing degree of the composite material is different, and the resins with different curing degrees also respond differently to temperature. For the experimental results, the temperature responses of the embedded carbon nanopaper sensors during the cooling phase of different curing cycles are not identical. The DSC method has been introduced to measure the curing degree. In the experiment, DSC was used to measure the curing degree of six groups of different curing systems. The curing degree and resistance temperature coefficient are sorted as shown in Table1:Table 1
Correlated changes in resistance for five curing regimes.
Temperature (°C)Degree of cure %12011150.981050.95850.81700.75The change of resistance is mainly caused by two reasons: the resistance change after the conductive structure is changed and the resistance change caused by the sensitive response of the sensor to temperature. The structure of the sensor’s solidification response to temperature is shown in Figure3.Figure 3
Sensor response to temperature system.Due to the negative temperature coefficient of the sensor itself, the resistance decreases as the temperature increases, and the response of the resistance to temperature changes is not particularly obvious. Compared with the resistance resulting from the temperature-sensitive behavior, the resistance changes in the two stages are of two orders of magnitude and have different growth trends. Therefore, the resistance change in the first stage of curing is mainly due to the resin flow changing the conductive structure. This also proves from another perspective that the contact resistance plays a major role. In the second stage of the curing experiment, the temperature in this stage remains unchanged, and the temperature-sensitive behavior does not produce resistance changes. The internal resin curing shrinkage and final stabilization is the main reason for the resistance change at this stage. Both the temperature and resistance during heating are shown in Figure4.Figure 4
Graph of temperature and resistance changes during heating.With the help of modern technology, real-time control of structures is possible based on information acquired by sensors. In the process of material production, use and maintenance, 3D woven composite materials are prone to internal damage such as degumming, air bubbles, and fiber breakage that are not visible on the surface due to external impact and strong collision, resulting in the reduction of the overall bearing strength and bearing capacity of the material, resulting in potential safety hazards. The main defect types of composite materials and their influence on material properties are shown in Table2. Therefore, it is of great practical significance to study the nondestructive testing (NDE, Nondestructive Evaluation) technology of 3D braided composites, especially the health monitoring of 3D braided composite parts based on carbon nanotube (CNT) wire.Table 2
Composite defect types and their impact on properties.
Defect typePerformance impact under defect correspondenceLayeredIt has a serious impact on the overall performance of the composite materialFractureThe strength in the direction of the broken fiber decreases by about 20%RippleThe bearing strength is lost by about 25%, and the lifespan is decreased by about 10%Pores are too largeThe strength loss is small, and the life is reduced by 50%Surface crackBearing strength decreased by 40%–50%The advancement of modern science and technology has provided modern fiber manufacturers with a wide variety of materials, and the creation of fiber art products is no longer limited by traditional fiber materials. Through modern craftsmanship, traditional fiber materials are changed to form new high-tech fiber materials, providing artists with more creative choices. Many new materials such as synthetic materials, metal fibers, and glass and ceramic fibers also provide artists with more modern Fiber Art Creation. Through special processing technology, these new materials will undergo different changes in texture, some become flexible, and some are rigid. At the same time, compared with traditional materials, the new materials have more morphological plasticity. Like perforated plastics and rubbers, they can exhibit very rich variations on demand, increasing the freedom of artistic conception. Fiber creation artists should be more advanced than traditional materials in the expression of creative concepts, which is the difference between modern new materials. Through fiber creation attempts to express and realize personal emotions. Both traditional fiber materials and modern new composite materials can express artistic information and ideas through artistic products, under the condition of desire and motivation expressed through works.


## 4. Modern Fiber Exploration of Carbon Nanotube Composites

### 4.1. Thermal Conductivity of Modern Fibers under Composites

The heat conduction of solid materials is mainly through electrons, phonons, and photons, and for polymer materials, phonons are mainly used for heat conduction. For most materials, there is a peak in thermal conductivity as the temperature changes. The thermal conductivity of composite materials is simulated by setting a uniform packing density system and melting point. The normalized heat flow autocorrelation function and its thermal conductivity results obtained from the simulation are shown in Figures5 and 6.Figure 5
Heat flow correlation function (a) and thermal conductivity (b) of composites at 280 K.
(a)(b)Figure 6
Heat flow correlation function (a) and thermal conductivity (b) of composites at 320 K.
(a)(b)According to Figures5 and 6, the law of the heat flow correlation function and the time change is judged by the change of the normalized heat flow autocorrelation function and the thermal conductivity of the composite material at temperatures of 280 K and 320 K. When the data changes level off and fluctuates around 0, then this is the performance of the function leveling off. If the change in the function value is not time-dependent, then the function value simply decays to 0. The heat flow autocorrelation functions and thermal conductivity images are similar for temperature settings of 280 K, 310 K, 340 K, and 370 K. All simulated thermal conductivity results are given in Table 3.Table 3
Thermal conductivity of carbon nanotubes at different temperatures.
Temperature (k)Thermal conductivity (w/mk)2800.593100.713401.123700.75The established model was simulated and calculated by the molecular dynamics equilibrium method, and the thermal conductivity of polyethylene at different temperatures was obtained. When the temperature is 310 K, the thermal conductivity of polyethylene is only 0.71, the thermal conductivity first increases and then decreases, and a central peak appears at the same time. The thermal conductivity reaches a maximum of 1.12, exceeding polyethylene generally considered to be less than 1. Table3 shows the change of thermal conductivity of polyethylene with temperature. When the temperature is less than 340 K, the thermal conductivity increases with the increase of temperature, but the increasing trend gradually weakens; when the temperature continues to increase above 340 K, the thermal conductivity of polyethylene decreases.Since phonon mobility increases with temperature, so does thermal conductivity, so thermal conductivity increases with temperature. At higher temperatures, the phonon vibrations are enhanced, the interaction or friction of the phonons is enhanced, and the resulting diffusion increases, thereby reducing the mean free path of the phonons and slowing down heat transfer. Therefore, at higher temperatures, the thermal conductivity decreases with increasing temperature. Enhanced phonon motion increases thermal conductivity with increasing temperature, but on the other hand, phonon scattering decreases thermal conductivity.


### 4.2. Mechanical and Thermodynamic Properties of Carbon Nanotube-Epoxy Composites

As the concept of various art categories became more and more blurred, modern fiber art entered a new era, driven by the development of artistic performance in the 20th century. Fiber art refers to practical or decorative, or three-dimensional or flat art, using different fibers as materials and using various traditional or modern creative tools and equipment. Although modern fiber art is an innovation on the basis of traditional fiber art, due to the different materials of fiber creation, the form of artistic realization will change, and the artistic ideas, information, and concepts conveyed will also change accordingly. Compared with the pure resin system, the addition of carboxylated multi-walled carbon nanotubes (MWCNTs-COOH) resulted in a certain improvement in the flexural strength and flexural modulus of the composites. This is mainly due to the addition of MWCNTs-COOH to increase the modulus of the epoxy-amine resin system, which is beneficial to improve the interfacial properties of the composites.From the experimental data in Figure7, it can be seen that after adding MWCNTs-NH2, the flexural strength and flexural modulus of T350 carbon fiber composites are increased by 50% and 57%, respectively, compared with the pure resin system, and they are increased by 23% in T550, it can be seen that the improvement of T350 is more obvious. Similarly, after adding MWCNTs-COOH, the flexural strength and flexural modulus of T350 increased by 28% and 14%, respectively, compared with the pure resin system, and T550 increased by 7.7%, respectively. The results show that the flexural strength and flexural modulus of the composite material are more significantly enhanced, and the flexural strength and flexural modulus of the carbon fiber of the pure resin system are lower than those of the composite material. Therefore, modern fibers using composite materials have better usability and ductility for artistic creation.Figure 7
Comparison of flexural strength and flexural modulus of composites with different contents of carbon fiber. (a) Bending strength. (b) Flexural modulas.
(a)(b)Figure8 shows the change in curing of the two composites at different temperature stages and the corresponding change in the physical state of the resin matrix during composite fabrication. The decrease in sensor resistance from the beginning changes from 20°C to 170°C is more obvious in the first stage. Compared with the MWCNTs-COOH, the resistance change of the MWCNTs-NH2 carbon nanotube sensor reflects different performances at each stage. This allows easier penetration of resin molecules into the conductive structure, resulting in expansion or even rupture of the contact between the conductive tube and the sheet structure. Therefore, when the temperature is from 20°C to 170°C, as the curing process progresses, the crosslink density increases and the system viscosity decreases.Figure 8
Curing process of composites over time.


## 4.1. Thermal Conductivity of Modern Fibers under Composites

The heat conduction of solid materials is mainly through electrons, phonons, and photons, and for polymer materials, phonons are mainly used for heat conduction. For most materials, there is a peak in thermal conductivity as the temperature changes. The thermal conductivity of composite materials is simulated by setting a uniform packing density system and melting point. The normalized heat flow autocorrelation function and its thermal conductivity results obtained from the simulation are shown in Figures5 and 6.Figure 5
Heat flow correlation function (a) and thermal conductivity (b) of composites at 280 K.
(a)(b)Figure 6
Heat flow correlation function (a) and thermal conductivity (b) of composites at 320 K.
(a)(b)According to Figures5 and 6, the law of the heat flow correlation function and the time change is judged by the change of the normalized heat flow autocorrelation function and the thermal conductivity of the composite material at temperatures of 280 K and 320 K. When the data changes level off and fluctuates around 0, then this is the performance of the function leveling off. If the change in the function value is not time-dependent, then the function value simply decays to 0. The heat flow autocorrelation functions and thermal conductivity images are similar for temperature settings of 280 K, 310 K, 340 K, and 370 K. All simulated thermal conductivity results are given in Table 3.Table 3
Thermal conductivity of carbon nanotubes at different temperatures.
Temperature (k)Thermal conductivity (w/mk)2800.593100.713401.123700.75The established model was simulated and calculated by the molecular dynamics equilibrium method, and the thermal conductivity of polyethylene at different temperatures was obtained. When the temperature is 310 K, the thermal conductivity of polyethylene is only 0.71, the thermal conductivity first increases and then decreases, and a central peak appears at the same time. The thermal conductivity reaches a maximum of 1.12, exceeding polyethylene generally considered to be less than 1. Table3 shows the change of thermal conductivity of polyethylene with temperature. When the temperature is less than 340 K, the thermal conductivity increases with the increase of temperature, but the increasing trend gradually weakens; when the temperature continues to increase above 340 K, the thermal conductivity of polyethylene decreases.Since phonon mobility increases with temperature, so does thermal conductivity, so thermal conductivity increases with temperature. At higher temperatures, the phonon vibrations are enhanced, the interaction or friction of the phonons is enhanced, and the resulting diffusion increases, thereby reducing the mean free path of the phonons and slowing down heat transfer. Therefore, at higher temperatures, the thermal conductivity decreases with increasing temperature. Enhanced phonon motion increases thermal conductivity with increasing temperature, but on the other hand, phonon scattering decreases thermal conductivity.


## 4.2. Mechanical and Thermodynamic Properties of Carbon Nanotube-Epoxy Composites

As the concept of various art categories became more and more blurred, modern fiber art entered a new era, driven by the development of artistic performance in the 20th century. Fiber art refers to practical or decorative, or three-dimensional or flat art, using different fibers as materials and using various traditional or modern creative tools and equipment. Although modern fiber art is an innovation on the basis of traditional fiber art, due to the different materials of fiber creation, the form of artistic realization will change, and the artistic ideas, information, and concepts conveyed will also change accordingly. Compared with the pure resin system, the addition of carboxylated multi-walled carbon nanotubes (MWCNTs-COOH) resulted in a certain improvement in the flexural strength and flexural modulus of the composites. This is mainly due to the addition of MWCNTs-COOH to increase the modulus of the epoxy-amine resin system, which is beneficial to improve the interfacial properties of the composites.From the experimental data in Figure7, it can be seen that after adding MWCNTs-NH2, the flexural strength and flexural modulus of T350 carbon fiber composites are increased by 50% and 57%, respectively, compared with the pure resin system, and they are increased by 23% in T550, it can be seen that the improvement of T350 is more obvious. Similarly, after adding MWCNTs-COOH, the flexural strength and flexural modulus of T350 increased by 28% and 14%, respectively, compared with the pure resin system, and T550 increased by 7.7%, respectively. The results show that the flexural strength and flexural modulus of the composite material are more significantly enhanced, and the flexural strength and flexural modulus of the carbon fiber of the pure resin system are lower than those of the composite material. Therefore, modern fibers using composite materials have better usability and ductility for artistic creation.Figure 7
Comparison of flexural strength and flexural modulus of composites with different contents of carbon fiber. (a) Bending strength. (b) Flexural modulas.
(a)(b)Figure8 shows the change in curing of the two composites at different temperature stages and the corresponding change in the physical state of the resin matrix during composite fabrication. The decrease in sensor resistance from the beginning changes from 20°C to 170°C is more obvious in the first stage. Compared with the MWCNTs-COOH, the resistance change of the MWCNTs-NH2 carbon nanotube sensor reflects different performances at each stage. This allows easier penetration of resin molecules into the conductive structure, resulting in expansion or even rupture of the contact between the conductive tube and the sheet structure. Therefore, when the temperature is from 20°C to 170°C, as the curing process progresses, the crosslink density increases and the system viscosity decreases.Figure 8
Curing process of composites over time.


## 5. Conclusion

The processed carbon nanotube composite material is more heat resistant than the pure carbon nanotube material, and the bending strength and bending modulus are also significantly improved, after adding MWCNTs-NH2 and MWCNTs-COOH, the T350 was increased by 28% and 14%, respectively, and the effect was obvious, which can also shine in the production process of modern fiber art. This modern fiber art composite material is more perfect in genre and specific performance. Composite materials are added to fiber art in a new form of expression, and there is a broad space for development and comprehensive utilization in artistic creation. More and more fiber artists are creating art through new composite materials. The materials of new composite materials can show different artistic effects and realize the freedom of the entire creative process. Art is moving forward, artists are using their passion and creativity to transform various objects and techniques into magic, and modern fiber art is entering the realm of pure art with the help of objects and techniques.



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*Source: 5880370-2022-08-28.xml*