# Mechanical and Dielectric Properties of Aligned Electrospun Fibers
## 3 Mechanical and Dielectric Properties of Nanofibers
### Mechanical Properties
#### 3.1.1 PAN Nanofibers and Carbon Fillers  
[PERSON] (1998) reported that PAN-based carbon fibers have higher tensile strengths and reasonable tensile moduli compared to pitch-based carbon (micro-size) fibers [135]. PAN precursor is used for carbon nanofiber (CNF) production in nanocomposite structures [136] and in energy storage devices [137] due to their good electrospinning property, high carbonization yield, excellent nanostructure, ultrahigh specific surface area, good electrical conductivity, and stability. PAN is soluble in polar solvents like dimethylformamide (DMF), dimethylsulfone (DMSO), dimethylsulfoxide (DMSO), and dimethylacetamide (DMAc) [13]. Among organic solvents, DMF and DMSO are known to be good solvents of PAN and for production of high-performance PAN fibers, DMSO is preferred [138]. [PERSON] et al. (2017) observed that carbon nanofibers obtained from hot-drawn samples demonstrated strength as high as 5.4 GPa and modulus 287 GPa as shown in Figure 7a,b. Here, 400 nm PAN nanofibers reached a maximum strength (5.4 GPa) after hot-drawn and carbonized at 1100 \({}^{\circ}\)C [139]. As shown in Figure 8a, the thinnest fiber had the highest strength when compared to other thicker fibers. Moreover, it is evident from Figure 8b that the thinnest fiber had the highest modulus. [PERSON] et al. (2013) [140] studied simultaneous improvement in strength, modulus, and toughness in ultrafine as-spun PAN electrospun nanofibers as shown in Figure 8a,b. A reduction of as-spun PAN nanofiber diameter from 2.8 um to 100 nm resulted in higher modulus, strength, and toughness. The 100 nm annealed PAN fibers showed a modulus of 48 GPa and strength of 1.75 GPa. This study recorded dramatic increase in strength and modulus for nanofibers finer than 200-250 nm. Figure 7: (**a**) Typical stress–strain curve and (**b**) the average fiber diameter of carbon nanofibers (CNFs) [139]. [PERSON] et al. (2013) [104] compared the result with [PERSON] et al. (2011) [105] and showed the dependence of fiber diameter on strength and modulus as shown in Figure 9. As the fiber diameter decreases, the tensile strength and modulus increase. [PERSON] et al. (2013) observed that individual PAN nanofibers with 108 nm in diameter, heat treated at 800 \({}^{\circ}\)C, showed a maximum modulus of 262 GPa and strength of 7.3 GPa. [PERSON] et al. (2011) [105] showed that individual PAN nanofibers with 9 wt.% and other given parameters had the stress-strain relationship shown in Figure 10. The plot shows a linear relationship until 125 MPa and thereafter a strain hardening region where crystallinity occurs. The maximum ultimate strength was found with 1 kV/cm and 430 nm in diameter. [PERSON] et al. demonstrated that increase in carbonization temperature in CNFs monotonically increases elastic modulus, while highest strength of CNFs was observed at a carbonization temperature of 1400 \({}^{\circ}\)C. This study revealed the fiber diameter and carbonization temperature had effect on strength and modulus of PAN nanofibers. Figure 8: (**a**) Stress–strain graph of as-spun polyacrylonitrile (PAN) nanofibers. (**b**) Strength and modulus of annealed nanofibers. (Reprinted with permission from Reference [140]. Copyright (2004) American Chemical Society). Figure 9: Strength and modulus of individual carbon nanofiber obtained from PAN nanofiber mat [104]. [PERSON] et al. (2015) [1] reported that tensile strength of carbon nanofiber mats can be approximately estimated as the sum of individual nanofibers as shown in Figure 11. The nanofiber mat reached their maximum strength where the curves dropped sharply, which means the majority of nanofibers break simultaneously. [PERSON] et al. (2015) showed that a quantitative relationship exists between the tensile strength of a nanofiber mat and that of individual nanofibers as in Figure 12. The tensile strength of nanofiber mat is described by Equation (3). Figure 11: Stress–strain curve of carbon nanofiber mats [1]. Figure 10: Stress–strain relationship of individual PAN nanofibers [105].