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fiber SCs. (c–f) The voltage distribution and energy distribution of the two structures simulated by ANSYS Maxwell software.

      Source: Reproduced with permission [52]. © 2018, Wiley‐VCH.

      According to the following equation, the energy densities (E) and capacitance (C) can be calculated:

      (2.1)normal upper C equals StartFraction upper Q Over upper V EndFraction d upper E equals d upper Q asterisk upper V

upper Q 1 equals upper C 10 upper V 1 plus upper C 12 left-parenthesis upper V 1 minus upper V 2 right-parenthesis

      Then capacitance matrix is derived from Eq. (2.2) as:

      (2.3)StartBinomialOrMatrix upper Q 1 Choose upper Q Baseline 2 EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column upper C 10 plus upper C 12 2nd Column minus upper C 12 2nd Row 1st Column upper C 20 plus upper C 21 2nd Column minus upper C 21 EndMatrix StartBinomialOrMatrix upper V 1 Choose upper V 2 EndBinomialOrMatrix

      Where Q represents the quantity of electric charge, V stands for voltage.

      A capacitance ratio of 5.14 : 1 was obtained between the two structures, confirming and explaining the better electrochemical performances of the coaxial SCs coming from the shorter distance between positive and negative electrode, more uniform potential distribution and better conductivity. But the fabrication process of the coaxial SCs is much more complicated in comparison with twisted devices. These simulation results provide a theoretical support to the design of the fiber SCs from the views of the device configuration, which can be applied and extended to other filed that refers to the devices structures.

      2.2.1.1 Fabrication of Stretchable Parallel SCs

Schematic illustration of typical fabrication methods of 1D parallel fiber SCs: (a) Schematic illustration of the fabrication process of the fiber SCs by embedding in pre-strained stretchable substrate, (b) CV curves of the stretchable devices under stretching and folding.

      Source: Reproduced with permission [56]. © 2017, Wiley‐VCH.

      (c) Schematic illustration of the fabrication process of the fiber SCs by twisting sandwich fiber with double side electrode, (d) CV curves measured during successive stretch, twist, release and untwist process.

      Source: Reproduced with permission [57]. © 2016, American Chemical Society.

      Different from the first embedded method, the second parallel SCs always employ the elastic materials as the stretchable substrate. In 2016, Choi et al. introduced stretchable SCs with sandwich fiber, the schematic illustration of the fabrication process was presented in Figure 2.3c [57]. The assembled method can be summarized as four steps: (i) Preparation of fiber shaped substrate. The dielectric silicone rubber (Ecoflex 0030) was processed as a sheet with a length of 30 mm by the conventional reaction of commercially available resins in a rectangular and then cut into ∼2 mm thick. (ii) Pre‐stretching the fiber shaped silicone rubber. The as‐prepared core fiber was stretched along the axial direction by 300% of its length. (iii) Covering electrode material on the surface of the core fiber. CNT aerogel sheets that extract from a multiwalled carbon nanotube (MWNT) forest served as electrode materials, which is attached on both sides of the silicone rubber fiber. The direction normal to the CNT electrode was coved with a PU film to prevent electrical shortage by residual CNT bundles during CNT wrapping. The strong adhesion between the CNT electrode and the silicone rubber fiber was guaranteed by continual dropping ethanol during CNT wrapping, which also protects the CNT surface from delamination. Then, the PU mask was mechanically removed from the silicone rubber fiber with CNT coat. 4: Release the fiber. The CNT electrode materials after release archived a uniform waved electrode. The electrical resistance of the CNT electrode materials is about 179 Ω cm−1 at the CNT loading of 2.31 mg cm−2 for each side, which is benefit to the electrochemical performances of the stretchable fiber SCs. Figure 2.3d showed the CV curves of the fiber SCs measured during successive stretch, twist, release and untwist process. Importantly, when applied a successive stretch, twist, release and untwist deformation during charge and discharge, the electrochemical performance of the fiber devices didn't change. The stretch test also showed an imperceptible nuance under various strains ranging from 0% to 200%.

      2.2.1.2 Fabrication of Stretchable Twisted SCs

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