Ion Conduction In Crystalline Polymer Electrolytes For Lithium Ion Batteries
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Ion Conduction In Crystalline Polymer Electrolytes For Lithium Ion Batteries
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Author : Shankar Ram Chithur Viswanathan
language : en
Publisher:
Release Date : 2021
Ion Conduction In Crystalline Polymer Electrolytes For Lithium Ion Batteries written by Shankar Ram Chithur Viswanathan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Polyethylene oxide (PEO) based Solid Polymer Electrolytes (SPEs) are safe and efficient alternatives to liquid/gel-based electrolytes. In addition to improving safety and design flexibility, SPEs could allow the use of lithium metal anode which can theoretically improve energy density 10-folds than commercially used lithium graphite anode. However, SPEs suffer from low Li+ ion conductivity. In most SPEs, the conductivity is linked to PEO segmental motion. Attempts to increase polymer dynamics reduce the mechanical strength of SPEs. Thus, it is necessary to decouple conductivity from the mechanical strength of the polymer. Conduction through the crystalline domain was never considered possible until the discovery of a PEO/salt co-crystal [PEO6], which was found to be more conductive than its amorphous counterpart. In PEO6 [the crystal structure co-crystallizes 6 PEO ether oxygens to one Li-anion pair], two PEO chains fold around Li+ in a non-helical fashion forming an approximate cylindrical "tunnel" with lithium atoms distributed along the cylinder central axis. Each lithium atom coordinates five ether oxygens; the anions are outside the tunnel and there is no direct bonding between the anions and the Li+. Due to its unique tunnel-like structure, PEO6 conducts Li+ based on a mechanism that decouples the conductivity and segmental motion of the polymer. However, these polymer electrolytes have not been used for battery applications because these studies used low molecular weight PEO (1000 g/mol) to achieve high crystallinity of the PEO6 phase. At this low molecular weight, the polymer does not confer the high modulus required. In SPEs with high molecular weight PEO, conduction through PEO6 is unfavorable as the tunnels fold to form lamellar structures and increase the conduction pathway. In this study, we explore conduction in high molecular weight [600000 g/mol] crystalline polymer electrolytes at EO: Li = 6:1. At this molecular weight, although four lithium salts [LiPF6, LiAsF6, LiSbF6, and LiClO4] can form PEO6, we focus our study on PEO6-LiClO4, which displays the highest conductivity than with other salt complexes. But this conductivity of PEO6LiClO4 drops by an order of magnitude after 2 months of thermal annealing. This is also accompanied by the changes in the XRD pattern which is uncharacteristic of any phases of PEO-LiClO4. Thus to explain this change, we explore the possibility of defects like vacancy, extra salt, and interstitial lithium in PEO6. In addition to being enthalpically stable, these defects also display the peculiar peaks of long-time annealed samples. While the change in the XRD pattern of a long-time annealed PEO6 can be explained by a combination of defects, based on their relative stability, it is more likely to be due to the "trapped" PEO6 structure. In this structure, in contrast to PEO6 where lithium atoms are at the center of the tunnel, one of the Li+ is "trapped" in the periphery of the tunnel coordinating with four ether oxygens and one anion, distorting the PEO6 tunnel. Because this crystal transformation is detrimental to conduction in PEO6, we use a percolated network of high aspect ratio fillers (cellulose nanowhiskers) to stabilize PEO6 tunnels over long distances. The patterned arrangement of the --OH surface group, which has a Lewis acidic character allows it to interact with either the anions or ether oxygen on the PEO chain. In addition, the distance between primary alcohol groups on the cellulose surface along the axial direction closely matches with the lattice parameter of PEO6 along the tunnel direction. This results in a low energy penalty [0.08 eV] for constraining PEO6 on the surface of the whisker, making it a suitable nucleation agent for PEO6LiClO4. Although these patterned cellulose nanowhiskers do stabilize PEO6 tunnels resulting in no change in XRD pattern even after a year of annealing, the room temperature conductivity (6 x10-6 S/cm) is still below the target value (10-3 S/cm). To improve the conductivity further, we draw inspiration from crystalline ceramic conductors, which have utilized doping [adding or substituting a small percentage of impurities to the host material] strategies to increase conductivity. By replacing 0.5-10% LiClO4 with NaClO4 in PEO6LiClO4, we demonstrate an order of magnitude increase in room temperature conductivity with the highest effect at 1% doping. This increase is not correlated with the glass transition temperature. Up to 1%, doping disrupts PEO6 crystallization. Above 1 %, diffraction peaks arise between 10-15o which cannot be due to PEO6 but resemble another polymer salt co-crystal, PEO3. A stable structure for PEO6 with NaClO4 is determined computationally, whereas only structures for PEO3 and PEO8 have been observed experimentally. Due to doping, larger sodium cations could either be accommodated into PEO6 or could end up not being part of the PEO6 lattice, resulting in a vacancy in PEO6. From DFT calculations, we determine that it is 0.92 eV more energetically favorable to swap sodium with lithium in PEO6 than to form PEO6 with vacancy. We conclude the increase in conductivity to be a consequence of weaker coordination of sodium to ether oxygen which increases the "bottleneck" size for conduction. In the sodium doping study, the presence of PEO3 peaks in XRD was correlated with increase an increase in conductivity. This is contrary to the popular belief that PEO3 is non-conductive. In contrast to PEO6, in PEO3, only one chain wraps around the Li+ in a helical fashion resulting in three-fold coordination of ether oxygen and two-fold coordination of anions. Due to tighter coordination of the lithium atoms with the neighboring anions, and lack of uncoordinated neighboring sites in PEO3, the activation energy for lithium hop as reported in PEO3LiCF3SO3 was found to be high [~1 eV]1-2, resulting in low ionic conductivity. If this gridlock is reduced by creating more vacancies, lithium atoms in PEO3 could become more mobile. To test this hypothesis, we create vacancies in PEO3 by reducing the concentration of LiClO4 from EO: Li = 3:1. We observe several orders of improvement in conductivity with a 20% reduction in salt concentration from EO: Li = 3:1, with no change in crystal structure or crystallinity up to 30% concentration deviation. Surprisingly, this change in conduction is accompanied by an increase in activation energy, indicating a change in the mechanism of conduction. To explain this change, we use DFT to find the activation energy for several conduction pathways in PEO3 including lithium diffusion: along the strand, across the strand, into a vacancy, and anion diffusion. In contrast to the previously held view that PEO3 has activation energy [~1eV], we conclude that the activation energy of PEO3LiClO4 can vary from 0.42- 1.3 eV depending on the conduction pathway. Thus, using both experiments and simulations we demonstrate the potential of crystalline polymer electrolytes and develop tools to understand the conduction mechanism in them. Although we did not reach the target conductivity, the findings from this work are important to design fast conduction solid polymer electrolytes.
Metal Organic Framework Mof Assisted Ion Conduction In Solid Polymer Electrolytes For Application In Lithium Ion Batteries
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Author : Nagma Zerin
language : en
Publisher:
Release Date : 2021
Metal Organic Framework Mof Assisted Ion Conduction In Solid Polymer Electrolytes For Application In Lithium Ion Batteries written by Nagma Zerin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Solid polymer electrolytes (SPEs) are safer and cleaner alternatives to the flammable organic liquid electrolytes used in rechargeable lithium-ion batteries. Due to having the potential to tune stiffness, SPEs can prevent dendrite formation while being used with the lithium-metal anode of high energy density. The most common SPE is polyethylene oxide (PEO) dissolving a lithium salt (e.g., LiClO4). PEO is popular due to its ability to dissolve lithium salts easily and commercial availability at a reasonable cost. However, these electrolytes have very low ionic conductivity at room temperature (less than 10^-5 S/cm), which does not meet the performance demands for practical battery applications. It is commonly believed that lithium-ion conduction in PEO-based electrolytes only depends on polymer segmental motion in amorphous regions. Thus, to increase polymer mobility associated conductivity, a considerable amount of research is focused on lowering the glass transition temperature (Tg) of SPEs. However, this approach compromises the SPE stiffness, which makes it incompatible with the lithium-metal anode. Crystalline solid polymer electrolytes, commonly known as polymer-salt co-crystals, are promising alternatives to dissociate conductivity from polymer mobility and increase stiffness. Unfortunately, these crystals are poor ion conductors on their own. There are not many studies that attempt to increase conduction through polymer-salt co-crystals. This research aims to improve conduction through these crystals and understand their mechanism through structural analysis. To achieve our goal, we incorporate Metal-Organic framework (MOF), with a high aspect ratio, as the nanofiller. We choose MOF due to its flexibility to tune surface chemistry and dimension as well as filler shape. We analyze the effect of two shapes of MOF, one nanosheet (Cu MOF/C2n2d) and the other nanowhisker (Ni MOF/Nnd), on 5 different SPE compositions: EO:Li=14:1, 10:1, 8:1, 6:1, and 3:1 [EO= Ether oxygen, Li= Lithium]. These compositions form 3 types of crystals depending on the lithium-ion content: PEO, PEO6, and PEO3. While PEO6 and PEO3 are conductive polymer-salt co-crystals, PEO is an insulator. In PEO6, two PEO chains wrap around each other to form a cylindrical tunnel-like structure. The lithium ions conduct through the tunnels, while the anions stay outside. In PEO3, the lithium ions and anions form an ion chain, which wraps around PEO. The lithium ions slide along PEO while interacting with the anions. We have achieved significant improvement in crystalline conduction with only 2 wt% Cu MOF loading. We obtain our best conductivity at EO:Li=8:1, where 2 wt% Cu MOF produces greater than 10^-5 S/cm conductivity at room temperature. At EO:Li=6:1, the % conductivity increase is between 200-900% in the entire temperature range with 2 wt% Cu MOF, which is a significant achievement for an electrolyte containing high molecular weight PEO6. We have discovered that the shape of the MOF filler and thermal annealing time play very important roles in crystalline conductivity. 2D Cu MOF has higher conductivity than 1D Ni MOF for all the compositions, and 10 days of thermal annealing produces more effective conductive crystals than those produced after a longer annealing time. Conductivity drops significantly after one month as a result of excessive bulk crystallization. For practical battery applications, it would be imperative to control the extent of the crystallinity of the crystalline polymer electrolytes. We recommend crosslinking the composites during initial thermal annealing to hold the effective crystal structures in place. Although we are still quite far away from reaching the target room-temperature conductivity (10^-3 S/cm) for commercial battery applications, this study is the first demonstration of MOF-assisted crystalline conduction. In the field of MOF nanofillers, this opens up the opportunity to explore a novel mechanism for improving conductivity, where ion conduction is decoupled from polymer segmental motion. The combined use of crystalline polymer electrolyte and MOF has the potential to limit anion movement and dendrite formation, which paves the way to design a safe and efficient battery.
Ion Transport In Semicrystalline Solid Polymer Electrolytes
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Author : Shan Cheng
language : en
Publisher:
Release Date : 2014
Ion Transport In Semicrystalline Solid Polymer Electrolytes written by Shan Cheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Crystallization categories.
Solid polymer electrolytes (SPEs) with both high room temperature ionic conductivity and mechanical integrity are highly desirable for all-solid-state lithium batteries. Linear polyethylene oxide (PEO) represents the simplest yet most attractive solvating polymer due to its capability to form complex with a selected number of alkali metal salt, especially lithium salt. The ether oxygen on PEO backbone coordinates with Li+ and the transport of the latter is facilitated through segmental motion of the polymer chain. However, the highly crystalline nature due to stereoregularity and flexibility of the polymer chain complicate the ion transport mechanism. PEO crystallization has been long considered to be detrimental to ion transport as it results in a decrease of the effective fraction of amorphous conducting phase, slower polymer chain dynamics and more tortuous pathways for ion transport. However, a quantitative analysis of crystallization effect on the ionic conductivity is challenging since these factors are always coupled. In this dissertation, we demonstrated that the two factors, namely tethered chain/dynamic and tortuosity/structural effects can be decoupled by preparing polymer membranes with controlled crystal orientation and measuring the in-plane and through-plane conductivity of the orientated membrane. Moderate conductivity anisotropy as a result of PEO lamellar orientation was first observed in a solution cast PEO SPE. We further used graphene oxide to enhance the crystal orientation, hence the conductivity anisotropy. To quantitatively characterize the crystallization effect, a model electrolyte system consists of PEO single crystals with well controlled crystal structure, size, crystallinity and orientation were fabricated. Ion conduction was confined within the chain fold region, and guided by the crystalline lamellae. We demonstrated that at low ion content, the in-plane conductivity was 1000-2000 times greater than through-plane one due to the tortuosity effect, which was described using Nielsen's permeability model. Contradictory to the general view, the dynamic effect was negligible at moderate ion contents and the overall conductivity was mainly controlled by crystal orientation, strong Li-PEO interaction and Li+ aggregation. Our results demonstrated that semicrystalline polymer can be viewed as a two phase model which morphologically mimicking the popular systems such as block copolymers and polyolefin porous membranes. By controlling crystallization behavior, mechanically robust semi-crystalline SPE with high room temperature conductivity is feasible.
De Brettes Seigneurs Du Cros De Cieux De Masrocher Etc Marquis De Brettes Du Cros En Limosin
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Author :
language : en
Publisher:
Release Date :
De Brettes Seigneurs Du Cros De Cieux De Masrocher Etc Marquis De Brettes Du Cros En Limosin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Solid State Ionics Materials Devices Procs Of The 7th Asian Conf
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Author : B V R Chowdari
language : en
Publisher: World Scientific
Release Date : 2000-10-27
Solid State Ionics Materials Devices Procs Of The 7th Asian Conf written by B V R Chowdari and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-27 with Science categories.
Solid state ionics, being a multidisciplinary area, is expected to grow at a faster rate in the new millennium, prompting the discovery of new materials and devices, as well as helping to optimize the known devices, especially the portable power sources and display systems. The Asian Society for Solid State Ionics (ASSSI) plays a significant role in bringing together researchers from the Asian countries, every two years, to exchange notes and ideas, to foster friendship and collaboration, and to discuss the prospects.The topics covered in this volume are: ion dynamics, theoretical modeling, ion-conducting polymers, gels and ceramics, glasses, crystalline materials including nano-phases, composites, electrode/electrolyte interfaces and novel experimental techniques. Papers on crystalline materials deal with ion conduction in Li, Na, Ag, Tl, F and O-containing compounds. Materials and device aspects have received wide coverage, especially the areas of lithium ion batteries (LIBs) and solid oxide fuel cells (SOFCs).Rechargeable high energy density LIBs, especially those employing immobilized gel or polymer electrolyte, are the favorite portable power sources in the new millennium. As expected, a large number of papers on both cathodes and polymer electrolytes for LIBs were presented at the conference. The papers on fuel cells almost exclusively deal with SOFCs, indicating the great importance being given to this area in Japan and China. A breakthrough in materials and technology of SOFC is expected in the coming decade. This volume will be useful not only to the active researchers in the field but also to youngsters entering the exciting area of solid state ionics.
Ion Conduction Mechanisms In Polymer Electrolytes For Lithium Batteries And Fuel Cells And Crystal Engineering Of Cyclophosphazenes
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Author : David Kim Yong Lee
language : en
Publisher:
Release Date : 2010
Ion Conduction Mechanisms In Polymer Electrolytes For Lithium Batteries And Fuel Cells And Crystal Engineering Of Cyclophosphazenes written by David Kim Yong Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Fast Ion Transport In Solids
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Author : B. Scrosati
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fast Ion Transport In Solids written by B. Scrosati and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The main motivation for the organization of the Advanced Research Workshop in Belgirate was the promotion of discussions on the most recent issues and the future perspectives in the field of Solid State lonics. The location was chosen on purpose since Belgirate was the place were twenty years ago, also then under the sponsorship of NATO, the very first international meeting on this important and interdisciplinary field took place. That meeting was named "Fast Ion Transport in Solids" and gathered virtually everybody at that time having been active in any aspect of motion of ions in solids. The original Belgirate Meeting made for the first time visible the technological potential related to the phenomenon of the fast ionic transport in solids and, accordingly, the field was given the name "Solid State lonics". This field is now expanded to cover a wide range of technologies which includes chemical sensors for environmental and process control, electrochromic windows, mirrors and displays, fuel cells, high performance rechargeable batteries for stationary applications and electrotraction, chemotronics, semiconductor ionics, water electrolysis cells for hydrogen economy and other applications. The main idea for holding an anniversary meeting was that of discussing the most recent issues and the future perspectives of Solid State lonics just twenty years after it has started at the same location on the lake Maggiore in North Italy.
Solid State Ionics
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Author : B. V. R. Chowdari
language : en
Publisher: World Scientific
Release Date : 2000
Solid State Ionics written by B. V. R. Chowdari and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Technology & Engineering categories.
Solid atate ionics, being a multidisciplinary area, is expected to grow at a faster rate in the new millennium, prompting the discovery of new materials and devices, as well as helping to optimize the known devices, especially the portable power sources and display systems. The Asian Society for Solid State Ionics (ASSSI) plays a significant role in bringing together researchers from the Asian countries, every two years, to exchange notes and ideas, to foster friendship and collaboration, and to discuss the prospects. The topics covered in this volume are: ion dynamics, theoretical modeling, ion-conducting polymers, gels and ceramics, glasses, crystalline materials including nano-phases, composites, electrode/electrolyte interfaces and novel experimental techniques. Papers on crystalline materials deal with ion conduction in Li, Na, Ag, Tl, F and O-containing compounds. Materials and device aspects have received wide coverage, especially the areas of lithium ion batteries (LIBs) and solid oxidefuel cells,(SOFCs). Rechargeable high energy density LIBs, especially those employing immobilized gel or polymer electrolyte, are the favorite portable power sources in the new millennium. As expected, a large number of papers on both cathodes and polymer electrolytes for LIBs were presented at the conference. The papers on fuel cells almost exclusively deal with SOFCs, indicating the great importance being given to this area in Japan and China. A breakthrough in materials and technology of SOFC is expected in the coming decade. This volume will be useful not only to the active researchers in the field but also to youngsters entering the exciting area of solid state ionics.
Polymer Single Crystals
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Author : Phillip Herbert Geil
language : en
Publisher:
Release Date : 1963
Polymer Single Crystals written by Phillip Herbert Geil and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Crystalline polymers categories.
A Novel Ion Conductive Gel Polymer Electrolyte For Sodium Air Battery Application
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Author : Yuan Xue
language : en
Publisher:
Release Date : 2017
A Novel Ion Conductive Gel Polymer Electrolyte For Sodium Air Battery Application written by Yuan Xue and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
"The innovation of batteries is urgently required due to the world-wide energy crisis and extensive adoption of renewable energy sources. Secondary batteries attract increased and significant research interests as alternative energy storage devices, for instance, lithium-ion battery. In decades, a lot of efforts have been devoted to lithium-ion battery in terms of fabrication, operation and optimization. Lithium-ion battery exhibits high energy density ascribing to its high energy capacity and light molar mass. The usage of lithium-ion battery technology is still limited, however, by the high capital cost of lithium metal and lack of lithium deposition methodology. Sodium-based batteries are developed as an appealing candidate for replacing lithium-based batteries since sodium is a more economic choice and sodium-based batteries are more suitable for large scale application. A special attention will be paid to sodium-air battery, which is environmentally friendly, low cost with high energy density, in the new energy storage system development. To enable sodium-based battery, the sodium ion conducting electrolyte is the key determinant that governs the batteries' usable power, operating potential, durability, safety, cost, etc. Most electrolytes which are widely used nowadays adopt liquid or solid states formulations to boost the ion conduction; however, corrosion, reduction in lifetime and low ionic conductivity have been observed. Consequently, developing a new sodium conducting electrolyte remains a key challenge in the application of sodium-based batteries. The goal of the thesis is to develop a robust and high efficient sodium ion conducting electrolyte which will be able for sodium-based batteries application. The thesis, firstly, deals with the research for the gel polymer electrolyte (GPE), consisting of polymer blend matrix (poly(methyl methacrylate)/polycarbonate), organic liquids (ethylene carbonate (EC) and propylene carbonate (PC)) and sodium tetrafluoroborate (NaBF4). This new, high sodium ion conductive GPE was fabricated through solution casting technique. The addition of NaBF4 decreased the crystallinity of the polymer blend matrix, while providing more charge carriers to enhance the ionic conductivity. The peak ionic conductivity of 5.67×10-4 S cm-1 was obtained for the GPE with 25 wt.% NaBF4, which increases two orders of magnitude when compared to the GPE without NaBF4, which has a value of 1.03×10-6 S/cm. The temperature dependence of ionic conductivity behavior agrees with the Arrhenius equation when temperature elevated from 20 oC to 90 oC. The activation energies for GPEs with concentrations of 5 wt.%, 15 wt.% and 25 wt% NaBF4 are found to be 0.13, 0.17 and 0.28 eV respectively. GPEs were confirmed to be electrochemically stable in a potential range of -5 V to 5 V by the cyclic voltammetry test. The transference numbers of GPEs varied from 0.83 to 0.93 illustrated that GPEs are ionic conductive electrolytes. Emerging from the solution-casted GPE, the thesis employs free radical polymerization for PMMA-based cross-linked GPE as sodium-ion transport enhancement. The cross-linked GPE exhibits higher ionic conductivity than that of GPE with polymer blend matrix, good mechanical property and low cost. In the cross-linked GPE system, NaBF4 was substituted by sodium hexafluorophosphate (NaPF6). NaPF6 will dissolve in organic solvents more easily than NaBF4 due to its lower dissociation energy than that of NaBF4. The highest ionic conductivity obtained was 1.33×10-3 S cm-1 for the cross-linked GPE with 20 wt.% NaPF6, which is much higher than the highest ionic conductivity of GPE with PMMA/polycarbonate matrix. The Shore A durometer test revealed that the NaPF6 additions enhanced the hardness of cross-linked GPEs. Activation energies calculated based on Arrhenius equation for cross-linked GPEs with 10 wt.%, 20 wt.% and 30 wt.% NaPF6 were 0.13, 0.10 and 0.16 eV, respectively. The electrochemical window for cross-linked was valid from -2.5 V to 2.5 V and the transference numbers was ranging from 0.9 to 0.96. This work demonstrates that the adoption of cross-linking technique and NaPF6 opens the door to facile synthesis of sodium ion conductive GPEs The successful synthesis of the cross-linked GPE motivates us to explore the possibility to develop fabric-reinforced cross-linked GPE (FRCL GPE) constructed by a cross-linked polymer host with an embedded thin layer of fabric substrate, organic liquids PC/EC and NaPF6. The novel FRCL GPEs with reduced weight have been successfully fabricated and characterized. The SEM images confirmed that the fabric was embedded inside the cross-linked GPE. The highest ionic conductivity of FRCL GPE is 3.01×10-4 S cm-1 for the FRCL GPE with 20 wt.% NaPF6, which is comparable with other composite GPEs in which the highest ionic conductivity is 0.3 mS cm-1. The values of activation energies are 0.12 eV, 0.11 eV and 0.15 eV for FRCL GPEs with 15 wt.%, 20 wt.% and 25 wt.% NaPF6, respectively. This result agrees with ionic conductivity tendency that the lower activation energy offers FRCL GPE higher ionic conductivity. The electrochemical window was defined from -3 V to 3 V from cyclic voltammetry measurement, which is a wide range to cover the reactions for sodium-based batteries. The transference numbers observed for FRCL GPEs with various NaPF6 are in the range of 0.927~0.966. The values indicate the conductivity of FRCL GPEs is predominately contributed by ions motion, the electron transfer can be neglected. The final test of mechanical properties strongly confirmed the importance of fabric reinforcement for cross-linked GPEs. The strength of FRCL GPE is ten times of that of cross-linked GPE without reinforcement. The results make the FRCL GPE a promising electrolyte with good mechanical stability to be used for battery applications. Future efforts will be expected to improve the specific energy density of the energy storage devices, further elevate the ionic conductivity and mechanical property."--Pages ix-xii.