Humidity gating device and manufacturing method thereof

Through the braided structure of fiber solid electrolyte and fibrous positive and negative electrodes, the problem of traditional humidity gated devices being unable to self-energize and have poor flexibility is solved, and self-drive, flexible and concealed humidity monitoring is achieved, which is suitable for wearable devices.

CN119269589APending Publication Date: 2025-01-07SUZHOU INST FOR ADVANCED STUDY USTC +1
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Patent Information

Application Number
CN202411467494.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-21
Publication Date
2025-01-07

AI Technical Summary

Technical Problem

Traditional humidity gated devices are unable to self-energize and lack flexibility and concealment, limiting their use in wearable and concealed applications.

Method used

The fiber solid electrolyte is woven together with the fiber-like positive electrode and negative electrode. The ionic conductivity of the fiber-like positive electrode and negative electrode responds to the change in environmental humidity, causing the fiber-like positive electrode and negative electrode to undergo redox reaction, output electrical signals, realize self-drive function, and pass the braiding technology. Improve flexibility and concealment.

Benefits of technology

It realizes the self-drive function without external power supply, has good flexibility and concealment, is suitable for humidity monitoring of wearable devices, and has a simple structure, low cost and short response time.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention provides a humidity gating device and a manufacturing method thereof, and belongs to the technical field of sensing. The humidity gating device comprises a fiber solid electrolyte, wherein the ionic conductivity of the fiber solid electrolyte changes in response to the change of the humidity of an environment to be measured; the fibrous positive electrode and the fibrous negative electrode are respectively contacted with two ends of the fibrous solid electrolyte; wherein in response to the change of the ionic conductivity of the fibrous solid electrolyte, the rate of the redox reaction between the fibrous positive electrode and the fibrous negative electrode is changed, so that electric signals output by the fibrous positive electrode and the fibrous negative electrode are changed, and the electric signals are used for representing the humidity of the environment to be measured. The humidity gating device provided by the invention can realize a self-driving function, and use of large power supply equipment is avoided.
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Description

Technical Field

[0001] At least one embodiment of the present invention relates to a sensor, and more particularly to a humidity gating device and a method for manufacturing the same. Background Art

[0002] Humidity gating devices are a common type of sensor that can monitor environmental humidity and biological system activities and output signals that are easy to read. Humidity gating devices are widely used in various fields, including health care, human-computer interaction, and artificial intelligence technology. Currently, common humidity gating devices mainly include resistive, capacitive, micro-electromechanical systems, weight, quartz oscillator, light intensity, surface acoustic wave, etc. Although the above-mentioned humidity gating devices have excellent humidity response performance, the current mainstream humidity gating devices still have certain defects. For example, resistive and capacitive humidity gating devices cannot be self-driven and require external power supply equipment for power supply. Traditional micro-electromechanical systems and quartz oscillator humidity gating devices are large in size, poor in flexibility and concealment, which limits their application in wearable and other fields. Summary of the invention

[0003] In view of this, it is necessary to propose a new type of humidity gating device and its manufacturing method to address the technical problems that traditional humidity gating devices cannot be self-powered and do not have high flexibility and concealment.

[0004] According to an embodiment of one aspect of the present invention, a humidity gating device is provided, comprising: a fibrous solid electrolyte, the ionic conductivity of the fibrous solid electrolyte changes in response to changes in the humidity of an environment to be measured; and a fibrous positive electrode and a fibrous negative electrode, respectively contacting two ends of the fibrous solid electrolyte; wherein, in response to changes in the ionic conductivity of the fibrous solid electrolyte, the rates of redox reactions occurring in the fibrous positive electrode and the fibrous negative electrode change, causing electrical signals output by the fibrous positive electrode and the fibrous negative electrode to change, and the electrical signals are used to characterize the humidity of the environment to be measured.

[0005] According to an embodiment of another aspect of the present invention, a method for manufacturing a humidity gating device is provided, comprising: preparing a fibrous solid electrolyte; separately preparing a fibrous positive electrode and a fibrous negative electrode; and weaving the fibrous positive electrode, the fibrous negative electrode, and the fibrous solid electrolyte together; wherein the fibrous positive electrode and the fibrous negative electrode are in contact with two ends of the fibrous solid electrolyte, respectively.

[0006] According to the humidity gating device provided by the above embodiment of the present invention, when the ambient humidity acts on the humidity gating device, the ionic conductivity of the fiber solid electrolyte changes in response to the change of the ambient humidity. In response to the change of the ionic conductivity of the fiber solid electrolyte, the rate of the redox reaction occurring in the fiber positive electrode and the fiber negative electrode changes, so that the electrical signal output by the fiber positive electrode and the fiber negative electrode changes. The humidity gating device does not require an external power supply to provide additional energy for it, and can realize the self-driving function, avoiding the use of large power supply equipment.

[0007] According to the humidity gating device provided by the above embodiment of the present invention, the fibrous solid electrolyte, the fibrous positive electrode, and the fibrous negative electrode are all flexible and can be woven or combined with a fabric carrier, so that the humidity gating device has good flexibility and concealment. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present invention, but are not intended to limit the present invention.

[0009] Figure 1 A three-dimensional schematic diagram of a humidity gating device woven on a fabric carrier provided by an embodiment of the present invention;

[0010] Figure 2 A schematic flow chart of a method for manufacturing a humidity gating device provided in an embodiment of the present invention;

[0011] Figure 3 An optical photograph of a fiber solid electrolyte provided by an embodiment of the present invention;

[0012] Figure 4 A scanning electron microscope image of a fiber solid electrolyte provided by an embodiment of the present invention;

[0013] Figure 5 An optical photograph and an enlarged view thereof of a humidity gating device woven on a fabric carrier provided by an embodiment of the present invention;

[0014] Figure 6 A single response / recovery curve of the humidity gating device provided in an embodiment of the present invention to ambient humidity;

[0015] Figure 7 The response curve of the humidity gating device provided in the embodiment of the present invention to the ambient humidity within 200 hours;

[0016] Figure 8 The response / recovery curve of the humidity gating device provided by the embodiment of the present invention to the same humidity source at different distances; and

[0017] Fig. 9The response / recovery curve of the humidity gating device provided in the embodiment of the present invention to human breathing.

[0018] Description of reference numerals:

[0019] 1- fabric carrier;

[0020] 2-Fiber solid electrolyte;

[0021] 3-Fiber-shaped positive electrode;

[0022] 4-Fiber-shaped negative electrode. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. However, the present invention can be implemented in different forms and should not be construed as being limited to the embodiments set forth herein. On the contrary, providing these embodiments will make the invention thorough and complete and fully convey the scope of the present invention to those skilled in the art. In the accompanying drawings, for clarity, the sizes and relative sizes of layers and regions may be exaggerated, and the same reference numerals throughout represent the same elements.

[0024] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the existence of the features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0025] Figure 1 A schematic diagram of a humidity gating device woven on a fabric carrier provided in an embodiment of the present invention.

[0026] According to an exemplary embodiment of the present invention, the present invention provides a humidity gating device, referring to Figure 1 As shown, including:

[0027] A fibrous solid electrolyte 2, the ionic conductivity of the fibrous solid electrolyte 2 changes in response to changes in the humidity of the environment to be measured; and a fibrous positive electrode 3 and a fibrous negative electrode 4, wherein the fibrous positive electrode 3 and the fibrous negative electrode 4 are respectively in contact with the two ends of the fibrous solid electrolyte 2; wherein, in response to changes in the ionic conductivity of the fibrous solid electrolyte 2, the rates of the redox reactions occurring in the fibrous positive electrode 3 and the fibrous negative electrode 4 change, causing the electrical signals output by the fibrous positive electrode 3 and the fibrous negative electrode 4 to change, and the electrical signals are used to characterize the humidity of the environment to be measured.

[0028] According to an embodiment of the present invention, the humidity gating device is woven on a fabric carrier 1. The material of the fabric carrier 1 is not limited here, for example, it can be nylon fabric or fiber fabric; the type of the fabric carrier 1 is not limited here, for example, it can be any one of a mask, gloves and clothing.

[0029] According to an embodiment of the present invention, under the influence of the change of humidity in the external environment, the ionic conductivity of the fiber solid electrolyte 2 will change. The fiber solid electrolyte 2 is hydrophilic and sensitive to humidity. The fiber solid electrolyte 2 is, for example, a composite fiber material composed of one or at least two of two-dimensional nanomaterial fibers, hydrogel fibers, and cellulose fibers.

[0030] According to an embodiment of the present invention, the ions released by the fiber solid electrolyte 2 include any one of metal ions and hydrogen ions; the metal ions are any one of lithium ions, sodium ions, potassium ions, zinc ions and manganese ions.

[0031] According to an embodiment of the present invention, the size of the fiber solid electrolyte 2 is in the micron level, for example, the diameter of the fiber solid electrolyte 2 is 10-20 μm, for example, 10 μm, 12 μm, 15 μm, 20 μm, but not limited to the values ​​listed.

[0032] According to the embodiment of the present invention, in a dry environment, the voltage signal output by the humidity gating device is close to zero. When the external environment humidity acts on the humidity gating device, the electrical signal output by the humidity gating device will change because the ionic conductivity of the fiber solid electrolyte 2 changes in response to the change in the environmental humidity. Therefore, the change in the external environment humidity can be judged according to the change in the electrical signal of the humidity gating device.

[0033] According to an embodiment of the present invention, the fibrous positive electrode 3 and the fibrous negative electrode 4 are asymmetric electrodes capable of constructing a redox potential difference, and the fibrous positive electrode 3 and the fibrous negative electrode 4 are any one of copper wire, zinc wire, silver wire, MXene fiber, graphene fiber, and black phosphorus fiber.

[0034] According to an embodiment of the present invention, the humidity gating device is woven on a fabric carrier 1 , and the fibrous positive electrode 3 and the fibrous negative electrode 4 are arranged in parallel at both ends of the fibrous solid electrolyte 2 and are in contact with both ends of the fibrous solid electrolyte 2 .

[0035] According to an embodiment of the present invention, the humidity gating device is woven on a fabric carrier 1 , and the fibrous positive electrode 3 and the fibrous negative electrode 4 are cross-arranged at both ends of the fibrous solid electrolyte 2 and are in contact with both ends of the fibrous solid electrolyte 2 .

[0036] According to an embodiment of the present invention, the humidity gating device is woven on a fabric carrier 1 , and the fibrous positive electrode 3 , the fibrous negative electrode 4 and the fibrous solid electrolyte 2 are arranged on the fabric carrier 1 in a pattern.

[0037] According to an embodiment of the present invention, the humidity gating device is not woven on a fabric carrier, and the fibrous positive electrode 3, the fibrous negative electrode 4 and the fibrous solid electrolyte 2 are woven into one.

[0038] According to an embodiment of the present invention, both the fibrous positive electrode 3 and the fibrous negative electrode 4 have lead-out electrodes, and the electrical signals between the fibrous positive electrode 3 and the fibrous negative electrode 4 are output to an external monitoring device through the two lead-out electrodes, thereby realizing the monitoring of the humidity of the environment or biological system. The lead-out electrodes may be, for example, copper wires.

[0039] According to the humidity gating device provided by the above embodiment of the present invention, when the ambient humidity acts on the humidity gating device, the ionic conductivity of the fiber solid electrolyte changes in response to the change of the ambient humidity; in response to the change of the ionic conductivity of the fiber solid electrolyte, the electrical signals output by the fiber positive electrode and the fiber negative electrode change. The humidity gating device does not require an external power supply to provide additional energy for it, and can realize a self-driving function, avoiding the use of large power supply equipment.

[0040] According to the embodiment of the present application, the humidity gating device can also realize cyclic charging and discharging. Specifically, the humidity gating device is charged by electrically connecting the positive and negative electrodes of the external power supply to the fibrous positive electrode / fibrous negative electrode.

[0041] According to the humidity gating device provided by the above embodiment of the present invention, the response / recovery time of the humidity gating device is short, and the response to the ambient humidity can be effectively achieved.

[0042] According to the embodiments of the present invention, the fiber solid electrolyte, fiber positive electrode and fiber negative electrode of the humidity gating device have excellent flexibility and mechanical properties, and can be sewn on the surface of fabrics such as masks and clothes by weaving, which is concealed and can perform real-time health monitoring of the human body. In addition, the humidity gating device provided by the embodiments of the present invention has a simple structure, low cost and is easy to mass produce.

[0043] Figure 2 A schematic flow chart of a method for manufacturing a humidity gating device provided in an embodiment of the present invention.

[0044] According to an exemplary embodiment of the present invention, the present invention provides a method for manufacturing a humidity gating device, referring to Figure 2 As shown, it includes: operation S01 to operation S03.

[0045] Operation S01, preparing a fiber solid electrolyte 2.

[0046] According to an embodiment of the present invention, the fibrous solid electrolyte 2 is obtained from cellulose or two-dimensional nanomaterials by wet spinning.

[0047] In operation S02, a fibrous positive electrode 3 and a fibrous negative electrode 4 are prepared respectively.

[0048] Operation S03 , weaving the fibrous solid electrolyte 2 , the fibrous positive electrode 3 and the fibrous negative electrode 4 together; wherein the fibrous positive electrode 3 and the fibrous negative electrode 4 are in contact with both ends of the fibrous solid electrolyte 2 , respectively.

[0049] The designed humidity gating device and its manufacturing method are schematically described below. It should be noted that the example description is only a specific embodiment of the present invention and cannot limit the protection scope of the present invention.

[0050] Example 1

[0051] refer to Figure 1 As shown, a proton battery-type fibrous humidity gating device is manufactured by using a fabric glove as a fabric carrier 1, bacterial cellulose nanofibers as a fibrous solid electrolyte 2, a fibrous copper wire as a positive electrode 3, and a fibrous zinc wire as a negative electrode 4.

[0052] Preparation of bacterial cellulose nanofibers. Specifically, 20 mL of bacterial cellulose nanofibers with a concentration of 10 mg / mL were diluted evenly; 0.1 M calcium chloride solution was injected into a glass petri dish; the bacterial cellulose nanofiber dilution was loaded into a syringe; the bacterial cellulose nanofiber dilution was pushed into a calcium chloride coagulation bath at a uniform speed using a syringe; the bacterial cellulose nanofibers in the calcium chloride coagulation bath were collected; the collected bacterial cellulose nanofibers were soaked in the aqueous solution for 1 hour and then taken out to dry.

[0053] Figure 3 This is an optical photograph of the fiber solid electrolyte provided by an embodiment of the present invention.

[0054] Figure 4 This is a scanning electron microscope image of the fiber solid electrolyte provided in an embodiment of the present invention.

[0055] refer to Figure 3 , Figure 4 As shown, the test results of optical photographs and scanning electron microscope images show that the prepared fibrous solid electrolyte is fibrous.

[0056] A fibrous positive electrode and a fibrous negative electrode were prepared. Specifically, purchased copper wire and zinc wire were ground and polished.

[0057] Figure 5 Optical photograph and magnified view of the humidity gating device woven on a fabric carrier provided in an embodiment of the present invention.

[0058] refer to Figure 5 As shown, the fibrous positive electrode 3, the fibrous negative electrode 4 and the bacterial cellulose nanofiber solid electrolyte 2 are sewn on the outer surface of the fabric glove 1. The fibrous positive electrode 3 and the fibrous negative electrode 4 are woven closely to the two ends of the bacterial cellulose nanofiber solid electrolyte 2 to obtain a proton battery type fibrous humidity gating device.

[0059] Figure 6 This is a single response / recovery curve of the humidity gating device provided in an embodiment of the present invention to ambient humidity.

[0060] refer to Figure 6 As shown in the figure, in response to the change of the humidity of the external environment, the voltage output by the humidity gated device changes, and the response / recovery time is 1.15 s / 3.23 s. It can be seen that the response / recovery time of the humidity gated device is short. This is because the size of the solid electrolyte is micron-level, and the specific surface area of ​​the fiber-shaped solid electrolyte is relatively large, which can fully and quickly contact the moisture in the environment to be tested, so that the ionic conductivity of the fiber solid-state battery material changes rapidly, thereby making the response / recovery time of the device short.

[0061] Figure 7 The following is a response curve of the humidity gating device provided in an embodiment of the present invention to the ambient humidity within 200 hours.

[0062] refer to Figure 7 As shown in the figure, the voltage signal output by the humidity gated device remains basically unchanged after being kept in the same humidity environment for 200 hours, which indicates that the humidity gated device has good stability in the working state. This is because the fiber solid electrolyte has good humidity sensitivity. When the humidity in the test environment changes, the device responds, and when the test environment is dry, the device does not respond, which can reduce the loss of the device and increase the service life of the device; and the mechanical properties of the fiber positive electrode, fiber negative electrode and fiber solid electrolyte are good, so that the prepared device can be used for a long time.

[0063] Figure 8 The following are response / recovery curves of the humidity gating device provided in an embodiment of the present invention to humidity sources at different distances.

[0064] refer to Figure 8 As shown, the humidity gating device monitors the same humidity source at different distances. The monitoring results show that as the distance between the humidity source and the humidity gating device increases, the voltage signal responded by the humidity gating device becomes smaller.

[0065] Example 2

[0066] refer to Figure 1As shown, a fabric mask is used as a fabric carrier 1, cellulose nanofibers are used as fiber solid electrolytes 2, fibrous copper wires are used as positive electrodes 3, and fibrous zinc wires are used as negative electrodes 4 to manufacture a proton battery type fibrous humidity gating device.

[0067] Preparation of solid electrolyte cellulose nanofibers.

[0068] Specifically, 20 mL of polyvinyl alcohol with a concentration of 20 mg / mL was mixed evenly with trifluoromethanesulfonic acid; 0.1 M calcium chloride solution was injected into a glass culture dish; the composite polyvinyl alcohol polymer was loaded into a syringe; the composite polyvinyl alcohol polymer was pushed into a calcium chloride coagulation bath at a uniform speed using a syringe; the polyvinyl alcohol cellulose nanofibers in the calcium chloride coagulation bath were soaked for 1 hour and then taken out to dry.

[0069] A fibrous positive electrode and a fibrous negative electrode were prepared. Specifically, purchased copper wire and zinc wire were ground and polished.

[0070] The fibrous positive electrode, fibrous negative electrode and polyvinyl alcohol cellulose nanofiber solid electrolyte are sewn onto the inner surface of the mask, wherein the fibrous positive electrode and the fibrous negative electrode are woven tightly onto the two ends of the polyvinyl alcohol cellulose nanofiber solid electrolyte to obtain a proton battery-type fibrous humidity gating device, which is used to monitor the user's breathing condition in real time.

[0071] Fig. 9 The response / recovery curve of the humidity gating device provided in the embodiment of the present invention to human breathing.

[0072] refer to Fig. 9 As shown, in response to the change of environmental humidity caused by periodic human breathing, the voltage output by the humidity gate device changes periodically.

[0073] Example 3

[0074] refer to Figure 1 As shown, a zinc ion battery-type fibrous humidity gating device is manufactured by using a fabric glove as a fabric carrier 1, cellulose nanofibers as a fibrous solid electrolyte 2, fibrous VO2 as a positive electrode 3, and a fibrous zinc wire as a negative electrode 4.

[0075] Preparation of cellulose nanofibers as fibrous solid electrolytes.

[0076] Specifically, 20 mL of cellulose nanofibers with a concentration of 10 mg / mL were diluted; 0.1 M calcium chloride solution was injected into a glass culture dish; the cellulose nanofiber dilution was loaded into a syringe; the cellulose nanofiber dilution was pushed into a calcium chloride coagulation bath at a uniform speed using a syringe; the cellulose nanofibers in the calcium chloride coagulation bath were soaked for 1 hour and then taken out to dry.

[0077] A fiber-shaped negative electrode was prepared. Specifically, purchased zinc wire was ground and polished.

[0078] Prepare a fibrous positive electrode. Specifically, 2 mmol V2O5 powder and 6 mmol H2C2O4 were dissolved in 12 mL of distilled water and stirred at 75°C for about 2 hours to obtain a dark blue solution. Then 3 mL of 30% H2O2 was added and stirred for about 20 minutes to obtain a brown solution. It was then transferred to a 100 mL high-pressure reactor and reacted at 180°C for 12 hours. After the reaction, it was centrifuged three times with deionized water and ethanol and vacuum dried to obtain VO2 powder. The VO2 powder was evenly mixed with polyurethane (PU) at a ratio of 20:1 to form a fiber.

[0079] The above-mentioned fibrous negative electrode 4, fibrous positive electrode 3 and fibrous solid electrolyte 2 are sewn onto the inner surface of the glove 1, wherein the fibrous positive electrode 3 and the fibrous negative electrode 4 are in contact with the fibrous solid electrolyte 2 respectively, to obtain a zinc ion battery type fibrous humidity gating device.

[0080] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A humidity gating device, characterized in that: include: A fiber solid electrolyte (2), wherein the ionic conductivity of the fiber solid electrolyte (2) changes in response to a change in humidity of an environment to be measured; as well as A fibrous positive electrode (3) and a fibrous negative electrode (4) are respectively in contact with two ends of the fibrous solid electrolyte (2); In response to a change in the ionic conductivity of the fiber solid electrolyte (2), the rate of the redox reaction occurring in the fiber positive electrode (3) and the fiber negative electrode (4) changes, causing the electrical signal output by the fiber positive electrode (3) and the fiber negative electrode (4) to change, and the electrical signal is used to characterize the humidity of the environment to be measured.

2. The humidity gating device according to claim 1, characterized in that: The fibrous solid electrolyte (2) comprises a composite fiber material consisting of one or at least two of two-dimensional nanomaterial fibers, hydrogel fibers and cellulose nanofibers.

3. The humidity gating device according to claim 1, characterized in that: The ions released by the oxidation-reduction reaction between the fiber-shaped positive electrode (3) and the fiber-shaped negative electrode (4) include any one of metal ions and hydrogen ions; Preferably, the metal ion is any one of lithium ion, sodium ion, potassium ion, zinc ion and manganese ion.

4. The humidity gating device according to claim 1, characterized in that: The fibrous positive electrode (3) and the fibrous negative electrode (4) are asymmetric electrodes to construct a potential difference for a redox reaction.

5. The humidity gating device according to claim 4, characterized in that: The fibrous positive electrode (3) and the fibrous negative electrode (4) are any one of copper wire, zinc wire, silver wire, MXene fiber, graphene fiber, and black phosphorus fiber.

6. The humidity gating device according to claim 1, characterized in that: The humidity gate control device is woven on a fabric carrier (1). The fabric carrier (1) comprises any one of nylon fabric and fiber fabric.

7. The humidity gating device according to claim 6, characterized in that: The fibrous positive electrode (3) and the fibrous negative electrode (4) are in contact with both ends of the fibrous solid electrolyte (2) in a parallel arrangement.

8. The humidity gating device according to claim 1, characterized in that: The fibrous positive electrode (3) and the fibrous negative electrode (4) are respectively in contact with the two ends of the fibrous solid electrolyte (2) in a cross arrangement, so that the fibrous positive electrode (3), the fibrous negative electrode (4) and the fibrous solid electrolyte (2) are woven into one.

9. The humidity gating device according to claim 1 or 6, characterized in that: The fibrous positive electrode (3) and the fibrous negative electrode (4) are in contact with both ends of the fibrous solid electrolyte (2) in a patterned arrangement.

10. A method for manufacturing a humidity gating device according to any one of claims 1 to 9, characterized in that: include: Preparation of fiber solid electrolyte (2); Prepare a fibrous positive electrode (3) and a fibrous negative electrode (4) respectively; as well as A fibrous solid electrolyte (2), a fibrous positive electrode (3) and a fibrous negative electrode (4) are woven together; wherein the fibrous positive electrode (3) and the fibrous negative electrode (4) are in contact with two ends of the fibrous solid electrolyte (2) respectively.