High performance battery separator membrane
The MgF2-coated separator membrane addresses the limitations of conventional polyolefin membranes by enhancing mechanical and thermal stability, improving charge transfer, and enabling faster electrolyte filling, thus improving battery cell performance across different chemistries.
Patent Information
- Application Number
- JP2024167101
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2024-03-13
- Filing Date
- 2024-09-26
- Publication Date
- 2025-09-29
AI Technical Summary
Conventional separator membranes made of polyolefins lack mechanical stability above their melting temperature, are ineffective against dendrite-induced short circuits, and have low surface energy, limiting electrolyte wettability and charge transport, thereby restricting the performance and charging rates of secondary battery cells.
A high-performance separator membrane comprising a porous support with a magnesium fluoride (MgF2) coating that controls pore size distribution and surface energy, enhancing mechanical and thermal stability, and improving charge transfer.
The MgF2-coated separator membrane provides improved mechanical stability, faster electrolyte filling, increased charge transfer, and extended thermal operating range, enabling better performance in various battery chemistries.
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Figure 2025141767000001_ABST
Abstract
Description
[Technical Field]
[0001] A secondary battery cell may include a separator membrane between the battery cell anode and the battery cell cathode. The separator membrane serves to prevent direct contact between the electrodes of the secondary battery cell, avoiding short circuits and potential hazards. Typically, the separator membrane comprises a porous, electrically insulating material, such as porous polyethylene or porous polypropylene, to block the flow of electrons between the anode and cathode while allowing the passage of ions. This permselectivity facilitates the movement of ions through the secondary battery cell's electrolyte, thereby driving the electrochemical reactions that generate electricity.
[0002] In some embodiments, the separator membrane comprises a porous support and a magnesium fluoride (MgF) coating on at least a portion of the porous support, wherein the pore size distribution of the separator membrane and the surface energy of the separator membrane are determined, at least in part, by the MgF coating.
[0003] In some embodiments, the separator membrane comprises a porous support and an MgF2 material coating at least a portion of the porous support, the MgF2 material partially determining the pore size distribution of the separator membrane.
[0004] In some embodiments, the separator membrane comprises a porous support and an MgF2 material at least partially coating the support membrane, the MgF2 material at least partially controlling the surface energy of the separator membrane. [Brief explanation of the drawings]
[0005] [Figure 1A] 1A-1C show examples of high performance separator membranes described herein. [Figure 1B] 1A-1C show examples of high performance separator membranes described herein. [Figure 1C] 1A-1C show examples of high performance separator membranes described herein. [Figure 1D]1A-1C show examples of high performance separator membranes described herein. [Figure 1E] 1A-1C show examples of high performance separator membranes described herein. [Figure 1F] 1A-1C show examples of high performance separator membranes described herein. [Figure 1G] 1A-1C show examples of high performance separator membranes described herein. [Figure 2] 1A-1C show related examples of battery cells including the high performance separator membranes described herein.
[0006] [Mode for Carrying Out the Invention] In the following description of example detailed embodiments, reference will be made to the accompanying drawings, in which the same reference numbers in different drawings may identify the same or similar elements.
[0007] Typical secondary battery cells include polyolefin separator membranes. Notably, polyolefins are phase stable up to their melting temperature. For example, polyethylene has a melting temperature of approximately 85 degrees Celsius (°C) to approximately 135°C. This means that typical separator membranes (e.g., separator membranes comprising polyolefins or similar materials) cannot provide mechanical stability above the melting temperature of the separator membrane material. Furthermore, conventional membrane separators are not effective mechanical barriers against short circuits due to dendrites that can damage the separator membrane. In addition, polyolefins and other similar materials have relatively low surface energies, which limit electrolyte wettability and reduce charge transport of active species (e.g., because the electrolyte cannot adequately wet the separator membrane surface). Secondary battery cells utilizing standard separator material chemistries exhibit performance limitations that affect the usability of the secondary battery cells in various applications, as well as limiting maximum charging rates.
[0008] Some embodiments described herein provide high-performance separator membranes. In some embodiments, the separator membrane comprises a porous support and a magnesium fluoride (MgF) coating on at least a portion of the porous support. Here, the pore size distribution and surface energy of the separator membrane are at least partially determined by the MgF coating.
[0009] In some embodiments, the versatility of the separator membranes described herein is increased (e.g., compared to conventional separator membranes) by enabling the porosity and / or surface energy of the separator membrane to be engineered (e.g., the porosity and / or surface energy can be controlled to achieve a desired goal). Additionally, the separator membranes described herein provide improved thermal and mechanical stability. Furthermore, the separator membranes described herein can be used with a variety of battery cell chemistries, such as ternary lithium (Li-NMC), lithium iron phosphate (LFP), lithium sulfur, sodium ion, or other types of battery cell chemistries. Furthermore, the separator membranes described herein provide improved charge transfer through the separator membrane, thereby improving battery cell performance, reducing charge times, and increasing maximum charge / discharge currents. Additional details are provided below.
[0010] 1A-1G are diagrams illustrating an example of a high-performance separator membrane 100 (hereinafter referred to as separator membrane 100). In some embodiments, as shown in FIGS. 1A-1D, separator membrane 100 can include a porous support 102 and an MgF2 coating 106 on at least a portion of (i.e., at least partially coating) porous support 102.
[0011] In the example shown in FIG. 1A, the porous support 102 includes a support body 103 having a plurality of openings 104 (e.g., holes) formed therein, the openings 104 defining the pores of the porous support 102. In the example shown in FIG. 1B, the porous support 102 includes a support body 103 defined by a plurality of support elements 104, where the support elements 104 are connected such that the porous support 102 has openings 105 between the support elements 104, where the openings 105 define the pores of the porous support 102. In some embodiments, as shown in the examples shown in FIGS. 1A and 1B, the porous support 102 has a substantially planar surface, and the MgF2 coating 106 is formed on this planar surface of the porous support 102. However, in some embodiments, the porous support 102 may have a non-planar surface, and the MgF2 coating 106 may be formed on this non-planar surface of the porous support 102, an example of which is illustrated in FIG. 1C. In another example embodiment, as shown in Figure 1D, the porous support 102 can be formed from a plurality of support fibers 107 connected to form the porous support 102 (e.g., such that there are openings between the support fibers 107 of the porous support 102). In some embodiments, the pore size distribution of the separator membrane 100 and / or the surface energy of the separator membrane 100 are at least partially determined by the MgF2 coating 106, as described in more detail below.
[0012] 1A-1D are provided as examples for illustrative purposes. In fact, the porous support 102 may comprise any type of support having an open membrane structure such that the porous support 102 is inherently porous. In some embodiments, the porous support 102 may be formed using a variety of techniques, such as fibrous materials, chemical etching, laser cutting, or punching.
[0013] In some embodiments, the porous support 102 can comprise one or more organic materials, such as organic polymers. In some embodiments, the porous support 102 can comprise one or more inorganic materials, such as inorganic polymers. In some embodiments, the porous support 102 can comprise a combination of organic and inorganic materials (e.g., a combination of one or more organic polymers and one or more inorganic polymers). Non-limiting examples of organic polymers that can be included in the porous support 102 include thermoplastic (e.g., polyesters, polyolefins, polycarbonates, polyamides, polyimides, polyiminoethers, polyurethanes, polyanilines, polyarylethers, acrylics, acrylates, polyvinyl esters, polyethers, polythiols, silicones, fluorocarbons, copolymers thereof, etc.), thermosetting (e.g., epoxies, polyurethanes, acrylates, melamine formaldehyde, urea formaldehyde, phenol formaldehyde, etc.), or energy-curable materials (e.g., acrylates, epoxies, vinyls, vinyl esters, styrenes, silanes, etc.). Non-limiting examples of inorganic polymers that can be included in the porous support 102 include silanes, siloxanes, titanates, zirconates, aluminates, silicates, phosphazenes, polyborazylenes, polythiazyls, or glasses (e.g., borosilicate glasses, alkali glasses, alkali-free glasses, metal oxide glasses, etc.). In some embodiments, the porosity of the porous support 102 alone can be greater than the desired porosity of the separator membrane 100. Thus, the formation of the MgF2 coating 106 can be performed to control the porosity of the separator membrane 100 (e.g., by reducing the porosity compared to the porosity of the porous support 102 alone).
[0014] The MgF2 coating 106 is a coating on the porous support 102. In some embodiments, the MgF2 coating 106 determines, at least in part, the surface energy and / or pore size distribution of the separator membrane 100. That is, the MgF2 coating 106 (e.g., alone or in combination with one or more materials, as described below) can define the surface energy of the separator membrane 100 and / or can define the pore size distribution (e.g., porosity) of the separator membrane 100. In some embodiments, applying the MgF2 coating 106, a chemically inert material, to the porous support 102 improves the performance of the separator membrane 100 by increasing its surface energy. With respect to battery cell chemistries, the lower the surface energy of the separator membrane, the more repulsive the separator membrane's surface. Thus, a low surface energy slows the electrolyte filling of the battery cell. Compared to materials used in conventional separator membranes, MgF2 inherently has a higher surface energy than polyolefin materials, improving the wetting of the separator membrane 100 containing the MgF2 coating 106 and shortening the electrolyte filling time during battery cell assembly. Furthermore, the MgF2 coating 106 improves charge transfer during charging of a battery cell containing the separator membrane 100 while also improving the battery's discharge performance. Additionally, the use of MgF2 allows for the control of the porosity scale of the separator membrane 100. Conventional separator membranes have fixed porosity distributions and material properties, which pose challenges in controlling the wettability and porosity scale. This is important because during operation, charge carriers may be able to travel between the anode and cathode, while the remaining battery chemicals must be separated. MgF2 controls porosity at various levels. Therefore, the MgF2 coating 106 can be formed to control the surface energy and porosity of the separator membrane 100. Generally, higher surface energy is beneficial to charge interactions in the electrolyte chemistry and provides improved pore distribution.Thus, the MgF2 coating 106 may enable the separator membrane 100 to be used for smaller species requiring separation, such as battery chemistries comprising lithium sulfate (Li2S4), and therefore may improve the selectivity of the separator membrane.
[0015] In some embodiments, the separator membrane 100 may include a magnesium oxide (MgO), magnesium oxide fluoride (MgF2), or a combination thereof on or within at least a portion of the MgF2 coating 106. x F y O z , where 1≦x≦4, 1≦y≦5, 1≦z≦4), or alumina (Al2O3). In some embodiments, these one or more other materials may help to further determine or define the surface energy of separator membrane 100 (e.g., by increasing the surface energy compared to MgF2 coating 106 alone) and / or help to further determine or define the pore size distribution of separator membrane 100. More generally, these one or more other materials may help to control the matching of wetting characteristics or improve or increase the surface energy of separator membrane 100, as defined from the surface chemical composition of separator membrane 100 to the properties of the electrolyte, and may also provide a desired pore size distribution of separator membrane 100. In some embodiments, these one or more other materials may increase the range of achievable surface energies of separator membrane 100 (e.g., compared to MgF2 alone).
[0016] For example, in some embodiments, separator membrane 100 can include MgO material 108 on or within at least a portion of MgF coating 106. FIG. 1E illustrates an example of separator membrane 100 including MgO material 108. In some embodiments, the formation of MgO material 108 can be tunable (e.g., during manufacturing of separator membrane 100) to provide further control (e.g., further increase) of the surface energy of separator membrane 100, thereby further improving the electrolyte wetting of separator membrane 100. As a result, MgO material 108 can help enable faster electrolyte filling after a battery cell including separator membrane 100 is assembled, which in turn can result in improved charge transfer of a battery cell including separator membrane 100.
[0017] As another example, separator membrane 100, in some embodiments, can include Al2O3 material 110 in at least a portion of MgF2 coating 106. FIG. 1F illustrates an example of separator membrane 100 including Al2O3 material 110. In some embodiments, Al2O3 material 110 allows for further control of the surface energy of separator membrane 100 (e.g., further increasing it compared to MgF2 alone). In some embodiments, terminating MgF2 coating 106 with a separate layer material, such as Al2O3 material 110, may allow for control of the surface energy of separator membrane 100 or the wetting characteristics of separator membrane 100 (e.g., for a given battery cell electrolyte and battery cell configuration).
[0018] As another example, in some embodiments, the separator membrane 100 may include MgF2 on or within at least a portion of the MgF2 coating 106. x F y O z In some embodiments, the material may include Mg x F y O z The material may further allow for control or improvement of one or more properties of the separator membrane 100 (e.g., surface energy or electrolyte wettability). xF y O z The material may comprise any material on a continuum between pure MgF2 and pure MgO. In some embodiments, the transition between the MgF2 coating 106 and the MgO material 108 is x F y O z It may be composed of various species of materials, and its formulation may be designed to provide a controlled or desired surface energy and / or pore size distribution for the separator membrane 100 .
[0019] In some embodiments, one or more materials of separator membrane 100 can determine, at least in part, the pore size distribution of separator membrane 100 and / or the surface energy of separator membrane 100. For example, the MgF coating 106 and one or more other materials (e.g., MgO material 108, Al2O3 material 110, and / or Mg x F y O z The pore size distribution and / or surface energy of separator membrane 100 can be determined, at least in part, by the MgF2 coating 106 and one or more other materials. In some embodiments, the surface energy of separator membrane 100 can be designed to be within a range of about 35 milliNewtons per meter (mN / m) to about 1000 mN / m. Notably, different battery cell concepts may require different surface energies of separator membrane 100 for optimal performance, and the surface energy of separator membrane 100 can be designed (e.g., by controlled formation of MgF2 coating 106 and one or more other materials) for a given battery cell concept or application. In some embodiments, the pore size distribution comprises pore sizes ranging from about 2 nanometers (nm) to about 1000 nm. In particular, different battery cell concepts may require different pore size distributions in the separator membrane 100 for optimal performance, and the pore size distribution of the separator membrane 100 may be engineered (e.g., by controlled formation of the MgF2 coating 106 and one or more other materials) for a given battery cell concept or application.
[0020] In some embodiments, one or more materials of the separator membrane 100 (e.g., MgF2 coating 106, MgO material 108, Al2O3 material 110, and / or Mg x F y O z By adjusting or controlling the process techniques and / or process conditions (e.g., pressure, deposition rate, etc.) for the deposition of one or more materials, the microstructure of the one or more materials, and therefore the pore size and pore size distribution of the separator membrane 100, can be engineered (e.g., to meet battery cell performance requirements for a given application). In some embodiments, process gases associated with the formation of one or more materials, such as nitrogen (N), argon (Ar), and oxygen (O), can be used in various blend ratios in connection with controlling the formation of the one or more materials. In some embodiments, a given one of the one or more materials of the separator membrane 100 can be formed using vacuum deposition, wet chemical vapor deposition, or another type of process. In some embodiments, the vacuum process associated with the formation of the MgF coating 106 and / or one or more other materials of the separator membrane 100 can be performed in a temperature range of about 1000°C. -6 The process can be carried out at pressures ranging from 100 torr to about 100 millitorr (mtorr). The substrate temperature or surface activation technique, among other things, can affect the layer growth, orientation, or microstructure of the MgF coating 106 or one or more other materials. In some embodiments, an engineered balance of amorphous relative to crystalline phases controls the microstructure and pore distribution of the separator membrane 100.
[0021] In some embodiments, the stoichiometry of materials, including doping of one or more other materials in the MgF2 coating 106 and / or separator membrane 100, can be utilized to engineer one or more properties of the separator membrane 100. In some embodiments, the stoichiometry of one or more other materials in the MgF2 coating 106 and / or separator membrane 100 can be engineered by co-evaporation and / or coating chamber conditions. That is, the water vapor and oxygen content during deposition can be adjusted to balance the ratio of MgO to MgF2, and the ratio of MgO to MgF2, and the ratio of MgF2 to MgF2. x F y O zIn some embodiments, the MgO phase can improve the wetting behavior of MgF by increasing the surface energy of the separator membrane 100, as described above, which also improves the rate of charge transfer through the separator membrane 100.
[0022] In some embodiments, a gas phase chemical vapor deposition process may be utilized that uses vaporized precursor materials that react in the gas phase or on the surface of the porous support 102 to form a porous layer of MgF2 that forms the MgF2 coating 106. The chemical vapor deposition process may be performed, for example, at a temperature of about 1000. -6 The process can be carried out at a pressure range from 1000 mTorr to about 1000 mTorr. Additional materials (MgO, Mg x F y O z The ratio of MgF2 to MgF2 (e.g., MgF2, Al2O3, or other oxides) can be engineered through the use of additional precursors and process gases. By adding plasma during the process, it is possible to engineer the microstructure of the MgF2 coating 106 and engineer the porosity and / or surface energy of the separator membrane 100. FIG. 1G shows an example of a separator membrane 100 formed using a gas-phase chemical vapor deposition process. As shown in FIG. 1G, the gas-phase chemical vapor deposition method allows the MgF2 coating 106 to fill the pores as needed along the surface of the porous support 102.
[0023] In some embodiments, the gas phase chemical vapor deposition process can be carried out by using evaporated precursors that adsorb onto the surface of the porous substrate and fill the pores of the porous support 102 before forming a layer of MgF2 on the surface of the porous support 102.
[0024] In some embodiments, a liquid coating process can be used to form a layer on a porous substrate that can form colloidal particles and / or a polymer network. In some embodiments, the layer can be crosslinked via light, heat, or chemical reaction to form a porous layer of MgF2 on the porous support 102.
[0025] In this manner, the porosity of separator membrane 100 can be engineered, i.e., increasing the versatility of separator membrane 100 (e.g., allowing separator membrane 100 to be used in a variety of battery chemistries and applications). Additionally, the surface energy of separator membrane 100 can be engineered, i.e., improving the performance of a battery cell including separator membrane 100 and / or the performance of an assembly of battery cells including separator membrane 100.
[0026] Furthermore, in some embodiments, the thickness of the separator membrane 100 can be reduced (e.g., compared to conventional separator membranes that include laminates with two or more material layers to achieve a desired porosity distribution). Additionally, the separator membranes 100 described herein provide mechanical stability with respect to stretching and cell deformation while providing chemical stability with respect to battery cell chemistries (e.g., different components and electrolytes). Furthermore, the separator membranes 100 provide mechanical and chemical stability against dendrite penetration. Additionally, the separator membranes 100 can have improved thermal stability, i.e., a reduced likelihood of melting, and can further extend the thermal operating range (e.g., thermal performance can be improved by increasing the thickness of the MgF2 coating 106 and / or one or more other materials). Additionally, the separator membranes 100 described herein reduce electrolyte injection time during battery cell assembly (e.g., compared to battery cells constructed with conventional separator membranes). In some embodiments, the separator membranes 100 described herein provide improved performance for a variety of battery cell chemistries, including, but not limited to, solid-state lithium battery cells, lithium-sulfur battery cells, sodium-ion battery cells, or other types of battery cell chemistries.
[0027] As noted above, Figures 1A-1G are provided as examples, and other examples may differ from what is described with respect to Figures 1A-1G.
[0028] 2 is a diagram illustrating an example related battery cell 200 including the high performance separator membrane 100 described herein. As shown in FIG. 2, the battery cell 200 includes an anode 202 (e.g., a lithium (Li) anode), a cathode 204 (e.g., a sulfur (S) cathode), and the separator membrane 100 with (at least) an MgF2 coating 106.
[0029] In the example shown in FIG. 2, the improved porosity distribution provided by the separator membrane 100 allows lithium polysulfide (Li x S y , x>2, y>2) from the cathode side of the battery cell 200 to the anode side of the battery cell 200, which would otherwise cause the performance of the battery cell 200 to gradually decrease over time. As shown in FIG. 2, the lithium ions (Li + ) can pass through separator membrane 100. In particular, conventional polyolefin separator membranes do not block the passage of polysulfides, meaning that separator membrane 100 has improved performance (compared to lithium-ion batteries using conventional polyolefin separator membranes).
[0030] As noted above, Figure 2 is provided as an example. Other examples may differ from what is described with respect to Figure 2.
[0031] The foregoing disclosure has been presented for purposes of illustration and description, and is not intended to be exhaustive or to limit the embodiments to the precise form disclosed. Modifications and variations may be made in light of the foregoing disclosure or may be acquired from practice of the embodiments.
[0032] Combinations of particular features recited in the claims and / or disclosed in the specification are not intended to limit the disclosure of various embodiments. Indeed, many of these features may be combined in ways not recited in the claims and / or disclosed in the specification. While each dependent claim listed below may directly depend on only one claim, the disclosure of various embodiments includes each dependent claim in combination with all other claims in the set. As used herein, the phrase "at least one" of a list of items refers to any combination of those items, including single elements. For example, "at least one of a, b, or c" covers a, b, c, ab, ac, bc, and abc, as well as any combination of multiple of the same items.
[0033] No element, act, or instruction used herein should be construed as essential or required unless expressly stated as such. Additionally, as used herein, the articles "a" and "an" are intended to include one or more items and may be used interchangeably with "one or more." Additionally, as used herein, the article "the" is intended to include one or more items referenced in connection with the article "the" and may be used interchangeably with "one or more." Additionally, as used herein, the term "set" is intended to include one or more items (e.g., related items, unrelated items, or a combination of related and unrelated items) and may be used interchangeably with "one or more." Where only one item is intended, the phrase "only one" or similar expression may be used. Additionally, as used herein, terms such as "have," "having," and "having" are intended to be open-ended terms. Additionally, the phrase "based on" is intended to mean "based at least in part on," unless expressly stated otherwise. Also, as used herein, the term "or" is intended to be inclusive when used consecutively and can be used interchangeably with "and / or" (such as when used in combination with "either" or "only one of") unless expressly stated otherwise.
Claims
1. A separator membrane, A porous carrier; Magnesium fluoride (MgF) coated on at least a portion of the porous support 2 )and, Equipped with The pore size distribution and the surface energy of the separator membrane are determined by the MgF 2 determined at least in part by the coating, Separator membrane.
2. MgF 2 Alumina (Al) is deposited on at least a portion of the coating. 2 O 3 10. The separator membrane of claim 1 further comprising a .sup.2 (.alpha.) material.
3. The MgF 2 10. The separator membrane of claim 1, further comprising a magnesium oxide (MgO) material on or within at least a portion of the coating.
4. The MgF 2 Magnesium fluoride oxide (Mg x F y O z , where 1≦x≦4, 1≦y≦5, 1≦z≦4) material.
5. The separator membrane of claim 1 , wherein the porous support comprises at least one of an organic material or an inorganic material.
6. 10. The separator membrane of claim 1, wherein the surface energy of the separator membrane is in the range of about 35 milliNewtons per meter (mN / m) to about 1000 mN / m.
7. 10. The separator membrane of claim 1, wherein the pore size distribution comprises pore sizes ranging from about 2 nanometers (nm) to about 1000 nm.
8. A separator membrane, A porous carrier; Magnesium fluoride (MgF) at least partially coating the porous support 2 )and, Equipped with The MgF 2 The material partially determines the pore size distribution of the separator membrane. Separator membrane.
9. 9. The separator membrane of claim 8, wherein the pore size distribution of the separator membrane comprises pore sizes ranging from about 2 nanometers (nm) to about 1000 nm.
10. The MgF 2 The separator membrane of claim 8 , wherein a material at least partially controls the surface energy of the separator membrane.
11. 11. The separator membrane of claim 10, wherein the surface energy of the separator membrane is in the range of about 35 milliNewtons per meter (mN / m) to about 1000 mN / m.
12. The MgF 2 Alumina (Al) is deposited on at least a portion of the coating. 2 O 3 10. The separator membrane of claim 8 further comprising a .sup.2+.sup.2 .OMEGA.) material.
13. The MgF 2 10. The separator membrane of claim 8, further comprising a magnesium oxide (MgO) material on or within at least a portion of the coating.
14. The MgF 2 Magnesium fluoride oxide (Mg x F y O z 10. The separator membrane of claim 8, further comprising a 100% SiO2 (where 1≦x≦4, 1≦y≦5, 1≦z≦4) material.
15. The separator membrane of claim 8 , wherein the porous support comprises an organic material, an inorganic material, or a combination thereof.
16. A separator membrane, A porous carrier; Magnesium fluoride (MgF) at least partially coating the porous support 2 )and, The MgF 2 a material that at least partially controls the surface energy of the separator membrane; Separator membrane.
17. The MgF 2 17. The separator membrane of claim 16, wherein the material partially determines the pore size distribution of the separator membrane.
18. The MgF 2 Alumina (Al) is deposited on at least a portion of the coating. 2 O 3 17. The separator membrane of claim 16, further comprising a .sup.2+ ...
19. The MgF 2 17. The separator membrane of claim 16, further comprising a magnesium oxide (MgO) material on or within at least a portion of the coating.
20. The MgF 2 Magnesium fluoride oxide (Mg x F y O z 17. The separator membrane of claim 16, further comprising a 1≦x≦4, 1≦y≦5, 1≦z≦4) material.