Patent Application
20220115692
This disclosure generally relates to a stretchable battery.
Recent technological advances and the continual miniaturization of electronics have diminished the divide between humans and technology. Increasingly, humans are in close contact with electronic devices in the form of personal computers, portable smartphones, and wearable electronics. These electronics are typically stiff, and do not conform to the human body. Looking to the future, there is substantial interest in developing electronics that are more intimate with the human body. Such applications include human-facing soft robotics, sensors that conform to human skin, and electronic devices that can be implanted directly into human tissue. Recent advances in stretchable electronics have facilitated these applications; from strain-engineered rigid-island structures to intrinsically stretchable semiconducting polymers and circuits, soft electronics are rapidly becoming a reality. However, there is a substantial constraint for the development of soft and stretchable electronics due to the lack of an adequate, portable power source. While some flexible battery materials have been proposed, there is still a substantial gap in the ability to fabricate stretchable battery materials to fabricate electronics that intimately couple to the human body.
To address the demand for stretchable batteries, several approaches have been proposed. Strategies for stretchable batteries include strain-engineering rigid electrodes to conform to applied strain either through interconnected rigid-islands, formation of a buckled electrode structure, or wrapping active materials around a stretchable cylindrical rod. While these strategies show promise for stretchable forms of energy storage, their intensive fabrication processes are at substantial economic odds with the low-cost slurry process used to form commercial battery materials. Other approaches to fabricating stretchable batteries involve using composite mixtures of active materials and elastomer molecules to create intrinsically stretchable battery materials. While this approach shows promise from an economic standpoint, the elastomers used to make intrinsically stretchable battery materials generally are not ionically conductive, specifying that these stretchable batteries use liquid electrolytes in their operation.
There are safety hazards associated with using liquid electrolytes in lithium-ion batteries. For a stretchable battery application in intimate contact with the human body, the safety hazards associated with electrolyte leakage and flammability are exacerbated. Desirably, stretchable battery materials would utilize a solid polymer electrolyte. However, a stretchable polymer electrolyte with sufficient ionic conductivity for battery operation has not been reported. The use of gel electrolytes is a desirable compromise for stretchable batteries with sufficient ionic conductivity. While stretchable gel electrolytes have been reported, these gel-electrolytes typically have poor mechanical properties, and thus could lead to shorting when used in a stretchable battery.
It is against this background that a need arose to develop embodiments of this disclosure.
Stretchable batteries are desired for applications in which soft electronics interface directly with the human body. However, other approaches for stretchable batteries rely on costly strain-engineering approaches. Herein, some embodiments are directed to a supramolecular polymeric design to fabricate a stretchable lithium ion conductor (SLIC). SLIC utilizes orthogonally functional hydrogen bonding domains and ionically conductive domains to create an ultra-resilient polymer electrolyte with high ionic conductivity. Implementation of SLIC as a binder material allows for the formation of stretchable Li-ion battery electrodes via a slurry process. Combining the SLIC-based electrolytes and electrodes allows the fabrication of an all-stretchable battery with excellent performance even when deformed or stretched to about 70% of its original length.
Advantages of some embodiments of this disclosure include: 1) decoupling of mechanical properties from ionic conductivity, which allows for a highly resilient lithium-ion battery electrolyte that also has excellent ionic conductivity; 2) excellent mechanical properties allows for the creation of intrinsically stretchable electrodes, which can achieve higher mass loading at a much lower cost; and 3) dynamic bonding allows for the formation of continuous interface and so a liquid electrolyte can be omitted.
A stretchable lithium ion conductor has applications in stretchable batteries, supercapacitors, fuel cells, and other electrochemical energy storage devices. Applications for stretchable batteries include use in soft robotics, wearable electronics, and implanted electronic devices.
In some embodiments, a battery includes: 1) an anode; 2) a cathode; and 3) a solid or gel electrolyte disposed between the anode and the cathode, wherein the electrolyte includes a supramolecular polymer formed of, or including, molecules crosslinked through dynamic bonds, and each of the molecules includes an ionically conductive domain.
In additional embodiments, an electrode includes: 1) an active electrode material; 2) conductive fillers; and 3) a supramolecular polymer formed of, or including, molecules crosslinked through dynamic bonds, each of the molecules includes an ionically conductive domain, and the active electrode material and the conductive fillers are dispersed in the supramolecular polymer.
In further embodiments, a battery includes the electrode of any of the foregoing embodiments.
Other aspects and embodiments of this disclosure are also contemplated. The foregoing summary and the following detailed description are not meant to restrict this disclosure to any particular embodiment but are merely meant to describe some embodiments of this disclosure.
For a better understanding of the nature and objects of some embodiments of this disclosure, reference should be made to the following detailed description taken in conjunction with the accompanying drawings.
FIG. 17. Adhesion energy of SLIC-3 and other polymers.
In some embodiments of the battery 100, the dynamic bonds include hydrogen bonds. Other types of reversible (or dynamic), relatively weak bonds, such as coordination bonds (e.g., metal-ligand bonds) or electrostatic interactions, can be included in addition to, or in place of, hydrogen bonds. In some embodiments, each of the molecules includes a hydrogen bonding domain 122. In some embodiments, the hydrogen bonding domain 122 includes an oxygen-containing functional group, a nitrogen-containing functional groups, or both. In some embodiments, the hydrogen bonding domain 122 includes one or more of hydroxyl, amine, and carbonyl-containing functional groups. In some embodiments, the hydrogen bonding domain 122 can include a carbonyl-containing functional group. Carbonyl-containing functional groups include the moiety C═O. Examples of carbonyl-containing functional groups include amide, ester, urea, 2-ureido-4-pyrimidone, and carboxylic acid functional groups. In some embodiments, the hydrogen bonding domain 122 can include a nitrogen-containing functional group, such as selected from amine, amide, urea, and 2-ureido-4-pyrimidone. Amine, amide, urea, and 2-ureido-4-pyrimidone include the moiety —NHR, where R can be hydrogen or a moiety different from hydrogen. Certain functional groups, such as amide, urea, and ureidopyrimidone, include both the C═0 moiety as well as the —NHR moiety.
In some embodiments of the battery 100, the ionically conductive domain 120 includes a polyalkylene oxide chain. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A)n— where n is an integer that is 2 or greater, and A is an alkylene, such as ethylene or propylene. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A1)n1(—O—A2)n2— where n1 is an integer that is 1 or greater, n2 is an integer that is 1 or greater, and A1 and A2 are different alkylenes, such as selected from ethylene and propylene. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A1)n1(—O—A2)n2(—O—A1)n3— where n1 is an integer that is 1 or greater, n2 is an integer that is 1 or greater, n3 is an integer that is 1 or greater, and A1 and A2 are different alkylenes, such as selected from ethylene and propylene. Other ionically conductive domains, such as polyethylenimine chains, polyacrylonitrile chains, polyethylene carbonate chains, or perfluoropolyether chains, can be included in addition to, or in place of, polyalkylene oxide chains.
In some embodiments of the battery 100, the electrolyte 106 further includes lithium cations 118 dispersed in the supramolecular polymer 116. Other types of metal cations, such as sodium cations, can be included in addition to, or in place of, lithium cations. In some embodiments, a concentration of the metal ions (e.g., lithium ions 118) can be at least about 0.01% by weight relative to a total weight of the electrolyte 106, such as at least about 0.03% by weight, at least about 0.05% by weight, at least about 0.08% by weight, at least about 0.1% by weight, at least about 0.2% by weight, at least about 0.3% by weight, or at least about 0.4% by weight, and up to about 0.5% by weight or greater, up to about 0.7% by weight or greater, up to about 1% by weight or greater, or up to about 1.5% by weight or greater.
In some embodiments of the battery 100, the electrolyte 106 further includes fillers 114 dispersed in the supramolecular polymer 116. In some embodiments, the fillers 114 include ceramic fillers. In some embodiments, a concentration of the fillers 114 can be at least about 0.1% by weight relative to a total weight of the electrolyte 106, such as at least about 0.3% by weight, at least about 0.5% by weight, at least about 0.8% by weight, at least about 1% by weight, or at least about 2% by weight, and up to about 3% by weight or greater, or up to about 4% by weight or greater.
In some embodiments of the battery 100, the supramolecular polymer has a glass transition temperature that is no greater than about 25° C., such as from about −100° C. to about 25° C., from about −100° C. to about 0° C., from about −100° C. to about −25° C., from about −50° C. to about 25° C., from about −50° C. to about 0° C., or from about 0° C. to about 25° C.
In some embodiments of the battery 100, the electrolyte 106 has an ionic conductivity of at least about 10−6 S/cm at room temperature (25° C.), such as at least about 3×10−6 S/cm, at least about 5×10−6 S/cm, at least about 8×10−6 S/cm, at least about 10−5 S/cm, at least about 3×10−5 S/cm, at least about 5×10−5 S/cm, at least about 8×10−5 S/cm, or at least about 10−4 S/cm, and up to about 10−3 S/cm or greater.
In some embodiments of the battery 100, the electrolyte 106 has an ultimate tensile stress of at least about 0.1 MPa, such as at least about 0.5 MPa, at least about 1 MPa, at least about 1.5 MPa, at least about 2 MPa, or at least about 2.5 MPa, and up to about 3 MPa or greater, or up to about 4 MPa or greater. In some embodiments, the electrolyte 106 has an extensibility (or percentage elongation-at-break) of at least about 30%, at least about 40%, at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 100%, at least about 200%, at least about 300%, at least about 400%, at least about 500%, at least about 1,000%, at least about 1,500%, or at least about 2,000%, and up to about 2,500% or greater.
In some embodiments of the battery 100, at least one of the anode 102 or the cathode 104 includes a supramolecular polymer having the foregoing characteristics specified for the electrolyte 106. In some embodiments, the anode 102 includes a supramolecular polymer, along with an active anode material and conductive fillers dispersed in the supramolecular polymer. In some embodiments, the cathode 104 includes a supramolecular polymer, along with an active cathode material and conductive fillers dispersed in the supramolecular polymer. In some embodiments, the conductive fillers include carbonaceous fillers.
In some embodiments of the electrode 200, the dynamic bonds include hydrogen bonds. Other types of reversible (or dynamic), relatively weak bonds, such as coordination bonds (e.g., metal-ligand bonds) or electrostatic interactions, can be included in addition to, or in place of, hydrogen bonds. In some embodiments, each of the molecules includes a hydrogen bonding domain 212. In some embodiments, the hydrogen bonding domain 212 includes an oxygen-containing functional group, a nitrogen-containing functional groups, or both. In some embodiments, the hydrogen bonding domain 212 includes one or more of hydroxyl, amine, and carbonyl-containing functional groups. In some embodiments, the hydrogen bonding domain 212 can include a carbonyl-containing functional group. Carbonyl-containing functional groups include the moiety C═O. Examples of carbonyl-containing functional groups include amide, ester, urea, 2-ureido-4-pyrimidone, and carboxylic acid functional groups. In some embodiments, the hydrogen bonding domain 212 can include a nitrogen-containing functional group, such as selected from amine, amide, urea, and 2-ureido-4-pyrimidone. Amine, amide, urea, and 2-ureido-4-pyrimidone include the moiety —NHR, where R can be hydrogen or a moiety different from hydrogen. Certain functional groups, such as amide, urea, and ureidopyrimidone, include both the C═O moiety as well as the —NHR moiety.
In some embodiments of the electrode 200, the ionically conductive domain 210 includes a polyalkylene oxide chain. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A)n— where n is an integer that is 2 or greater, and A is an alkylene, such as ethylene or propylene. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A1)n1(—O—A2)n2— where n1 is an integer that is 1 or greater, n2 is an integer that is 1 or greater, and A1 and A2 are different alkylenes, such as selected from ethylene and propylene. In some embodiments, the polyalkylene oxide chain is in the form of (—O—A1)n1(—O—A2)n2(—O—A1)n3— where n1 is an integer that is 1 or greater, n2 is an integer that is 1 or greater, n3 is an integer that is 1 or greater, and A1 and A2 are different alkylenes, such as selected from ethylene and propylene. Other ionically conductive domains, such as polyethylenimine chains, polyacrylonitrile chains, polyethylene carbonate chains, or perfluoropolyether chains, can be included in addition to, or in place of, polyalkylene oxide chains.
In some embodiments of the electrode 200, the electrode 200 further includes lithium cations 208 dispersed in the supramolecular polymer 206. Other types of metal cations, such as sodium cations, can be included in addition to, or in place of, lithium cations. In some embodiments, a concentration of the metal cations (e.g., lithium ions 208) can be at least about 0.01% by weight relative to a total weight of the electrode 200, such as at least about 0.03% by weight, at least about 0.05% by weight, at least about 0.08% by weight, at least about 0.1% by weight, at least about 0.2% by weight, at least about 0.3% by weight, or at least about 0.4% by weight, and up to about 0.5% by weight or greater, or up to about 0.7% by weight or greater.
In some embodiments of the electrode 200, the electrode 200 has an ionic conductivity of at least about 10−6 S/cm at room temperature (25° C.), such as at least about 3×10−6 S/cm, at least about 5×10−6 S/cm, at least about 8×10−6 S/cm, at least about 10−5 S/cm, at least about 3×10−5 S/cm, at least about 5×10−5 S/cm, at least about 8×10−5 S/cm, or at least about 10−4 S/cm, and up to about 10−3 S/cm or greater.
In some embodiments of the electrode 200, the electrode 200 has an ultimate tensile stress of at least about 0.1 MPa, such as at least about 0.5 MPa, at least about 1 MPa, at least about 1.5 MPa, at least about 2 MPa, or at least about 2.5 MPa, and up to about 3 MPa or greater, or up to about 4 MPa or greater. In some embodiments, the electrode 200 has an extensibility (or percentage elongation-at-break) of at least about 30%, at least about 40%, at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 100%, at least about 200%, at least about 300%, at least about 400%, at least about 500%, or at least about 900%, and up to about 1,500% or greater.
In further embodiments, a battery includes the electrode 200 of any of the foregoing embodiments.
The following example describes specific aspects of some embodiments of this disclosure to illustrate and provide a description for those of ordinary skill in the art. The example should not be construed as limiting this disclosure, as the example merely provides specific methodology useful in understanding and practicing some embodiments of this disclosure.
In this example, supramolecular polymer engineering is introduced to form gel polymer electrolytes with excellent mechanical properties. By embedding hydrogen bonding 2-ureido-4-pyrimidone (UPy) moieties into an ionically conductive polymer backbone, an ultra-resilient polymer electrolyte is formed that has mechanical properties that are decoupled from the ionic conductivity. This polymer, called a stretchable lithium ion conductor (SLIC), can be used as a resilient polymer electrolyte and has an ionic conductivity of about 2×10−4 S cm−1 when gelled with a moderate amount (e.g., about 20 wt. %) of a plasticizer. The extreme resilience of this polymer electrolyte allows for the fabrication of intrinsically stretchable battery materials that do not involve strain engineering or liquid electrolyte. Furthermore, the dynamic hydrogen bonding of this polymer allows for the formation of excellent interfaces between an electrode and electrolyte components. These interfaces allow for the formation of stretchable lithium-ion batteries with continuous ion transport between various components. The strategy reported here of using supramolecular dynamic bonding to form stretchable ion conductors opens a new pathway for fabricating strong, resilient materials for stretchable lithium-ion batteries.
The mechanical properties of the as-synthesized SLIC molecules are of importance when assessing the feasibility of the polymer for use as a robust stretchable electrolyte.
One of the major advantages of the SLIC system for use as a polymer electrolyte is the decoupling of the Tg from the mechanical properties of the polymer through the use of orthogonally functional hydrogen bonding and ion conducting domains. The Vogel-Tamman-Fulcher (VTF) equation dictates that a lower Tg in a polymer electrolyte leads to higher ionic conductivity. As such, efforts for polymer electrolyte have focused on reducing the Tg of polymer electrolytes in order to improve ionic conductivity. However, lowering the Tg of a polymer can be deleterious to the strength of a polymer, and so a polymer electrolyte with a low Tg can lead to hazards such as short circuiting via external puncture or from dendrite formation. For stretchable batteries, the dangers of short-circuit due to soft and weak polymer electrolytes are exacerbated when the battery is stretched. Because of these dangers, polymer engineering strategies have been developed to overcome the trade-off between Tg and mechanical strength of a polymer electrolyte. One strategy is based on a polystyrene (PS)-polyethylene oxide (PEO) block copolymer, in which the PS block provides mechanical strength and the PEO block provides ionic conductivity. Other strategies include nanoscale-phase separation, crosslinking with hairy nanoparticles, and addition of ceramic fillers. However, these strategies result in rigid electrolytes, and thus are not suitable for application as stretchable polymer electrolytes. Herein, the SLIC system provides a strategy based on supramolecular engineering to decouple the ionic conductivity from the mechanical strength of a polymer electrolyte.
To confirm this hypothesis, polymer electrolytes were created by dissolving a lithium salt (lithium bis(trifluoromethanesulfonyl)imide (LiTFSI)) into the polymer and casting a film. Ion transport properties were investigated with and without the presence of di(ethylene glycol)dimethyl ether (DEGDME) as a plasticizer. Experimentally, about 20 wt. % LiTFSI and about 20 wt. % DEGDME were chosen in the formation of polymer electrolyte films to enhance the ionic conductivity and mechanical properties of the samples.
The mechanical properties of the SLIC-based polymer electrolytes can determine their performance as a solid electrolyte. Addition of LiTSFI salt causes a decrease in the mechanical properties of the SLIC based electrolytes. This is potentially due to the Li+ driven ionic crosslinking of the soft segments or the plasticizing TFSI anion interfering with the formation of the UPy domains. Indeed,
Finally, when evaluating the performance of the SLIC electrolyte for a stretchable battery, the performance of the electrolyte under strain is considered.
Development of a stretchable electrode material can allow stretchable lithium ion batteries. Other approaches to form stretchable electrode materials either utilize cost-intensive micro/nano scale engineering, or involve coating a small amount of active material onto an elastic support. Intrinsically stretchable electrodes could be fabricated by replacing a binder in electrode materials with a stretchable one. Because SLIC is a polymer with excellent mechanical properties as well as ionic conductivity, it is a candidate for making stretchable composite electrode materials. By using a slurry process, large-scale, free standing electrodes are formed based on mixtures of lithium iron phosphate (LFP), carbon black, and SLIC electrolyte.
One challenge for batteries with solid or gel electrolyte is achieving good interfacial contact and ionic conductivity between the electrode and electrolyte layers. Because of the dynamic nature of the UPy bonds, it is expected that the SLIC electrodes will be able to form strong interfaces with the SLIC electrolyte developed in the previous section.
Battery testing on these stretchable electrode and electrolyte materials was first conducted in coin cells in order to determine their performance in a lithium-ion battery.
The foregoing demonstrates the ability to use SLIC as a material to fabricate high-performance stretchable electrolyte and electrode materials that can interface well with each other and operate in a half-cell battery configuration. As a final demonstration, it is shown that SLIC can be used to fabricate an all-stretchable battery.
To demonstrate the ability to fabricate full cells based on the stretchable SLIC electrode and electrolyte component, a lithium titanate (LTO) anode was fabricated in the same manner as the LFP electrode.
To demonstrate the stretchability of the batteries based on all-SLIC components, the PDMS-encapsulated full cells were operated both unstretched and with about 60% strain applied (
In conclusion, the stretchable lithium ion conductor, SLIC, is a rationally designed, supramolecular polymer than allows the fabrication of high-performance materials for stretchable lithium ion batteries. SLIC's design incorporates orthogonally functional components that provide both high ionic conductivity and excellence resilience. Using this design to overcome the characteristic tradeoff between ionic conductivity and mechanical robustness, fabrication is made of a resilient polymer electrolyte. Additionally, the ultra-robust and ionically conductive nature of the SLIC polymers lends them as excellent binder materials to create stretchable composite electrodes using a slurry casting processes. Combining these stretchable materials allows for the creation of a fully stretchable lithium ion battery based on SLIC materials.
All reagents were purchased from Sigma Aldrich and used without purification unless otherwise specified. NMR spectroscopy was conducted using an Inova 300 MHz spectrometer for 7Li NMR. Polymer/salt/additive mixtures were dissolved to a concentration of about 5 wt. % in deuterated chloroform (CDCl3), and placed into 5 mm borosilicate NMR tubes. CDCl3 does interfere with solvation of LiTFSI as indicated by the lack of 7Li peak in a neat LiTFSI-CDCl3 mixture. In all instances, samples were prepared and tightly sealed in NMR tubes in the nitrogen environment.
SLIC polymers were dissolved in tetrahydrofuran (THF) along with an appropriate amount of vacuum-dried LiTFSI and about 14 nm fumed SiO2. The viscous solution was cast into a Teflon mold, and dried for about 24 hours at room temperature (RT). After drying at RT, the film was further dried for about 24 hours at about 60° C. in a vacuum oven and for about 24 hours in a nitrogen filled glovebox. Resulting films were about 75-200 μm thick. To use, the films were peeled, punched, and plasticized in the confines of the nitrogen glovebox.
SLIC polymer and LiTFSI were dissolved in N-methyl-2-pyrrolidone to make a viscous liquid. Active material (LFP/LTO, MTI), and carbon black (Timcal SuperP) were then added in appropriate ratios and mixed using a dual asymmetric centrifugal mixer (FlackTek). Resulting slurries were doctor bladed onto either a Teflon block or current collector and then dried for about 12 hours at RT and about 24 hours at about 70° C. under vacuum. Films were rapidly transferred into a nitrogen-filled glovebox, peeled, and then cut to the appropriate size.
All electrochemical measurements were preformed using a Biologic VSP-300 potentiostat. Temperature controlled experiments utilized an Espec environmental chamber. Electrochemical impedance measurements were conducted by sandwiching polymer films in a symmetric stainless steel (SS||SS) coin cell. A Teflon spacer of about 150 μm was used to ensure no thickness change during the measurement. A frequency range of about 7 MHz to about 100 mHz with a polarization amplitude of about 50 mV was used. Temperature-dependent ionic conductivity was measured from 0 to about 70° C. with equilibration time of about 1 hour at each temperature. Strain-dependent ionic conductivity was conducted by connecting the potentiostat into the glovebox and measuring the impedance between two stainless steel disks clamped onto the stretched polymer film with a fixed amount of pressure. For other electrochemical tests, samples were transferred hermetically to an argon filled glovebox. Electrochemical stability was probed using a Li||SS cell at about 40° C. over a range of 0 to about 4 V with a scan rate of about 0.25 mV/s. Lithium transference number was calculated using a Li||Li symmetric cell at about 40° C. with a polarization of about 50 mV.
Non-stretchable battery tests were conducted using an Arbin battery cycler in 2032 coin cells. An about 2 cm2 disk of plasticized electrolyte was placed on top of a freshly scraped about 1 cm2 Li disk. An about 1 cm2 composite electrode coated onto an aluminum current collector was placed on top of the electrolyte and the stack was sealed in the coin cell.
Stretchable current collectors were fabricated by evaporating gold onto a thin (about 20 μm) film of SLIC-3. The evaporation rate was about 8 Å s−1. The strain-dependence of electronic resistance was measured using a Keithly LCR meter with a custom-made stretch station. To make stretchable batteries, the composite electrode slurry was doctor-bladed directly onto the Au@SLIC film. Following drying, Au@SLIC+electrode slurries were transferred into the nitrogen filled glovebox. In the glovebox, the SLIC electrolyte was plasticized, and the components were assembled in the following order: Au@SLIC+LTO||SLIC electrolyte||Au@SLIC+LFP. Aluminum tabs were taped to the edge of the Au@SLIC current collectors, and the entire stack was sandwiched between two slabs of PDMS (EcoFlex DragonSkin 10 Medium) and sealed with a coating of liquid PDMS. Following overnight curing, the battery was transferred out of the glovebox and probed electrochemically. For long-term cycling measurements, stretchable battery components were sealed in coin-cells to reduce the moisture permeability. Typical stretchable batteries had an active material area of about 1 cm2. For the LED demonstration, two stretchable batteries with an active material area of about 1 cm2 were connected in parallel after sealing in PDMS.
As used herein, the singular terms “a,” “an,” and “the” may include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to an object may include multiple objects unless the context clearly dictates otherwise.
As used herein, the terms “substantially,” “substantial,” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can refer to instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. When used in conjunction with a numerical value, the terms refer to a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.
As used herein, the term “size” refers to a characteristic dimension of an object. Thus, for example, a size of an object that is spherical can refer to a diameter of the object. In the case of an object that is non-spherical, a size of the non-spherical object can refer to a diameter of a corresponding spherical object, where the corresponding spherical object exhibits or has a particular set of derivable or measurable characteristics that are substantially the same as those of the non-spherical object. When referring to a set of objects as having a particular size, it is contemplated that the objects can have a distribution of sizes around the particular size. Thus, as used herein, a size of a set of objects can refer to a typical size of a distribution of sizes, such as an average size, a median size, or a peak size.
Additionally, amounts, ratios, and other numerical values are sometimes presented herein in a range format. It is to be understood that such range format is used for convenience and brevity and should be understood flexibly to include numerical values explicitly specified as limits of a range, but also to include all individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly specified. For example, a ratio in the range of about 1 to about 200 should be understood to include the explicitly recited limits of about 1 and about 200, but also to include individual ratios such as about 2, about 3, and about 4, and sub-ranges such as about 10 to about 50, about 20 to about 100, and so forth.
While the disclosure has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the true spirit and scope of the disclosure as defined by the appended claims. In addition, many modifications may be made to adapt a particular situation, material, composition of matter, method, operation or operations, to the objective, spirit and scope of the disclosure. All such modifications are intended to be within the scope of the claims appended hereto. In particular, while certain methods may have been described with reference to particular operations performed in a particular order, it will be understood that these operations may be combined, sub-divided, or re-ordered to form an equivalent method without departing from the teachings of the disclosure. Accordingly, unless specifically indicated herein, the order and grouping of the operations are not a limitation of the disclosure.
This application claims the benefit of U.S. Provisional Application No. 62/794,481, filed Jan. 18, 2019, the contents of which are incorporated herein by reference in their entirety.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2020/014071 | 1/17/2020 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62794481 | Jan 2019 | US |
