Lithium iron phosphate positive electrode and preparation method and application thereof
By constructing a highly efficient conductive network using graphene and carbon nanotube composite conductive agents, the problem of insufficient loading of cathode materials in lithium-ion batteries was solved, resulting in lithium-ion batteries with high energy density and stability, simplifying the manufacturing process and improving production efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGZHOU GREAT POWER ENERGY & TECH CO LTD
- Filing Date
- 2026-02-10
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies struggle to increase the active material loading of cathode materials in lithium-ion batteries, resulting in insufficient battery energy density and complex manufacturing processes with low production efficiency.
A composite conductive agent of graphene and carbon nanotubes is used to replace the traditional powdered conductive agent, thereby constructing a highly efficient conductive network, increasing the active material loading of the lithium iron phosphate cathode, and simplifying the preparation process. By pre-preparing the slurry and mixing it with the adhesive, material agglomeration is avoided, and uniform mixing of materials is achieved.
It improves the active material loading and conductivity of lithium iron phosphate cathodes, enhances the energy density and stability of lithium-ion batteries, simplifies the manufacturing process, and improves production efficiency.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of battery technology, and particularly relates to a lithium iron phosphate cathode, its preparation method, and its application. Background Technology
[0002] Lithium-ion batteries need to continuously improve their energy density while meeting safety and other comprehensive technical requirements. The basic approach is to continuously develop combinations of high-energy-density battery materials and optimize cell design and manufacturing processes. Therefore, it is essential to provide an optimized method for manufacturing high-load lithium-ion batteries to improve cell energy density and optimize related manufacturing processes.
[0003] Currently, the main methods for developing high specific energy density technologies include: 1) increasing the surface density of the cathode coating and increasing the usable space through cathode compaction. However, the compaction density of cathode materials is currently difficult to improve effectively and cannot reach 2.7 g / cm³. 3 The method requires high electrode toughness and high strength in the winding process; 2) Reduce the amount and proportion of auxiliary materials used in the positive electrode feeding process, such as reducing the content of conductive agent or binder to increase the loading of positive electrode active material, thereby achieving high specific energy. However, in this method, if the content of conductive agent is insufficient, a conductive network cannot be formed, the electrode conductivity decreases, and the internal resistance increases. Although the loading of active material is increased, its effective utilization rate decreases, leading to incomplete capacity release. If the content of binder is insufficient, the electrode is prone to detachment during the volume change process of charging and discharging, resulting in separation of active material from current collector. Therefore, in the current scheme, the content of conductive agent needs to be above 1.5%, and the content of binder needs to be above 2% to maintain the positive electrode material skeleton. Consequently, the maximum ratio of positive electrode active material is only about 96%, which cannot be further increased.
[0004] In addition, regarding the homogenization process of the positive electrode in manufacturing, the existing technology still uses a dual planetary mixer to dry mix the active material and auxiliary materials, add adhesive to knead, and then stir vigorously to make pulp and adjust viscosity. The disadvantages of this technology are that the process is more complex and the pulp production efficiency is low. Summary of the Invention
[0005] In order to overcome at least one of the problems existing in the prior art, one of the objectives of the present invention is to provide a lithium iron phosphate cathode, which has a high cathode active material loading and produces a battery with high energy density, good conductivity, and good stability.
[0006] The second objective of this invention is to provide a method for preparing the above-mentioned lithium iron phosphate cathode.
[0007] The third objective of this invention is to provide a lithium-ion battery.
[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A first aspect of the present invention provides a lithium iron phosphate cathode, the lithium iron phosphate cathode comprising a cathode active layer; the cathode active layer comprising the following components by mass percentage: 97-98% lithium iron phosphate, 0.2-0.5% composite conductive agent, and 1.5-2.5% polyvinylidene fluoride; the composite conductive agent comprising graphene and carbon nanotubes; the mass ratio of graphene to carbon nanotubes being 1:(0.1-0.5); and the D50 particle size of the graphene being 1-3 μm.
[0009] Existing formulations often include positive electrode active materials, conductive agents, dispersants, CNTs, PVDF, etc., with binder content around 2% and positive electrode active material content between 95% and 96%. Furthermore, the addition of conductive agents and other auxiliary materials typically further reduces the active material ratio. Traditional electrodes require the addition of conductive agents such as carbon black, but these materials have low bulk density. Therefore, this invention does not include powdered conductive agents or other related additives. Instead, it utilizes a combination of sheet-like graphene and tubular carbon nanotubes to construct a highly efficient conductive network. The conductivity of graphene (approximately 10⁻⁶) is... 6 The S / m ratio is much higher than that of carbon black, thereby reducing the volume ratio of inactive materials and further increasing the loading of active materials in the lithium iron phosphate cathode to 97~98%. The resulting lithium iron phosphate cathode has good conductivity and low impedance, resulting in lithium-ion batteries with high capacity, high energy density and stable voltage platform.
[0010] In some embodiments of the present invention, the mass ratio of graphene to carbon nanotube is 1:(0.15~0.4); in some specific embodiments of the present invention, the mass ratio of graphene to carbon nanotube is 1:(0.2~0.3).
[0011] In some embodiments of the present invention, the compaction density of the positive electrode active layer is 2.6~2.7 g / cm³. 3 .
[0012] In some embodiments of the present invention, the lithium iron phosphate cathode further includes a cathode current collector; specifically, the cathode current collector is stacked with the cathode active layer.
[0013] In some embodiments of the present invention, the thickness of the positive current collector is 10~20μm.
[0014] In some embodiments of the present invention, the positive current collector is made of carbon-coated aluminum foil.
[0015] A second aspect of the present invention provides a method for preparing a lithium iron phosphate cathode as described in the first aspect of the present invention, comprising the following steps: mixing lithium iron phosphate, a composite conductive agent, polyvinylidene fluoride and a solvent to prepare a cathode slurry; and drying the cathode slurry to form a cathode active layer, thereby obtaining the lithium iron phosphate cathode.
[0016] In some embodiments of the present invention, the positive electrode slurry is applied to a positive electrode substrate, and after drying and compaction, a positive electrode active layer is formed; the areal density of the positive electrode slurry applied to the positive electrode substrate is 422~435 g / m³. 2 .
[0017] In some embodiments of the present invention, the composite conductive agent and the polyvinylidene fluoride are first mixed with a solvent to prepare a conductive slurry and a polyvinylidene fluoride adhesive; then, lithium iron phosphate, the conductive slurry and the polyvinylidene fluoride adhesive are mixed to prepare a positive electrode slurry.
[0018] The above preparation process eliminates the need for a dry material mixing step, which shortens the preparation time. Furthermore, since the slurry and adhesive are prepared in advance, the materials can be mixed more uniformly, avoiding material agglomeration. Even if there are slight quality differences in the raw materials, a slurry that meets the requirements can still be produced. The positive electrode slurry prepared by the above method has good fluidity and few bubbles, which is conducive to obtaining a positive electrode active layer with uniform thickness and a smooth surface.
[0019] In some embodiments of the present invention, the solid content of the conductive paste is 4-8 wt%; in some embodiments of the present invention, the solid content of the conductive paste is 5-7 wt%.
[0020] A third aspect of the present invention provides a lithium-ion battery, wherein the positive electrode of the lithium-ion battery is the lithium iron phosphate positive electrode described in the first aspect of the present invention, or the lithium iron phosphate positive electrode prepared by the preparation method described in the second aspect of the present invention.
[0021] In some embodiments of the present invention, the negative electrode of the lithium-ion battery comprises a stacked negative electrode current collector and a negative electrode active layer; the negative electrode active layer comprises the following components in mass percentage: 96-97% carbon-coated artificial graphite, 0.6-1% conductive carbon black, 2-2.5% polyacrylic acid, and 0.5-1% styrene-butadiene rubber.
[0022] In some embodiments of the present invention, the negative electrode of the lithium-ion battery is prepared by applying a negative electrode slurry onto a negative electrode current collector, drying and compacting it; the negative electrode slurry contains a solvent and various components of the negative electrode active layer.
[0023] In some embodiments of the present invention, the areal density of the negative electrode slurry applied on the negative electrode substrate is 207~217 g / m³. 2 .
[0024] In some embodiments of the present invention, the negative electrode current collector is a copper foil.
[0025] In some embodiments of the present invention, the thickness of the negative electrode current collector is 4~8 μm.
[0026] In some embodiments of the present invention, the compaction density of the negative electrode active layer is 1.45~1.52 g / cm³. 3 .
[0027] In some embodiments of the present invention, the electrolyte of the lithium-ion battery comprises the following components by mass percentage: 10-14% lithium hexafluorophosphate, 4-6% lithium difluorosulfonylimide, 4-8% additives, and 80-85% solvent; the additives comprise the following components by mass percentage: 2-5% vinylene carbonate, 1.5-2% fluorovinyl carbonate, and 0.5-1% ethylene sulfate; the solvent comprises ethylene carbonate, methyl ethyl carbonate, and dimethyl carbonate; the mass ratio of ethylene carbonate, methyl ethyl carbonate, and dimethyl carbonate is 1:(0.5-1.5):(0.5-1.5).
[0028] In some embodiments of the present invention, the separator of the lithium-ion battery is a polyolefin-ceramic composite separator; in some specific embodiments of the present invention, the separator of the lithium-ion battery is composed of a 7μm PE layer, a 2μm ceramic layer, a 1μm PVDF layer and a 1μm PVDF layer.
[0029] In some embodiments of the present invention, the separator thickness of the lithium-ion battery is 10~12μm.
[0030] The beneficial effects of this invention are: This invention uses graphene of a specific particle size and carbon nanotubes in a certain compound ratio to form a composite conductive agent, which has excellent conductivity. A small amount of addition can build a highly efficient conductive network, thereby reducing the volume ratio of inactive materials. The lithium iron phosphate cathode prepared using this composite conductive agent has the advantages of high loading of positive electrode active material and high compaction density, and can be used to prepare lithium-ion batteries with high energy density. Attached Figure Description
[0031] Figure 1 This is a flowchart of the preparation process of the positive electrode slurry in Example 1.
[0032] Figure 2 This is a scanning electron microscope image of the graphene used in Example 1.
[0033] Figure 3 Electrochemical impedance spectroscopy of cells used in Application Example 1 and Comparative Example 2.
[0034] Figure 4The graphs show the 1C / 1C room temperature cycling test results of the batteries in Application Example 1 and Application Comparative Example 1.
[0035] Figure 5 The graphs show the 1C / 1C high-temperature cycling test results of the batteries in Application Example 1 and Application Comparative Example 1. Detailed Implementation
[0036] The following specific embodiments further illustrate the content of the present invention in detail. It should also be understood that the following embodiments are only for further explanation of the present invention and should not be construed as limiting the scope of protection of the present invention. Non-essential improvements and adjustments made by those skilled in the art based on the principles described herein are all within the scope of protection of the present invention. The specific process parameters, etc., in the following examples are merely examples within a suitable range; that is, those skilled in the art can make selections within a suitable range based on the description herein, and are not intended to be limited to the specific data in the examples below. Unless otherwise specified, the raw materials, reagents, or apparatus used in the following embodiments and comparative examples can be obtained from conventional commercial sources or by existing known methods.
[0037] Example 1 A lithium iron phosphate cathode comprises a 13 μm thick carbon-coated aluminum foil and a cathode active layer coated on the carbon-coated aluminum foil. The cathode active layer, by mass percentage, comprises: 97.6% lithium iron phosphate (LFP), 0.4% composite conductive agent, and 2% polyvinylidene fluoride (PVDF); the composite conductive agent is composed of graphene and carbon nanotubes in a mass ratio of 4:1.
[0038] The preparation process steps of the above-mentioned lithium iron phosphate cathode are as follows: (1) Preparation of positive electrode slurry: The process flow diagram for the preparation of positive electrode slurry is as follows. Figure 1 As shown, (A) represents step 1, and (B) represents steps 2-4; the specific steps are as follows: Step 1: Mix the PVDF adhesive with the NMP solvent and homogenize to obtain the PVDF adhesive solution; Step 2: Mix the positive electrode active material LFP, 60% of the total mass of PVDF adhesive (obtained in Step 1), and solvent NMP to wet the positive electrode powder. The amount of NMP added should be adjusted according to the actual condition of the slurry. Step 3: Mix the composite conductive agent with NMP to prepare a graphene conductive slurry with a solid content of 6wt% in advance; add the remaining 40% PVDF adhesive (prepared in Step 1) and the graphene conductive slurry to the slurry in Step 2 for homogenization and uniform mixing. Step 4: Add the remaining NMP to the slurry and stir vigorously. After the viscosity at the outlet is qualified, sieve to obtain the positive electrode slurry. The amount of solvent NMP is set according to the required solid content of the positive electrode slurry. In this example, the solid content of the positive electrode slurry is 60±2wt%.
[0039] (2) The positive electrode slurry from step (1) is coated onto a 13 μm thick carbon-coated aluminum foil, dried, and rolled to obtain a lithium iron phosphate positive electrode. The areal density of the positive electrode slurry coating is 430 g / m². 2 .
[0040] Application Example 1 The specific manufacturing process steps for a lithium-ion battery are as follows: (1) Positive electrode: A lithium iron phosphate positive electrode was prepared according to the method in Example 1; (2) Negative electrode sheet: comprising a 6μm copper foil and a negative electrode active layer coated on the copper foil; by mass percentage, the composition of the negative electrode active layer is: 96.4% carbon-coated artificial graphite, 0.8% conductive carbon black, 2.3% polyacrylic acid, and 0.5% styrene-butadiene rubber. The negative electrode sheet is prepared by mixing the negative electrode active layer components with a solvent to form a negative electrode slurry, coating the negative electrode slurry onto the copper foil, drying, and rolling to obtain the negative electrode sheet. The coating surface density of the negative electrode slurry is 210 g / m². 2 The compaction density of the negative electrode is taken as 1.5 g / cm³. 3 .
[0041] (3) Electrolyte: The electrolyte is composed of 10% lithium hexafluorophosphate, 6% lithium difluorosulfonyl imide, 4% additives (including 2% vinylene carbonate, 1.5% fluoroethylene carbonate, and 0.5% ethylene sulfate) and 80% solvent by mass percentage. The solvent is ethylene carbonate, methyl ethyl carbonate and dimethyl carbonate in a mass ratio of 1:1.3:0.5.
[0042] (4) Separator: 7+2+1+1 ceramic coated separator (specifically composed of 7μm PE layer, 2μm ceramic layer, 1μm PVDF layer and 1μm PVDF layer), with a total thickness of 11μm.
[0043] (5) The above positive electrode, negative electrode and separator are wound into a core, and then assembled, baked, injected with liquid for the first time, aged at high temperature, formed under negative pressure, injected with liquid for the second time, placed at room temperature, restrained and charged, aged at high temperature, placed at room temperature, capacity test and K test to obtain a lithium-ion battery.
[0044] Comparative Example 1 A lithium iron phosphate cathode comprises a 13 μm thick carbon-coated aluminum foil and a cathode active layer coated on the carbon-coated aluminum foil. The cathode active layer comprises, by mass percentage: 96.5% lithium iron phosphate (LFP), 0.5% carbon nanotubes (CNTs), 1% conductive carbon black (SP), and 2% polyvinylidene fluoride (PVDF).
[0045] The preparation process steps of the above-mentioned lithium iron phosphate cathode are as follows: (1) Preparation of positive electrode slurry: First, lithium iron phosphate and conductive carbon black are mixed, then some PVDF and some NMP are added and stirred for a certain period of time. Then, CNT, the remaining PVDF and the remaining NMP are added and mixed to obtain the positive electrode slurry. The solid content of the positive electrode slurry is 60±2wt%.
[0046] (2) Preparation of lithium iron phosphate cathode: Same as step (2) in Example 1.
[0047] Application Comparative Example 1 A lithium-ion battery differs from Application Example 1 in that the positive electrode is replaced with the lithium iron phosphate positive electrode prepared in Comparative Example 1, while all other conditions are the same as in Application Example 1.
[0048] Comparative Example 2 A lithium iron phosphate cathode differs from Example 1 in that the active layer of the cathode does not contain a composite conductive agent, while all other conditions are the same as in Example 1.
[0049] Application Comparative Example 2 A lithium-ion battery differs from Application Example 1 in that the positive electrode is replaced with the lithium iron phosphate positive electrode prepared in Comparative Example 2, while all other conditions are the same as in Application Example 1.
[0050] Performance testing (1) The lithium iron phosphate cathodes prepared in the examples and comparative examples were subjected to extreme compaction tests. The specific steps are as follows: 1) Adjust the roller pressure to a certain value (the pressure causes a large change in thickness), and adjust the roller gap distance (the roller gap is for fine-tuning the thickness). 2) Adjust the roll gap according to the actual thickness, setting the roll gap from large to small, while the thickness also decreases from large to small. 3) Take a 1256.64mm round piece from the left, center, and right sides of the electrode sheet after the rollers along the TD direction. 2 The thickness t1 and weight m1 of the disc were measured, and the disc measured 1256.64 mm. 2 Given the weight of the empty foil (m2) and its thickness (t2), calculate the actual compaction density using the following formula: PD = (m1 - m2) / [1256.64 × (t1 - t2)] × 10 9 .
[0051] 4) After the electrode compaction test is completed, its elongation is measured. The elongation test is to take an electrode with a length of 80cm~1m, measure the length of the electrode before and after rolling, and record them as L1 and L2 respectively. The calculation formula is: elongation = (L2-L1) / L1.
[0052] (2) The lithium-ion batteries prepared by the application example and the application comparison example were subjected to a 1P / 1P constant capacity test at room temperature (25°C).
[0053] (3) The lithium-ion batteries prepared by the application examples and the application comparison examples were subjected to EIS electrochemical impedance spectroscopy tests.
[0054] (4) The lithium-ion batteries prepared in the application examples and application comparison examples were subjected to 1C / 1C room temperature (25°C) cycle test and 1C / 1C high temperature (45°C) cycle test.
[0055] Table 1. Ultimate compaction test results of the cathodes of Example 1 and Comparative Example 1
[0056] As shown in Table 1, in both Example 1 and the Comparative Example, the ultimate compaction roller pressure and roller gap were adjusted to the maximum. After compaction, the Comparative Example 1 achieved 2.5 fold light transmission, while Example 1 achieved 3 fold light transmission, with one positive and one negative side accounting for 1 fold. Compared to Comparative Example 1, Example 1 can increase the positive electrode active material loading by 1.1% and can also increase the ultimate compaction density of the positive electrode material.
[0057] Furthermore, in the preparation process of the positive electrode slurry in Example 1, the dry material mixing process is directly eliminated compared to the traditional process, which can shorten the dry material mixing time, improve production efficiency, and shorten the preparation time by about 30 minutes. Because a slurry and a binder are used, the materials can be mixed more uniformly, avoiding material agglomeration. Even with slight quality differences in the raw materials, a slurry that meets the requirements can be produced. The positive electrode slurry prepared by the method in Example 1 has good fluidity and few bubbles, which is beneficial for obtaining a positive electrode active layer with uniform thickness and a smooth surface.
[0058] In Example 1, a pre-prepared 6wt% solid-content graphene conductive paste, PVDF adhesive, and NMP solvent were used to wet and mix the active material LFP main material powder. The specific mixing order can be replaced and controlled. For example, the LFP powder can be mixed with the graphene conductive paste, some solvent, and binder, and then the remaining binder and solvent can be added. The preparation effect is the same as in Example 1.
[0059] Table 2. Capacity data of 1P / 1P cells for Application Example 1 and Application Comparison Example 1
[0060] As can be seen from Table 2, the lithium-ion battery prepared by Application Example 1 of the present invention has a higher energy density than Application Comparative Example 1, which shows that the positive electrode material prepared by Example 1 can increase the proportion of positive electrode active material, significantly improve the capacity and energy density of the cell, and the voltage plateau of the battery is not affected.
[0061] Figure 2 This is a scanning electron microscope (SEM) image of the graphene used in Example 1. It can be seen that the graphene has a sheet-like structure with a sheet diameter (D50) of 1-3 μm.
[0062] Figure 3 The electrochemical impedance spectroscopy (EIS) of the cells in Application Example 1 and Comparative Application Example 2 is shown. It can be seen that, compared to Comparative Application Example 2 without the addition of the graphene and carbon nanotube composite conductive agent, the addition of 0.4% composite conductive agent (composed of graphene and carbon nanotubes) to the positive electrode of Application Example 1 effectively reduced the charge transfer impedance.
[0063] Figure 4 The graphs show the 1C / 1C room temperature cycling test results of the batteries in Application Example 1 and Application Comparative Example 1. Figure 5 The graphs show the 1C / 1C high-temperature cycling test results of the batteries in Application Example 1 and Comparative Example 1. From... Figures 4-5 As can be seen, the battery of Application Example 1 of this invention has a 1C / 1C room temperature cycle count trend of up to 3000 cycles and a 1C / 1C high temperature cycle count trend of up to 1500 cycles. Its room temperature cycle performance and high temperature cycle performance are both better than those of the battery of Application Comparative Example 1.
[0064] In summary, this invention uses graphene of a specific particle size and carbon nanotubes in a certain compound ratio to form a composite conductive agent, which has excellent conductivity. A small amount of the composite conductive agent can be added to build a highly efficient conductive network, thereby reducing the volume ratio of inactive materials. The lithium iron phosphate cathode prepared using this composite conductive agent has the advantages of high loading of positive electrode active material and high compaction density, and can be used to prepare lithium-ion batteries with high energy density.
Claims
1. A lithium iron phosphate cathode, characterized in that, The lithium iron phosphate cathode includes a cathode active layer; the cathode active layer comprises the following components by mass percentage: 97-98% lithium iron phosphate, 0.2-0.5% composite conductive agent, and 1.5-2.5% polyvinylidene fluoride; the composite conductive agent comprises graphene and carbon nanotubes; the mass ratio of graphene to carbon nanotubes is 1:(0.1-0.5); the D50 particle size of the graphene is 1-3 μm.
2. The lithium iron phosphate cathode according to claim 1, characterized in that, The compaction density of the positive electrode active layer is 2.6~2.7 g / cm³. 3 .
3. The lithium iron phosphate cathode according to claim 1, characterized in that, The lithium iron phosphate cathode also includes a cathode current collector; the thickness of the cathode current collector is 10~20μm.
4. A method for preparing a lithium iron phosphate cathode as described in any one of claims 1 to 3, characterized in that, The process includes the following steps: mixing lithium iron phosphate, a composite conductive agent, polyvinylidene fluoride, and a solvent to prepare a positive electrode slurry; drying the positive electrode slurry to form a positive electrode active layer, thereby obtaining the lithium iron phosphate positive electrode.
5. The preparation method according to claim 4, characterized in that, The positive electrode slurry is applied to the positive electrode substrate, and after drying and compaction, it forms the positive electrode active layer; the areal density of the positive electrode slurry applied to the positive electrode substrate is 422~435 g / m³. 2 .
6. The preparation method according to claim 4, characterized in that, First, the composite conductive agent and the polyvinylidene fluoride are mixed with solvents to prepare a conductive slurry and a polyvinylidene fluoride adhesive; then, lithium iron phosphate, the conductive slurry and the polyvinylidene fluoride adhesive are mixed to prepare a positive electrode slurry.
7. The preparation method according to claim 6, characterized in that, The solid content of the conductive paste is 4~8wt%.
8. A lithium-ion battery, characterized in that, The positive electrode of the lithium-ion battery is a lithium iron phosphate positive electrode according to any one of claims 1 to 3, or a lithium iron phosphate positive electrode prepared by any one of claims 4 to 7.
9. The lithium-ion battery according to claim 8, characterized in that, The negative electrode of the lithium-ion battery includes a negative electrode current collector and a negative electrode active layer; the negative electrode active layer includes the following components by mass percentage: 96~97% carbon-coated artificial graphite, 0.6~1% conductive carbon black, 2~2.5% polyacrylic acid, and 0.5~1% styrene-butadiene rubber.
10. The lithium-ion battery according to claim 8, characterized in that, The electrolyte of the lithium-ion battery comprises the following components by mass percentage: 10-14% lithium hexafluorophosphate, 4-6% lithium difluorosulfonylimide, 4-8% additives, and 80-85% solvent; the additives comprise the following components by mass percentage: 2-5% vinylene carbonate, 1.5-2% fluorovinyl carbonate, and 0.5-1% ethylene sulfate; the solvent comprises ethylene carbonate, methyl ethyl carbonate, and dimethyl carbonate; the mass ratio of ethylene carbonate, methyl ethyl carbonate, and dimethyl carbonate is 1:(0.5-1.5):(0.5-1.5).