A photo-crosslinked polyacrylic acid-based aqueous adhesive and its preparation method and application

Abstract

The present invention belongs to the technical field of lithium ion batteries, and discloses a photocrosslinked polyacrylic acid-based aqueous binder and its preparation method and application. The polyacrylic acid-based aqueous binder is abbreviated as AA-MEA-CMCS / DES, and choline chloride and urea are dissolved in deionized water, and stirred in a water bath at 80-90°C to form a low eutectic solvent. Acrylic acid monomer and ethanolamine monomer are added and stirred, and then a photoinitiator and carboxymethyl chitosan are added and stirred until completely dissolved. The above mixed solution is irradiated with a mixed light source of 395nm and 365nm. The binder has excellent water solubility, ionic conductivity and flexibility, can effectively suppress the volume expansion problem of silicon-based negative electrode during the cycle, significantly improve the cycle stability of the battery, and can be applied in the field of lithium ion batteries.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium batteries, and more specifically, relates to a photo-crosslinked polyacrylic acid-based aqueous adhesive, a preparation method thereof, and an application thereof. Background Art

[0002] Building a new energy storage system that combines high energy density, environmental friendliness, and economy is the core demand for promoting the innovation of portable electronic devices and electric vehicles. As the most competitive energy storage carrier, the continuous breakthrough of lithium-ion batteries in energy density directly determines the improvement of the endurance of terminal devices. However, commercial graphite anodes have a lithium storage capacity that is close to the theoretical limit (372 mAhg -1 ), which significantly restricts the iterative upgrade of battery performance. The development of new energy storage systems with low cost, environmental friendliness and high energy density is of great significance to the industrialization of portable electronic devices and electric vehicles. In this context, silicon-based anode materials have a very high theoretical specific capacity (~4200 mAhg -1 ) has become a very promising alternative, but the dramatic volume expansion of micron silicon during charge and discharge (~300%) can easily lead to electrode structure damage and cycle performance degradation. Therefore, the same high theoretical specific capacity (~2600 mAhg -1 ) and has smaller volume expansion of micron SiO x The negative electrode has become one of the most promising candidate materials. However, SiO x The inherent volume expansion of anodes remains a major challenge hindering their large-scale commercial application. In previous studies, researchers have used various strategies such as nanoengineering, coating, and efficient bonding design to buffer volume expansion and improve the electrochemical performance of silicon-based anodes. However, the complex manufacturing process in nanoengineering and the capacity sacrifice caused by coating have caused concerns about increased costs and reduced capacity. In this context, the development of efficient binder systems with multiple functional properties is seen as a feasible solution to the problem of structural instability of silicon-based anodes.

[0003] As the link that tightly connects the electrode material and the current collector, the binder determines the mechanical structural stability of the entire electrode. The ideal silicon-based negative electrode binder not only has strong mechanical properties, but more importantly, it is compatible with the active material. The specific requirements are as follows: (1) It has an excellent ion conduction network to compensate for the intrinsic conductivity defects of the silicon material; (2) It forms a strong interface adhesion with the active particles to ensure the deformation resistance of the electrode structure; (3) It establishes an efficient stress dissipation mechanism to buffer the volume change during the cycle; (4) It maintains a stable interface with the current collector. Existing research has accelerated lithium ion transmission by constructing coordination bonds through functional group design (such as ether groups in PEO and amino groups in PEI), or introduced polar groups such as hydroxyl and carboxyl groups to enhance covalent bonds or van der Waals interface bonding, and even used novel concepts such as self-healing and dynamic cross-linking to improve the stability of the binder. However, these systems are generally limited to the optimization of a single performance and it is difficult to meet the balance between multiple requirements. Summary of the Invention

[0004] In order to solve the above-mentioned deficiencies and shortcomings of the prior art, the present invention aims to provide a photo-crosslinked polyacrylic acid-based aqueous adhesive, which is a novel adhesive system based on photo-crosslinking and molecular cooperative assembly strategy. x A three-dimensional adaptive network structure is constructed within the negative electrode. This binder not only optimizes the ion conduction path and dissipates mechanical stress, but also dynamically repairs electrode interface damage through multiple intermolecular forces.

[0005] Another object of the present invention is to provide a method for preparing the aforementioned photocrosslinked polyacrylic acid-based aqueous binder. This method uses choline chloride and urea as raw materials to prepare a deep eutectic solvent. Acrylic acid and ethanolamine monomers, along with a photoinitiator and carboxymethyl chitosan, are then added. Ultraviolet light is used to initiate crosslinking to form a stable polymer network structure.

[0006] Another object of the present invention is to provide an application of the above-mentioned photo-crosslinked polyacrylic acid-based water-based adhesive.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A photo-crosslinked polyacrylic acid-based water-based adhesive, abbreviated as AA-MEA-CMCS / DES, is prepared by dissolving choline chloride and urea in deionized water, stirring in a water bath at 80-90°C to form a deep eutectic solvent (DES), adding acrylic acid monomer (AA) and ethanolamine monomer (MEA) and stirring, then adding a photoinitiator and carboxymethyl chitosan (CMCS) and stirring until completely dissolved. The mixed solution is then irradiated with a mixed light source of 395nm and 365nm to produce the adhesive.

[0009] Preferably, the molar ratio of the choline chloride to the urea is 2:1; the mass ratio of the total mass of the choline chloride and urea to deionized water is 1:(4-8); the photoinitiator is 2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone (photoinitiator I2959); the photoinitiator is 0.1-0.5wt% of the total mass of the acrylic acid monomer and the monoethanolamine monomer; the carboxymethyl chitosan is 0.3-0.5wt% of the total mass of the acrylic acid monomer and the monoethanolamine monomer; and the mass ratio of the low eutectic solvent, the acrylic acid monomer and the ethanolamine monomer is 8.37:(3-4):1.

[0010] Preferably, the irradiation time is 1 to 2 h.

[0011] The preparation method of the photo-crosslinked polyacrylic acid-based aqueous adhesive comprises the following steps:

[0012] S1. Dissolve choline chloride and urea in deionized water and stir in a water bath at 80-90°C to form a homogeneous deep eutectic solvent.

[0013] S2. The acrylic acid monomer and ethanolamine monomer were added to a deep eutectic solvent and stirred, and then a photoinitiator and carboxymethyl chitosan were added and stirred until completely dissolved to obtain a mixed solution;

[0014] S3. The mixed solution was transferred to a UV lamp and irradiated with a mixed light source of 395 nm and 365 nm to prepare a polyacrylic acid-based water-based adhesive.

[0015] Preferably, the stirring time in step S1 is 90 to 120 minutes.

[0016] Application of the photo-crosslinked polyacrylic acid-based aqueous binder in lithium-ion batteries.

[0017] Preferably, the negative electrode material of the lithium ion battery is SiO x , 0 <x<2。

[0018] This paper constructs a water-based conductive adhesive (AA-MEA-CMCS / DES) with an innovative structure in a deep eutectic solvent (DES) environment through photocrosslinking and electrostatic / hydrogen bond self-assembly strategies. During the molecular network construction process of the adhesive, acrylic acid monomer (AA) is polymerized by UV light to form a three-dimensional skeleton structure. This crosslinked network gives the material the necessary mechanical strength and can effectively resist SiO xThe volume change stress generated by the negative electrode during the charge and discharge process. At the same time, the introduction of ethanolamine monomer (MEA) not only provides elastic links, but its hydroxyl group (–OH) also forms an extensive hydrogen bond network with the carboxyl group of carboxymethyl chitosan (CMCS) and the DES component. This dynamic and reversible secondary bonding gives the material significant flexibility and energy dissipation capabilities. The abundant polar groups on the AA-MEA-CMCS / DES molecular chain can also react with SiO x The Si–OH bonds on the surface of the negative electrode material form supramolecular interactions. This chemical bonding mechanism significantly enhances the interfacial bonding strength between the binder and the silicon oxide particles. In addition, DES plays multiple key roles in this system. Its inherent ionic conductivity and the carboxylate (–COO) on the CMCS molecular chain - ) and protonated amino groups (–NH 3+ ) and other charged groups work together to build an efficient lithium ion transmission channel, which increases the ionic conductivity (σ) by three orders of magnitude. x A protective layer is formed on the surface of the negative electrode, which can effectively inhibit the decomposition reaction of the electrolyte.

[0019] The electrode preparation and battery assembly process of the binder of the present invention are as follows: silicon oxide material (SiO x ) as the active material, mixed with conductive carbon black (Super P) and the aforementioned binders in a mass ratio of (7-8):(1-2):1. Deionized water was added, degassed, and stirred to form a uniform slurry. The slurry was evenly coated onto a copper foil current collector, vacuum-dried at 80°C for 12 hours, and then punched into 14 mm diameter disc electrodes. The battery was assembled in an argon-protected glove box. A metallic lithium sheet was used as the counter electrode. The electrolyte system consisted of 1 M LiPF₆ dissolved in an EC / DEC (1:1 v / v) solvent mixture, with 10% FEC and 1% VC added as film-forming additives. CR2032 coin cells were ultimately used for packaging testing.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] The binder of the present invention has excellent water solubility, ionic conductivity and flexibility, can effectively suppress the volume expansion problem of the silicon-based negative electrode during the cycle process, and significantly improve the cycle stability of the battery.

[0022] The SiO xDuring the UV-light cross-linking process of the negative electrode binder, polyacrylic acid (PAA) formed through photopolymerization of acrylic acid provides a stable three-dimensional skeleton structure for the entire binder system through its rigid molecular backbone. Simultaneously, the introduction of the hydroxyethyl flexible chain segment (–CH2–CH2–OH) in the ethanolamine molecule significantly improves the flexibility and deformation resistance of the molecular network. Furthermore, the abundant polar functional groups, such as hydroxyl and carboxyl groups, in carboxymethyl chitosan not only form multiple hydrogen bonds with the silicon-based active material but also produce synergistic cross-linking with the PAA network, significantly enhancing the binder's interfacial adhesion properties.

[0023] The SiO x The unique advantages of negative electrode binders in ion transport stem primarily from structural features such as the high free ion concentration and continuous ion migration pathways within the DES. Furthermore, the abundant polar functional groups (such as –NH2, –OH, and –COOH) within the CMCS molecule can form multiple hydrogen bond networks with DES components, providing ordered pathways for ion transport. This leads to efficient ion and electron transport within the polymer network, ultimately significantly improving the ionic conductivity of the binder system.

[0024] The SiO x The negative electrode binder is prepared by photocrosslinking, the synthesis process is simple and easy, and the three-dimensional crosslinked network gives it excellent mechanical adaptability to buffer the SiO x The volume expansion effect of the material and the rich polar groups ensure high-strength adhesion with the current collector and active materials, while the introduction of the deep eutectic solvent provides an efficient channel for lithium ion conduction. These characteristics can better withstand SiO x The volume change during the charge and discharge process of the electrode contributes to the x The structural integrity of the electrode during cycling, thereby improving the SiO x Negative electrode cycling stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 4. FTIR spectra of choline chloride, urea, and the deep eutectic solvent (DES) formed by the choline chloride, urea, and the urea in Example 1;

[0026] Figure 2 FTIR spectra of acrylic acid monomer (AA), ethanolamine monomer (MEA), carboxymethyl chitosan (CMCS), deep eutectic solvent (DES) and AA-MEA-CMCS / DES polymer binder in Application Example 1;

[0027] Figure 3 The figure is a rate performance diagram of button batteries prepared in Application Example 1 and Comparative Examples 1-2;

[0028] Figure 4 For application example 1 at 500 mA g -1 Comparison of the cycle performance of button batteries prepared in Example 1-2 under current density. DETAILED DESCRIPTION

[0029] The present invention will be further described below in conjunction with specific examples, but should not be construed as limiting the present invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art. Unless otherwise specified, the reagents, methods and equipment used in the present invention are conventional reagents, methods and equipment in the art.

[0030] The acrylic acid monomer used in the examples of the present invention has a purity of >99%; the ethanolamine monomer has a purity of >99%; and the degree of substitution of carboxymethyl chitosan is >80% (ACS, an analytical reagent that complies with the standards of the American Chemical Society). The photoinitiator 2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone (photoinitiator I2959) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. Example

[0031] 5.58 g of choline chloride and 4.8 g of urea were dissolved in 50 g of deionized water, and stirred continuously in a water bath at 80° C. for 90 min to fully dissolve and form a uniform deep eutectic solvent (DES).

[0032] 3.73 g of acrylic acid monomer (AA) and 1.24 g of ethanolamine monomer (MEA) were added to the above-mentioned deep eutectic solvent and stirred until the monomers were fully dispersed in the solvent to obtain a mixed solution;

[0033] 0.01 g of photoinitiator 2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone (photoinitiator I2959) and 0.311 g of carboxymethyl chitosan were added to the mixed solution obtained in step 1 and stirred until completely dissolved to ensure the uniformity and efficiency of the subsequent photocrosslinking reaction. The mixed solution was transferred to an ultraviolet lamp and irradiated with a mixed light source of 395 nm and 365 nm for 1 hour to obtain a polyacrylic acid-based water-based adhesive.

[0034] Figure 1 The Fourier transform infrared spectra of choline chloride (Choline Chloride), urea (Urea) and the deep eutectic solvent (DES) formed by the two in Example 1 are shown in FIG. Figure 1 It can be seen that 1676cm in the urea molecule -1 The C=O stretching vibration peak at 1610 cm-1 is red-shifted to 1610 cm-1 in DES. -1 , accompanied by 960cm -1 Choline chloride quaternary ammonium salt group CN +The intensity of the vibration peak weakens, revealing the formation of the DES solution. Figure 2 The Fourier infrared spectrogram of the acrylic monomer (AA), ethanolamine monomer (MEA), carboxymethyl chitosan (CMCS), deep eutectic solvent (DES), and AA-MEA-CMCS / DES polymer binder for Example 1 is as Figure 2 shown. In terms of the photopolymerization reaction system, it shows that the C=C stretching vibration peak at 1630 cm -1 and the =C–H bending vibration peak at 810 cm -1 in the acrylic monomer (AA) completely disappear after the reaction. At the same time, a characteristic CH2 bending vibration peak of the polyacrylic acid (PAA) main chain appears at 1452 cm -1 . This series of changes provides conclusive evidence for the ultraviolet light-induced double bond cleavage and polymerization reaction of acrylic acid. At the same time, the systematic displacement of the characteristic peaks of each component's functional groups further confirms the existence of various supramolecular interactions between the components.

[0035] Application Example 1

[0036] Mix the active material SiO x (0 < x < 2), conductive agent Super P, and the polyacrylic acid-based binder AA-MEA-CMCS / DES of Example 1 in a mass ratio of 7:2:1. After adding 600 - 800 mL of deionized water, put it into a defoamer and stir for 20 - 30 min to obtain a uniformly dispersed slurry. Coating the obtained slurry onto a copper foil, after vacuum drying at 80 °C for 12 h, cut it into circular electrode sheets with a diameter of 14 mm, denoted as AA-MEA-CMCS / DES@SiO x electrode sheets. Transfer these electrode sheets into a glove box filled with argon for battery assembly. In the battery, a lithium sheet is used as the counter electrode, the electrolyte uses 1 mol / L LiPF6 as the solute, and ethylene carbonate (EC) and diethyl carbonate (DEC) with a volume ratio of 1:1 as the solvent. Among them, 10 wt% fluoroethylene carbonate (FEC) and 1 wt% vinylene carbonate (VC) are used as additives, and a CR2032 coin cell is assembled.

[0037] Comparative Example 1

[0038] Dissolve 5.58 g of choline chloride and 4.8 g of urea in 50 g of deionized water, and continuously stir in a water bath at 80 °C for 90 min to ensure complete dissolution and form a uniform deep eutectic solvent (DES).

[0039] Add 3.73 g of acrylic monomer (AA) and 1.24 g of ethanolamine monomer (MEA) to the above deep eutectic solvent (DES) and continue to stir evenly to make the monomers fully dispersed in the solvent, obtaining a mixed solution;

[0040] 0.01 g of photoinitiator I2959 was added to the above mixed solution and stirred until completely dissolved to ensure the uniformity and efficiency of the subsequent photocrosslinking reaction. Then the mixed solution was transferred under an ultraviolet lamp and irradiated with a mixed light source of 395 nm and 365 nm for 1 h to obtain a polymer binder without carboxymethyl chitosan, denoted as AA-MEA / DES binder.

[0041] The active material SiO with a mass ratio of 7:2:1 x (0 < x < 2), conductive agent Super P and the AA-MEA / DES binder of Comparative Example 1 were mixed, 600 - 800 mL of deionized water was added, and then it was put into a defoamer and stirred for 20 - 30 min to obtain a uniformly dispersed slurry. The obtained slurry was coated on a copper foil, vacuum dried at 80 °C for 12 h, and then cut into circular electrode sheets with a diameter of 14 mm, denoted as AA-MEA / DES@SiO x electrode sheets. The electrode sheets were transferred into a glove box filled with argon for battery assembly. In the battery, a lithium sheet was used as the counter electrode, the electrolyte had 1 mol / L of LiPF6 as the solute and ethylene carbonate (EC) and diethyl carbonate (DEC) with a volume ratio of 1:1 as the solvent. Among them, 10 wt% of fluoroethylene carbonate (FEC) and 1 wt% of vinylene carbonate (VC) were used as additives, and a CR2032 coin cell was used for assembly.

[0042] Comparative Example 2

[0043] 3.73 g of acrylic acid monomer (AA) and 1.24 g of ethanolamine monomer (MEA) were dissolved in 50 g of deionized water and continuously stirred evenly to fully disperse the monomers in the solvent to obtain a mixed solution.

[0044] 0.01 g of photoinitiator (I2959) and 0.31 g of carboxymethyl chitosan were added to the mixed solution and stirred until completely dissolved to ensure the uniformity and efficiency of the subsequent photocrosslinking reaction. Then the mixed solution was transferred under an ultraviolet lamp and irradiated with a mixed light source of 395 nm and 365 nm for 1 h to obtain a polymer binder without deep eutectic solvent, denoted as AA-MEA-CMCS / H2O.

[0045] The active material SiO with a mass ratio of 7:2:1 xWhen (0 < x < 2), the conductive agent Super P is mixed with the AA-MEA / DES binder in Comparative Example 2. After adding 600 - 800 mL of deionized water, it is put into a defoaming machine and stirred for 20 - 30 min to obtain a uniformly dispersed slurry. The obtained slurry is coated on a copper foil, vacuum dried at 80 °C for 12 h, and then cut into circular electrode sheets with a diameter of 14 mm, denoted as AA-MEA-CMCS / H2O electrode sheets. These electrode sheets are transferred to a glove box filled with argon for battery assembly. In the battery, a lithium sheet is used as the counter electrode. The electrolyte uses 1 mol / L LiPF6 as the solute and ethylene carbonate (EC) and diethyl carbonate (DEC) with a volume ratio of 1:1 as the solvent. Among them, 10 wt% fluoroethylene carbonate (FEC) and 1 wt% vinylene carbonate (VC) are used as additives, and a CR2032 coin-type battery is assembled.

[0046] The coin-type batteries assembled in Application Example 1 and Comparative Examples 1 - 2 are left standing at 28 °C for 12 h and then their electrochemical performance is tested by constant current in a Neware test system. The test conditions are: current density 500 mA g -1 ; voltage window 0.1 - 1.5 V. Figure 3 is the rate performance graph of the coin-type batteries prepared in Application Example 1 and Comparative Examples 1 - 2. As can be seen from Figure 3 it that the AA-MEA-CMCS / DES@SiO x electrode sheet exhibits the most excellent rate performance. The discharge specific capacities at current densities of 0.2C, 0.5C, 1C, 2C, and 3C are 1310.46, 1178.92, 764.81, 629.79, and 369.12 mAh g -1 respectively. It is worth noting that when the current density is restored from 3C to 0.2C, its discharge specific capacity can be restored to 1349.8 mAh g -1 , showing good capacity reversibility. The rate performance of the AA-MEA / DES@SiO x electrode sheet is somewhat reduced, while the performance of the AA-MEA-CMCS / H2O@SiO x electrode sheet is the least ideal, and it can only provide discharge specific capacities of 742.36, 615.2, 403.87, 267.22, and 142.51 mAh g -1 under the same current density conditions, indicating the significant advantage of the AA-MEA-CMCS / DES binder in improving the rate performance of the electrode.

[0047] Figure 4 is the comparison graph of the cycle performance of the coin-type batteries prepared in Application Example 1 at a current density of 500 mA g -1 and Comparative Examples 1 - 2. As can be seen from Figure 4It can be seen that the electrode assembled with the AA-MEA-CMCS / DES binder of the present invention has a capacity retention rate of 87.92% after 200 cycles (after two activation cycles), and still maintains a high reversible capacity of 986.97 mAh g -1 after 320 cycles, showing excellent cycling stability. In contrast, the cycling performance of the AA-MEA / DES@SiO x electrode significantly decreases, and the discharge specific capacity is only 739.9 mAh g -1 after 190 cycles, and the capacity retention rate drops to 66.48%. The AA-MEA-CMCS / H2O@SiO x electrode shows the worst performance, and the capacity rapidly decays to 171.34 mAh g -1 after 320 cycles. The results show that the electrode assembled with the photo-crosslinked polyacrylic acid-based aqueous binder (AA-MEA-CMCS / DES) of the present invention exhibits excellent cycling stability, which can effectively inhibit the volume expansion of the SiO x (0 < x < 2) anode material during the charge and discharge process of the electrode, enabling the SiO x anode to exhibit good cycling stability.

[0048] The above embodiments are the preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent substitution methods and are all included in the protection scope of the present invention.

Claims

1. A photo-crosslinked polyacrylic acid-based aqueous adhesive, characterized in that: The polyacrylic acid-based aqueous binder, abbreviated as AA-MEA-CMCS / DES, is prepared by dissolving choline chloride and urea in deionized water, stirring in a water bath at 80-90°C to form a deep eutectic solvent; then adding acrylic acid monomer and ethanolamine monomer and stirring, and then adding a photoinitiator and carboxymethyl chitosan and stirring until completely dissolved, and irradiating the mixed solution with a mixed light source of 395nm and 365nm. The molar ratio of choline chloride to urea is 2:1; the mass ratio of the total mass of the choline chloride and urea to deionized water is 1:(4-8); the photoinitiator is 2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone, and the photoinitiator is 0.1-0.5wt% of the total mass of the acrylic acid monomer and the monoethanolamine monomer; the carboxymethyl chitosan is 0.3-0.5wt% of the total mass of the acrylic acid monomer and the monoethanolamine monomer; and the mass ratio of the deep eutectic solvent, acrylic acid monomer, and ethanolamine monomer is 8.37:(3-4):

1.

2. The photo-crosslinked polyacrylic acid-based adhesive according to claim 1, characterized in that The irradiation time is 1 to 2 hours.

3. The method for preparing a photo-crosslinked polyacrylic acid-based aqueous adhesive according to claim 1 or 2, characterized in that: The following steps are involved: S1. Dissolve choline chloride and urea in deionized water, and stir the mixed solution in a water bath at 80-90°C to form a uniform deep eutectic solvent; S2. The acrylic acid monomer and the ethanolamine monomer were added to the deep eutectic solvent and stirred, and then the photoinitiator and carboxymethyl chitosan were added and stirred until completely dissolved to obtain a mixed solution; S3. The mixed solution is transferred to an ultraviolet lamp and irradiated with a mixed light source of 395 nm and 365 nm to obtain a polyacrylic acid-based water-based adhesive.

4. The method for preparing a photo-crosslinked polyacrylic acid-based aqueous adhesive according to claim 3, wherein: The stirring time in step S1 is 90 to 120 minutes.

5. Use of the photo-crosslinked polyacrylic acid-based aqueous binder according to claim 1 or 2 in lithium-ion batteries.

6. Use of the photo-crosslinked polyacrylic acid-based aqueous binder in lithium-ion batteries according to claim 5, characterized in that: The negative electrode material of the lithium ion battery is SiO x , 0 <x<2。

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