JP2003151628A - Non-aqueous secondary battery - Google Patents

Abstract

(57) [Problem] To provide a non-aqueous secondary battery having high capacity and excellent charge / discharge cycle characteristics. SOLUTION: In a non-aqueous secondary battery using carbon sulfide as a positive electrode active material and metallic lithium as a negative electrode active material, tetraglyme and 1,1 are used as electrolyte solvents.
A non-aqueous secondary battery is formed using a mixed solvent in which dimethoxyethane is added to a base solvent composed of either or both of 3-dioxolane and dimethyl sulfoxide in a volume ratio of 2% or more and 30% or less based on the total electrolyte solvent. As the carbon polysulfide, a general formula (CS _x ) _n (where,
x is 0.9 to 2.0, and n is a number of 4 or more).

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a non-aqueous secondary battery, and more specifically, it uses polysulfide carbon as a positive electrode active material and metallic lithium as a negative electrode active material, and has high capacity and charge / discharge cycle characteristics. It relates to an excellent non-aqueous secondary battery.

[0002]

2. Description of the Related Art Currently, a lithium ion secondary battery is mainly used as a power source for portable equipment. The reason for this is that the lithium-ion secondary battery is lighter in weight and higher in voltage than conventional secondary batteries represented by NiCd secondary batteries and nickel-hydrogen secondary batteries. Can be mentioned.

However, the current lithium ion secondary battery uses a metal oxide such as LiCoO ₂ for the positive electrode,
Graphite is used for the negative electrode, and the capacity limit is approaching from their theoretical capacities, while on the other hand, there is a tendency for safety to decrease due to higher energy density. Further, with the recent decrease in the voltage of ICs, there is an increasing demand for secondary batteries that have a high capacity and can be driven at a low voltage.

[0004]

DISCLOSURE OF THE INVENTION
In order to meet such demands, polysulfide carbon is used as a positive electrode active material.
As a negative electrode active material using metallic lithium.
Developed a pond and added it to the specification of Japanese Patent Application No. 2001-81831.
As described, dimethylsulfoxide, sulfolane, etc.
A solvent having a sulfur atom in the molecule of R,₁O (CH₂CH
₂O)_zR₂(R ₁, R₂Is an alkyl group having 1 to 4 carbon atoms
And Z is 1 ≦ Z ≦ 14)
A side solvent or a mixed solvent thereof is used as an electrolyte solvent.
The high capacity and charge / discharge cycle characteristics
We have developed a non-aqueous secondary battery with excellent properties. But Naga
And this battery also shows that the decrease in capacity after cycling is small enough.
However, there was still room for improvement.

In view of the above circumstances, the present invention provides a non-aqueous secondary battery using polysulfide carbon as a positive electrode active material and metallic lithium as a negative electrode active material, which has high capacity and charge / discharge cycle characteristics. It is intended to provide an excellent non-aqueous secondary battery.

[0006]

The present invention is directed to a non-aqueous secondary battery using polysulfide carbon as a positive electrode active material and metallic lithium as a negative electrode active material, and tetraglyme and 1,3-as the electrolyte solvent. The above problem is solved by using a mixed solvent in which dimethoxyethane is added to the basic solvent containing either or both of dioxolane and dimethyl sulfoxide in an amount of 2% or more and 30% or less by volume ratio to the total electrolyte solution solvent.

That is, Japanese Patent Application No. 2001-81831
The electrolytic solution as shown in, for example, when the LiCF ₃ SO ₃ is dissolved in a mixed solvent of dimethyl sulfoxide and tetraglyme, which has the most excellent characteristics in the examples, the battery after the charge / discharge cycle is disassembled. Observation revealed that the surface of the lithium negative electrode turned black from the beginning of the cycle, and further erosion of the surface of the negative electrode locally proceeded as the cycle proceeded. Therefore, as a result of further studies by adding third and fourth solvents to the electrolytic solution, it was found that by mixing dimethoxyethane, it is possible to maintain a high discharge capacity and obtain excellent cycle characteristics. It was The behavior of metallic lithium in the charge / discharge reaction is such that dissolution and precipitation of lithium are repeated, but by adding dimethoxyethane, the black color change of the negative electrode at the beginning of the cycle is suppressed faintly. It is considered that the reaction with was suppressed. Furthermore, since there is little variation unevenness on the surface of the negative electrode, the dissolution-precipitation reaction of metallic lithium is progressing uniformly, and there is no local erosion,
It can be considered that the avoidance of current concentration in a part is the cause of less cycle deterioration.

[0008]

BEST MODE FOR CARRYING OUT THE INVENTION In the present invention, the base solvent of the electrolyte solvent is tetraglyme (tetraethylene glycol dimethyl ether) and either or both of 1,3-dioxolane and dimethyl sulfoxide, and tetraglyme. Has an affinity for carbon polysulfide, enhances reversibility by interacting with carbon polysulfide during the charge / discharge process, and contributes to obtain a non-aqueous secondary battery with excellent cycle characteristics. 3-Dioxolane and dimethylsulfoxide have lower viscosities than tetraglyme, and when used in combination with tetraglyme, the cycle characteristics are further improved. Dimethyl sulfoxide also has an affinity for carbon polysulfide.

And, these tetraglyme and 1,3-
The ratio of either or both of dioxolane and dimethyl sulfoxide is not particularly limited,
The volume ratio is preferably 4: 1 to 0.5: 1.

The amount of dimethoxyethane added to the base solvent consisting of the above tetraglyme and either or both of 1,3-dioxolane and dimethylsulfoxide is such that the volume ratio of dimethoxyethane to the total solvent is dimethoxyethane. Is 2 to 30%. That is, if the amount of dimethoxyethane added is less than the above amount, the effect is small, and if it is more than the above amount, the capacity decreases. As long as dimethoxyethane is added in the above-mentioned specific ratio to the base solvent consisting of either or both of tetraglyme and 1,3-dioxolane or dimethylsulfoxide, a solvent other than that, such as ethylene carbonate, Propylene carbonate, γ-butyrolactone, tetrahydrofuran, dimethyl carbonate, diethyl carbonate, methyl ethyl carbonate and the like may be added.

The electrolyte is the above tetraglyme and 1,3-
Representative examples of alkali metal halogen salts such as lithium and sodium or perchlorates and trifluoromethanesulfonates in a mixed solvent prepared by adding dimethoxyethane to a base solvent composed of either or both of dioxolane and dimethyl sulfoxide. It is prepared by dissolving an electrolyte salt such as a salt of a fluorine-containing compound. Specific examples of the electrolyte salt include, for example, LiF, LiCl,
LiClO ₄ , LiPF ₆ , LiBF ₄ , LiAs
F ₆ , LiSbF ₆ , LiCF ₃ SO ₃ , LiC ₄ F ₉
SO ₃ , LiCF ₃ CO ₂ , Li ₂ C ₂ F ₄ (SO ₃ )
₂ , LiN (RfSO ₂ ) (Rf′SO ₂ ), LiN
(RfOSO ₂ ) (Rf′OSO ₂ ), LiC (RfS
O ₂ ) ₃ , LiC _n F _{2n + 1} SO ₃ (n ≧ 2), LiN
(RfOSO ₂ ) ₂ [wherein Rf and Rf ′ are fluoroalkyl groups] and the like can be used alone or in admixture of two or more. The concentration of the electrolyte salt in the electrolytic solution is not particularly limited, but is preferably 0.3 mol / l or more, and 0.4 mol / l.
1 or more is more preferable, 1.7 mol / l or less is preferable, and 1.5 mol / l or less is more preferable. In the present invention, tetraglyme and 1,3-dioxolane or either or both of dimethylsulfoxide are used as a base solvent, and dimethoxyethane is added to the base solvent. This is only because of the relationship with the Japanese Patent Application No. 2001-81831. In preparing the electrolytic solution, dimethoxyethane was mixed with tetraglyme, 1,3-dioxolane, dimethylsulfoxide and the like. Good.

Further, in the present invention, the above-mentioned electrolytic solution may be used in a liquid state, or may be used in a gel state by gelling with a gelling agent.

Examples of such a gelling agent include linear polymers such as polyethylene oxide and polyacrylonitrile or copolymers thereof, and polyfunctional monomers which are polymerized by irradiation with actinic rays such as ultraviolet rays and electron beams (for example, , Pentaerythritol tetraacrylate, ditrimethylolpropane tetraacrylate,
Ethoxylated pentaerythritol tetraacrylate,
Obtained from polymers obtained from tetrafunctional or higher-functional methacrylates such as dipentaerythritol hydroxypentaacrylate and dipentaerythritol hexaacrylate, and from monomers that polymerize by utilizing the reaction between active hydrogen of amine compounds and urethane isocyanate groups. A polymer or the like is used. In particular, as the gelling agent, a polymer having a urea structure polymerized by utilizing the reaction between the active hydrogen of the amine compound and the isocyanate group of urethane as described above is preferable.

In the present invention, although the composition of the carbon polysulfide used as the positive electrode active material is slightly different depending on the synthesis conditions, when the composition is represented by the general formula (CS _x ) _n , x is 0.9 to 0.9. It is preferably 2.0 and n is 4 or more. That is, when x is smaller than 0.9, a large amount of C—S—C bonds that are not involved in charging / discharging is included in addition to the disulfide bonds involved in charging / discharging, and the capacity tends to decrease. Is more than 2.0, a large amount of polysulfide segment represented by —S _y — (y ≧ 3) is contained in the molecule, and the stability of the molecule may be decreased, and the reversibility during charge / discharge may be decreased. is there. That is, x is 0.9 to
A carbon polysulfide in the range of 2.0 is preferable because the existence ratio of disulfide bonds involved in charge / discharge in the molecule becomes high, and among them, carbon polysulfide in which x is 1.0 to 1.7 is a molecule. The presence ratio of the disulfide bond involved in charge / discharge is particularly high, which is preferable. And n is 4
The above is preferable because when n is 3 or less, it is difficult to produce a polysulfide carbon having a disulfide bond, and even if it can be produced, the capacity as an active material is low and the polysulfide is dissolved in an electrolytic solution. May be less useful. Considering the workability, this n is preferably 100 or more, and no matter how large it is, no problem arises, but normally n of up to about 100,000 is practically suitable.

[0015]

EXAMPLES Next, the present invention will be described more specifically with reference to examples. However, the present invention is not limited to only those examples. In the following examples and the like,% when indicating the concentration of a solution or dispersion and% when indicating composition, yield, etc. represent mass% unless otherwise noted.

In the following examples, etc., only the electrolytic solution (more accurately, the electrolytic solution solvent) is different,
Since the other constituent members are common, the common part will be described first.

First, polysulfide carbon used as a positive electrode active material was synthesized as follows. 100 g of sodium sulfide nonahydrate (Na ₂ S.9H ₂ O) was mixed at a volume ratio of 1: 1 to obtain a mixed solvent of ethanol and water 300
It was dissolved in ml, 53.4 g of elemental sulfur was added thereto, and the mixture was reacted at room temperature for 1 hour. Then the solvent was removed in vacuo and the residue was treated with N-methyl-2-pyrrolidone 7
Dissolve it in 00 ml and add hexachlorobutadiene to 17.
2 g was added and reacted at room temperature for 1 hour. Then, it was repeatedly washed with pure water, acetone, and ethanol three times in this order, and dried in vacuum for 15 hours while maintaining at 40 ° C. to obtain a brown solid compound as an intermediate product. The yield of this brown solid compound was 32 g.

Elemental analysis of the obtained compound is carried out,
The average composition was determined. For C, N and H, fully automatic elemental analyzer [Viber EL manufactured by Sebel Hegna Co., Ltd.
(Trade name)], the analysis was performed under the conditions of sample decomposition furnace temperature: 950 ° C., reduction furnace temperature: 500 ° C., helium flow rate: 200 ml / min, oxygen flow rate: 20-25 ml / min.
In addition, S was analyzed by the flask combustion method-measurement of barium acetate using trimethylene blue as an indicator. As a result, C: 7.0%, S: 92.3%,
It was found that N: 0.2% or less and H: 0.3% or less. This can be expressed by a general formula as (CS _4.9 ) _n . Also, trace amounts of N and H were detected as impurities, which are considered to be residual components of the solvent.

Next, 10 g of the intermediate product consisting of the brown solid compound was added to a ship-shaped alumina (aluminum oxide).
The container was placed in the container, the alumina container containing the intermediate product was placed in the core of an alumina heating furnace, and the atmosphere was replaced with argon gas having a purity of 99.999% by volume until the oxygen concentration was 100 ppm or less. The temperature was changed as shown below, and heat treatment was performed at 200 ° C. That is, the temperature was raised from room temperature to 60 ° C. in 0.5 hours, kept at 60 ° C. for 1 hour, then raised to 120 ° C. in 1 hour, and
The intermediate product was maintained at 20 ° C. for 1 hour, heated to 200 ° C. for 1.5 hours, and maintained at 200 ° C. for 6 hours to remove a part of sulfur in the intermediate product, thereby converting the intermediate product into polysulfide carbon. Changed to.

After the treatment, the reaction product was taken out from the alumina container after cooling to room temperature to obtain about 3 g of carbon black polysulfide having a black metallic luster. As a result of elemental analysis, the above carbon polysulfide was represented by the general formula and was (CS _1.55 ) _n . Since hexachlorobutadiene used as a reaction component in the production of the above-mentioned carbon polysulfide is a compound having 4 carbon atoms, the n value of the above (CS _1.55 ) _n is 4 or more, and mainly a multiple of 4 molecules is synthesized. it is conceivable that.

Next, this carbon polysulfide was subjected to X-ray diffraction measurement using CuKα rays by a powder X-ray diffractometer [RINT2000 (trade name) manufactured by Rigaku Corporation]. The measurement conditions are voltage: 40 kV, current: 150 mA,
Scan speed: 2 ° / min, sampling: 0.02 °,
Total number of times: 5 times. The X-ray diffraction pattern of the carbon polysulfide obtained by this X-ray diffraction measurement is 25.5 °.
It only had a broad peak at. Further, in this polysulfide carbon, peaks corresponding to unsaturated bonds of carbon and disulfide bonds of sulfur were observed by Raman analysis, but peaks corresponding to bonds corresponding to the polysulfide segment were not observed.

Then, in the production of the battery, the positive electrode is
The above-mentioned carbon polysulfide and carbon black as a conductive auxiliary agent were mixed in advance in a mass ratio of 75:15, and this mixture was added to a binder solution in which polyvinylidene fluoride as a binder was dissolved in n-methyl-2-pyrrolidone. The binder was added so that the binder ratio was 10% with respect to the total solid content, and the mixture was mixed to prepare a positive electrode mixture-containing paste. The paste containing the positive electrode mixture was applied to an aluminum foil by a doctor blade method in a predetermined amount, dried, pressed, and then cut into a predetermined size.

The above positive electrode is fixed to a positive electrode can via an aluminum spacer, while on the negative electrode side, a metal lithium foil is fixed to the negative electrode can via a nickel spacer to form a negative electrode, and the positive electrode and the negative electrode are separated from each other. A separator made of polyethylene non-woven fabric is placed in the container, and after injecting each of the electrolytic solutions described below, a polypropylene annular gasket is used to seal the gap between the positive electrode can and the negative electrode can to a thickness of 2 mm.
Then, a coin-shaped non-aqueous secondary battery having a diameter of 16 mm was assembled.

Then, the prepared battery is charged / discharged and its characteristics are examined. The charging / discharging conditions are as follows: current density at discharge 0.3 mA / cm ² , termination at 1.5 V, current density at charge 0. Constant current-constant voltage charging was performed at 3 mA / cm ² and 2.6 V.

Example 1 An electrolytic solution was prepared by dissolving LiCF ₃ SO _{3 in an amount} of 1 mol / l in a mixed solvent in which tetraglyme, 1,3-dioxolane and dimethoxyethane were mixed at a volume ratio of 49: 49: 2. I used one.

Example 2 An electrolytic solution was prepared by dissolving 1 mol / l of LiCF ₃ SO ₃ in a mixed solvent in which tetraglyme, 1,3-dioxolane and dimethoxyethane were mixed at a volume ratio of 35:35:30. I used one.

Comparative Example 1 As an electrolytic solution, LiC was added to a mixed solvent in which tetraglyme and 1,3-dioxolane were mixed at a volume ratio of 50:50.
The one prepared by dissolving 1 mol / l of F ₃ SO ₃ was used.

Comparative Example 2 As an electrolytic solution, tetraglyme, 1,3-dioxolane and dimethoxyethane were used in a volume ratio of 49.5: 49.5:
1 mol of LiCF ₃ SO ₃ in the mixed solvent mixed in 1.
What was prepared by dissolving / l was used.

Comparative Example 3 LiCF ₃ SO ₃ was prepared as an electrolytic solution by dissolving 1 mol / l of LiCF ₃ SO ₃ in a mixed solvent of tetraglyme, 1,3-dioxolane and dimethoxyethane mixed at a volume ratio of 30:30:40. I used one.

With respect to the batteries of Examples 1 and 2 and Comparative Examples 1 to 3, the initial discharge capacity and the discharge capacity after 10 cycles were measured. The results are shown in Table 1 by the discharge capacity per unit weight of the polysulfide carbon as the positive electrode active material.

[0031]

[Table 1]

As is clear from the results shown in Table 1, the battery of Example 1 in which 2% by volume of dimethoxyethane was added to the solvent of the whole electrolyte solution and 30% of dimethoxyethane in the volume ratio of the solvent to the whole electrolyte solution were added. The battery of Example 2 had a large initial discharge capacity, and also had a large discharge capacity after 10 cycles as compared with the batteries of Comparative Examples 1 to 3, a high capacity, and excellent charge-discharge cycle characteristics.

On the other hand, the battery of Comparative Example 1 containing no dimethoxyethane, the battery of Comparative Example 2 containing a small amount of dimethoxyethane, and the battery of Comparative Example 3 containing a large amount of dimethoxyethane were 10 The discharge capacity after cycling was small, the charge-discharge cycle characteristics were inferior to the batteries of Examples 1 and 2, and the battery of Comparative Example 3 had a small initial discharge capacity.

Example 3 As electrolyte, tetraglyme and 1,3-dioxolane
And dimethoxyethane in a volume ratio of 47.5: 47.5:
LiCF was added to the mixed solvent mixed at 5: 5.₃SO ₃1m
The prepared solution was dissolved in ol / l.

Example 4 As an electrolytic solution, LiCF was mixed with a mixed solvent of tetraglyme, 1,3-dioxolane, dimethoxyethane and ethylene carbonate at a volume ratio of 45: 45: 8: 2.
A prepared product in which ₃ SO ₃ was dissolved at 1 mol / l was used.

Comparative Example 4 As an electrolytic solution, tetraglyme, 1,3-dioxolane and ethylene carbonate were mixed at a volume ratio of 47.5: 47.
The one prepared by dissolving 1 mol / l of LiCF ₃ SO ₃ in the mixed solvent mixed at 5: 5.5 was used.

Comparative Example 5 As an electrolytic solution, tetraglyme, 1,3-dioxolane and propylene carbonate were mixed at a volume ratio of 47.5: 4.
A solvent prepared by dissolving LiCF ₃ SO _{3 in an amount} of 1 mol / l in a mixed solvent of 7.5: 5 was used.

Comparative Example 6 As an electrolytic solution, tetraglyme, 1,3-dioxolane and methyl ethyl carbonate were mixed in a volume ratio of 47.5: 4.
A solvent prepared by dissolving LiCF ₃ SO _{3 in an amount} of 1 mol / l in a mixed solvent of 7.5: 5 was used.

Comparative Example 7 As electrolyte, tetraglyme and 1,3-dioxolane
And dimethyl carbonate in a volume ratio of 47.5: 47.
LiCF was added to the mixed solvent mixed at 5: 5.₃SO ₃1m
What was prepared by dissolving ol / l was used.

Comparative Example 8 As an electrolytic solution, tetraglyme, 1,3-dioxolane and tetrahydrofuran were mixed at a volume ratio of 47.5: 47.
LiCF ₃ SO ₃ was added to a mixed solvent of 5: 5 in an amount of 1 m.
What was prepared by dissolving ol / l was used.

Comparative Example 9 LiCF ₃ SO ₃ was dissolved at 1 mol / l in a mixed solvent of tetraglyme, 1,3-dioxolane and sulfolane mixed at a volume ratio of 47.5: 47.5: 5 as an electrolytic solution. What was prepared by using was used.

Comparative Example 10 As an electrolytic solution, tetraglyme, 1,3-dioxolane and γ-butyrolactone were mixed at a volume ratio of 47.5: 47.
LiCF ₃ SO ₃ was added to a mixed solvent of 5: 5 in an amount of 1 m.
What was prepared by dissolving ol / l was used.

Comparative Example 11 Tetraglyme, 1,3-dioxolane and acetonitrile were used as an electrolytic solution in a volume ratio of 47.5: 47.5: 5.
1 mol / mL of LiCF ₃ SO ₃ in the mixed solvent mixed in
What was prepared by dissolving was used.

For the batteries of Examples 3 to 4 and Comparative Examples 4 to 11, the initial discharge capacity and the discharge capacity after 10 cycles were measured in the same manner as in Example 1. The results are shown in Table 2.
Shows the discharge capacity per unit weight of carbon polysulfide as the positive electrode active material.

[0045]

[Table 2]

As is clear from the results shown in Table 2, the battery of Example 3 to which dimethoxyethane was added and the battery of Example 4 to which dimethoxyethane and another solvent were added had a large initial discharge capacity and 10 The discharge capacity after cycling was large, and the capacity was high and the charge / discharge cycle characteristics were excellent.
The batteries of Comparative Examples 4 to 11 in which a solvent other than dimethoxyethane was added to a state of not containing dimethoxyethane at all had poor charge-discharge cycle characteristics, and the batteries of Comparative Examples 4 to 7 and Comparative Examples 10 to 11 were The initial discharge capacity was also small.

Example 5 As an electrolytic solution, LiCF ₃ SO ₃ was added to a mixed solvent prepared by mixing tetraglyme, 1,3-dioxolane, dimethyl sulfoxide, dimethoxyethane at a volume ratio of 45: 22.5: 22.5: 10. What was prepared by dissolving 1 mol / l was used.

Comparative Example 12 As an electrolytic solution, tetraglyme, 1,3-dioxolane and dimethyl sulfoxide were mixed at a volume ratio of 50:25:25.
1 mol / mL of LiCF ₃ SO ₃ in the mixed solvent mixed in
What was prepared by dissolving was used.

Regarding the batteries of Example 5 and Comparative Example 12 described above, the initial discharge capacity and 10
The discharge capacity after the cycle was measured. The results are shown in Table 3 by the discharge capacity per unit weight of the carbon polysulfide as the positive electrode active material.

[0050]

[Table 3]

As is clear from the results shown in Table 3, the battery of Example 5 in which dimethoxyethane was added to the base solvent consisting of tetraglyme, 1,3-dioxolane and dimethylsulfoxide had a large initial discharge capacity, Moreover, the discharge capacity after 10 cycles was large, and the capacity was high and the charge / discharge cycle characteristics were excellent.

On the other hand, in the battery of Comparative Example 12 to which dimethoxyethane was not added, the discharge capacity at the first time was large, but the discharge capacity after 10 cycles was small and the charge / discharge cycle characteristics were poor.

[0053]

As described above, in the present invention, in a non-aqueous secondary battery in which polysulfide carbon is used as the positive electrode active material and metallic lithium is used as the negative electrode active material, tetraglyme and 1 A non-aqueous secondary battery having high capacity and excellent charge / discharge cycle characteristics can be obtained by using a mixed solvent obtained by adding dimethoxyethane in a specific ratio to a base solvent composed of 1,3-dioxolane or dimethyl sulfoxide or both. Could be provided.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Toshihiro Nakai             Hitachima, 1-88, Torora, Ibaraki City, Osaka Prefecture             Within Kucsel Co., Ltd. (72) Inventor Yoshishi Iizuka             Hitachima, 1-88, Torora, Ibaraki City, Osaka Prefecture             Within Kucsel Co., Ltd. F term (reference) 5H029 AJ03 AJ05 AK00 AL12 AM02                       AM05 AM07 HJ02                 5H050 AA07 AA08 BA16 CA00 CB12                       HA02

Claims (2)

[Claims] 1. A non-aqueous secondary battery using polysulfide carbon as a positive electrode active material and metallic lithium as a negative electrode active material, wherein tetraglyme and 1,
A non-aqueous secondary battery characterized by using a mixed solvent prepared by adding dimethoxyethane in an amount of 2% or more and 30% or less by volume ratio to the total electrolyte solvent to a base solvent made of either or both of 3-dioxolane and dimethylsulfoxide. . 2. The carbon polysulfide has the general formula (CS
The non-aqueous secondary battery according to claim 1, wherein _x ) _n (wherein x is 0.9 to 2.0 and n is a number of 4 or more).