JP7484150B2 - Method for producing polyamide and monomer composition - Google Patents

Description

The present invention relates to a method for producing polyamide and a monomer composition that can be used in the method for producing polyamide.

As global warming and the depletion of petroleum resources become more serious, the use of biomass plastics has attracted attention from the perspective of protecting the global environment. Examples of biomass plastics that have been developed include polylactic acid and polybutylene succinate, and more recently biopolyethylene. However, these biomass plastics have poor heat resistance, with melting points below 180°C. An effective method for improving the heat resistance of plastics is to use aromatic monomers or alicyclic monomers, but the types of aromatic monomers and alicyclic monomers derived from biomass are limited. Among these, polyamides using 2,5-bis(aminomethyl)tetrahydrofuran obtained from biomass have been studied in recent years (Non-Patent Document 1).

New Developments in Wood Chemicals, CMC Publishing Co., Ltd., First Edition published on August 31, 2007

However, the properties and improvements of polyamides using 2,5-bis(aminomethyl)tetrahydrofuran as a raw material diamine have not been fully investigated. In particular, as a result of the investigations conducted by the present inventors, it was found that polyamides using 2,5-bis(aminomethyl)tetrahydrofuran as a raw material diamine may have poor appearance after heating or a low 5% mass loss temperature.
The present invention aims to solve the above problems, and has an object to provide a method for producing a polyamide that has excellent appearance after heating and high heat resistance, and a monomer composition for producing the polyamide.

In view of the above problems, the present inventors have conducted research and found that the above problems can be solved by reacting a diamine such as 2,5-bis(aminomethyl)tetrahydrofuran, which is a raw material monomer for polyamide, in a state in which the diamine is in slight excess over a dicarboxylic acid.
Specifically, the above problems were solved by the following means.
<1> A method for producing a polyamide, comprising: heating a composition containing a diamine represented by formula (1), a dicarboxylic acid, and a solvent, removing the solvent to obtain a prepolymer, and heating the prepolymer under reduced pressure to obtain a polyamide, wherein a molar ratio of diamine to dicarboxylic acid contained in the composition is 1.00<diamine/dicarboxylic acid.
Formula (1)
(In formula (1), n is an integer from 0 to 5.)
<2> The method for producing a polyamide according to <1>, wherein the diamine represented by the formula (1) is 2,5-bis(aminomethyl)tetrahydrofuran.
<3> The method for producing a polyamide according to <1> or <2>, wherein the dicarboxylic acid includes an aromatic dicarboxylic acid.
<4> The method for producing a polyamide according to any one of <1> to <3>, wherein the dicarboxylic acid includes an aliphatic dicarboxylic acid.
<5> The method for producing a polyamide according to any one of <1> to <4>, wherein the dicarboxylic acid includes at least one selected from the group consisting of phthalic acid, isophthalic acid, terephthalic acid, glutaric acid, adipic acid and sebacic acid.
<6> The method for producing a polyamide according to any one of <1> to <5>, wherein the molar ratio of diamine/dicarboxylic acid is 1.00<diamine/dicarboxylic acid≦1.10.
<7> The method for producing a polyamide according to any one of <1> to <5>, wherein the molar ratio of diamine/dicarboxylic acid is 1.00<diamine/dicarboxylic acid≦1.06.
<8> A monomer composition comprising a diamine represented by formula (1), a dicarboxylic acid, and a solvent, wherein a molar ratio of the diamine to the dicarboxylic acid contained in the monomer composition satisfies 1.00<diamine/dicarboxylic acid.
Formula (1)
(In formula (1), n is an integer from 0 to 5.)

The present invention makes it possible to provide a method for producing a polyamide that has excellent appearance after heating and high heat resistance, and a monomer composition for producing the polyamide.

1 is a graph showing the relationship between the molar ratio of diamine to dicarboxylic acid (A/C ratio) and the 5% mass loss temperature for polyamides of Examples and Comparative Examples. 1 is a graph showing the relationship between yellowing index (ΔYI) and number average molecular weight (Mn) for polyamides of Examples and Comparative Examples.

The present invention will be described in detail below. In this specification, the word "-" is used to mean that the numerical values before and after it are included as a lower limit and an upper limit.
In this specification, measurements, various physical properties and characteristic values are those at 23° C. unless otherwise specified.
In this specification, "parts by mass" indicates the relative amount of a component, and "% by mass" indicates the absolute amount of a component.

The method for producing a polyamide of the present invention comprises heating a composition containing a diamine represented by formula (1), a dicarboxylic acid and a solvent (hereinafter sometimes referred to as a "monomer composition") to remove the solvent to obtain a prepolymer, and heating the prepolymer under reduced pressure conditions to obtain a polyamide, wherein the molar ratio of diamine to dicarboxylic acid contained in the composition is 1.00<diamine/dicarboxylic acid.
Formula (1)
(In formula (1), n is an integer from 0 to 5.)
By adopting such a constitution, a polyamide having excellent appearance after heating and high heat resistance can be obtained. More specifically, a polyamide having a high 5% mass loss temperature while maintaining a low yellowing index (ΔYI) can be obtained.
This mechanism is presumed to be as follows, although it is not limited thereto. That is, the diamine represented by formula (1) contains a tetrahydrofuran ring, and the tetrahydrofuran ring is likely to coordinate a proton to an oxygen atom. Therefore, it is presumed that the tetrahydrofuran ring is decomposed with cleavage during polymerization of the diamine and the dicarboxylic acid. In the present invention, it is presumed that the decomposition caused by the cleavage of the tetrahydrofuran ring can be suppressed by making the ratio of the diamine higher than that of the dicarboxylic acid.
The production method of the present invention will now be described in detail.

The monomer composition used in the present invention is a raw material for polyamide, and contains diamine, dicarboxylic acid, solvent, and other components that are mixed as necessary. Specifically, as described above, the monomer composition contains diamine represented by formula (1), dicarboxylic acid, and solvent, and the molar ratio (A/C ratio) of diamine to dicarboxylic acid contained in the composition is 1.00<diamine/dicarboxylic acid. By setting the molar ratio (A/C ratio) of diamine to dicarboxylic acid as described above, a polyamide having excellent appearance after heating and high heat resistance can be obtained.
The lower limit of the A/C ratio is preferably 1.01≦A/C, more preferably 1.02≦A/C, and may be 1.02<A/C. The upper limit of the A/C ratio is preferably A/C≦1.10, more preferably A/C≦1.09, even more preferably A/C≦1.08, even more preferably A/C≦1.07, even more preferably A/C<1.07, even more preferably A/C≦1.06, and may be A/C<1.06. By making the A/C ratio equal to or less than the upper limit, the appearance after heating can be further improved while the heat resistance can be further improved.
In particular, by satisfying 1.02≦A/C<1.07, and further by satisfying 1.02≦A/C≦1.06, the 5% mass loss temperature can be set to 390° C. or higher, which is of great practical value.
In the present invention, the A/C ratio is a value rounded off to two decimal places. Therefore, for example, an A/C ratio of 1.01 means an A/C ratio of 1.005 or more and less than 1.015.

Next, the diamine represented by formula (1) contained in the monomer composition will be described.
Formula (1)
(In formula (1), n is an integer from 0 to 5.)

In the above formula (1), n is preferably each independently 1 or 2, and more preferably 1.
The diamine represented by formula (1) is preferably 2,5-bis(aminomethyl)tetrahydrofuran.
The monomer composition may contain only one type of diamine represented by formula (1), or may contain two or more types.

The monomer composition may contain a diamine other than the diamine represented by formula (1) without departing from the spirit of the present invention. Examples of diamines other than the diamine represented by formula (1) include aliphatic diamines (including alicyclic diamines) and aromatic diamines.

For specific examples of aliphatic diamines, refer to paragraph 0016 of WO 2016/056340, the contents of which are incorporated herein by reference. For specific examples of aromatic diamines, refer to paragraph 0052 of WO 2017/126409, the contents of which are incorporated herein by reference.
Another example of the diamine is 2,5-bis(aminomethyl)furan.
In the present invention, the proportion of the diamine represented by formula (1) in the diamine contained in the monomer composition is preferably 90% by mass or more, more preferably 95% by mass or more, and even more preferably 99% by mass or more, and may be substantially 100% by mass. "Substantially 100% by mass" means that all diamines other than diamines unintentionally contained as impurities or the like are the diamine represented by formula (1).

Next, the dicarboxylic acid contained in the monomer composition will be described.
The type of dicarboxylic acid contained in the monomer composition is not particularly limited, and a wide variety of known dicarboxylic acids can be used, with aromatic dicarboxylic acids and/or aliphatic dicarboxylic acids being preferred.

Examples of aliphatic dicarboxylic acids include succinic acid, glutaric acid, adipic acid, pimelic acid, suberic acid, azelaic acid, sebacic acid, dodecanedicarboxylic acid, 4,4'-methylenebis(2-methylcyclohexane-1-carboxylic acid), 4,4'-methylenebis(cyclohexane-1-carboxylic acid), decahydro-1,4-naphthalenedicarboxylic acid, 4,4'-oxobis(cyclohexane-1-carboxylic acid) and 4,4'-thiobis(cyclohexane-1-carboxylic acid), of which succinic acid, glutaric acid, adipic acid, pimelic acid, suberic acid, azelaic acid, sebacic acid and dodecanedicarboxylic acid are preferred, and glutaric acid, adipic acid and sebacic acid are more preferred.

Examples of aromatic dicarboxylic acids include isophthalic acid, terephthalic acid, orthophthalic acid, 1,2-naphthalenedicarboxylic acid, 1,3-naphthalenedicarboxylic acid, 1,4-naphthalenedicarboxylic acid, 1,5-naphthalenedicarboxylic acid, 1,6-naphthalenedicarboxylic acid, 1,7-naphthalenedicarboxylic acid, 1,8-naphthalenedicarboxylic acid, 2,3-naphthalenedicarboxylic acid, 2,6-naphthalenedicarboxylic acid, and 2,7-naphthalenedicarboxylic acid, with isophthalic acid and terephthalic acid being more preferred, and terephthalic acid being even more preferred.

In the present invention, it is particularly preferred that the dicarboxylic acid contained in the monomer composition includes at least one selected from the group consisting of phthalic acid, isophthalic acid, terephthalic acid, glutaric acid, adipic acid and sebacic acid, with terephthalic acid being more preferred.
The monomer composition may contain only one kind of dicarboxylic acid, or may contain two or more kinds of dicarboxylic acids.

The monomer composition used in the present invention may contain raw material monomers constituting polyamide other than the above diamines and dicarboxylic acids. Specific examples include lactams such as ε-caprolactam, valerolactam, laurolactam, and undecalactam, and aminocarboxylic acids such as 11-aminoundecanoic acid and 12-aminododecanoic acid. In the monomer composition used in the present invention, the total ratio of diamines and dicarboxylic acids among the raw material monomers (raw material monomers such as diamines, dicarboxylic acids, lactams, and aminocarboxylic acids) that are constituent units of polyamide is preferably 70% by mass or more, more preferably 80% by mass or more, even more preferably 90% by mass or more, even more preferably 95% by mass or more, even more preferably 98% by mass or more, and even more preferably substantially 100% by mass. Substantially 100% by mass means that all raw material monomers other than impurities and other unintentionally contained monomers are diamines or dicarboxylic acids.

Next, the solvent contained in the monomer composition will be described. As the solvent, any known solvent can be used as long as it does not deviate from the spirit of the present invention, and examples of the solvent include water, methanol, and ethanol, with water being preferred.
The ratio of the solvent in the monomer composition used in the present invention is, for example, 20 to 80% by mass. The monomer composition used in the present invention preferably contains 90% by mass or more of water in the solvent, and may contain 95% by mass or more of water, or may contain 99% by mass or more of water.
The monomer composition used in the present invention may contain only one type of solvent, or may contain two or more types. When two or more types are contained, the total amount is preferably within the above range.

In addition to the above, the monomer composition used in the present invention may contain other components such as additives that are commonly used in the synthesis of polyamides. Specific examples include reaction accelerators, antioxidants, catalysts, dyes, pigments, chain limiters, lubricants, flame retardants, light stabilizers, plasticizers, and nucleating agents. Other components include sodium acetate and calcium acetate for preventing gelation or fisheyes. The total amount of the other components in the monomer composition is preferably 3 parts by mass or less, and more preferably 1 part by mass or less, per 100 parts by mass of the raw material monomers contained in the monomer composition.

As described above, the production method of the present invention includes heating a composition (monomer composition) containing the diamine represented by formula (1), a dicarboxylic acid and a solvent, and removing the solvent to obtain a prepolymer.
That is, by heating the monomer composition and removing the solvent, the diamine and the dicarboxylic acid are usually polymerized in a molten state to form a prepolymer. The removal of the solvent is usually performed after the heating of the monomer composition, but the removal of the solvent may be started during the heating of the monomer composition. In addition, when removing the solvent, it is preferable to remove the condensed water together. The removal of the solvent is performed by releasing the solvent from the reaction system (for example, the reaction vessel) to the outside of the system.

The heating temperature in the stage of obtaining the prepolymer of the monomer composition is preferably 150° C. or higher, more preferably 180° C. or higher, and even more preferably 190° C. or higher. By setting it to the lower limit or higher, it is possible to increase the degree of polymerization while more effectively suppressing discoloration of the prepolymer. In addition, the heating temperature of the monomer composition is preferably 260° C. or lower, more preferably 250° C. or lower, even more preferably 230° C. or lower, and even more preferably 220° C. or lower. By setting it to the upper limit or lower, it is possible to more effectively suppress discoloration of the prepolymer.
The heating time is preferably 0.5 hours or more, more preferably 1 hour or more, and the upper limit of the heating time is preferably 4 hours or less, more preferably 3 hours or less.

The monomer composition may be pressurized when heated in the step of obtaining the prepolymer. In this case, the pressure is preferably 0.1 MPa or more. By setting the pressure at or above the lower limit, the formation of the prepolymer from the diamine and the dicarboxylic acid can be more effectively promoted. In addition, the pressure is preferably 5 MPa or less.

Here, preferred physical properties of the prepolymer will be described.
The prepolymer is a polymer having two or more amide bonds, and has a weight average molecular weight of usually 3,000 or more, preferably 5,000 or more, and usually 20,000 or less, more preferably 15,000 or less.
The number average molecular weight of the prepolymer is usually 2,000 or more, preferably 3,000 or more, and usually 10,000 or less, more preferably 8,000 or less.

The method for producing polyamide of the present invention further includes heating the prepolymer under reduced pressure conditions to obtain a polyamide. By heating the prepolymer under reduced pressure conditions (preferably under vacuum conditions), additional polymerization proceeds to obtain a polyamide with a higher molecular weight.

The heating temperature of the prepolymer (heating temperature during solid-state polymerization) is preferably 220°C or higher, more preferably 230°C or higher, even more preferably 240°C or higher, and even more preferably 245°C or higher. By setting it to the lower limit or higher, the late polycondensation (solid-state polymerization) of the prepolymer tends to proceed more effectively. In addition, the heating temperature of the prepolymer is preferably 300°C or lower, more preferably 280°C or lower, even more preferably 270°C or lower, and even more preferably 260°C or lower. By setting it to the upper limit or lower, denaturation and discoloration can be more effectively suppressed.
The heating time of the prepolymer is preferably 0.25 hours or more, more preferably 0.5 hours or more, and the upper limit of the heating time is preferably 5 hours or less, more preferably 3 hours or less.

Next, preferred physical properties of the polyamide after solid-state polymerization obtained by the production method of the present invention will be described. The weight-average molecular weight of the polyamide after solid-state polymerization obtained by the production method of the present invention is preferably 30,000 or more, more preferably 40,000 or more, and may be 50,000 or more, 60,000 or more, 70,000 or more, or may be 80,000 or more. In addition, the weight-average molecular weight may be, for example, 300,000 or less, 200,000 or less, or 150,000 or less.
The number average molecular weight of the polyamide obtained by the production method of the present invention after solid-state polymerization is preferably 5,000 or more, more preferably 8,000 or more, and even more preferably 10,000 or more, and may be 11,000 or more, or may be 13,000 or more. Moreover, the number average molecular weight is, for example, 50,000 or less, 30,000 or less, or 20,000 or less.
The polyamide polydispersity (Mw/Mn) obtained by the production method of the present invention after solid-state polymerization may be 1.5 or more, or may be 2.0 or more. By making it equal to or more than the lower limit, the mechanical strength of the obtained polyamide tends to be higher. In addition, the polydispersity (Mw/Mn) of the polyamide is preferably 10.0 or less, more preferably 8.0 or less. By making it equal to or less than the upper limit, the heat resistance is high because of the small amount of oligomers, and the moldability tends to be good.
The weight average molecular weight and the number average molecular weight are measured by the method described in the Examples below.

Next, preferred physical properties of the polyamide obtained after solid-phase polymerization by the production method of the present invention will be described.
The 5% mass loss temperature of the polyamide after solid-state polymerization obtained by the production method of the present invention is preferably 371° C. or more, more preferably 380° C. or more, even more preferably 385° C. or more, and even more preferably 390° C. or more. By making it equal to or higher than the lower limit (particularly, 390° C. or more), it can be preferably used in applications requiring heat resistance. The upper limit of the 5% mass loss temperature of the polyamide after solid-state polymerization is not particularly limited, but may be, for example, 410° C. or less, or 400° C. or less.
The 5% mass loss temperature is measured by the method described in the Examples section below.

The yellowing index (ΔYI) of the polyamide obtained by the production method of the present invention is preferably 30 or less, more preferably 20 or less, even more preferably 15 or less, even more preferably 13 or less, and even more preferably 12 or less. By making it equal to or less than the upper limit, a molded product with more suppressed coloring can be obtained. The lower limit of the ΔYI of the polyamide is not particularly set, but for example, 1 or more is practical, and even 5 or more sufficiently satisfies the required performance.
ΔYI is measured by the method described in the Examples below.

Next, applications of the polyamide obtained by the production method of the present invention will be described.
The polyamide obtained by the production method of the present invention can be used as a resin composition containing the polyamide, and further, as a molded article obtained by molding the resin composition.
Details of the resin composition, the molding method of the molded article, the use of the molded article, and the like can be found in paragraphs 0026 to 0040 of JP-A-2019-026686, paragraph 0039 of JP-A-2018-165298, and paragraphs 0045 to 0048 of JP-A-2018-087319. The contents of these can be referred to, and are incorporated herein by reference.

The present invention will be explained in more detail below with reference to examples. The materials, amounts used, ratios, processing contents, processing procedures, etc. shown in the following examples can be changed as appropriate without departing from the spirit of the present invention. Therefore, the scope of the present invention is not limited to the specific examples shown below.

<Synthesis Example of 2,5-bis(aminomethyl)tetrahydrofuran>
In a 300cc capacity autoclave reaction vessel, 20.70g (0.1641mol) of weighed 2,5-bis(aminomethyl)furan (manufactured by Carbosyns, FB187031801), 120mL of tetrahydrofuran, and 8.00g of Rh catalyst-containing material (manufactured by N.E. Chemcat, 317-160042) were placed, and after sufficient replacement with nitrogen, hydrogen was filled up to 6MPaG. After reacting at 90°C for 1 hour, the reaction solution was taken out of the reaction vessel and pressure-filtered under an Ar atmosphere. The product was distilled off to obtain a crude product, which was then purified by distillation at reduced pressure of 1hPa and 130°C.
The Rh catalyst-containing material is Rh catalyst powder supported on carbon, and is 55% by mass water and 45% by mass Rh catalyst, of which 5% by mass Rh and 40% by mass carbon.

Comparative Example 1
<Synthesis of polyamide>
In a 30 cc capacity autoclave reaction vessel, 0.740 g (4.43 mmol) of weighed terephthalic acid (manufactured by Fujifilm Wako Pure Chemical Industries, Ltd., PTM6633), 1.00 g of pure water, and 0.593 g (4.43 mmol) of 2,5-bis(aminomethyl)tetrahydrofuran synthesized above were placed, and after sufficient replacement with nitrogen, the system was heated to 200°C while stirring. After one and a half hours, the generated water and the charged water were removed from the system, and heating was continued for another 30 minutes. After the reaction, the prepolymer was removed from the reaction vessel, and post-polycondensation was carried out for one hour in a vacuum dryer at 250°C to obtain a polyamide.

<Measurement of weight average molecular weight (Mw) and number average molecular weight (Mn)>
The Mw and Mn of the polyamide were measured by gel permeation chromatography. 5 mL of 1,1,1,3,3,3-hexafluoroisopropanol was added to 10 mg of the polyamide obtained in the above Synthesis Example, and the mixture was filtered through a membrane filter (pore size: 0.2 μm) to obtain a sample solution.
The measurement was performed using a GPC-104 (using an RI detector) manufactured by Shoko Scientific Co., Ltd. The column used was a Shodex GPC LF-404 manufactured by Showa Denko K.K. If the above-mentioned gel permeation chromatography device and column are discontinued and difficult to obtain, other devices having equivalent performance may be used.
Eluent: 1,1,1,3,3,3-hexafluoroisopropanol (+10 mmol sodium trifluoroacetate)
The measurement conditions are as follows.
Flow rate: 0.3 mL/min Column temperature: 40° C.
Standard material: polymethyl methacrylate Sample concentration: 0.2% by weight/volume
Injection volume: 10 μL
The dispersity (Mw/Mn) was calculated from the values of Mw and Mn measured above.

<5% mass loss temperature>
The polyamide obtained in the above synthesis example was heated from 30°C to 400°C at a heating rate of 10.5°C/min. An aluminum disk was used as a reference. The initial mass of the polyamide was taken as 100%, and the temperature at which the mass became 95% was defined as the 5% mass reduction temperature. The unit was °C.
For the measurement, a TGDTA7220 manufactured by Hitachi High-Tech Science Corporation was used.

<Yellowing Index (ΔYI)>
Using hexafluoroisopropanol as a solvent, 42.5 mg of the polyamide obtained in the above synthesis example was dissolved in 60 mL of the solvent to adjust the concentration to the same, to obtain a sample solution. The yellowness index (YI) of the solvent and the sample solution was determined, and the difference between the yellowness index of the sample solution and the solvent was defined as the yellowness index (ΔYI).
The measurement was performed using a Spectro Color Meter SE2000 manufactured by Nippon Denshoku Industries Co., Ltd.

Examples 1 to 6
In Comparative Example 1, the molar ratio of diamine to dicarboxylic acid (A/C ratio) was changed as shown in Table 1, but the other procedures were the same.
The prepolymer obtained in Example 2 had Mw of 5,732, Mn of 3,653, and a 5% mass loss temperature of 329°C.
The results are shown in Table 1 below.

In Table 1 above, "*" indicates that the polyamide was not completely dissolved in the solvent, and the measurement was performed using the dissolved portion obtained by filtration.

The above results are shown in FIG. 1 and FIG.
1 is a graph showing the relationship between the molar ratio of diamine to dicarboxylic acid (A/C ratio) and the 5% mass loss temperature for polyamides of Examples and Comparative Examples. From the left, the plots are for Comparative Example 1, Example 1, Example 2, Example 3, Example 4, Example 5, and Example 6.
2 is a graph showing the relationship between ΔYI and Mn for the polyamides of the Examples and Comparative Examples. From the left, the plots are for Comparative Example 1, Example 1, Example 2, Example 3, and Example 5.

Claims (6)

A composition comprising a diamine represented by formula (1), a dicarboxylic acid, and a solvent , the composition comprising diamine represented by formula (1) in an amount of 90 mass% or more of the diamine contained in the composition, and removing the solvent to obtain a prepolymer;
heating the prepolymer under reduced pressure to obtain a polyamide;
A method for producing a polyamide comprising the steps of:
The method for producing a polyamide, wherein the molar ratio of the diamine represented by formula (1) and the dicarboxylic acid contained in the composition satisfies 1.02≦diamine represented by formula (1) /dicarboxylic acid<1.08.
Formula (1)

(In formula (1), n is an integer from 0 to 5.) The method for producing a polyamide according to claim 1, wherein the diamine represented by formula (1) is 2,5-bis(aminomethyl)tetrahydrofuran. The method for producing a polyamide according to claim 1 or 2, wherein the dicarboxylic acid includes an aromatic dicarboxylic acid. The method for producing polyamide according to any one of claims 1 to 3, wherein the dicarboxylic acid includes an aliphatic dicarboxylic acid. The method for producing polyamide according to any one of claims 1 to 4, wherein the dicarboxylic acid includes at least one selected from phthalic acid, isophthalic acid, terephthalic acid, glutaric acid, adipic acid, and sebacic acid. A monomer composition comprising a diamine represented by formula (1), a dicarboxylic acid, and a solvent, wherein the proportion of the diamine represented by formula (1) in the diamines contained in the monomer composition is 90 mass% or more, and a molar ratio of the diamine represented by formula (1) to the dicarboxylic acid contained in the monomer composition is 1.02≦diamine represented by formula (1) /dicarboxylic acid<1.08.
Formula (1)

(In formula (1), n is an integer from 0 to 5.)