Polyimide resin for high-frequency substrate material, composition, polyimide film, laminate, substrate for circuit, antenna, polyamic acid for high-frequency substrate material, and composition

Abstract

A polyimide resin for a high-frequency substrate material comprising an acid anhydride and a diamine, the acid anhydride being at least one compound selected from the group consisting of compounds represented by general formula (A-1), and the diamine being at least one compound selected from the group consisting of compounds represented by general formula (B-1) and compounds represented by general formula (B-2).　

Description

Polyimide resin, composition, polyimide film, laminate, circuit board, and antenna for use as high-frequency substrate materials, and polyamic acid and composition for use as high-frequency substrate materials

[0001] The present disclosure relates to polyimide resins, compositions, polyimide films, laminates, circuit boards, and antennas for use as high-frequency substrate materials, as well as polyamic acids and compositions for use as high-frequency substrate materials.

[0002] Polyimide resins with low dielectric loss tangents and low linear expansion coefficients have been studied as materials for high-frequency substrates (see, for example, Patent Document 1). Conventionally, a low dielectric constant and a low linear expansion coefficient are generally in a trade-off relationship, and it has been difficult to achieve both, and no polyimide resin for use as a high-frequency substrate material that achieves both a low dielectric constant and a low linear expansion coefficient has been found.

[0003] JP 2023-088880 A

[0004] An object of the present disclosure is to provide a polyimide resin for use as a high-frequency substrate material that has both a low dielectric constant and a low coefficient of linear expansion.

[0005] <1> A polyimide resin for use as a high-frequency substrate material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2): In the general formula (A-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 0 to 3, and when l is 0, it represents that there is no bond; m represents an integer of 0 to 3; n represents an integer of 0 to 5; and when n is 0, at least one R １ has a fluorine atom, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-2), R １are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom, each m independently represents an integer of 0 to 2, and o represents an integer of 0 to the maximum number of substituents. <2> The polyimide resin according to <1>, wherein general formula (A-1) is either of the following general formula (A-1a) or the following general formula (A-1b): In the general formula (A-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom; and m represents an integer of 0 to 3. In the general formula (A-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, n represents an integer of 1 to 5, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３<3> The polyimide resin according to <1> or <2>, wherein the general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), and the general formula (B-2) is the following general formula (B-2a): In the general formula (B-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and o represents an integer of 0 to 4. In the general formula (B-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; m represents an integer of 1 to 3; and o represents an integer of 0 to the maximum number of substituents. In the general formula (B-2a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom, and o represents an integer of 0 to 8. <4> A polyimide resin for use as a high-frequency substrate material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). In the general formulas (A-2a) to (A-2g), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; 1 represents an integer of 1 to 3; ２are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. In the general formula (B-3), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-4), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, each m independently represents an integer of 0 to 2, and o represents an integer of 0 to the maximum number of substituents. <5> The polyimide resin according to <4> above, wherein the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and the general formula (B-4) is the following general formula (B-4a): In the general formula (B-3a), R １are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and o represents an integer of 0 to 4. In the general formula (B-3b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; m represents an integer of 1 to 3; and o represents an integer of 0 to the maximum number of substituents. In the general formula (B-4a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom, and o represents an integer of 0 to 8. <6> The polyimide resin according to any one of <1> to <5>, having a dielectric constant of 2.6 or less at 10 GHz and a linear expansion coefficient of 50 ppm / K or less. <7> A polyimide resin having a structural unit represented by the following general formula (1): In the general formula (1), R ａ (CO) ４ The R moiety represents a tetravalent group derived from a tetravalent tetracarboxylic acid having two or more carbon atoms. ｂ (N) ２the moiety represents a tetravalent group derived from a divalent diamine having two or more carbon atoms, and the free volume fraction and average number of adjacent atoms of the amorphous polyimide resin in an equilibrium state at a temperature of 300 K and a pressure of 1 atm, calculated by molecular dynamics calculation, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of adjacent atoms is 3.94 to 4.95, the average number of adjacent atoms is the average number of adjacent atoms per number of atoms constituting the system of the molecular dynamics calculation, and the number of adjacent atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) Atomic pairs sharing one side of a Voronoi cell with each atom as a kernel point, (b) Atomic pairs separated by four bonds or more, or Atomic pairs between different molecules. <8> The polyimide resin according to <7> above, wherein the free volume fraction is 0.23 to 0.32 and the average number of adjacent atoms is 3.90 to 4.60. <9> The polyimide resin according to <7> above, wherein the free volume fraction is 0.23 to 0.32 and the average number of adjacent atoms is 3.90 to 4.60, and wherein the polyimide resin does not contain a trifluoromethyl group. <10> The polyimide resin according to <7> above, wherein the free volume fraction is 0.24 to 0.32 and the average number of adjacent atoms is 3.90 to 4.50, and wherein the polyimide resin does not contain a trifluoromethyl group. <11> The polyimide resin according to <7>, wherein the free volume fraction is 0.28 to 0.32 and the average number of adjacent atoms is 3.90 to 4.50, and the polyimide resin does not have a trifluoromethyl group.<12> The polyimide resin according to any one of <1> to <11>, wherein the free volume fraction and the average number of adjacent atoms of the polyimide resin in an amorphous state, calculated by molecular dynamics calculation, in an equilibrium state at a temperature of 300 K and a pressure of 1 atm, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38, and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38, and the average number of adjacent atoms is 3.94 to 4.95; the average number of adjacent atoms is the average of the number of adjacent atoms per number of atoms constituting the system of the molecular dynamics calculation, and the number of adjacent atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) A pair of atoms sharing one side of a Voronoi cell with each atom as a generating point; (b) A pair of atoms separated by four bonds or more, or a pair of atoms between different molecules. <13> A composition for a high-frequency substrate material, containing the polyimide resin according to any one of <1> to <12>. <14> A polyimide film for a high-frequency substrate material, containing the polyimide resin according to any one of <1> to <12>. <15> A laminate having a metal layer and a layer containing the polyimide resin according to any one of <1> to <12>. <16> A circuit board having the laminate according to <15>. <17> An antenna having the circuit board according to <16>. <18> The antenna according to claim 17, which is a millimeter-wave antenna. <19> A polyamic acid for use as a high-frequency substrate material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2): In the general formula (A-1), R １are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 0 to 3, and when l is 0, it represents that there is no bond; m represents an integer of 0 to 3; n represents an integer of 0 to 5; and when n is 0, at least one R １ has a fluorine atom, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-2), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom, each m independently represents an integer of 0 to 2, and o represents an integer of 0 to the maximum number of substituents. <20> A polyamic acid for use as a high-frequency substrate material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4): In the general formulas (A-2a) to (A-2g), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; 1 represents an integer of 1 to 3; ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. In the general formula (B-3), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-4), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, each m independently represents an integer of 0 to 2, and o represents an integer of 0 to the maximum number of substituents. <21> A composition for a high-frequency substrate material, comprising the polyamic acid according to <19> or <20> above, and a solvent.

[0006] According to the present disclosure, it is possible to provide a polyimide resin for use as a high-frequency substrate material that has both a low dielectric constant and a low coefficient of linear expansion.

[0007] Fig. 1 is a cross-sectional view showing an example of a laminate according to this embodiment. Fig. 2 is a cross-sectional view showing another example of a laminate according to this embodiment. Fig. 3 is a graph plotting the free volume fraction and the average number of adjacent atoms in a molecular dynamics simulation of an example. Fig. 4 is a graph plotting the measured values ​​of the dielectric constant and the measured values ​​of the linear expansion coefficient. Fig. 5 is a graph showing the relationship between the experimental value and the calculated value of the molecular dynamics simulation for the dielectric constant at a frequency of 10 GHz. Fig. 6 is a graph showing the relationship between the experimental value and the calculated value of the linear expansion coefficient in a molecular dynamics simulation.

[0008] (Polyimide Resin for High-Frequency Substrate Materials) The polyimide resin for high-frequency substrate materials of the present disclosure is a polyimide resin used in applications for high-frequency substrate materials, which combines a low dielectric constant and a low linear expansion coefficient. The polyimide resin (1) has a specific chemical structure as described in the first embodiment, (2) has a specific chemical structure as described in the second embodiment, (3) satisfies the free volume fraction and average number of adjacent atoms as described in the third embodiment, or (4) satisfies both (1) or (2) and (3). Here, "high frequency" refers to a high-frequency band of 10 GHz or higher, a frequency band of 30 GHz to 300 GHz known as millimeter waves (radio wave wavelengths of 1 mm to 10 mm), a frequency band of 24.25 GHz to 52.6 GHz corresponding to fifth-generation mobile communication systems (5G), etc., all of which can be appropriately selected depending on the intended application. The polyimide resin preferably has a dielectric constant of 2.6 or less at 10 GHz and a linear expansion coefficient of 50 ppm / K or less.

[0009] The polyimide resin for use as a high-frequency substrate material according to the present disclosure is based on the following findings made by the present inventors. Conventionally, a low dielectric constant and a low linear expansion coefficient have generally been in a trade-off relationship, making it difficult to achieve both. However, as shown in the examples described below, the present inventors performed molecular dynamics simulations using amorphous polyimide resins to identify two parameters: "free volume fraction" and a newly defined "average number of adjacent atoms." They found that these two parameters correlate with the calculated values ​​of the dielectric constant and linear expansion coefficient. Furthermore, by evaluating the relationships between the experimental values ​​of the dielectric constant and linear expansion coefficient for numerous known polyimide resins, they found that a high "free volume fraction" contributes to a low dielectric constant and a low linear expansion coefficient, and that a low "average number of adjacent atoms" contributes to a low dielectric constant. Based on these findings, they discovered that a polyimide resin that achieves both a low dielectric constant and a low linear expansion coefficient can be identified using the free volume fraction and the average number of adjacent atoms as indicators. Furthermore, the chemical structure of a polyimide resin that has both a low dielectric constant and a low linear expansion coefficient was identified through the molecular dynamics simulation.

[0010] [First Embodiment] A polyimide resin for use as a high-frequency substrate material in a first embodiment of the present disclosure is a polyimide resin comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2):

[0011] <Acid Anhydride> The acid anhydride is at least one selected from the group consisting of compounds represented by the following general formula (A-1). In one embodiment, it is preferably at least one selected from the group consisting of compounds represented by the following general formula (A-1a) and compounds represented by any one of the following general formulas (A-1b). The acid anhydride may be used alone or in combination of two or more.

[0012]

[0013] In the general formula (A-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent.

[0014] The substituent may be any group having a structure that can be substituted for the target, and examples thereof include one or more selected from the group consisting of halogen, hydroxyl group, alkoxy group, alkylcarbonyl group, alkylcarbonyloxy group, alkoxycarbonyl group, arylcarbonyloxy group, aryloxycarbonyl group, and aryl group. The number of the substituents may be selected from integers (e.g., 1, 2, 3, etc.) within the range from 1 to the maximum number that can be substituted (hereinafter referred to as the "maximum number of substituents").

[0015] The R １ are each independently selected from the group consisting of hydrogen, fluorine, an alkyl group having 1 to 4 carbon atoms, and a fluoroalkyl group having 1 to 4 carbon atoms, and are preferably selected from the group consisting of hydrogen, fluorine, a methyl group (—CH ３ ), and a trifluoromethyl group (—CF ３In addition, when n=0, at least one of the R １ has a fluorine atom. When n=0, one of the R １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, an alkyl group having 1 to 4 carbon atoms, and a fluoroalkyl group having 1 to 4 carbon atoms; １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, a methyl group, and a trifluoromethyl group.

[0016] In the general formula (A-1), l represents an integer of 0 to 3, and when l is 0, it indicates that there is no bond, and is preferably 0, 1, or 2, and more preferably 0 or 1. m represents an integer of 0 to 3, and is preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer of 0 to 5, and is preferably an integer of 0 to 3, and more preferably 0 or 1.

[0017] In the general formula (A-1), R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ is a fluoroalkyl group which may have a substituent. ２ The substituents in the above R １ The substituents described above can be appropriately selected, but halogens other than fluoro and alkyl groups having 1 to 4 carbon atoms are preferred. ２ is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R ２ are each independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; １ is a trifluoromethyl group, and the other R １are each independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0018] In the general formula (A-1), each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of

[0019] In the general formula (A-1), R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. ３ The substituents in the above R １ The substituents described above can be appropriately selected. ３ is more preferably each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0020] In one embodiment, the general formula (A-1) is preferably either the following general formula (A-1a) or the following general formula (A-1b). The following general formula (A-1a) is one embodiment of the general formula (A-1) where n = 0. The following general formula (A-1b) is one embodiment of the general formula (A-1) where l = 0 and m = 0.

[0021]

[0022] In the general formula (A-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom. １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms; １is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0023] In the general formula (A-1a), m represents an integer of 0 to 3, preferably 0, 1 or 2, and more preferably 0 or 1.

[0024]

[0025] In the general formula (A-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0026] In the general formula (A-1b), n represents an integer of 1 to 5, preferably an integer of 1 to 3, and more preferably 1.

[0027] In the general formula (A-1b), R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ is a fluoroalkyl group which may have a substituent. ２ is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R ２ are each independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; １ is a trifluoromethyl group, and the other R １ are each independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0028] In the general formula (A-1b), each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of

[0029] In the general formula (A-1b), R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. ３ is more preferably each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0030] <Diamine> The diamine is at least one selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2). In one embodiment, the general formula (B-1) is preferably either the following general formula (B-1a) or the following general formula (B-1b), and the general formula (B-2) is preferably the following general formula (B-2a). The diamine may be used alone or in combination of two or more types.

[0031]

[0032] In the general formula (B-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0033] In general formula (B-1), l represents an integer of 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer of 0 to 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer of 0 to 5, preferably an integer of 0 to 3, and more preferably 0 or 1. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0034] In the general formula (B-1), R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ is a fluoroalkyl group which may have a substituent. ２ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected, but halogens other than fluoro and alkyl groups having 1 to 4 carbon atoms are preferred. ２ is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R ２ are each independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; １ is a trifluoromethyl group, and the other R １ are each independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0035] In the general formula (B-1), each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of

[0036] In the general formula (B-1), R ３are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. ３ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. ３ is more preferably each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0037] The diamine compound represented by the general formula (B-1) has two amino groups (—NH ２ When m is 0, the two amino groups can be substituted at any two positions on the benzene ring shown at the left end of general formula (B-1), and when m is 1, 2, or 3, the two amino groups can be substituted at any two positions on the fused benzene ring.

[0038]

[0039] In the general formula (B-2), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom. １ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms; １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0040] In the general formula (B-2), each m independently represents an integer of 0 to 2, and is preferably 0 or 1, and more preferably 0. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0041] The diamine, which is a compound represented by the general formula (B-2), has two amino groups (—NH ２ When m is 0, the two amino groups can be substituted at any two positions on the benzene rings shown at both ends of the general formula (B-2), and they may be substituted on the same benzene ring, or they may be substituted on each of the two benzene rings. When m is 1 or 2, the two amino groups can be substituted at any two positions on the two condensed benzene rings, and they may be substituted on the same condensed benzene ring, or they may be substituted on each of the two condensed benzene rings.

[0042] In one embodiment, the general formula (B-1) is preferably either the following general formula (B-1a) or the following general formula (B-1b), and the general formula (B-2) is preferably the following general formula (B-2a). The following general formula (B-1a) is one embodiment of the general formula (B-1) where m = 0 and n = 0. The following general formula (B-1b) is one embodiment of the general formula (B-1) where n = 0. The following general formula (B-2a) is one embodiment of the general formula (B-2) where m = 0.

[0043]

[0044] In the general formula (B-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ is preferably each independently selected from the group consisting of fluorine and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of fluorine and a methyl group.

[0045] In the general formula (B-1a), o represents an integer of 0 to 4, preferably an integer of 1 to 4, and more preferably an integer of 2 to 4.

[0046]

[0047] In the general formula (B-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0048] In general formula (B-1b), m represents an integer of 1 to 3, preferably 1 or 2, and more preferably 1. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer that is 25% or more of the maximum number of substituents, and more preferably an integer that is 50% or more of the maximum number of substituents.

[0049]

[0050] In the general formula (B-2a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom. １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms; １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0051] In the general formula (B-2a), o represents an integer of 0 to 8, preferably an integer of 2 to 8, and more preferably an integer of 4 to 8.

[0052] [Second Embodiment] A polyimide resin for use as a high-frequency substrate material in a second embodiment of the present disclosure is a polyimide resin comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4):

[0053] <Acid Anhydride> The acid anhydride is at least one selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g): The acid anhydride may be used alone or in combination of two or more.

[0054]

[0055] In the general formulas (A-2a) to (A-2g), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, an alkyl group having 1 to 4 carbon atoms, and a fluoroalkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, a methyl group, and a trifluoromethyl group.

[0056] In the general formulae (A-2a) to (A-2g), l represents an integer of 1 to 3, and is preferably 1 or 2.

[0057] In the general formulas (A-2a) to (A-2g), R ２are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. ２ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. ２ are each independently preferably selected from the group consisting of hydrogen, fluorine, an alkyl group having 1 to 4 carbon atoms, and a fluoroalkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, a methyl group, and a trifluoromethyl group.

[0058] <Diamine> The diamine is at least one selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). In one embodiment, the general formula (B-3) is preferably either the following general formula (B-3a) or the following general formula (B-3b), and the general formula (B-4) is preferably the following general formula (B-4a). The diamine may be used alone or in combination of two or more types.

[0059]

[0060] In the general formula (B-3), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0061] In general formula (B-3), l represents an integer of 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer of 0 to 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer of 0 to 5, preferably an integer of 0 to 3, and more preferably 0 or 1. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0062] In the general formula (B-3), R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R ２ is a fluoroalkyl group which may have a substituent. ２ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. ２ is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R ２ are each independently selected from the group consisting of hydrogen, fluorine, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; １ is a trifluoromethyl group, and the other R １ are each independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0063] In the general formula (B-3), each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of

[0064] In the general formula (B-3), R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３may be bonded to each other to form a cycloalkyl group. ３ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. ３ is more preferably each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0065]

[0066] In the general formula (B-4), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ The substituent in the formula (A-1) is R １ The substituents described above can be appropriately selected. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0067] In general formula (B-4), each m independently represents an integer of 0 to 2, and is preferably 0 or 1, and more preferably 0. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer of 25% or more of the maximum number of substituents, and more preferably an integer of 50% or more of the maximum number of substituents.

[0068] In one embodiment, the general formula (B-3) is preferably either the following general formula (B-3a) or the following general formula (B-3b), and the general formula (B-4) is preferably the following general formula (B-4a). The following general formula (B-3a) is one embodiment of the general formula (B-3) where m = 0 and n = 0. The following general formula (B-3b) is one embodiment of the general formula (B-3) where n = 0. The following general formula (B-4a) is one embodiment of the general formula (B-4) where m = 0.

[0069]

[0070] In the general formula (B-3a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ is preferably each independently selected from the group consisting of fluorine and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of fluorine and a methyl group.

[0071] In the general formula (B-3a), o represents an integer of 0 to 4, preferably an integer of 1 to 4, and more preferably an integer of 2 to 4.

[0072]

[0073] In the general formula (B-3b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. １ are each independently preferably selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms, and more preferably selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0074] In general formula (B-3b), m represents an integer of 1 to 3, preferably 1 or 2, and more preferably 1. o represents an integer of 0 to the maximum number of substituents, and is preferably an integer that is 25% or more of the maximum number of substituents, and more preferably an integer that is 50% or more of the maximum number of substituents.

[0075]

[0076] In the general formula (B-4a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom. １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms; １ is fluorine, and the other R １ are each independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

[0077] In the general formula (B-4a), o represents an integer of 0 to 8, preferably an integer of 2 to 8, and more preferably an integer of 4 to 8.

[0078] [Third Embodiment] A polyimide resin for use as a high-frequency substrate material in a third embodiment of the present disclosure is a polyimide resin having a structural unit represented by the following general formula (1): In the general formula (1), R ａ (CO) ４ The R moiety represents a tetravalent group derived from a tetravalent tetracarboxylic acid having two or more carbon atoms. ｂ (N) ２The moiety represents a tetravalent group derived from a divalent diamine having two or more carbon atoms. The free volume fraction and average number of neighboring atoms of the polyimide resin in an amorphous state, calculated by molecular dynamics calculation at an equilibrium state at a temperature of 300 K and a pressure of 1 atm, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of neighboring atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of neighboring atoms is 3.94 to 4.95. The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the system of the molecular dynamics calculation, and the number of neighboring atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) atom pairs that share one side of a Voronoi cell with each atom as a kernel point; (b) atom pairs that are four bonds or more apart, or atom pairs between different molecules.

[0079] -Free volume fraction- "Free volume" is the volume per unit mass of a molecule at a certain temperature and pressure, i.e., the specific volume v, minus the occupied volume v of that molecule. ０ This can be expressed as a free volume vf using the following formula 1. Also, the "free volume fraction" is the free volume vf per specific volume v, and can be expressed as a free volume fraction f using the following formula 2. (Formula 1) vf = v - v ０ (Formula 2) f=(v−v ０ ) / v

[0080] The free volume fraction in this embodiment is the free volume fraction of the amorphous polyimide resin at equilibrium at a temperature of 300 K and a pressure of 1 atm, calculated by molecular dynamics calculation, and can be calculated using the following formula 3. Specifically, the free volume fraction can be calculated using the polymer property automatic calculation system RadonPy (open source software) and Python library molecular dynamics calculation. Based on the coordinates of each atom in the equilibrium state in the molecular dynamics simulation described below, the free volume fraction f can be calculated using the following formula 3. The van der Waals radius of each atom in the following formula 3 was calculated using the value calculated based on the GAFF2 force field (Reference 1 below). Reference 1: X. He, V. H. Man, W. Yang, T.-S. Lee, and J. Wang, A Fast and High-Quality Charge Model for the Next Generation General AMBER Force Field, J. Chem. Phys. 153, 114502 (2020).

[0081] (Formula 3)

[0082] - Average number of neighboring atoms - The average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the system of the molecular dynamics calculation. The number of neighboring atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) Atomic pairs that share one side of a Voronoi cell with each atom as a kernel point (b) Atomic pairs that are four bonds or more apart, or atomic pairs between different molecules

[0083] Specifically, the number of adjacent atoms is calculated by molecular dynamics calculation as the total number of atom pairs that satisfy the following (a) and (b): (a) atom pairs (pairs of kernel points) that share a Voronoi edge in a Voronoi diagram calculated with each atom as a kernel point (b) atom pairs that are four bonds or more apart, or atom pairs between different molecules In a system with periodic boundary conditions, the total number of pairs that satisfy (a) and (b) (i.e., the number of adjacent atoms) can be divided by the number of atoms that make up the system to calculate the average number of adjacent atoms.

[0084] The average number of adjacent atoms in this embodiment is the average number of adjacent atoms calculated by molecular dynamics calculation in an equilibrium state of the polyimide resin in an amorphous state at a temperature of 300 K and a pressure of 1 atm. The average number of adjacent atoms per atom can be calculated by performing Voronoi polyhedron analysis with each atom as a kernel point based on the coordinates of each atom in the equilibrium state in a molecular dynamics simulation described below, and dividing the total number of atom pairs in the amorphous cell that satisfy (a) and (b) by the total number of atoms constituting the amorphous cell.

[0085] The free volume fraction and the average number of adjacent atoms preferably satisfy the following condition (1) or (2), and also satisfy any one of the following conditions (3) to (6): According to the molecular dynamics simulation described below, when the following condition (1) or (2) is satisfied, it is possible to achieve both a low dielectric constant of 2.6 or less at 10 GHz and a low linear expansion coefficient of 50 ppm / K or less: (1) the free volume fraction is 0.23 to 0.38, and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38, and the average number of adjacent atoms is 3.94 to 4.95.

[0086] (3) The free volume fraction is 0.23 to 0.32, and the average number of adjacent atoms is 3.90 to 4.60. When the condition (3) is satisfied, it is possible to achieve both a low dielectric constant and a low linear expansion coefficient, that is, a dielectric constant of 2.5 or less at 10 GHz and a linear expansion coefficient of 40 ppm / K or less.

[0087] (4) The free volume fraction is 0.23 to 0.32, the average number of adjacent atoms is 3.90 to 4.60, and the polymer does not contain a trifluoromethyl group. When the condition (4) is satisfied, the dielectric constant at 10 GHz is 2.5 or less, and the linear expansion coefficient is 40 ppm / K or less, so that both a low dielectric constant and a low linear expansion coefficient can be achieved.

[0088] (5) The free volume fraction is 0.24 to 0.32, the average number of adjacent atoms is 3.90 to 4.50, and the polymer does not contain a trifluoromethyl group. When the condition (5) is satisfied, the dielectric constant at 10 GHz is 2.5 or less, and the linear expansion coefficient is 30 ppm / K or less, so that both a low dielectric constant and a low linear expansion coefficient can be achieved.

[0089] (6) The free volume fraction is 0.28 to 0.32, the average number of adjacent atoms is 3.90 to 4.50, and the polymer does not contain a trifluoromethyl group. When the condition (6) is satisfied, the dielectric constant at 10 GHz is 2.5 or less, and the linear expansion coefficient is 20 ppm / K or less, so that both a low dielectric constant and a low linear expansion coefficient can be achieved.

[0090] [Fourth Embodiment] A polyimide resin for use as a high-frequency board material in a fourth embodiment of the present disclosure is the polyimide resin for use as a high-frequency board material in the first embodiment or the polyimide resin for use as a high-frequency board material in the second embodiment, wherein the free volume fraction and the average number of adjacent atoms of the polyimide resin in an amorphous state, calculated by molecular dynamics calculation, in an equilibrium state at a temperature of 300 K and a pressure of 1 atm, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of adjacent atoms is 3.94 to 4.95, wherein the average number of adjacent atoms is the average number of adjacent atoms per number of atoms constituting the system in the molecular dynamics calculation, and wherein the number of adjacent atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) Atomic pairs that share one edge of a Voronoi cell with each atom as a kernel point. (b) Atomic pairs that are four bonds or more apart, or atomic pairs between different molecules.

[0091] The polyimide resin for use as a high-frequency substrate material in the first embodiment and the polyimide resin for use as a high-frequency substrate material in the second embodiment can be selected as appropriate from the items described in the first and second embodiments, respectively. The conditions for the free volume fraction and the average number of adjacent atoms can be selected as appropriate from the items described in the third embodiment. The free volume fraction and the average number of adjacent atoms preferably satisfy the condition (1) or (2) and any one of the conditions (3) to (6).

[0092] [Characteristics] Each of the polyimide resins for high frequency substrate materials in the first to fourth embodiments preferably has a dielectric constant of 2.6 or less at 10 GHz and a linear expansion coefficient of 50 ppm / K or less.

[0093] -Dielectric Constant- The dielectric constant of the polyimide resin at 10 GHz is preferably 2.6 or less, more preferably 2.5 or less, and even more preferably 2.4 or less.

[0094] Specifically, the dielectric constant of the polyimide resin at 10 GHz can be measured by the SPDR method (resonator method) using a vector network analyzer (E5063A, manufactured by Keysight Corporation) for a polyimide film obtained by the polyimide film manufacturing method described below. Note that the polyimide film used as a measurement sample is left to stand at a temperature of 23±1°C and a humidity of 50±5% RH for 24 hours or more before use.

[0095] Furthermore, as a method for calculating the dielectric constant of the polyimide resin at 10 GHz by molecular dynamics simulation, the following procedure can be specifically mentioned, as will be explained in the molecular dynamics simulation described later.

[0096] The length of the dielectric relaxation function (e.g., 100 ns) and the time length for calculating the dipole moment (e.g., 500 ns) are set by molecular dynamics calculation, and the dipole moment of the target substance is calculated. This generates time-series data of the dipole moment. Next, a high-pass filter is designed based on the received calculation conditions. The cutoff frequency of the high-pass filter is the reciprocal of the length of the dielectric relaxation function. If the length of the dielectric relaxation function is 100 ns, the cutoff frequency is 10 MHz. Next, the designed high-pass filter is used to remove low-frequency components from the time-series data of the dipole moment. In other words, a frequency band equal to or greater than the cutoff frequency is extracted from the time-series data of the dipole moment. This generates time-series data of the dipole moment after filtering, from which low-frequency components (e.g., less than 10 GHz) have been removed.

[0097] Next, the time series data of the dipole moment after filtering is defined as M(t), and the dielectric relaxation function Φ(t) is calculated using equation (1). The calculated dielectric relaxation function Φ(t) is fitted using equation (2). Furthermore, the fitted dielectric relaxation function Φ is calculated by Fourier transform of equation (3). ｆｉｔ (t) is frequency resolved, whereby a frequency-dependent complex permittivity is obtained, and the permittivity at a frequency of 10 GHz can be calculated from the real part of the complex permittivity at a frequency of 10 GHz.

[0098] Here, by removing low-frequency components (e.g., less than 10 GHz) that are susceptible to local effects in the simulation from the time-series data of the dipole moment, the dielectric relaxation function of the target material, polyimide resin, can be derived with high accuracy.

[0099]

[0100]

[0101]

[0102] - Linear expansion coefficient - The linear expansion coefficient means the ratio of the amount of deformation ΔL per 1 K (Kelvin) or 1° C. of temperature change to the original length L. The linear expansion coefficient of the polyimide resin is preferably 50 ppm / K or less, more preferably 40 ppm / K or less, still more preferably 30 ppm / K or less, and particularly preferably 20 ppm / K or less.

[0103] Specifically, the linear expansion coefficient of the polyimide resin can be measured using a thermomechanical analyzer (EXSTAR6000TMA / SS6000, manufactured by SII NanoTechnology Inc.) for a polyimide film obtained by the polyimide film manufacturing method described below, under the following measurement conditions. --Measurement Conditions-- First stage: The sample is heated to 150°C at a heating rate of 5°C / min to remove absorbed water. Second stage: The sample is air-cooled to room temperature at a heating rate of 5°C / min. Third stage: The main measurement is performed at a heating rate of 5°C / min. The average value of the linear expansion coefficients in the temperature range of 50°C to 200°C during this measurement is calculated and used as the linear expansion coefficient of the target polyimide film.

[0104] Furthermore, as a method for calculating the linear expansion coefficient of the polyimide resin by molecular dynamics simulation, the following procedure can be specifically mentioned, as will be explained later in the molecular dynamics simulation. First, the volume expansion coefficient α is calculated from the following formula based on the fluctuations of the volume V and enthalpy H in the equilibrium calculation: Ｐ Calculate [see Reference 2 below]. Ｂ is the Boltzmann constant and T is the temperature. Reference 2: MP Allen and DJ Tildesley, Computer Simulation of Liquids (Clarendon Press, New York, 1989).

[0105]

[0106] Next, assuming the system is isotropic, the linear expansion coefficient α L is derived.

[0107]

[0108] The dielectric loss tangent of the polyimide resin is preferably 0.0040 or less, more preferably 0.0035 or less, and even more preferably 0.0030 or less. Since the dielectric loss is proportional to the product of the square root of the dielectric constant and the dielectric loss tangent, a dielectric loss tangent of 0.0040 or less can effectively reduce the dielectric loss.

[0109] Specifically, the dielectric loss tangent of the polyimide resin can be measured by a vector network analyzer (E5063A, manufactured by Keysight) at a frequency of 1 GHz or 10 GHz using the SPDR method (resonator method) for a polyimide film obtained by the polyimide film manufacturing method described below. Note that the polyimide film used as a measurement sample is left to stand at a temperature of 23±1°C and a humidity of 50±5% RH for 24 hours or more before use.

[0110] -Glass Transition Point- The glass transition temperature of the polyimide resin is preferably 260° C. or higher, more preferably 280° C. or higher, and even more preferably 300° C. or higher. When the glass transition temperature is 260° C. or higher, the polyimide resin can be used as a material for high-frequency substrates having good solder heat resistance and dimensional stability.

[0111] The haze of the polyimide resin is preferably 20% or less, more preferably 10% or less, and even more preferably 5% or less. When the haze is 20% or less, the visibility of alignment marks can be ensured in the photolithography process when a laminate is formed and in the subsequent mounting process of a high-frequency substrate, making the polyimide resin suitable for use.

[0112] Specifically, the haze of the polyimide resin can be measured for a polyimide film obtained by the polyimide film manufacturing method described below using a spectroscopic haze meter (HSP-150Vis, manufactured by Murakami Color Research Laboratory Co., Ltd.) The average thickness of the polyimide film as a measurement sample is preferably 5 μm or more and 80 μm or less.

[0113] - Breaking elongation - The breaking elongation of the polyimide resin is preferably 20% or more, more preferably 25% or more, and even more preferably 30% or more. When the breaking elongation is 20% or more, the polyimide film is less likely to break during transport in the production process, and good productivity is maintained. Furthermore, when made into a flexible printed circuit board, bending resistance is maintained, and cracks and wiring breaks are less likely to occur during the mounting process.

[0114] The tensile modulus of the polyimide resin is preferably 5 GPa or more, more preferably 6 GPa or more, and even more preferably 7 GPa or more. When the tensile modulus is 5 GPa or more, the amount of elongation of the film when tension is applied during film transport in the polyimide film production process is suppressed, and dimensional stability is maintained.

[0115] Specifically, the breaking elongation and tensile modulus of the polyimide resin can be measured using a polyimide film obtained by the polyimide film manufacturing method described below, cut into a strip of 10 mm width and 80 mm length, using a Tensilon universal testing machine (RTM-100, manufactured by Orientec Co., Ltd.) in accordance with Japanese Industrial Standards (JIS K 7127: 1999). The width of the measurement sample is 10 mm, the chuck spacing is 50 mm, the test speed is 50 mm / min, and the number of measurements, n=10, is used to calculate the average value.

[0116] [Method for Synthesizing Polyimide Resin] The method for synthesizing the polyimide resin is not particularly limited, and any known method can be selected depending on the purpose. For example, equimolar amounts of an acid anhydride and a diamine are polymerized to synthesize a polyamic acid (polyamic acid), which is a precursor of polyimide. The resulting polyamic acid is then heated at a temperature of 200°C or higher or a catalyst is used to promote an imidization (dehydration and cyclization) reaction, thereby obtaining a polyimide. A tetracarboxylic acid corresponding to the acid anhydride may be used instead of or in combination with the acid anhydride. When multiple acid anhydrides and / or multiple diamines are used, the resulting polyamic acid and polyimide resin may be a random copolymer, a block copolymer, or a mixture thereof.

[0117] The polyamic acid and the composition containing the polyamic acid can be synthesized, for example, by the following procedure. A thermometer and a stirring rod with a stirring blade are placed in a 300 mL four-neck separable flask. Next, a solvent (e.g., dimethylacetamide, DMAC) is added under a dry nitrogen stream, and the temperature is raised to 60°C. After the temperature is raised, a diamine is added and dissolved while stirring. Next, an equimolar amount of an acid anhydride is added, and the acid anhydride and diamine are polymerized with stirring. The mixture is then cooled to room temperature, and a solvent is added as necessary, followed by filtration to obtain a composition containing polyamic acid.

[0118] The reaction temperature for polymerizing the acid anhydride and the diamine is preferably -20°C to 150°C, more preferably 0°C to 100°C. The reaction time is preferably 0.1 to 24 hours, more preferably 0.5 to 12 hours. The number of moles of the acid anhydride and the number of moles of the diamine used in the reaction are preferably equal. The closer the amount of the acid anhydride and the diamine to a polyamic acid, the more likely it is that a polyimide film with excellent mechanical properties will be obtained.

[0119] The method for synthesizing the polyimide from the polyamic acid by the imidization reaction can be, for example, the following procedure. The resulting composition containing the polyamic acid is applied (e.g., spin-coated) onto a substrate. Then, the composition is dried using a hot plate (e.g., at 80°C for 5 minutes). Subsequently, the composition is heated at a temperature of 200°C or higher to form a polyimide resin film on the substrate. Examples of the method for heating at a temperature of 200°C or higher include, for example, using an oven in a nitrogen atmosphere (oxygen concentration of 20 ppm or less), increasing the temperature from 50°C at a heating rate of 4°C / min, heating at 180°C for 30 minutes, and subsequently heating at 350°C for 30 minutes.

[0120] [Method for Identifying Polyimide Resin] The method for identifying the polyimide resin is not particularly limited and can be appropriately selected depending on the purpose. For example, a method can be used in which the polyimide resin is analyzed by infrared attenuated total reflection spectroscopy (IR-ATR) using a Fourier transform infrared spectrometer (FT-IR) to identify constituent components such as acid anhydrides and diamines. FT-IR measurement can be performed using, for example, a Nicolet 6700 (manufactured by Thermo Fisher Scientific K.K.).

[0121] (Polyamic Acid for High-Frequency Substrate Material) The polyamic acid for high-frequency substrate material according to the present disclosure is used in applications as a material for high-frequency substrates, and is a precursor of the polyimide resin for the high-frequency substrate material according to the present disclosure, which has both a low dielectric constant and a low linear expansion coefficient, and is (1) a precursor of the polyimide resin for the high-frequency substrate material according to the first embodiment, or (2) a polyamic acid that is a precursor of the polyimide resin for the high-frequency substrate material according to the second embodiment.

[0122] [First Embodiment] A polyamic acid for a high-frequency board material in a first embodiment of the present disclosure is a precursor of a polyimide resin for a high-frequency board material in the first embodiment, and is a polyamic acid comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by general formula (A-1) above, and the diamine is one or more compounds selected from the group consisting of compounds represented by general formula (B-1) above and compounds represented by general formula (B-2).

[0123] The acid anhydride and diamine can be appropriately selected from those described in the polyimide resin for high frequency substrate materials in the first embodiment.

[0124] [Second Embodiment] A polyamic acid for a high-frequency board material in a second embodiment of the present disclosure is a precursor of a polyimide resin for a high-frequency board material in the second embodiment, and is a polyamic acid comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4):

[0125] The acid anhydride and diamine can be appropriately selected from those described in the polyimide resin for high frequency substrate materials in the second embodiment.

[0126] (Composition for High-Frequency Substrate Material) [First Embodiment] The composition for high-frequency substrate material in the first embodiment of the present disclosure contains a polyimide resin and may further contain other components such as a solvent as necessary. Suitable examples of the polyimide resin include the polyimide resin for high-frequency substrate material in the first embodiment, the polyimide resin for high-frequency substrate material in the second embodiment, the polyimide resin for high-frequency substrate material in the third embodiment, and the polyimide resin for high-frequency substrate material in the fourth embodiment. These may be used alone or in combination of two or more. The composition for high-frequency substrate material in the first embodiment can be suitably prepared by subjecting the composition for high-frequency substrate material in the second embodiment to an imidization reaction.

[0127] [Second Embodiment] A composition for a high-frequency substrate material according to a second embodiment of the present disclosure contains a polyamic acid and a solvent, and may further contain other components as necessary. Suitable examples of the polyamic acid include the polyamic acid for the high-frequency substrate material according to the first embodiment and the polyamic acid for the high-frequency substrate material according to the second embodiment. These may be used alone or in combination of two or more.

[0128] <Solvent> The solvent is not particularly limited and can be appropriately selected depending on the purpose, and examples thereof include water, N-methyl-2-pyrrolidone, N,N-dimethylformamide, N,N-dimethylacetamide, N,N-dimethylisobutyramide, 3-methoxy-N,N-dimethylpropionamide, 3-butoxy-N,N-dimethylpropionamide, γ-butyrolactone, ethyl lactate, 1,3-dimethyl-2-imidazolidinone, N,N′-dimethylpropylene urea, 1,1,3,3-tetramethylurea, dimethyl sulfoxide, sulfolane, propylene glycol monomethyl ether, propylene glycol monomethyl ether acetate, diethylene glycol ethyl methyl ether, diethylene glycol dimethyl ether, etc. These may be used alone or in combination of two or more.

[0129] The content of the solvent is not particularly limited and can be appropriately selected depending on the purpose, but is preferably 150 parts by mass or more, more preferably 200 parts by mass or more, relative to 100 parts by mass of the polyimide resin and / or polyamic acid in the composition. The content of the solvent is preferably 2,000 parts by mass or less, more preferably 1,000 parts by mass or less. When the content of the solvent is 150 parts by mass or more but 2,000 parts by mass or less, the viscosity becomes suitable for coating, and the thickness of the composition after coating and the resulting polyimide film can be easily adjusted.

[0130] <Other Components> Examples of the other components include a catalyst for catalyzing imidization and a dehydrating agent.

[0131] - Catalyst - Examples of the catalyst include amines. Examples of the amines include aliphatic tertiary amines such as trimethylamine and triethylenediamine; aromatic tertiary amines such as dimethylaniline; and heterocyclic tertiary amines such as isoquinoline, pyridine, and β-picoline. These may be used alone or in combination of two or more. Among these, heterocyclic tertiary amines are preferred, and β-picoline is more preferred.

[0132] - Dehydrating Agent - Examples of the dehydrating agent include aliphatic carboxylic acid anhydrides such as acetic anhydride, propionic anhydride, and butyric anhydride; and aromatic carboxylic acid anhydrides such as benzoic anhydride. These may be used alone or in combination of two or more. Among these, acetic anhydride and benzoic anhydride are preferred, and acetic anhydride is more preferred.

[0133] The contents of the catalyst and the dehydrating agent are not particularly limited and can be appropriately selected depending on the purpose, but are preferably 0.05 mol to 10 mol, more preferably 0.1 mol to 5 mol, and even more preferably 0.5 mol to 3 mol, relative to 1 mol of the amic acid unit of the polyamic acid.

[0134] Furthermore, the composition for a high-frequency board material in the first embodiment may contain other components such as inorganic particles, a thermal crosslinking agent, a thermal acid generator, a leveling agent, a viscosity modifier, an antioxidant, an inorganic pigment, an organic pigment, or a dye.

[0135] -Inorganic Particles- The composition for high-frequency substrate materials in the first embodiment and the polyimide film described below may contain inorganic particles for the purpose of further improving the heat resistance of the polyimide film or reducing the linear expansion coefficient. Examples of the inorganic particles include metal inorganic particles such as platinum, gold, palladium, silver, copper, nickel, zinc, aluminum, iron, cobalt, rhodium, ruthenium, tin, lead, bismuth, and tungsten; and metal oxide inorganic particles such as silicon oxide (silica), titanium oxide, aluminum oxide, zinc oxide, tin oxide, tungsten oxide, zirconium oxide, calcium carbonate, and barium sulfate. The shape and content of the inorganic particles are not particularly limited and can be appropriately selected depending on the purpose. Furthermore, it is preferable to uniformly disperse the inorganic particles in the composition and polyimide film, and known means can be used to achieve this.

[0136] (Polyimide Film for High-Frequency Substrate Material) The polyimide film for high-frequency substrate material of the present disclosure contains a polyimide resin and may further contain other components as necessary. Suitable examples of the polyimide resin include the polyimide resin for high-frequency substrate material in the first embodiment, the polyimide resin for high-frequency substrate material in the second embodiment, the polyimide resin for high-frequency substrate material in the third embodiment, and the polyimide resin for high-frequency substrate material in the fourth embodiment. These may be used alone or in combination of two or more.

[0137] The average thickness of the polyimide film is not particularly limited and can be appropriately selected depending on the purpose, but is preferably 3 μm or more, more preferably 5 μm or more, and even more preferably 10 μm or more. If the average thickness is 3 μm or more, sufficient mechanical properties can be obtained as a circuit substrate. Furthermore, the average thickness is preferably 200 μm or less, more preferably 100 μm or less, and even more preferably 80 μm or less. If the average thickness is 80 μm or less, sufficient toughness can be obtained as a circuit substrate.

[0138] The polyimide film can be suitably used for films used in circuit boards such as flexible printed circuit boards, coverlay films, heat-resistant insulating tapes, heat-resistant adhesive tapes, high-density magnetic recording bases, capacitors, and the like.

[0139] [Method for Producing Polyimide Film] The method for producing the polyimide film is not particularly limited and can be appropriately selected depending on the purpose. Examples include: (I) a production method comprising the steps of applying a composition containing polyamic acid onto a substrate and drying it, and heating the resulting coating film to imidize it; and (II) a production method comprising the steps of casting a composition containing polyamic acid onto a heated substrate, imidizing it to form a gel film, peeling the resulting gel film from the substrate, and heat-treating the peeled gel film.

[0140] The substrate is not particularly limited and can be appropriately selected depending on the purpose. Examples include glass substrates; metal substrates such as stainless steel drums, endless stainless steel belts, and aluminum foil. The temperature of the substrate is preferably 30°C to 200°C, more preferably 40°C to 150°C, and even more preferably 50°C to 120°C. The drying temperature of the gel film is preferably 150°C to 500°C, more preferably 180°C to 400°C, and even more preferably 200°C to 300°C. The heat treatment temperature of the dried polyimide film is preferably 200°C or higher, more preferably 300°C or higher, and even more preferably 350°C or higher. The gel film and polyimide film may be stretched in the conveyance direction or width direction in each step.

[0141] The obtained polyimide film may further be subjected to annealing treatment or adhesion enhancing treatment (for example, electrical treatment such as corona treatment or plasma treatment, or blast treatment).

[0142] (Laminate) The laminate of the present disclosure has a metal layer and a layer containing a polyimide resin, and may further have other layers as necessary. The layer containing a polyimide resin is preferably the polyimide film of the present disclosure.

[0143] <Metal Layer> The material of the metal layer is not particularly limited and can be appropriately selected depending on the purpose, and examples thereof include copper or a copper alloy, stainless steel or an alloy thereof, nickel or a nickel alloy, and aluminum or an aluminum alloy. Among these, copper and a copper alloy are preferred, and a copper alloy containing copper and one or more components selected from the group consisting of nickel, zinc, iron, chromium, cobalt, molybdenum, tungsten, vanadium, beryllium, titanium, tin, manganese, aluminum, phosphorus, and silicon is more preferred. As the metal layer, a metal foil formed by rolling or electroplating is preferred, and a copper foil or a copper alloy foil is more preferred.

[0144] The metal-clad laminate can be obtained by laminating the metal layer and the layer containing the polyimide resin. The metal layer can also have an anti-corrosion layer, a heat-resistant layer, a silane coupling agent, or the like formed on the surface of the metal layer.

[0145] The thickness of the metal layer is not particularly limited as long as it can exhibit sufficient function depending on the purpose. The surface of the metal layer is preferably smooth in order to reduce transmission loss, and preferably has an Ra of 1.0 μm or less.

[0146] As long as the laminate comprises the metal layer and the layer containing the polyimide resin, there are no limitations on the lamination form. For example, the polyimide film and the metal layer may be directly laminated together, or the polyimide film and the metal layer may be laminated together via an adhesive layer.

[0147] The laminate may be a laminate 10 (single-sided metal-clad laminate) in which a metal layer 3 is laminated on one side of a polyimide film 1, optionally via an adhesive layer 2, as shown in FIG. 1, or a laminate 20 (double-sided metal-clad laminate) in which a metal layer 3 is laminated on both sides of a polyimide film 1, optionally via an adhesive layer 2, as shown in FIG. 2.

[0148] The material of the adhesive layer is not particularly limited and can be appropriately selected depending on the purpose, and may be, for example, either a thermosetting resin or a thermoplastic resin. From the viewpoint of the heat resistance of the laminate, the adhesive layer is preferably a thermoplastic polyimide. The glass transition temperature of the thermoplastic polyimide is preferably 300°C or less, more preferably 280°C or less, and even more preferably 260°C or less. When the glass transition temperature is 300°C or less, sufficient adhesiveness can be exhibited when, for example, hot roll lamination is performed in the step of bonding a metal layer to a layer containing a polyimide resin.

[0149] [Method for Producing Laminate] The method for producing the laminate is not particularly limited and can be appropriately selected depending on the purpose. Examples include a method including a step of bonding a metal layer to a layer containing a polyimide resin via an adhesive layer; a method of directly forming a polyimide film on a metal layer; etc. Examples of methods for bonding a layer containing a polyimide resin to a metal layer include a method using a heat roll laminating device having one or more pairs of metal rolls; and a method using continuous processing using a double belt press. Among these, it is preferable to use a heat roll laminating device having one or more pairs of metal rolls because the device configuration is simple and it is advantageous in terms of maintenance costs.

[0150] (Circuit board) The circuit board of the present disclosure includes the laminate of the present disclosure, and may further include other components as necessary. If the metal layer in the laminate is etched to form a desired pattern wiring, the laminate can be suitably used as various flexible printed circuit boards for mounting miniaturized, high-density components. The applications of the present invention are not limited thereto, and the laminate can be used for various applications as long as it includes a metal layer.

[0151] (Antenna) The antenna of the present disclosure includes the circuit board of the present disclosure and may further include other components as necessary. The antenna is preferably a millimeter-wave antenna. "Millimeter-wave" refers to a frequency of 30 GHz to 300 GHz (a radio wave wavelength of 1 mm to 10 mm). The polyimide resin of the present disclosure can achieve both a low dielectric constant and a low coefficient of linear expansion, and therefore can be suitably used as a high-frequency band communication antenna that enables ultra-high-speed and large-capacity communication.

[0152] The present invention will be described in more detail below based on examples, but the present invention is not limited to the following examples.

[0153] <Molecular Dynamics Simulation of Polyimide> A molecular dynamics simulation was performed on a homopolymer having a specific structural unit to calculate the free volume fraction and average number of adjacent atoms in the amorphous state. Specifically, in the following steps S1 to S3, an appropriate computing device (including an input device, output device, CPU, memory, etc.) was used to obtain an equilibrium structure using the polymer property automatic calculation system RadonPy (open source software), and the free volume fraction was calculated from the equilibrium structure. In addition, a proprietary Python program was used to calculate the average number of adjacent atoms from the equilibrium structure using a method that utilizes a Voronoi diagram.

[0154] The polyimides used in the calculations included approximately 250 types of polyimides, including those with structures described in PolyInfo (https: / / polymer.nims.go.jp / ) and PI1M (Reference 3: Ruimin Ma and Tengfei Luo, J. Chem. Inf. Model., 60, 10 (2020)). Molecular dynamics simulations were performed on each polyimide.

[0155] Step S1: Amorphous data were obtained for polyimide, a homopolymer with specific structural units. A system was constructed in which 10 polyimide molecules, each with approximately 1,000 atoms per molecule (specifically, between 900 and 1,100), were arranged. The polyimide was then aggregated and cooled from 800 K to 300 K at a pressure of 1 atm. The cooling rate was 150 ps / K. This allowed for the acquisition of data on the initial structure of the amorphous system. For this calculation, the force field developed in Reference 4 below was used, and non-bonded and bonded interaction parameters were specified. Reference 4: J. Trag and D. Zahn, Improved GAFF2 Parameters for Fluorinated Alkanes and Mixed Hydro- and Fluorocarbons, J. Mol. Model. 25, 39 (2019).

[0156] Step S2: Subsequently, the motion of each atom was calculated by molecular dynamics simulation under conditions of a temperature of 300 K and a pressure of 1 atm. The coordinates of each atom in the equilibrium system at 500 ns were obtained.

[0157] <Calculation of free volume fraction by molecular dynamics simulation> Step S3-1 Next, the free volume fraction f was calculated using the polymer property automatic calculation system RadonPy based on the coordinates of each atom at the final time. The free volume fraction was derived using the following equation 3, and the van der Waals radius of each atom in the following equation 3 was calculated based on the GAFF2 force field (see Reference 1).

[0158] (Formula 3)

[0159] <Calculation of the Average Number of Neighboring Atoms by Molecular Dynamics Simulation> Step S3-2 Next, the average number of neighboring atoms in the system was calculated using the following method, based on the coordinates of each atom at the final time. The number of neighboring atoms was calculated as the total number of atom pairs that satisfy the following (a) and (b): (a) atom pairs that share a Voronoi edge (pairs of kernel points) in a Voronoi diagram calculated with each atom as a kernel point (b) atom pairs that are four bonds or more apart, or atom pairs between different molecules Next, the total number of pairs that satisfy the above (a) and (b) in a system with periodic boundary conditions (i.e., the number of neighboring atoms) was divided by the number of atoms that make up the system, and the resulting value was calculated as the average number of neighboring atoms.

[0160] <Calculation of Dielectric Constant at a Frequency of 10 GHz by Molecular Dynamics Simulation> Time series data of the dipole moment of polyimide was calculated by the following procedure, and the dielectric constant at a frequency of 10 GHz was calculated based on the time series data at frequencies of 10 GHz or higher.

[0161] Specifically, the dipole moment of the target substance was calculated using molecular dynamics calculations, with the length of the dielectric relaxation function set to 100 ns and the time length for calculating the dipole moment set to 500 ns. This generated time-series data for the dipole moment. Next, a high-pass filter was designed based on the accepted calculation conditions. The cutoff frequency of the high-pass filter was the inverse of the length of the dielectric relaxation function. Since the length of the dielectric relaxation function was set to 100 ns, the cutoff frequency was set to 10 MHz. Next, low-frequency components were removed from the time-series data for the dipole moment using the designed high-pass filter. In other words, a frequency band with a cutoff frequency of 10 MHz or higher was extracted from the time-series data for the dipole moment. This generated time-series data for the filtered dipole moment, with components below 10 MHz removed.

[0162] Next, the time series data of the dipole moment after filtering was defined as M(t), and the dielectric relaxation function Φ(t) was calculated using equation (1). The calculated dielectric relaxation function Φ(t) was fitted using equation (2). Furthermore, the fitted dielectric relaxation function Φ was obtained by Fourier transform of equation (3). ｆｉｔ(t) was subjected to frequency resolution, whereby the frequency-dependent complex permittivity was obtained, and the permittivity at a frequency of 10 GHz was calculated from the real part of the complex permittivity at a frequency of 10 GHz.

[0163]

[0164]

[0165]

[0166] <Calculation of linear expansion coefficient by molecular dynamics simulation> First, based on the fluctuations of the volume V and enthalpy H in the equilibrium calculation, the volume expansion coefficient α Ｐ was calculated. Ｂ represents the Boltzmann constant, and T represents the temperature.

[0167]

[0168] Next, assuming the system is isotropic, the linear expansion coefficient α L was derived.

[0169]

[0170] Figure 3 is a graph plotting the free volume fraction and the average number of adjacent atoms. In Figure 3, black dots indicate that the linear expansion coefficient and dielectric constant calculated by molecular dynamics simulation are 60 ppm / K or less and 2.5 or less, respectively.

[0171] Figure 4 is a graph plotting the measured values ​​of dielectric constant and linear expansion coefficient for various polymers. The measured values ​​were referenced from PolyInfo. Figure 4 suggests that there is generally a negative correlation between the two physical properties (correlation coefficient: -0.74), indicating that it is difficult to achieve both a low linear expansion coefficient and a low dielectric constant.

[0172] Therefore, by visualizing polyimides (black dots) that have both a low linear expansion coefficient and a low dielectric constant in Figure 3, it was found that polyimides with a low dielectric constant and a low linear expansion coefficient exist in the region of a high free volume fraction and a low average number of adjacent atoms. Specifically, it was found that a low dielectric constant and a low linear expansion coefficient can be achieved simultaneously when the free volume fraction and the average number of adjacent atoms satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of adjacent atoms is 3.94 to 4.95.

[0173] Here, the reason why polyimides with a high free volume fraction of 0.23 or more exhibit the properties of low dielectric constant and low linear expansion coefficient is as follows. Polyimides with a high free volume fraction have a rigid or bulky molecular structure as a characteristic of their molecular structure. In an amorphous state, polyimides with a rigid molecular structure maintain the shape of their molecular chains in a rod-like shape regardless of the arrangement of surrounding molecules, making it difficult for the molecular chains to flexibly change their structure and pack densely. This is thought to result in a sparse structure. Furthermore, polyimides with a bulky molecular structure are thought to have a sparse structure because the bulky moieties act as steric hindrances, inhibiting the free internal rotation of the molecular chains, preventing the molecular chains from flexibly changing their structure and packing densely. A sparse structure results in relatively smaller polarization per volume than a dense structure, reducing responsiveness to an electric field and contributing to a reduced dielectric constant. Therefore, polyimides with a high free volume fraction characterized by a rigid or bulky molecular structure are thought to have a low dielectric constant. Furthermore, in polyimides having a rigid or bulky structure, it is assumed that internal rotation of molecular chains is inhibited for the above-mentioned reasons, and therefore, changes in molecular mobility (changes in conformational rotation frequency) due to thermal energy are thought to be small. A small change in molecular mobility due to thermal energy means a small change in free volume with respect to changes in temperature, which in turn means a material with a small thermal expansion coefficient and a low linear expansion coefficient. Therefore, polyimides with a high free volume fraction, characterized by a rigid or bulky molecular structure, are thought to have a low linear expansion coefficient. For the above-mentioned reasons, a high free volume fraction of 0.23 or more contributes to a low dielectric constant and a low linear expansion coefficient.

[0174] Polyimides with a low average number of neighboring atoms of 4.95 or less are polyimides with a high content of sp3 hybridized carbon atoms, such as polyimides containing aliphatic or alicyclic structures. Because sp3 hybridized carbon atoms are surrounded by bonding atoms, they are less likely to contact non-bonding atoms. The average number of neighboring atoms represents the average number of non-bonding atoms surrounding each atom, so the higher the content of sp3 hybridized carbon atoms, the lower the average number of neighboring atoms. In contrast, aromatic polyimides containing a large amount of sp2 hybridized carbon atoms tend to exhibit a relatively high dielectric constant because the contribution of π electrons, which have high polarizability, is included in the dielectric constant. Therefore, as the ratio of sp3 hybridized carbon atoms to sp2 hybridized carbon atoms increases, the contribution of π electrons becomes relatively smaller, resulting in a lower dielectric constant. Therefore, a low average number of neighboring atoms of 4.95 or less contributes to a low dielectric constant.

[0175] From the above, it was found that a high free volume fraction contributes to a low dielectric constant and a low linear expansion coefficient, and a low average number of adjacent atoms contributes to a low dielectric constant. Therefore, a polyimide having a high free volume fraction and a low average number of adjacent atoms, which satisfies the above condition (1) or (2), achieves both a low dielectric constant and a low linear expansion coefficient.

[0176] <Comparison of Experimental Values ​​with Calculated Values ​​from Molecular Dynamics Simulation> For the polyimide properties of dielectric constant at a frequency of 10 GHz and linear expansion coefficient, the experimental values ​​of each polyimide for which experimental values ​​are known were compared with the calculated values ​​from molecular dynamics simulation. The results are shown in Figures 5 and 6. Specific examples of polyimides for which experimental values ​​are known include polymers described in PolyInfo and the following Reference 5. Reference 5: J.O. Simpson and A.K. St. Clair, Thin Solid Films, 308-309 (1997)

[0177] Figure 5 is a graph showing the relationship between experimental values ​​for dielectric constant at a frequency of 10 GHz and calculated values ​​obtained by molecular dynamics simulation, and Figure 6 is a graph showing the relationship between experimental values ​​for linear expansion coefficient and calculated values ​​obtained by molecular dynamics simulation. In Figures 5 and 6, each dot represents a polymer for which experimental values ​​obtained by molecular dynamics simulation are known, with the horizontal axis representing the experimental value and the vertical axis representing the calculated value. The correlation coefficients were 0.94 (Figure 5) and 0.91 (Figure 6), respectively, indicating a positive correlation.

[0178] 5 and 6, it was found that the physical property values ​​of the dielectric constant and linear expansion coefficient obtained by molecular dynamics simulation qualitatively represent the experimental values. From the above, the two parameters that can achieve both a low dielectric constant and a low linear expansion coefficient (calculated value), namely the free volume fraction and the average number of adjacent atoms, are effective parameters for designing materials with the dielectric constant and linear expansion coefficient as target physical properties.

[0179] Synthesis Example 1 Polyamic acid was synthesized by adding 3.5 g of 2,3,5,6-tetramethyl-1,4-phenylenediamine (TMPD), 4.8 g of 1,2,4,5-cyclohexanetetracarboxylic dianhydride (HPMDA), and N-methyl-2-pyrrolidone (NMP) to a flask under a nitrogen atmosphere and stirring the mixture at 25° C. for 96 hours. The resulting polyamic acid A had an Mw of 7,000.

[0180] Synthesis Example 2: Under a nitrogen atmosphere, 1.0 g of 2,4,6-trimethylbenzene-1,3-diamine, 5.9 mL of γ-butyrolactone, 1.5 g of N-ethylpiperidine, and 1.49 g of hexahydro-1H,3H-benzo[1,2-c:4,5-c']difuran-1,3,5,7-tetraone were added to a recovery flask and stirred at 160°C to 215°C for 4 hours. The mixture was then allowed to cool and purified by recrystallization with acetone to obtain 1.9 g of powder. When the IR spectrum of the obtained powder was measured, peaks corresponding to C═O and C═N, which are characteristic of imide groups, were confirmed. Therefore, it was confirmed that the corresponding polyimide was obtained according to the following reaction formula:

[0181] <Evaluation> The linear expansion coefficient at 20° C. to 200° C. and the relative dielectric constant of the polyimide obtained in Synthesis Example 2 were evaluated according to the following procedures.

[0182] <<Linear Expansion Coefficient>> First, a sheet having an average thickness of 25 μm was formed using the obtained polyimide as a sample, and the linear expansion coefficient of the polyimide at 20° C. to 200° C. was measured and evaluated using a thermomechanical analyzer (EXSTAR6000TMA / SS6000, manufactured by SII NanoTechnology Inc.) under the following measurement conditions.

[0183] --Measurement conditions-- First step: The sample is heated to 150°C at a rate of 5°C / min to remove absorbed water. Second step: The sample is air-cooled to room temperature at a rate of 5°C / min. Third step: The actual measurement is carried out at a rate of 5°C / min. The average linear expansion coefficient in the temperature range of 20°C to 200°C during this measurement is calculated and used as the linear expansion coefficient of the target polyimide. The "linear expansion coefficient of polyimide at 20°C to 200°C" was evaluated based on the following evaluation criteria.

[0184] -Evaluation Criteria- ◯: The linear expansion coefficient of the polyimide is 50 ppm / °C or less. ×: The linear expansion coefficient of the polyimide is more than 50 ppm / °C.

[0185] <<Dielectric Constant>> A sheet having an average thickness of 25 μm was formed as a sample using the obtained polyimide, and the dielectric constant of the polyimide was measured at 25° C. and 10 GHz by the SPDR method (resonator method) using a vector network analyzer (E5063A, manufactured by Keysight Corporation), and evaluated based on the following evaluation criteria.

[0186] -Evaluation Criteria- ◯: The relative dielectric constant of the polyimide is 2.6 or less. ×: The relative dielectric constant of the polyimide is more than 2.6.

[0187] As a result of evaluating the polyimide obtained in Synthesis Example 2, it was confirmed that the linear expansion coefficient at 20°C to 200°C was evaluated as "good" and the relative dielectric constant of the polyimide was evaluated as "good".

[0188] Although the embodiments have been described above, it will be understood that various changes in form and details can be made without departing from the spirit and scope of the claims.

[0189] This application claims priority based on Japanese Patent Application No. 2024-070589, filed on April 24, 2024, the entire contents of which are incorporated herein by reference.

[0190] REFERENCE SIGNS LIST 1 Polyimide film 2 Adhesive layer 3 Metal layer 10 Laminate 20 Laminate

Claims

1. A polyimide resin for use as a high-frequency circuit board material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2). In the general formula (A-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 0 to 3, and when l is 0, it represents that there is no bond; m represents an integer of 0 to 3; n represents an integer of 0 to 5; and when n is 0, at least one R １ has a fluorine atom, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-2), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom; each m independently represents an integer of 0 to 2; and o represents an integer of 0 to the maximum number of substituents.

2. The polyimide resin according to claim 1, wherein the general formula (A-1) is either the following general formula (A-1a) or the following general formula (A-1b): In the general formula (A-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom; and m represents an integer of 0 to 3. In the general formula (A-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, n represents an integer of 1 to 5, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group.

3. The polyimide resin according to claim 1 or 2, wherein the general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), and the general formula (B-2) is the following general formula (B-2a): In the general formula (B-1a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and o represents an integer of 0 to 4. In the general formula (B-1b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; m represents an integer of 1 to 3; and o represents an integer of 0 to the maximum number of substituents. In the general formula (B-2a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom; and o represents an integer of 0 to 8.

4. A polyimide resin for use as a high-frequency circuit board material, comprising an acid anhydride and a diamine, wherein the acid anhydride is at least one selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is at least one selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4). In the general formulas (A-2a) to (A-2g), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; 1 represents an integer of 1 to 3; ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. In the general formula (B-3), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-4), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; each m is independently an integer of 0 to 2; and o is an integer of 0 to the maximum number of substituents.

5. The polyimide resin according to claim 4, wherein the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and the general formula (B-4) is the following general formula (B-4a): In the general formula (B-3a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and o represents an integer of 0 to 4. In the general formula (B-3b), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; m represents an integer of 1 to 3; and o represents an integer of 0 to the maximum number of substituents. In the general formula (B-4a), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, １ has a fluorine atom; and o represents an integer of 0 to 8.

6. A polyimide resin according to any one of claims 1 to 5, having a dielectric constant of 2.6 or less at 10 GHz and a linear expansion coefficient of 50 ppm / K or less.

7. A polyimide resin having a structural unit of the following general formula (1): In the general formula (1), R ａ (CO) ４ The R moiety represents a tetravalent group derived from a tetravalent tetracarboxylic acid having two or more carbon atoms. ｂ (N) ２ the moiety represents a tetravalent group derived from a divalent diamine having two or more carbon atoms, and the free volume fraction and average number of neighboring atoms of the polyimide resin in an amorphous state, calculated by molecular dynamics calculation at an equilibrium state at a temperature of 300 K and a pressure of 1 atm, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of neighboring atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of neighboring atoms is 3.94 to 4.95, the average number of neighboring atoms is the average number of neighboring atoms per number of atoms constituting the system of the molecular dynamics calculation, and the number of neighboring atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) atom pairs that share one side of a Voronoi cell with each atom as a kernel point, and (b) atom pairs that are four bonds or more apart, or atom pairs between different molecules.

8. The polyimide resin according to claim 7, wherein the free volume fraction is 0.23 to 0.32 and the average number of adjacent atoms is 3.90 to 4.

60.

9. The polyimide resin according to claim 7, wherein the free volume fraction is 0.23 to 0.32, the average number of adjacent atoms is 3.90 to 4.60, and the polyimide resin does not contain a trifluoromethyl group.

10. The polyimide resin according to claim 7, wherein the free volume fraction is 0.24 to 0.32, the average number of adjacent atoms is 3.90 to 4.50, and the polyimide resin does not contain a trifluoromethyl group.

11. The polyimide resin according to claim 7, wherein the free volume fraction is 0.28 to 0.32, the average number of adjacent atoms is 3.90 to 4.50, and the polyimide resin does not contain a trifluoromethyl group.

12. The polyimide resin according to any one of claims 1 to 11, wherein the free volume fraction and the average number of adjacent atoms of the polyimide resin in an amorphous state, calculated by molecular dynamics calculations, in an equilibrium state at a temperature of 300 K and a pressure of 1 atm, satisfy the following condition (1) or (2): (1) the free volume fraction is 0.23 to 0.38 and the average number of adjacent atoms is 3.80 to 4.75, or (2) the free volume fraction is 0.24 to 0.38 and the average number of adjacent atoms is 3.94 to 4.95; the average number of adjacent atoms is the average number of adjacent atoms per molecule of the polyimide resin; the average number of adjacent atoms is the average number of adjacent atoms per number of atoms constituting the system of the molecular dynamics calculation; and the number of adjacent atoms is the total number of atom pairs that satisfy the following (a) and (b): (a) Atomic pairs that share one edge of a Voronoi cell with each atom as a kernel point. (b) Atomic pairs that are four bonds or more apart, or atomic pairs between different molecules.

13. A composition for use as a high-frequency substrate material, comprising the polyimide resin according to any one of claims 1 to 12.

14. A polyimide film for use as a high-frequency substrate material, comprising the polyimide resin according to any one of claims 1 to 12.

15. A laminate having a metal layer and a layer containing the polyimide resin according to any one of claims 1 to 12.

16. A circuit board comprising the laminate of claim 15.

17. An antenna having the circuit board according to claim 16.

18. The antenna of claim 17, which is a millimeter wave antenna.

19. A polyamic acid for use as a high-frequency circuit board material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-1) and compounds represented by the following general formula (B-2): In the general formula (A-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 0 to 3, and when l is 0, it represents that there is no bond; m represents an integer of 0 to 3; n represents an integer of 0 to 5; and when n is 0, at least one R １ has a fluorine atom, and R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-1), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ２ may be bonded to each other to form a cycloalkyl group, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-2), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R １ has a fluorine atom; each m independently represents an integer of 0 to 2; and o represents an integer of 0 to the maximum number of substituents.

20. A polyamic acid for use as a high-frequency circuit board material, comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formulas (A-2a) to (A-2g), and the diamine is one or more compounds selected from the group consisting of compounds represented by the following general formula (B-3) and compounds represented by the following general formula (B-4): In the general formulas (A-2a) to (A-2g), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; 1 represents an integer of 1 to 3; ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent. In the general formula (B-3), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; l represents an integer of 1 to 3; m represents an integer of 0 to 3; n represents an integer of 0 to 5; o represents an integer of 0 to the maximum number of substituents; R ２ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and at least one R ２ represents a fluoroalkyl group which may have a substituent, and each X is independently —O—, —C(R ３ ) ２ - and -SO ２ - is selected from the group consisting of R ３ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent, and two adjacent R ３ may be bonded to each other to form a cycloalkyl group. In the general formula (B-4), R １ are each independently selected from the group consisting of hydrogen, halogen, an alkyl group which may have a substituent, an alkoxy group which may have a substituent, an aromatic ring which may have a substituent, and a heterocycle which may have a substituent; each m is independently an integer of 0 to 2; and o is an integer of 0 to the maximum number of substituents.

21. A composition for use as a high-frequency substrate material, comprising the polyamic acid according to claim 19 or 20 and a solvent.

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