Polyimide resins, compositions, polyimide films, laminates, circuit boards, and antennas for high-frequency substrate materials, as well as polyamic acids and compositions for high-frequency substrate materials.

Abstract

To provide a polyimide resin for high-frequency substrate materials that achieves both a low dielectric constant and a low coefficient of thermal expansion. [Solution] A polyimide resin for high-frequency substrate material comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of compounds represented by formula (A-1), and the diamine is one or more selected from the group consisting of compounds represented by formula (B-1), etc. TIFF2026123010000073.tif55169 TIFF2026123010000074.tif48169

Description

[Technical Field]

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

[0002] Polyimide resins with low dielectric loss tangent and low coefficient of thermal expansion are being considered as materials for high-frequency substrates (see, for example, Patent Document 1). Conventionally, low dielectric constant and low coefficient of thermal expansion are generally in a trade-off relationship, making it difficult to achieve both, and a polyimide resin for high-frequency substrates that can achieve both low dielectric constant and low coefficient of thermal expansion has not been found. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2023-088880 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] This disclosure aims to provide a polyimide resin for high-frequency substrate materials that achieves both a low dielectric constant and a low coefficient of thermal expansion. [Means for solving the problem]

[0005] <1> It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1): The polyimide resin for high-frequency substrate materials 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). [ka] In the general formula (A-1), R 2 is 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 heterocyclic ring which may have a substituent, l represents an integer of 0 to 3, and when l is 0, it indicates that there is no bond, m represents an integer of 0 to 3, n represents an integer of 0 to 5, When n is 0, at least one R 1 has a fluorine atom, R 2 is 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 heterocyclic ring which may have a substituent, and two adjacent Rs 2 may combine with each other to form a cycloalkyl group, At least one R 2 is a fluoroalkyl group which may have a substituent, X is independently selected from the group consisting of -O-, -C(R 3 )2-, and -SO2-, R 3 is 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 heterocyclic ring which may have a substituent, and two adjacent Rs 3 may combine with each other to form a cycloalkyl group. [Chemical formula] In the general formula (B-1), R 1 is 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 heterocyclic ring 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 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-2), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <2> The above general formula (A-1) is one of the following general formulas (A-1a) and (A-1b). <1> This is the polyimide resin described in [reference]. [ka] In the above general formula (A-1a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R1 It has a fluorine atom, m represents an integer between 0 and 3. [ka] In the general formula (A-1b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer from 1 to 5. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. <3> The above general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), The above general formula (B-2) is the following general formula (B-2a) <1> or <2> This is the polyimide resin described in [reference]. [ka] In the general formula (B-1a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. [ka] In the general formula (B-1b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. n is [Momoyama 1], representing an integer from 1 to 3. 'o' represents an integer between 0 and the maximum number of substituents. [ka] In the general formula (B-2a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, 'o' represents an integer between 0 and 8. <4> It consists of an acid anhydride and a diamine, 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). The polyimide resin for high-frequency substrate materials 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). [ka] In the general formulas (A-2a) to (A-2g), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. [ka] In the general formula (B-3), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer between 0 and the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-4), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <5> The above general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), The above general formula (B-4) is the following general formula (B-4a) <4> This is the polyimide resin described in [reference]. [ka] In the general formula (B-3a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. [ka] In the general formula (B-3b), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. [ka] In the general formula (B-4a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, 'o' represents an integer between 0 and 8. <6> The dielectric constant at 10 GHz is 2.6 or less. The coefficient of linear expansion is 50 ppm / K or less, <1> from <5> It is a polyimide resin as described in any one of the items. <7> A polyimide resin having the structural unit of the following general formula (1), [ka] In the above general formula (1), R a The (CO)4 portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R b The (N)2 portion represents a tetravalent group derived from a divalent diamine with 2 or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The polyimide resin for high-frequency substrate materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules <8> The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms is 3.90 to 4.60, <7> This is the polyimide resin described in [reference]. <9> The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.60. The above, which does not have a trifluoromethyl group. <7> This is the polyimide resin described in [reference]. <10> The free volume fraction is 0.24 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.50. The above, which does not have a trifluoromethyl group. <7> This is the polyimide resin described in [reference]. <11> The free volume fraction is 0.28 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.50. The above, which does not have a trifluoromethyl group. <7> This is the polyimide resin described in [reference]. <12> The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The number of adjacent atoms is the total number of atom pairs that satisfy both (a) and (b) below, <1> from <11> It is a polyimide resin as described in any one of the items. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules <13> The aforementioned <1> from <12> This is a composition for high-frequency substrate materials containing the polyimide resin described in any one of the above. <14> The aforementioned <1> from <12> This is a polyimide film for high-frequency substrate materials containing the polyimide resin described in any one of the items. <15> Metal layer, The aforementioned <1> from <12> A laminate having a layer containing the polyimide resin described in any one of the items. <16> The aforementioned <15> This is a circuit board having the laminate described above. <17> The aforementioned <16> This is an antenna having a circuit board as described above. <18> The aforementioned millimeter-wave antenna <17> This is the antenna described in [the document]. <19> It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1): The diamine is a polyamic acid for high-frequency substrate materials, wherein 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). [ka] In the above general formula (A-1), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 0 and 3, and if l is 0, it indicates that there are no connections. m represents an integer between 0 and 3. n represents an integer from 0 to 5. If n is 0, then at least one R 1 It has a fluorine atom, R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-1), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer between 0 and the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group. at least one R 2 This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-2), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 1 It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <20> It consists of an acid anhydride and a diamine, 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). The diamine is a polyamic acid for high-frequency substrate materials, wherein 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). [ka] In the general formulas (A-2a) to (A-2g), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. [ka] In the general formula (B-3), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer between 0 and the maximum number of substituents. R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R 2This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-, R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. [ka] In the general formula (B-4), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents. <21> The aforementioned <19> or <20> This is a composition for high-frequency substrate materials containing the polyamic acid and solvent described above. [Effects of the Invention]

[0006] According to this disclosure, it is possible to provide a polyimide resin for high-frequency substrate materials that achieves both a low dielectric constant and a low coefficient of thermal expansion. [Brief explanation of the drawing]

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

[0008] (Polyimide resin for high-frequency substrate materials) The polyimide resin for high-frequency substrate materials of this disclosure is a polyimide resin used for applications as a material for high-frequency substrates, which achieves both a low dielectric constant and a low coefficient of thermal expansion, and is a polyimide resin that (1) has a specific chemical structure in the first embodiment, (2) has a specific chemical structure in the second embodiment, (3) satisfies the requirements for free volume fraction and average number of neighboring atoms in the third embodiment, or (4) satisfies (1) or (2) and (3) above. Here, "high frequency" refers to high-frequency bands of 10 GHz or higher, frequency bands of 30 GHz to 300 GHz (radio wave wavelengths of 1 mm to 10 mm) known as millimeter waves, and frequency bands of 24.25 GHz to 52.6 GHz compatible with fifth-generation mobile communication systems (5G). All of these can be appropriately selected depending on the intended use. The polyimide resin preferably has a dielectric constant of 2.6 or less at 10 GHz and a coefficient of thermal expansion of 50 ppm / K or less.

[0009] The polyimide resin for high-frequency substrate materials described herein is based on the following findings discovered by the inventors. In other words, conventionally, low dielectric constant and low coefficient of thermal expansion are generally in a trade-off relationship, making it difficult to achieve both. However, as shown in the examples described later, the inventors identified two parameters, "free volume fraction" and the newly defined "average number of neighboring atoms," through molecular dynamics simulations using amorphous polyimide resin, and found that these two parameters correlate with the calculated values ​​of dielectric constant and coefficient of thermal expansion. In addition, as a result of evaluating the relationship between the dielectric constant and coefficient of thermal expansion of numerous known polyimide resins and experimental values, they found that a high "free volume fraction" contributes to low dielectric constant and low coefficient of thermal expansion, and that a low "average number of neighboring atoms" contributes to low dielectric constant. From this, we found that a polyimide resin that achieves both a low dielectric constant and a low coefficient of thermal expansion can be identified using the free volume fraction and the average number of neighboring atoms as indicators. Furthermore, we identified the chemical structure of a polyimide resin that achieves both a low dielectric constant and a low coefficient of thermal expansion through molecular dynamics simulations.

[0010] [First Embodiment] The polyimide resin for high-frequency substrate material in the first embodiment of this disclosure is a polyimide resin comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more selected from the group consisting of compounds represented by the following general formula (A-1), and the diamine is one or more 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 aforementioned acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1). In one embodiment, it is preferable that the compound is selected from the group consisting of a compound represented by the following general formula (A-1a) and a compound represented by either of the following general formulas (A-1b). The aforementioned acid anhydride may be used alone or in combination of two or more types.

[0012] [ka]

[0013] In the above general formula (A-1), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle.

[0014] The substituent can be any group having a structure that can be substituted on the target, but examples include one or more selected from the group consisting of halogens, hydroxyl groups, alkoxy groups, alkylcarbonyl groups, alkylcarbonyloxy groups, alkoxycarbonyl groups, arylcarbonyloxy groups, aryloxycarbonyl groups, and aryl groups. The number of substituents can be selected from an integer within the range of one to the maximum number of substituents that can be substituted (hereinafter referred to as the "maximum number of substituents") (for example, one, two, three, etc.).

[0015] The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl group (-CH3), and trifluoromethyl group (-CF3). Furthermore, if n=0, at least one of the R 1 It contains a fluorine atom. If n=0, one of the above R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, a methyl group, and a trifluoromethyl group.

[0016] In the general formula (A-1) above, l represents an integer from 0 to 3, where l = 0 indicates no coupling, and is preferably 0, 1, or 2, and more preferably 0 or 1. m represents an integer between 0 and 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer between 0 and 5, preferably between 0 and 3, and more preferably 0 or 1.

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

[0018] In the above general formula (A-1), X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

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

[0020] In one embodiment, it is preferable that the general formula (A-1) is any one of the following general formula (A-1a) and the following general formula (A-1b). The following general formula (A-1a) is one embodiment among the embodiments where n = 0 in the general formula (A-1). The following general formula (A-1b) is one embodiment among the embodiments where l = 0 and m = 0 in the general formula (A-1).

[0021]

Chemical formula

[0022] In the general formula (A-1a), R 1 is 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 heterocyclic ring which may have a substituent, and at least one R 1 has a fluorine atom. One of the above Rs 1 is fluorine, and it is preferable that the other above Rs [[ID= forty-one]] 1 are independently selected from the group consisting of hydrogen, fluorine, and an alkyl group having 1 to 4 carbon atoms; one of the above Rs 1 is fluorine, and it is more preferable that the other above Rs 1 are independently selected from the group consisting of hydrogen, fluorine, and a methyl group.

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

[0024] [ka]

[0025] In the general formula (A-1b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is independently 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) above, n represents an integer from 1 to 5, preferably an integer from 1 to 3, and more preferably 1.

[0027] In the general formula (A-1b), R 2 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group, and at least one R 2 This is a fluoroalkyl group which may have substituents. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; one of the R 1 is a trifluoromethyl group, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0028] In the above general formula (A-1b), X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

[0029] In the general formula (A-1b), R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. The aforementioned R 3 It is more preferable that each of these elements be independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0030] <Diamine> The aforementioned 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 one embodiment, it is preferable that the general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), and it is preferable that the general formula (B-2) is the following general formula (B-2a). The aforementioned diamine may be used alone or in combination of two or more types.

[0031] [ka]

[0032] In the general formula (B-1), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (B-1) 1 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently 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 the general formula (B-1) above, l represents an integer from 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer between 0 and 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer between 0 and 5, preferably between 0 and 3, and more preferably 0 or 1. o represents an integer from 0 to the maximum number of substituents, 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 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 2 These may bond to each other to form a cycloalkyl group, and at least one R 2 This is a fluoroalkyl group which may have substituents. R in the above general formula (B-1) 2 The substituent in is R of the general formula (A-1) 1 The substituents described can be appropriately selected, but halogens other than fluorocarbons and alkyl groups having 1 to 4 carbon atoms are preferred. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, an alkyl group having 1 to 4 carbon atoms, and an aromatic ring; one of the R 1 is a trifluoromethyl group, and the other R 1However, it is more preferable that each is independently selected from the group consisting of hydrogen, a methyl group, a trifluoromethyl group, and a phenyl group.

[0035] In the above general formula (B-1), X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

[0036] In the general formula (B-1), R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. R in the above general formula (B-1) 3 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 3 It is more preferable that each of these elements be independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0037] The diamine compound represented by the general formula (B-1) has two amino groups (-NH2). 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 the 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] [ka]

[0039] In the general formula (B-2), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R1 It contains a fluorine atom. R in the above general formula (B-2) 1 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0040] In the general formula (B-2) above, each m independently represents an integer between 0 and 2, preferably 0 or 1, and more preferably 0. o represents an integer from 0 to the maximum number of substituents, 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 compound represented by the general formula (B-2) has two amino groups (-NH2). 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 may be substituted on the same benzene ring or 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 fused benzene rings, and may be substituted on the same fused benzene ring or on each of the two fused benzene rings.

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

[0043] [ka]

[0044] In the general formula (B-1a), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is 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) above, o represents an integer from 0 to 4, preferably an integer from 1 to 4, and more preferably an integer from 2 to 4.

[0046] [ka]

[0047] In the general formula (B-1b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is independently 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 the general formula (B-1b) above, m represents an integer from 1 to 3, and is preferably 1 or 2, and more preferably 1. o represents an integer from 0 to the maximum number of substituents, 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.

[0049] [ka]

[0050] In the general formula (B-2a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 1 It contains a fluorine atom. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

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

[0052] [Second Embodiment] The polyimide resin for high-frequency substrate material in the 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 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 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 aforementioned 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). The aforementioned acid anhydride may be used alone or in combination of two or more types.

[0054] [ka]

[0055] In the general formulas (A-2a) to (A-2g), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. From the above general formula (A-2a) to general formula (A-2g), R 1 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl groups, and trifluoromethyl groups.

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

[0057] In the general formulas (A-2a) to (A-2g), R 2 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. From the above general formula (A-2a) to general formula (A-2g), R 2 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 2 Preferably, each of these is independently selected from the group consisting of hydrogen, fluorine, C1-C4 alkyl groups, and C1-C4 fluoroalkyl groups, and more preferably selected from the group consisting of hydrogen, fluorine, methyl groups, and trifluoromethyl groups.

[0058] <Diamine> The aforementioned 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 one embodiment, it is preferable that the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and it is preferable that the general formula (B-4) is the following general formula (B-4a). The aforementioned diamine may be used alone or in combination of two or more types.

[0059] [ka]

[0060] In the general formula (B-3), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (B-3) 1 The substituent in is R of the general formula (A-1) 1The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently 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 the general formula (B-3) above, l represents an integer from 1 to 3, preferably 1 or 2, and more preferably 1. m represents an integer between 0 and 3, preferably 0, 1, or 2, and more preferably 0 or 1. n represents an integer between 0 and 5, preferably between 0 and 3, and more preferably 0 or 1. o represents an integer from 0 to the maximum number of substituents, 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 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 2 This is a fluoroalkyl group which may have substituents. R in the above general formula (B-3) 2 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. One of the R 2 is a fluoroalkyl group having 1 to 4 carbon atoms, and the other R 2 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, alkyl groups having 1 to 4 carbon atoms, and aromatic rings; one of the R 1 is a trifluoromethyl group, and the other R 1 However, it is more preferable that each is 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) above, X is independently -O-, -C(R 3 Selected from the group consisting of )2- and -SO2-.

[0064] In the general formula (B-3), R 3 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R 3 These may bond to each other to form a cycloalkyl group. R in the above general formula (B-3) 3 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 3 It is more preferable that each of these elements be independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

[0065] [ka]

[0066] In the general formula (B-4), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. R in the above general formula (B-4) 1 The substituent in is R of the general formula (A-1) 1 The substituents described in the above can be selected as appropriate. The aforementioned R 1 Preferably, each of these is independently 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 the general formula (B-4) above, each m independently represents an integer between 0 and 2, preferably 0 or 1, and more preferably 0. o represents an integer from 0 to the maximum number of substituents, 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, it is preferable that the general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), and it is preferable that the general formula (B-4) is the following general formula (B-4a). The following general formula (B-3a) is one of the embodiments of the above general formula (B-3) where m=0 and n=0. The following general formula (B-3b) is one of the embodiments of the above general formula (B-3) where n=0. The following general formula (B-4a) is one of the embodiments of the above general formula (B-4) where m=0.

[0069] [ka]

[0070] In the general formula (B-3a), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is 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) above, o represents an integer from 0 to 4, preferably an integer from 1 to 4, and more preferably an integer from 2 to 4.

[0072] [ka]

[0073] In the general formula (B-3b), R 1 Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. The aforementioned R 1 Preferably, each of these is independently 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 the general formula (B-3b) above, m represents an integer from 1 to 3, and is preferably 1 or 2, and more preferably 1. o represents an integer from 0 to the maximum number of substituents, 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.

[0075] [ka]

[0076] In the general formula (B-4a), R 1 Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle, and at least one R 1 It contains a fluorine atom. One of the R 1 is fluorine, and the other R 1 However, each is preferably independently selected from the group consisting of hydrogen, fluorine, and alkyl groups having 1 to 4 carbon atoms; one of the R 1 is fluorine, and the other R 1 However, it is more preferable that each is independently selected from the group consisting of hydrogen, fluorine, and methyl groups.

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

[0078] [Third Embodiment] The polyimide resin for high-frequency substrate material in the third embodiment of this disclosure is a polyimide resin having the following general formula (1) structural unit, [ka] In the above general formula (1), R a The (CO)4 portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R b The (N)2 portion represents a tetravalent group derived from a divalent diamine with two or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The polyimide resin for high-frequency substrate materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

[0079] -Free volume fraction- "Free volume" is the volume per unit mass of a molecule under constant temperature and pressure, i.e., the specific volume v, minus the volume occupied by that molecule v0. This can be expressed as the free volume vf using the following equation 1. Furthermore, the "free volume fraction" is the free volume vf per specific volume v, and can be expressed as the free volume fraction f using the following equation 2. (Formula 1) vf=v-v0 (Formula 2) f=(v-v0) / v

[0080] The free volume fraction in this embodiment is the free volume fraction of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, calculated by molecular dynamics calculations, and can be determined by the following formula 3. Specifically, the free volume fraction can be calculated using the polymer property automatic calculation system RadonPy (open-source software) and the Python library molecular dynamics calculation. Based on the coordinates of each atom in the equilibrium state in the molecular dynamics simulation described later, the free volume fraction f can be calculated using the following equation 3. In addition, the van der Waals radii of each atom in Equation 3 below were calculated based on the GAFF2 force field (see Reference 1 below). Reference 1: X. He, VH 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)

number

[0082] -Average number of neighboring atoms- The aforementioned average number of neighboring atoms is the average number of neighboring atoms per unit of atoms constituting the molecular dynamics calculation system. The number of adjacent atoms is the total number of atom pairs that satisfy both (a) and (b) below. (a) Atom pairs sharing an edge of the Voronoi cell with each atom as each parent point (b) Atom pairs separated by four or more bonds or atom pairs between different molecules

[0083] Specifically, the number of adjacent atoms is calculated by molecular dynamics calculation as the total number of atom pairs satisfying the following (a) and (b). (a) In the Voronoi diagram calculated with each atom as each parent point, atom pairs (parent point pairs) sharing a Voronoi edge (b) Atom pairs separated by four or more bonds or atom pairs between different molecules In a system with periodic boundary conditions, the total number of pairs (i.e., the number of adjacent atoms) satisfying the above (a) and (b) can be calculated as the average number of adjacent atoms by dividing the total number of pairs by the number of atoms constituting the system.

[0084] The average number of adjacent atoms in this embodiment is the average number of adjacent atoms in the equilibrium state at a temperature of 300 K and a pressure of 1 atm of the amorphous polyimide resin calculated by molecular dynamics calculation. Based on the coordinates of each atom in the equilibrium state in the molecular dynamics simulation described later, Voronoi polyhedron analysis is performed with each atom as each parent point, and the total number of atom pairs satisfying the above (a) and (b) in the amorphous cell is divided by the total number of atoms constituting the amorphous cell to calculate the average number of adjacent atoms per atom.

[0085] The free volume fraction and the average number of adjacent atoms preferably satisfy the following condition (1) or (2) and any one of the following conditions (3) to (6). When the following condition (1) or (2) is satisfied by the molecular dynamics simulation described later, a low dielectric constant and a low linear expansion coefficient can be achieved simultaneously, with a dielectric constant at 10 GHz of 2.6 or less and a 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 neighboring atoms is 3.94 to 4.95.

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

[0087] (4) The free volume fraction is 0.23 to 0.32, the average number of neighboring atoms is 3.90 to 4.60, and it does not have a trifluoromethyl group. When the above condition (4) is met, it is possible to achieve both a low dielectric constant and a low coefficient of thermal expansion, where the dielectric constant at 10 GHz is 2.5 or less and the coefficient of thermal expansion is 40 ppm / K or less.

[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 it does not have a trifluoromethyl group. When the above condition (5) is met, it is possible to achieve both a low dielectric constant and a low coefficient of thermal expansion, where the dielectric constant at 10 GHz is 2.5 or less and the coefficient of thermal expansion is 30 ppm / K or less.

[0089] (6) The free volume fraction is 0.28 to 0.32, the average number of neighboring atoms is 3.90 to 4.50, and it does not have a trifluoromethyl group. When the above condition (6) is met, it is possible to achieve both a low dielectric constant and a low coefficient of thermal expansion, where the dielectric constant at 10 GHz is 2.5 or less and the coefficient of thermal expansion is 20 ppm / K or less.

[0090] [Fourth Embodiment] The polyimide resin for high-frequency substrate material in the fourth embodiment of this disclosure is the polyimide resin for high-frequency substrate material in the first embodiment, or the polyimide resin for high-frequency substrate material in the second embodiment, The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300K and a pressure of 1atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The polyimide resin for high-frequency substrate materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom acting as a parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

[0091] The polyimide resin for the high-frequency substrate material in the first embodiment and the polyimide resin for the high-frequency substrate material in the second embodiment can be appropriately selected from the items described in the first embodiment and the second embodiment, respectively. The conditions for the free volume fraction and the average number of neighboring atoms can be appropriately selected from those described in the third embodiment. The free volume fraction and the average number of neighboring atoms are preferably such that they satisfy condition (1) or (2) and any of conditions (3) to (6).

[0092] [Characteristics] In each of the polyimide resins for high-frequency substrate materials in the first to fourth embodiments, it is preferable that the dielectric constant at 10 GHz is 2.6 or less, and the coefficient of thermal expansion is 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] The dielectric constant of the polyimide resin at 10 GHz can be measured specifically using the SPDR method (resonator method) with a vector network analyzer (E5063A, Keysight) for a polyimide film obtained by the polyimide film manufacturing method described later. The polyimide film used as a measurement sample should be left at a temperature of 23±1°C and a humidity of 50±5%RH for at least 24 hours before use.

[0095] Furthermore, a method for calculating the dielectric constant of the polyimide resin at 10 GHz using molecular dynamics simulation is as follows, as will be explained in the molecular dynamics simulation described later.

[0096] Molecular dynamics calculations are used to set the length of the dielectric relaxation function (e.g., 100 ns) and the time length for calculating the dipole moment (e.g., 500 ns), and then calculate the dipole moment of the target material. This generates time-series data of the dipole moment. Next, a high-pass filter is designed based on the accepted 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 will be 10 MHz. Next, the designed high-pass filter is used to remove low-frequency components from the dipole moment time series data. In other words, the frequency band above the cutoff frequency is extracted from the dipole moment time series data. This generates filtered dipole moment time series data from which low-frequency components (e.g., below 10 MHz) have been removed.

[0097] Next, taking the time-series data of the dipole moment after filtering as M(t), the dielectric relaxation function Φ(t) is calculated by Equation (1). The calculated dielectric relaxation function Φ(t) is fitted with Equation (2). Further, by performing the Fourier transform of Equation (3), the dielectric relaxation function Φ fit (t) is frequency-decomposed. Thereby, the frequency-dependent complex dielectric constant is obtained, and the dielectric constant at a frequency of 10 GHz can be determined from the real part of the complex dielectric constant at a frequency of 10 GHz.

[0098] Here, by removing the low-frequency components (for example, less than 10 MHz) that are easily affected by local effects of the simulation from the time-series data of the dipole moment, the dielectric relaxation function of the polyimide resin as the target substance can be accurately derived.

[0099] [Number]

[0100] [Number]

[0101] [Number]

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

[0103] [[ID=Specifically, the coefficient of linear expansion of the polyimide resin can be measured using a thermomechanical analyzer (EXSTAR6000TMA / SS6000, manufactured by SII Nanotechnology Co., Ltd.) on a polyimide film obtained by the polyimide film manufacturing method described later, under the following measurement conditions. --Measurement Conditions-- Stage 1: Heat the sample to 150°C at a rate of 5°C / min to remove adsorbed water. Stage 2: Cool to room temperature by air at a cooling rate of 5°C / minute. Stage 3: Perform the measurement at a heating rate of 5°C / minute. The average value of the linear expansion coefficient in the temperature range of 50°C to 200°C during this measurement is determined and used as the linear expansion coefficient of the target polyimide film.

[0104] Furthermore, a method for calculating the coefficient of linear expansion of the polyimide resin using molecular dynamics simulations is as follows, as will be explained in the molecular dynamics simulation section below. First, based on the fluctuations of volume V and enthalpy H in the equilibrium calculation, the volume expansion coefficient α is obtained from the following equation. P Calculate k [see reference 2 below]. B is the Boltzmann constant, and T represents temperature. Reference 2: MP Allen and DJ Tildesley, Computer Simulation of Liquids (Clarendon Press, New York, 1989).

[0105]

number

[0106] Next, assuming the isotropy of the system, the coefficient of linear expansion α is given by the following equation. L Derive the following.

[0107]

number

[0108] - Dielectric Loss Tangent - 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 dielectric loss is proportional to the product of the square root of the dielectric constant and the dielectric loss tangent, the dielectric loss can be effectively reduced by keeping the dielectric loss tangent below 0.0040.

[0109] The dielectric loss tangent of the polyimide resin can be measured specifically using a vector network analyzer (E5063A, Keysight) at a frequency of 1 GHz or 10 GHz by the SPDR method (resonator method) on a polyimide film obtained by the polyimide film manufacturing method described later. The polyimide film used as a measurement sample should be left at a temperature of 23 ± 1 °C and a humidity of 50 ± 5% RH for at least 24 hours 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. If the glass transition temperature is 260°C or higher, it can be used as a material for high-frequency substrates with good solder heat resistance and dimensional stability.

[0111] -Hayes- 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 alignment marks can be made visible in the photolithography process when the material is laminated, and in the subsequent mounting process of the high-frequency substrate, making it suitable for use.

[0112] The haze of the polyimide resin can be measured specifically using a spectroscopic haze meter (HSP-150Vis, manufactured by Murakami Color Technology Laboratory Co., Ltd.) on a polyimide film obtained by the polyimide film manufacturing method described later. The average thickness of the polyimide film used as the measurement sample is preferably 5 μm to 80 μm.

[0113] -Elongation at break- The elongation at break of the polyimide resin is preferably 20% or more, more preferably 25% or more, and even more preferably 30% or more. When the break elongation is 20% or more, tearing during film transport is less likely to occur in the polyimide film manufacturing process, thus maintaining good productivity. Furthermore, bending resistance is maintained when it is made into a flexible printed circuit board, making cracking and wiring breakage less likely during the mounting process.

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

[0115] Specifically, the elongation at break and tensile modulus of the polyimide resin can be measured using a Tensilon universal material tester (RTM-100, manufactured by Orientec Co., Ltd.) in accordance with Japanese Industrial Standards (JIS K 7127:1999), with a sample cut into strips 10 mm wide and 80 mm long from a polyimide film obtained by the polyimide film manufacturing method described later. The width of the sample to be measured is 10 mm, the chuck spacing is 50 mm, the test speed is 50 mm / minute, and the average value is calculated with n=10 measurements.

[0116] [Method for synthesizing polyimide resin] There are no particular limitations on the method for synthesizing the polyimide resin, and a known method can be appropriately selected depending on the purpose. For example, polyamic acid (polyamic acid), which is a precursor of polyimide, can be synthesized by polymerizing equimolar amounts of acid anhydride and diamine, and the obtained polyamic acid can be heated at a temperature of 200°C or higher, or an imidation (dehydration and cyclization) reaction can be carried out using a catalyst to obtain polyimide. Alternatively, a tetracarboxylic acid corresponding to the acid anhydride may be used in place 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 random copolymers, block copolymers, or mixtures 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 stirring blades are set in a 300 mL four-neck separable flask. Next, a solvent (e.g., dimethylacetamide, DMAC) is added under a stream of dry nitrogen and the temperature is raised to 60°C. After the temperature rises, the diamine is added while stirring and dissolved. Then, equimolar amounts of acid anhydride are added and stirred to polymerize the acid anhydride and diamine. After that, the mixture is cooled to room temperature, and if necessary, solvent is added and the mixture is filtered 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, and more preferably 0°C to 100°C. The reaction time is preferably 0.1 hours to 24 hours, and more preferably 0.5 hours to 12 hours. It is also preferable that the number of moles of acid anhydride and the number of moles of diamine used in the reaction are equal. Polyamic acids in which the amounts of acid anhydride and diamine are close to equal tend to yield polyimide films with high mechanical properties.

[0119] For example, the following procedure can be used to synthesize the polyimide from the polyamic acid by an imidation reaction. The resulting polyamic acid-containing composition is applied to a substrate (e.g., by spin coating). Then, it is dried using a hot plate (e.g., at 80°C for 5 minutes). Subsequently, a film-like polyimide resin can be formed on the substrate by heating at a temperature of 200°C or higher. As an example of a method for heating to a temperature of 200°C or higher, one could use an oven and, under a nitrogen atmosphere (oxygen concentration of 20 ppm or less), raise the temperature from 50°C at a rate of 4°C / minute, heat at 180°C for 30 minutes, and then continue heating at 350°C for 30 minutes.

[0120] [Method for identifying polyimide resins] There are no particular limitations on the method for identifying the polyimide resin, and a suitable method can be selected depending on the purpose. For example, one method is to analyze it using the infrared total internal reflection attenuation method (IR-ATR method) with a Fourier transform infrared spectrometer (FT-IR) to identify constituent components such as acid anhydrides and diamines. FT-IR measurements can be performed using, for example, a Nicolet 6700 (manufactured by Thermo Fisher Scientific Co., Ltd.).

[0121] (Polyamic acid for high-frequency substrate materials) The polyamic acid for high-frequency substrate materials of this disclosure is used in applications for high-frequency substrate materials and is a precursor of the polyimide resin for high-frequency substrate materials of this disclosure that achieves both a low dielectric constant and a low coefficient of thermal expansion, and is (1) a precursor of the polyimide resin for high-frequency substrate materials in the first embodiment, or (2) a precursor of the polyimide resin for high-frequency substrate materials in the second embodiment.

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

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

[0124] [Second Embodiment] The polyamic acid for high-frequency substrate materials in the second embodiment of this disclosure is a precursor of the polyimide resin for high-frequency substrate materials in the second embodiment, and is a polyamic acid comprising an acid anhydride and a diamine, wherein the acid anhydride is one or more 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 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 the diamine can be appropriately selected from those described in the polyimide resin for high-frequency substrate material in the second embodiment.

[0126] (Composition for high-frequency substrate materials) [First Embodiment] The composition for high-frequency substrate material in the first embodiment of this disclosure contains a polyimide resin and may further contain other components such as solvents as needed. 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 individually or in combination of two or more types. The composition for high-frequency substrate material in the first embodiment can be suitably prepared by imidizing the composition for high-frequency substrate material in the second embodiment.

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

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

[0129] There are no particular restrictions on the content of the solvent, and it can be appropriately selected depending on the purpose, but it is preferably 150 parts by mass or more, and more preferably 200 parts by mass or more, per 100 parts by mass of polyimide resin and / or polyamic acid in the composition. Furthermore, the solvent content is preferably 2000 parts by mass or less, and more preferably 1000 parts by mass or less. When the solvent content is between 150 parts by mass and 2000 parts by mass, the viscosity becomes suitable for coating, and the thickness of the coated composition and the resulting polyimide film can be easily adjusted.

[0130] <Other ingredients> Examples of the other components mentioned above include catalysts that catalyze imidation and dehydrating agents.

[0131] -catalyst- Examples of the catalysts mentioned above include amines. Examples of the aforementioned 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 individually 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 agents 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 individually or in combination of two or more. Among these, acetic anhydride and benzoic anhydride are preferred, with acetic anhydride being more preferred.

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

[0134] Furthermore, the composition for high-frequency substrate material in the first embodiment may also contain other components such as inorganic particles, thermal crosslinking agents, thermal acid generators, leveling agents, viscosity modifiers, antioxidants, inorganic pigments, organic pigments, and dyes.

[0135] -Inorganic particles- The composition for high-frequency substrate material in the first embodiment, and the polyimide film described later, may contain inorganic particles for the purpose of further improving the heat resistance of the polyimide film or reducing its coefficient of thermal expansion. 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 dioxide (silica), titanium dioxide, aluminum oxide, zinc oxide, tin oxide, tungsten oxide, zirconium oxide, calcium carbonate, and barium sulfate. There are no particular restrictions on the shape or content of the inorganic particles, and they can be appropriately selected depending on the purpose. Furthermore, it is preferable to uniformly disperse the inorganic particles in the composition and the polyimide film, and known methods can be applied.

[0136] (Polyimide film for high-frequency substrate materials) The polyimide film for high-frequency substrate materials of this disclosure contains a polyimide resin and may further contain other components as needed. 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 individually or in combination of two or more types.

[0137] The average thickness of the polyimide film is not particularly limited and can be appropriately selected depending on the purpose, but it 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 for use as a circuit board. 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 for use as a circuit board.

[0138] The polyimide film can be suitably used in films for 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 manufacturing polyimide film] There are no particular limitations on the method for producing the polyimide film, and an appropriate method can be selected depending on the purpose. For example, (I) a method comprising the steps of coating and drying a composition containing polyamic acid on a substrate, and heating the resulting coating to imide it; (II) a method comprising the steps of casting a composition containing polyamic acid on a heated substrate to imide it and form a gel film, peeling the gel film obtained from the substrate, and heat-treating the peeled gel film.

[0140] There are no particular restrictions on the substrate, and it can be appropriately selected according to 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 for the polyimide film after drying 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 transport direction or the width direction during each step.

[0141] The resulting polyimide film may be further subjected to annealing or adhesion-enhancing treatments (e.g., electrolytic treatments such as corona treatment or plasma treatment, or blast treatment).

[0142] (Laminated structure) The laminate of this disclosure comprises a metal layer and a layer containing a polyimide resin, and may further comprise other layers as needed. A suitable example of the layer containing the polyimide resin is the polyimide film of this disclosure.

[0143] <Metal layer> There are no particular restrictions on the material of the metal layer, and it can be appropriately selected depending on the purpose. Examples include copper or copper alloys, stainless steel or its alloys, nickel or nickel alloys, aluminum or aluminum alloys, etc. Among these, copper and copper alloys are preferred, and copper alloys 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 are more preferred. As the metal layer, a metal foil formed by rolling or electroplating is preferred, and copper foil or copper alloy foil is more preferred.

[0144] A metal-clad laminate can be obtained by laminating the metal layer and the layer containing the polyimide resin. Alternatively, a laminate with a rust-preventive layer, a heat-resistant layer, a silane coupling agent, etc., formed on the surface of the metal layer can also be used.

[0145] There are no particular restrictions on the thickness of the metal layer; any thickness that allows for sufficient functionality according to the purpose is acceptable. A smooth surface of the metal layer is preferable for reducing transmission loss, and Ra of 1.0 μm or less is preferred.

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

[0147] Furthermore, 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 via an adhesive layer 2 as needed, as shown in Figure 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 via an adhesive layer 2 as needed, as shown in Figure 2.

[0148] There are no particular restrictions on the material of the adhesive layer, and it can be appropriately selected depending on the purpose. For example, it may be either a thermosetting resin or a thermoplastic resin. From the viewpoint of the heat resistance of the laminate, it is preferable that the adhesive layer be a thermoplastic polyimide. The glass transition temperature of the thermoplastic polyimide is preferably 300°C or lower, more preferably 280°C or lower, and even more preferably 260°C or lower. When the glass transition temperature is 300°C or lower, sufficient adhesion can be achieved when bonding a metal layer to a polyimide resin layer, for example, when performing hot roll lamination.

[0149] [Method for manufacturing laminates] There are no particular limitations on the method for manufacturing the laminate, and it can be appropriately selected depending on the purpose. Examples include a method that includes a step of bonding a metal layer to a layer containing polyimide resin via an adhesive layer; and a method of directly forming a polyimide film on a metal layer. Methods for bonding a polyimide resin-containing layer to a metal layer include, for example, using a hot roll laminating apparatus having one or more pairs of metal rolls; and using a continuous process with a double belt press. Among these, it is preferable to use a hot roll laminating apparatus having one or more pairs of metal rolls because the apparatus configuration is simple and it is advantageous in terms of maintenance costs.

[0150] (Circuit board) The circuit board of this disclosure has the laminate of this disclosure and may further have other components as necessary. By etching the metal layer in the aforementioned laminate to form a desired pattern wiring, it can be suitably used as various flexible printed circuit boards for mounting miniaturized and high-density components. The applications of the present invention are not limited to this, and any laminate containing a metal layer can be used for a variety of applications.

[0151] (antenna) The antenna of this disclosure has the circuit board of this disclosure and may further have other components as necessary. The antenna is preferably a millimeter-wave antenna. "Millimeter wave" refers to frequencies between 30 GHz and 300 GHz (radio wave wavelengths between 1 mm and 10 mm). The polyimide resin of this disclosure can achieve both a low dielectric constant and a low coefficient of thermal expansion, making it suitable for use as a high-frequency communication antenna that enables ultra-high-speed and high-capacity communication. [Examples]

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

[0153] <Molecular dynamics simulation of polyimides> Molecular dynamics simulations were performed on homopolymers with specific structural units to calculate the free volume fraction of the amorphous state and the average number of neighboring atoms. Specifically, following steps S1 to S3 below, we used appropriate computing equipment (including input devices, output devices, CPU, memory, etc.) and the polymer property automatic calculation system RadonPy (open-source software) to obtain the structure in equilibrium state, and calculated the free volume fraction from the equilibrium structure. In addition, we used a proprietary Python program to calculate the average number of neighboring atoms from the equilibrium structure using a Voronoi diagram method.

[0154] Specifically, the polyimides used in the calculations included approximately 250 different types, such as those described in PolyInfo (https: / / polymer.nims.go.jp / ) and PI1M (Reference 3: Ruimin Ma and Tengfei Luo, J. Chem. Inf. Model., 60, 10 (2020)), and molecular dynamics simulations were performed for each polyimide.

[0155] Step S1 Data on the amorphous structure of polyimide, a homopolymer with specific structural units, was obtained. A system was constructed consisting of 10 polyimide molecules, each containing approximately 1000 atoms (more specifically, between 900 and 1100 atoms). The system, in an aggregated state, was cooled from 800K to 300K under 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. Furthermore, the force field developed in Reference 4 below was used in this calculation, and the non-bonding and bonding interaction parameters were defined. 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 Next, molecular dynamics simulations were used to calculate the motion of each atom under conditions of a temperature of 300 K and a pressure of 1 atm. The coordinates of each atom in the system at equilibrium after 500 ns were obtained.

[0157] <Calculation of free volume fraction using 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 point. The free volume fraction was derived using Equation 3 below, and the van der Waals radii of each atom in Equation 3 below were calculated based on the GAFF2 force field (reference 1 above).

[0158] (Formula 3)

number

[0159] <Calculation of the average number of neighboring atoms using molecular dynamics simulation> Step S3-2 Next, based on the coordinates of each atom at the final time point, the average number of neighboring atoms in the system was calculated using the following method. The number of adjacent atoms was calculated as the total number of atom pairs that satisfy both (a) and (b) below. (a) In a Voronoi diagram calculated with each atom as a generator point, pairs of atoms (pairs of generator points) that share a Voronoi edge. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules Next, the average number of neighboring atoms was calculated by dividing the total number of pairs (i.e., the number of neighboring atoms) that satisfy both (a) and (b) above within a system with periodic boundary conditions by the number of atoms constituting the system.

[0160] <Calculation of dielectric constant at a frequency of 10 GHz using molecular dynamics simulation> The time-series data of the dipole moment of polyimide was calculated using the following procedure, and the dielectric constant at a frequency of 10 GHz was calculated based on the aforementioned time-series data at frequencies of 10 GHz or higher.

[0161] Specifically, molecular dynamics calculations were used to calculate the dipole moment of the target material, with a dielectric relaxation function length of 100 ns and a time length of 500 ns for calculating the dipole moment. This generated time-series data of 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 set to the reciprocal of the length of the dielectric relaxation function, and since the length of the dielectric relaxation function was set to 100 ns, the cutoff frequency was set to 10 MHz. Next, the designed high-pass filter was used to remove low-frequency components from the dipole moment time series data. In other words, the frequency band with a cutoff frequency of 10 MHz or higher was extracted from the dipole moment time series data. This generated filtered dipole moment time series data from which components below 10 MHz had been removed.

[0162] Next, the time series data of the filtered dipole moment was denoted 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 the Fourier transform of equation (3). fit (t) was frequency-decomposed. This yielded the frequency-dependent complex permittivity, and the permittivity at 10 GHz was determined from the real part of the complex permittivity at 10 GHz.

[0163]

number

[0164]

number

[0165]

number

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

[0167]

number

[0168] Next, assuming the isotropy of the system, the coefficient of linear expansion α is given by the following equation. L This was derived.

[0169]

number

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

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

[0172] Therefore, when we visualized polyimides (black dots) that exhibit both low thermal expansion coefficient and low dielectric constant in Figure 3, we found that polyimides with low dielectric constant and low thermal expansion coefficient exist in regions with high free volume fraction and low average number of neighboring atoms. Specifically, it was found that a low dielectric constant and a low coefficient of thermal expansion can be achieved simultaneously when the free volume fraction and average number of neighboring atoms satisfy either condition (1) or (2) below. (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.

[0173] The reason why polyimides with a high free volume fraction of 0.23 or higher exhibit the properties of low dielectric constant and low coefficient of thermal expansion is as follows. Polyimides with a high free volume fraction are characterized by a rigid or bulky molecular structure. In the amorphous state, polyimides with a rigid molecular structure maintain the shape of their molecular chains in a rod-like manner regardless of the surrounding molecular arrangement. As a result, it is difficult for the molecular chains to flexibly change structure and pack densely, leading to a sparse structure. Similarly, polyimides with a bulky molecular structure are thought to have a sparse structure because the bulky parts act as steric hindrance, hindering the free internal rotation of the molecular chains. As a result, the molecular chains are unable to flexibly change structure and pack densely, leading to a sparse structure. Compared to a dense structure, a sparse structure results in relatively smaller polarization per unit volume, leading to reduced responsiveness to electric fields and contributing to a reduction in dielectric constant. Therefore, polyimides with a high free volume fraction, characterized by a rigid or bulky molecular structure, are considered to have a low dielectric constant. Furthermore, in polyimides with a rigid or bulky structure, it is assumed that internal rotation of the molecular chains is inhibited for the reasons mentioned above, and therefore the change in molecular mobility due to thermal energy (change in conformational rotation frequency) is considered to be small. A small change in molecular mobility due to thermal energy means that the change in free volume with respect to temperature changes is small, which in turn means that the coefficient of thermal expansion is small and the material has a low coefficient of linear expansion. Therefore, polyimides with a rigid or bulky molecular structure and a high free volume fraction are considered to have a low coefficient of linear expansion. For the reasons stated above, a high free volume fraction with a value of 0.23 or higher contributes to a low dielectric constant and a low coefficient of thermal expansion.

[0174] Polyimides with a low average number of neighboring atoms (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, the probability of them coming into contact with unbonded atoms is low. The average number of neighboring atoms represents the average number of unbonded atoms surrounding each atom; therefore, the higher the content of sp3 hybridized carbon atoms, the lower the average number of neighboring atoms. In contrast, aromatic polyimides containing many 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, and the dielectric constant decreases. Consequently, a low average number of neighboring atoms, such as 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 coefficient of linear expansion, and a low average number of neighboring atoms contributes to a low dielectric constant. Therefore, polyimides that satisfy the above conditions (1) or (2), have a high free volume fraction and a low average number of neighboring atoms, achieve both a low dielectric constant and a low coefficient of linear expansion.

[0176] <Comparison between experimental values ​​and calculated values ​​from molecular dynamics simulations> For polyimide properties, specifically the dielectric constant and coefficient of thermal expansion at a frequency of 10 GHz, we compared the experimental values ​​for each polyimide with those calculated from molecular dynamics simulations. The results are shown in Figures 5-6. Specifically, the polyimides for which experimental values ​​are publicly known were those described in PolyInfo and reference 5 below. Reference 5: JO Simpson and AK St.Clair, Thin Solid Films, 308-309 (1997)

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

[0178] Figures 5-6 show that the dielectric constant and coefficient of thermal expansion obtained through molecular dynamics simulations qualitatively represent the experimental values. Based on the above, the two parameters that can achieve both low dielectric constant and low coefficient of thermal expansion (calculated value)—free volume fraction and average number of neighboring atoms—are effective parameters for material design where dielectric constant and coefficient of thermal expansion are the desired physical properties.

[0179] (Comparative Synthesis Example 1) Under a nitrogen atmosphere, 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) were added to a flask and stirred at 25°C for 96 hours to synthesize polyamic acid. The obtained polyamic acid A had a Mw of 0.7 million. [ka]

[0180] (Comparative 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 1,2,4,5-cyclohexanetetracarboxylic dianhydride (HPMDA) were added to a round-bottom flask and stirred at 160°C to 215°C for 4 hours. After cooling, recrystallization with acetone was performed to obtain 1.9 g of powder. When the IR 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 by the following reaction equation. [ka]

[0181] <Rating> The coefficient of linear expansion and relative permittivity of the polyimide obtained in Comparative Synthesis Example 2 were evaluated at 20°C to 200°C using the following procedure.

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

[0183] --Measurement Conditions-- Stage 1: Heat the sample to 150°C at a rate of 5°C / min to remove adsorbed water. Stage 2: Cool to room temperature by air at a cooling rate of 5°C / minute. Stage 3: Perform the measurement at a heating rate of 5°C / minute. The average value of the linear expansion coefficient in the temperature range of 20°C to 200°C was determined and used as the linear expansion coefficient of the target polyimide. The linear thermal expansion coefficient of polyimide at 20°C to 200°C was evaluated based on the following evaluation criteria.

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

[0185] <<Relative permittivity>> As a sample, a sheet with an average thickness of 25 μm was formed using the obtained polyimide. The relative permittivity of the polyimide was measured at 25°C and 10 GHz using a vector network analyzer (E5063A, Keysight) by the SPDR method (resonance method), and the results were evaluated based on the following evaluation criteria.

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

[0187] The polyimide obtained in comparative synthesis example 2 was evaluated, and it was confirmed that the coefficient of linear expansion at 20°C to 200°C was "○" and the relative permittivity of the polyimide was also "○".

[0188] Although embodiments have been described above, it should be understood that various modifications to the form and details are possible without departing from the spirit and scope of the claims. [Explanation of Symbols]

[0189] 1. Polyimide film 2 Adhesive layer 3 metal layer 10 Laminate 20 Laminate

Claims

1. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1): A polyimide resin for high-frequency substrate materials, wherein the diamine is one or more 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). 【Chemistry 1】 In the above general formula (A-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 0 and 3, and if l is 0, it indicates that there are no connections. m represents an integer between 0 and 3. n represents an integer from 0 to 5. If n is 0, then at least one R １ It has a fluorine atom, R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ is 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 heterocyclic ring which may have a substituent, and two adjacent Rs ３ may be bonded to each other to form a cycloalkyl group. 【Chemistry 2】 In the general formula (B-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Transformation 3】 In the general formula (B-2), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and 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). 【Chemistry 4】 In the above general formula (A-1a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, m represents an integer between 0 and 3. 【Transformation 5】 In the general formula (A-1b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer from 1 to 5. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group.

3. The above general formula (B-1) is either the following general formula (B-1a) or the following general formula (B-1b), The polyimide resin according to claim 1 or 2, wherein the general formula (B-2) is the following general formula (B-2a). 【Transformation 6】 In the general formula (B-1a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. 【Transformation 7】 In the general formula (B-1b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. n represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. 【Transformation 8】 In the general formula (B-2a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, 'o' represents an integer from 0 to 8.

4. It consists of an acid anhydride and a diamine, 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). A polyimide resin for high-frequency substrate materials, wherein the diamine is one or more 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). 【Chemistry 9】 In the general formulas (A-2a) to (A-2g), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R ２ Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 【Chemistry 10】 In the general formula (B-3), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 11】 In the general formula (B-4), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

5. The above general formula (B-3) is either the following general formula (B-3a) or the following general formula (B-3b), The polyimide resin according to claim 4, wherein the general formula (B-4) is the following general formula (B-4a). 【Chemistry 12】 In the general formula (B-3a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 'o' represents an integer between 0 and 4. 【Chemistry 13】 In the general formula (B-3b), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. m represents an integer between 1 and 3. 'o' represents an integer between 0 and the maximum number of substituents. 【Chemistry 14】 In the general formula (B-4a), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, 'o' represents an integer from 0 to 8.

6. The relative permittivity at 10 GHz is 2.6 or less. The polyimide resin according to claim 1 or 4, wherein the coefficient of linear thermal expansion is 50 ppm / K or less.

7. A polyimide resin having the structural unit of the following general formula (1), 【Chemistry 15】 In the above general formula (1), R ａ (CO) ４ The portion represents a tetravalent group derived from a tetravalent tetracarboxylic acid with 2 or more carbon atoms, R ｂ (N) ２ The portion shows a tetravalent group derived from a divalent diamine with two or more carbon atoms. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300 K and a pressure of 1 atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The polyimide resin for high-frequency substrate materials is such that the number of adjacent atoms is the total number of atom pairs satisfying both (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom as the parent point. (b) Atomic pairs separated by four or more bonds, or atomic 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 neighboring atoms is 3.90 to 4.

60.

9. The free volume fraction is 0.23 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.

60. The polyimide resin according to claim 7, which does not have a trifluoromethyl group.

10. The free volume fraction is 0.24 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.

50. The polyimide resin according to claim 7, which does not have a trifluoromethyl group.

11. The free volume fraction is 0.28 to 0.32, and the average number of neighboring atoms satisfies 3.90 to 4.

50. The polyimide resin according to claim 7, which does not have a trifluoromethyl group.

12. The free volume fraction and average number of neighboring atoms of the amorphous polyimide resin in equilibrium at a temperature of 300 K and a pressure of 1 atm, as calculated by molecular dynamics calculations, satisfy the following conditions (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 molecular dynamics calculation system, The polyimide resin according to any one of claims 1, 4, and 7, wherein the number of adjacent atoms is the total number of atom pairs satisfying (a) and (b) below. (a) Atomic pairs that share one side of a Voronoi cell, with each atom as the parent point. (b) Atomic pairs separated by four or more bonds, or atomic pairs between different molecules

13. A composition for a high-frequency substrate material containing the polyimide resin according to any one of claims 1, 4, and 7.

14. A polyimide film for high-frequency substrate material containing the polyimide resin according to any one of claims 1, 4, and 7.

15. Metal layer, A laminate having a layer containing the polyimide resin according to any one of claims 1, 4, and 7.

16. A circuit board having the laminate described in claim 15.

17. An antenna having a circuit board as described in claim 16.

18. The antenna according to claim 17, which is a millimeter-wave antenna.

19. It consists of an acid anhydride and a diamine, The acid anhydride is one or more compounds selected from the group consisting of compounds represented by the following general formula (A-1): A polyamic acid for high-frequency substrate materials, wherein 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). 【Chemistry 16】 In the above general formula (A-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 0 and 3, and if l is 0, it indicates that there are no connections. m represents an integer between 0 and 3. n represents an integer from 0 to 5. If n is 0, then at least one R １ It has a fluorine atom, R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 17】 In the general formula (B-1), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ２ These may bond to each other to form a cycloalkyl group. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. [Chemistry 18] In the general formula (B-2), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R １ It has a fluorine atom, Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

20. It consists of an acid anhydride and a diamine, 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). A polyamic acid for high-frequency substrate materials, wherein the diamine is one or more 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). 【Chemistry 19】 In the general formulas (A-2a) to (A-2g), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. R ２ Each of these is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. 【Chemistry 20】 In the general formula (B-3), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. l represents an integer between 1 and 3. m represents an integer between 0 and 3. n represents an integer from 0 to 5. o represents an integer from 0 to the maximum number of substituents. R ２ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle. at least one R ２ This is a fluoroalkyl group which may have substituents, X is independently -O-, -C(R ３ ) ２ -, and -SO ２ - Selected from the group consisting of, R ３ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted aromatic ring, and optionally substituted heterocycle, and two adjacent R ３ These may bond to each other to form a cycloalkyl group. 【Chemistry 21】 In the general formula (B-4), R １ Each is independently selected from the group consisting of hydrogen, halogen, optionally substituted alkyl group, optionally substituted alkoxy group, optionally substituted aromatic ring, and optionally substituted heterocycle. Each m represents an integer between 0 and 2, independently. 'o' represents an integer between 0 and the maximum number of substituents.

21. A composition for high-frequency substrate materials containing the polyamic acid and solvent described in claim 19 or 20.

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