Abstract:
The present invention pertains to: a polymerizable compound represented by a formula (I); a polymerizable composition comprising the polymerizable compound and an initiator; a polymer obtained by polymerizing the polymerizable compound or the polymerizable composition; and an optically anisotropic article comprising the polymer. The present invention provides a polymerizable compound, a polymerizable composition, and a polymer that have a practical low melting point, exhibit excellent solubility in a general-purpose solvent, can be produced at low cost, and can produce an optical film that achieves uniform conversion of polarized light over a wide wavelength band, and also provide an optically anisotropic article.

Description:
This application is a national stage application under 35 U.S.C. §317 of International Patent Application No. PCT/JP2013/078103 filed on Oct. 16, 2013, which claims the benefit of foreign priority to Japanese Patent Application No. JP 2012-233672 filed on Oc. 23, 2012. 
     TECHNICAL FIELD 
     The present invention relates to a polymerizable compound, a polymerizable composition, and a polymer that may produce an optical film that achieves uniform conversion of polarized light over a wide wavelength band, and also relates to an optically anisotropic article. 
     A flat panel display (FPD) that utilizes an optical film (e.g., polarizer and retardation film) can achieve high-resolution display, and has been widely used as a display device that exhibits excellent performance. 
     Examples of the retardation film include a quarter-wave plate that converts linearly polarized light into circularly polarized light, a half-wave plate that changes the plane of vibration of linearly polarized light by 90°, and the like. Such a retardation film can achieve accurate conversion of specific monochromatic light so that ¼λ or ½λ retardation occurs. 
     However, known retardation films have a problem in that polarized light that passes through is converted into colored polarized light. Specifically, since a material that forms the retardation film has wavelength dispersion with respect to retardation, and a polarization state distribution corresponding to each wavelength occurs with respect to white light that includes different light beams in the visible region, it is impossible to achieve accurate ¼λ or ½λ retardation over the entire wavelength band. 
     In order to solve the above problem, various wideband retardation films that can achieve uniform retardation for light over a wide wavelength band (i.e., retardation films having reverse wavelength dispersion) have been studied (see Patent Documents 1 to 6). 
     It has been desired to reduce the thickness of the flat panel display as much as possible along with an improvement in performance and widespread use of mobile information terminals (e.g., mobile personal computer and mobile phone). Therefore, a reduction in thickness of the retardation film has also been desired. 
     It has been considered that it is most effective to produce a retardation film by applying a polymerizable composition that includes a low-molecular-weight polymerizable compound to a film substrate in order to reduce the thickness of the retardation film. Various low-molecular-weight polymerizable compounds having excellent wavelength dispersion, and various polymerizable compositions using such polymerizable compounds have been developed (see Patent Documents 7 to 24). 
     However, the low-molecular-weight polymerizable compounds or the polymerizable compositions disclosed in Patent Documents 7 to 24 have a number of problems in that reverse wavelength dispersion may be insufficient, or it may be difficult to apply the low-molecular-weight polymerizable compounds or the polymerizable compositions to a film due to a high melting point that is not suitable for an industrial process, or the temperature range in which liquid crystallinity is obtained may be very narrow, or solubility in a solvent generally used for an industrial process may be low. Moreover, since the above low-molecular-weight polymerizable compounds and the like are synthesized by performing a plurality of steps using a synthesis method that utilizes an expensive reagent, the production cost increases. 
     RELATED-ART DOCUMENT 
     Patent Document 
     
         
         Patent Document 1: JP-A-10-68816 
         Patent Document 2: JP-A-10-90521 
         Patent Document 3: JP-A-11-52131 
         Patent Document 4: JP-A-2000-284126 (US20020159005A1) 
         Patent Document 5: JP-A-2001-4837 
         Patent Document 6: WO2000/026705 
         Patent Document 7: JP-A-2002-267838 
         Patent Document 8: JP-A-2003-160540 (US20030102458A1) 
         Patent Document 9: JP-A-2005-208414 
         Patent Document 10: JP-A-2005-208415 
         Patent Document 11: JP-A-2005-208416 
         Patent Document 12: JP-A-2005-289980 (US20070176145A1) 
         Patent Document 13: JP-A-2006-330710 (US20090072194A1) 
         Patent Document 14: JP-A-2009-179563 (US20090189120A1) 
         Patent Document 15: JP-A-2010-31223 
         Patent Document 16: JP-A-2011-6360 
         Patent Document 17: JP-A-2011-6361 
         Patent Document 18: JP-A-2011-42606 
         Patent Document 19: JP-T-2010-537954 (US20100201920A1) 
         Patent Document 20: JP-T-2010-537955 (US20100301271A1) 
         Patent Document 21: WO2006/052001 (US20070298191A1) 
         Patent Document 22: U.S. Pat. No. 6,139,771 
         Patent Document 23: U.S. Pat. No. 6,203,724 
         Patent Document 24: U.S. Pat. No. 5,567,349 
       
    
     SUMMARY OF THE INVENTION 
     Technical Problem 
     The invention was conceived in view of the above situation. An object of the invention is to provide a polymerizable compound, a polymerizable composition, and a polymer that have a practical low melting point, exhibit excellent solubility in a general-purpose solvent, can be produced at low cost, and can produce an optical film that achieves uniform conversion of polarized light over a wide wavelength band, and also provide an optically anisotropic article. 
     Solution to Problem 
     The inventors of the invention conducted extensive studies in order to solve the above problem. As a result, the inventors found that an optical film that achieves uniform conversion of polarized light over a wide wavelength band, and exhibits satisfactory performance, can be produced at low cost by utilizing an optically anisotropic article produced using a polymer that is obtained by polymerizing a polymerizable compound represented by the following formula (I), or a polymerizable composition that includes the polymerizable compound and an initiator. This finding has led to the completion of the invention. 
     Several aspects of the invention provide the following polymerizable compound (see (1) to (7)), polymerizable composition (see (8) and (9)), polymer (see (10) and (11)), and optically anisotropic article (see (12)).
     (1) A polymerizable compound represented by the following formula (I),   

                                
wherein Y 1  to Y 8  are independently a chemical single bond, —O—, —S—, —O—C(═O)—, —C(═O)—O—, —O—C(═O)—O—, —NR 1 —C(═O)—, —C(═O)—NR 1 —, —O—C(═O)—NR 1 —, —NR 1 —C(═O)—O—, —NR 1 —C(═O)—NR 1 —, —O—NR 1 —, or —NR 1 —O—, R 1  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms,
     G 1  and G 2  are independently a substituted or unsubstituted divalent aliphatic group having 1 to 20 carbon atoms that optionally includes —O—, —S—, —O—C(═O)—, —C(═O)—O—, —O—C(═O)—O—, —NR 2 —C(═O)—, —C(═O)—NR 2 —, —NR 2 —, or —C(═O)—, provided that a case where the aliphatic group includes two or more contiguous —O— or —S— is excluded, R 2  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms,   Z 1  and Z 2  are independently an alkenyl group having 2 to 10 carbon atoms that is substituted with a halogen atom, or unsubstituted,   A x  is a group represented by the following formula (II),   

                                
wherein X is a nitrogen atom or a carbon atom, and R a  and R b  are independently a hydrogen atom, a substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, a substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, a substituted or unsubstituted cycloalkyl group having 3 to 18 carbon atoms, a substituted or unsubstituted aromatic hydrocarbon ring group having 1 to 20 carbon atoms, or a substituted or unsubstituted heteroaromatic ring group having 1 to 20 carbon atoms,
     A y  is a hydrogen atom, a substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, a substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, a substituted or unsubstituted cycloalkyl group having 3 to 12 carbon atoms, or the group represented by the formula (II),   A 1  is a substituted or unsubstituted trivalent aromatic group,   A 2  and A 3  are independently a substituted or unsubstituted divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms,   A 4  and A 5  are independently a substituted or unsubstituted divalent aromatic group having 4 to 30 carbon atoms,   Q 1  is a hydrogen atom, or a substituted or unsubstituted alkyl group having 1 to 6 carbon atoms, and m and n are independently 0 or 1.   (2) The polymerizable compound according to (1), wherein R a  and R b  in the formula (II) are independently a hydrogen atom, a substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, a substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, a substituted or unsubstituted cycloalkyl group having 3 to 18 carbon atoms, or a group among groups respectively represented by the following formulas (II-1) to (II-5),   

                                
wherein X a  is a nitrogen atom or a carbon atom, R X  are a hydrogen atom, a halogen atom, an alkyl group having 1 to 6 carbon atoms, a cyano group, a nitro group, an alkylsulfinyl group having 1 to 6 carbon atoms, an alkylsulfonyl group having 1 to 6 carbon atoms, a fluoroalkyl group having 1 to 6 carbon atoms, an alkoxy group having 1 to 6 carbon atoms, an alkylthio group having 1 to 6 carbon atoms, a monosubstituted amino group, a disubstituted amino group, an alkylsulfamoyl group having 1 to 6 carbon atoms, a dialkylsulfamoyl group having 2 to 12 carbon atoms, or —C(═O)—O—R 6 , and R 6  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms, provided that R X  are either identical or different, and an arbitrary C—R X  linkage is optionally substituted with a nitrogen atom.
     (3) The polymerizable compound according to (1), wherein A 1  is a substituted or unsubstituted trivalent benzene ring group, or a substituted or unsubstituted trivalent naphthalene ring group, and A 4  and A 5  are independently a substituted or unsubstituted phenylene group, or a substituted or unsubstituted naphthylene group.   (4) The polymerizable compound according to (1), wherein Y 1  to Y 8  are independently a chemical single bond, —O—, —O—C(═O)—, —C(═O)—O—, or —O—C(═O)—O—.   (5) The polymerizable compound according to (1), wherein Z 1  and Z 2  are independently CH 2 ═CH—, CH 2 ═C(CH 3 )—, or CH 2 ═C(Cl)—.   (6) The polymerizable compound according to (1), wherein G 1  and G 2  are independently a substituted or unsubstituted divalent aliphatic group having 1 to 12 carbon atoms that optionally includes —O—, —O—C(═O)—, —C(═O)—O—, or —C(═O)—, provided that a case where the aliphatic group includes two or more contiguous —O— is excluded.   (7) The polymerizable compound according to (1), wherein G 1  and G 2  are independently a divalent alkylene group having 1 to 12 carbon atoms.   (8) A polymerizable composition including at least one type of the polymerizable compound according to any one of (1) to (7).   (9) A polymerizable composition including the polymerizable compound according to any one of (1) to (7), and an initiator.   (10) A polymer obtained by polymerizing the polymerizable compound according to any one of (1) to (7), or the polymerizable composition according to (8) or (9).   (11) The polymer according to (10), the polymer being a liquid crystalline polymer.   (12) An optically anisotropic article including the polymer according to (11).   

     Advantageous Effects of the Invention 
     The polymerizable compound, the polymerizable composition, and the polymer according to the aspects of the invention make it possible to inexpensively obtain an optically anisotropic article that achieves uniform conversion of polarized light over a wide wavelength band, and exhibits satisfactory performance. 
     Since the optically anisotropic article according to one aspect of the invention is produced using the polymer according to one aspect of the invention, the optically anisotropic article can be produced at low cost, achieves uniform conversion of polarized light over a wide wavelength band, and exhibits satisfactory performance. 
     For example, an antireflective film may be produced by combining the film-shaped optically anisotropic article according to one aspect of the invention with a polarizer. The antireflective film may suitably be used to prevent reflection from a touch panel, an organic electroluminescent device, and the like. 
    
    
     DESCRIPTION OF EMBODIMENTS 
     A polymerizable compound, a polymerizable composition, a polymer, and an optically anisotropic article according to exemplary embodiments of the invention are described in detail below. 
     1) Polymerizable Compound 
     A polymerizable compound according to one embodiment of the invention is a compound represented by the formula (I) (compound (I)). 
     Y 1  to Y 8  in the formula (1) are independently a chemical single bond, —O—, —S—, —O—C(═O)—, —C(═O)—O—, —NR 1 —C(═O)—, —C(═O)—NR 1 —, —O—C(═O)—NR 1 —, —NR 1 —C(═O)—NR 1 —, —O—NR 1 —, or —NR 1 —O—. 
     R 1  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms. 
     Examples of the alkyl group having 1 to 6 carbon atoms represented by R 1  include a methyl group, an ethyl group, an n-propyl group, an isopropyl group, an n-butyl group, a sec-butyl group, a t-butyl group, an n-pentyl group, an n-hexyl group, and the like. 
     R 1  is preferably a hydrogen atom or an alkyl group having 1 to 4 carbon atoms. 
     It is preferable that Y 1  to Y 8  be independently a chemical single bond, —O—, —O—C(═O)—, —C(═O)—O—, or —O—C(═O)—O—. 
     G 1  and G 2  are independently a substituted or unsubstituted divalent aliphatic group having 1 to 20 carbon atoms. 
     Examples of the divalent aliphatic group having 1 to 20 carbon atoms include a divalent aliphatic group having a linear structure; a divalent aliphatic group having an alicyclic structure such as a saturated cyclic hydrocarbon (cycloalkane) structure or an unsaturated cyclic hydrocarbon (cycloalkene) structure; and the like. 
     Examples of a substituent that may substitute the divalent aliphatic group represented by G 1  and G 2  include a halogen atom such as a fluorine atom, a chlorine atom, a bromine atom, and an iodine atom; an alkoxy group having 1 to 6 carbon atoms, such as a methoxy group, an ethoxy group, an n-propoxy group, an isopropoxy group, an n-butoxy group, a sec-butoxy group, a t-butoxy group, an n-pentyloxy group, and an n-hexyloxy group; and the like. Among these, a fluorine atom, a methoxy group, and an ethoxy group are preferable. 
     The aliphatic group optionally includes —O—, —S—, —O—C(═O)—, —C(═O)—O—, —O—C(═O)—O—, —NR 2 —C(═O)—, —C(═O)—NR 2 —, —NR 2 —, or —C(═O)— (provided that a case where the aliphatic group includes two or more contiguous —O— or —S— is excluded). R 2  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms similar to that represented by R 1 , and is preferably a hydrogen atom or a methyl group. 
     —O—, —O—C(═O)—, —C(═O)—O—, and —C(═O)— are preferable as the group that is optionally included in the aliphatic group. 
     Specific examples of the aliphatic group that includes the above group include —CH 2 —CH 2 —O—CH 2 —CH 2 —, —CH 2 —CH 2 —S—CH 2 —CH 2 —, —CH 2 —CH 2 —O—C(═O)—CH 2 —CH 2 —, —CH 2 —CH 2 —C(═O)—O—CH 2 —CH 2 —, —CH 2 —CH 2 —C(═O)—O—CH 2 —, —CH 2 —O—C(═O)—O—CH 2 —CH 2 —, —CH 2 —CH 2 —NR 2 —C(═O)—CH 2 —CH 2 —, —CH 2 —CH 2 —C(═O)—NR 2 —CH 2 —, —CH 2 —NR 2 —CH 2 —CH 2 —, —CH 2 —C(═O)—CH 2 —, and the like. 
     It is preferable that G 1  and G 2  be independently a divalent aliphatic group having a linear structure (e.g., an alkylene group having 1 to 20 carbon atoms or an alkenylene group having 2 to 20 carbon atoms), more preferably an alkylene group having 1 to 12 carbon atoms (e.g., methylene group, ethylene group, trimethylene group, propylene group, tetramethylene group, pentamethylene group, hexamethylene group, or octamethylene group), and particularly preferably a tetramethylene group (—(CH 2 ) 4 —) or a hexamethylene group (—(CH 2 ) 6 —), in order to ensure that the intended effects of the invention can be more advantageously achieved. 
     Z 1  and Z 2  are independently an alkenyl group having 2 to 10 carbon atoms that is substituted with a halogen atom, or unsubstituted. 
     The number of carbon atoms of the alkenyl group is preferably 2 to 6. Examples of the halogen atom that may substitute the alkenyl group represented by Z 1  and Z 2  include a fluorine atom, a chlorine atom, a bromine atom, and the like. Among these, a chlorine atom is preferable. 
     Specific examples of the alkenyl group having 2 to 10 carbon atoms represented by Z 1  and Z 2  include CH 2 ═CH—, CH 2 ═C(CH 3 )—, CH 2 ═CH—CH 2 —, CH 3 —CH═CH—, CH 2 ═CH—CH 2 —CH 2 —, CH 2 ═C(CH 3 )—CH 2 —CH 2 —, (CH 3 ) 2 C═CH—CH 2 —, (CH 3 ) 2 C═CH—CH 2 —CH 2 —, CH 2 ═C(Cl)—, CH 2 ═C(CH 3 )—CH 2 —, CH 3 —CH═CH—CH 2 —, and the like. 
     It is preferable that Z 1  and Z 2  be independently CH 2 ═CH 2 —, CH 2 ═C(CH 3 )—, CH 2 ═C(Cl)—, CH 2 ═CH—CH 2 —, CH 2 ═C(CH 3 )—CH 2 —, or CH 2 ═C(CH 3 )—CH 2 —CH 2 —, more preferably CH 2 ═CH—, CH 2 ═C(CH 3 )—, or CH 2 ═C(Cl)—, and particularly preferably CH 2 ═CH 2 —, in order to ensure that the intended effects of the invention can be more advantageously achieved. 
     A x  is the group represented by the formula (II). 
     X in the formula (II) is a nitrogen atom or a carbon atom, and preferably a nitrogen atom. 
     R a  and R b  in the formula (II) are independently a hydrogen atom, a substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, a substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, a substituted or unsubstituted cycloalkyl group having 3 to 18 carbon atoms, a substituted or unsubstituted aromatic hydrocarbon ring group having 1 to 20 carbon atoms, or a substituted or unsubstituted heteroaromatic ring group having 1 to 20 carbon atoms. 
     Examples of the alkyl group having 1 to 20 carbon atoms (that is substituted or unsubstituted) that may be represented by R a  and R b  include a methyl group, an ethyl group, an n-propyl group, an isopropyl group, an n-butyl group, a sec-butyl group, a t-butyl group, an n-pentyl group, an isopentyl group, a neopentyl group, an n-hexyl group, an isohexyl group, an n-heptyl group, an n-octyl group, an n-nonyl group, an n-decyl group, an n-undecyl group, an n-dodecyl group, an n-tridecyl group, an n-tetradecyl group, an n-pentadecyl group, an n-hexadecyl group, an n-heptadecyl group, an n-octadecyl group, an n-nonadecyl group, an n-icosyl group, and the like. The number of carbon atoms of the substituted or unsubstituted alkyl group having 1 to 20 carbon atoms is preferably 1 to 12, and more preferably 1 to 6. 
     Examples of a substituent that may substitute the substituted or unsubstituted alkyl group having 1 to 20 carbon atoms include a halogen atom such as a fluorine atom and a chlorine atom; a cyano group; a substituted amino group such as a dimethylamino group; an alkoxy group having 1 to 6 carbon atoms, such as a methoxy group, an ethoxy group, and an isopropoxy group; an alkoxy group having 1 to 6 carbon atoms that is substituted with an alkoxy group having 1 to 6 carbon atoms, such as 
     a methoxymethoxy group and a methoxyethoxy group; a nitro group; an aryl group such as a phenyl group and a naphthyl group; a cycloalkyl group having 3 to 8 carbon atoms, such as a cyclopropyl group, a cyclopentyl group, and a cyclohexyl group; —C(═O)—R 4 ; —C(═O)—OR 4 ; —SO 2 R 4 ; a hydroxyl group; and the like. R 4  is an alkyl group having 1 to 6 carbon atoms, or an aryl group having 6 to 14 carbon atoms. 
     Examples of the alkenyl group having 2 to 20 carbon atoms (that is substituted or unsubstituted) that may be represented by R a  and R b  include a vinyl group, a propenyl group, an isopropenyl group, a butenyl group, a pentenyl group, a hexenyl group, a heptenyl group, an octenyl group, a decenyl group, an undecenyl group, a dodecenyl group, a tridecenyl group, a tetradecenyl group, a pentadecenyl group, a hexadecenyl group, a heptadecenyl group, an octadecenyl group, a nonadecenyl group, an icosenyl group, and the like. The number of carbon atoms of the substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms is preferably 2 to 12. 
     Examples of the cycloalkyl group having 3 to 18 carbon atoms (that is substituted or unsubstituted) that may be represented by R a  and R b  include a cyclopropyl group, a cyclobutyl group, a cyclopentyl group, a cyclohexyl group, a cycloheptyl group, a cyclooctyl group, a cyclodecyl group, a cyclododecyl group, and the like. 
     Examples of a substituent that may substitute the substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms and the substituted or unsubstituted cycloalkyl group having 3 to 18 carbon atoms include a halogen atom such as a fluorine atom and a chlorine atom; a cyano group; a substituted amino group such as a dimethylamino group; an alkoxy group having 1 to 6 carbon atoms, such as a methoxy group, an ethoxy group, and an isopropoxy group; a nitro group; an aryl group such as a phenyl group and a naphthyl group; a cycloalkyl group having 3 to 8 carbon atoms, such as a cyclopropyl group, a cyclopentyl group, and a cyclohexyl group; —C(═O)—R 4 ; —C(═O)—OR 4 ; —SO 2 R 4 ; a hydroxyl group; and the like. Note that R 4  is the same as defined above. 
     Examples of the aromatic hydrocarbon ring group having 1 to 20 carbon atoms (that is substituted or unsubstituted) include a benzene ring group, a naphthalene ring group, an anthracene ring group, and the like. 
     Examples of the heteroaromatic ring group having 1 to 20 carbon atoms (that is substituted or unsubstituted) include a monocyclic heteroaromatic ring group such as a pyrrole ring group, a furan ring group, a thiophene ring group, a pyridine ring group, a pyridazine ring group, a pyrimidine ring group, a pyrazine ring group, a pyrazole ring group, an imidazole ring group, an oxazole ring group, and a thiazole ring group; a fused heteroaromatic ring group such as a benzothiazole ring group, a benzoxazole ring group, a quinoline ring group, a phthalazine ring group, a benzimidazole ring group, a benzopyrazole ring group, a benzofuran ring group, and a benzothiophene ring group; and the like. 
     Examples of a substituent that may substitute the aromatic hydrocarbon ring group and the heteroaromatic ring group include a halogen atom such as a fluorine atom and a chlorine atom; a cyano group; an alkyl group having 1 to 6 carbon atoms, such as a methyl group, an ethyl group, and a propyl group; an alkenyl group having 2 to 6 carbon atoms, such as a vinyl group and an allyl group; an alkyl halide group having 1 to 6 carbon atoms, such as a trifluoromethyl group; a substituted amino group such as a dimethylamino group; an alkoxy group having 1 to 6 carbon atoms, such as a methoxy group, an ethoxy group, and an isopropoxy group; a nitro group; an aryl group such as a phenyl group and a naphthyl group; —C(═O)—R 4 ; —C(═O)—OR 4 ; —SO 2 R 4 ; and the like. Note that R 4  is the same as defined above. 
     The groups respectively represented by the formulas (II-1) to (II-5) are preferable as the substituted or unsubstituted aromatic hydrocarbon ring group having 1 to 20 carbon atoms and the substituted or unsubstituted heteroaromatic ring group having 1 to 20 carbon atoms. 
     X a  in the formulas (II-1) and (II-2) is a nitrogen atom or a carbon atom. 
     R X  are a hydrogen atom, a halogen atom (e.g., fluorine atom, chlorine atom, or a bromine atom), an alkyl group having 1 to 6 carbon atoms (e.g., methyl group or ethyl group), a cyano group, a nitro group, an alkylsulfinyl group having 1 to 6 carbon atoms (e.g., methylsulfinyl group or ethylsulfinyl group), an alkylsulfonyl group having 1 to 6 carbon atoms (e.g., methylsulfonyl group or ethylsulfonyl group), a fluoroalkyl group having 1 to 6 carbon atoms (e.g., trifluoromethyl group or pentafluoroethyl group), an alkoxy group having 1 to 6 carbon atoms (e.g., methoxy group or ethoxy group), an alkylthio group having 1 to 6 carbon atoms (e.g., methylthio group or ethylthio group), a monosubstituted amino group (e.g., methylamino group or ethylamino group), a disubstituted amino group (e.g., dimethylamino group or diethylamino group), an alkylsulfamoyl group having 1 to 6 carbon atoms (e.g., methylsulfamoyl group), a dialkylsulfamoyl group having 2 to 12 carbon atoms (e.g., dimethylsulfamoyl group), or —C(═O)—O—R 6 . R 6  is a hydrogen atom or an alkyl group having 1 to 6 carbon atoms. 
     R X  are either identical or different, and one to three C—R X  linkages are optionally substituted with a nitrogen atom. 
     It is preferable that all of R X  be a hydrogen atom. 
     Among the groups respectively represented by the formulas (II-1) to (II-5), the groups respectively represented by the formulas (II-3) and (II-4) are preferable, in order to ensure that the intended effects of the invention can be more advantageously achieved. 
     Examples of the group represented by the formula (II-3) include groups respectively represented by the following formulas, and the like. 
                                
wherein R X′  is the same as defined for R X . Note that the C—R X′  linkage is not substituted with a nitrogen atom.
 
     Examples of the group represented by the formula (II-4) include groups respectively represented by the following formulas, and the like. 
                                
wherein R X′  is the same as defined above.
 
     It is preferable that R b  be a hydrogen atom, and R a  be a group among the groups respectively represented by the formulas (II-1) to (II-5), or R a  and R b  be independently a group among the groups respectively represented by the formulas (II-1) to (II-5). It is more preferable that R b  be a hydrogen atom, and R a  be the group represented by the formula (II-4), or R a  and R b  be independently the group represented by the formula (II-3). 
     Groups respectively represented by the following formulas are preferable as A x . 
                                
wherein X and R X  are the same as defined above.
 
     Groups respectively represented by the following formulas are more preferable as A x . 
                                
wherein X is the same as defined above.
 
     The groups respectively represented by the following formulas are particularly preferable as A x . 
     
       
                 
         
             
             
         
      
     
     A y  is a hydrogen atom, a substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, a substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, a substituted or unsubstituted cycloalkyl group having 3 to 12 carbon atoms, or the group represented by the formula (II) similar to that represented by A x . 
     Examples of the substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, the substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, and the substituted or unsubstituted cycloalkyl group having 3 to 12 carbon atoms that may be represented by A y  include those mentioned above in connection with the substituted or unsubstituted alkyl group having 1 to 20 carbon atoms, the substituted or unsubstituted alkenyl group having 2 to 20 carbon atoms, and the substituted or unsubstituted cycloalkyl group having 3 to 12 carbon atoms that may be represented by R a  and R b . 
     A y  is preferably a hydrogen atom. 
     A 1  is a substituted or unsubstituted trivalent aromatic group. The trivalent aromatic group may be a trivalent carbocyclic aromatic group, or may be a trivalent heterocyclic aromatic group. It is preferable that the trivalent aromatic group be a trivalent carbocyclic aromatic group, more preferably a trivalent benzene ring group or a trivalent naphthalene ring group, and still more preferably a trivalent benzene ring group or a trivalent naphthalene ring group represented by a formula among the following formulas, in order to ensure that the intended effects of the invention can be more advantageously achieved. 
     Note that the substituents Y 1  and Y 2  are also included in the following formulas so that the bonding state can be readily understood (Y 1  and Y 2  are the same as defined above; hereinafter the same). 
     
       
                 
         
             
             
         
      
     
     A 1  is more preferably a group among groups respectively represented by the following formulas (A11) to (A25), still more preferably a group among the groups respectively represented by the formulas (A11), (A13), (A15), (A19), and (A23), and particularly preferably the group represented by the formula (A11) or the group represented by the formula (A23). 
     
       
                 
         
             
             
         
      
       
                 
         
             
             
         
       
     
     Examples of a substituent that may substitute the trivalent aromatic group represented by A 1  include those mentioned above in connection with a substituent that may substitute the aromatic ring included in A x . It is preferable that A 1  be unsubstituted. 
     A 2  and A 3  are independently a substituted or unsubstituted divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms. 
     Examples of the divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms include a cycloalkanediyl group having 3 to 30 carbon atoms, a divalent fused alicyclic group having 10 to 30 carbon atoms, and the like. 
     Examples of the cycloalkanediyl group having 3 to 30 carbon atoms include a cyclopropanediyl group; a cyclobutanediyl group such as a cyclobutane-1,2-diyl group and a cyclobutane-1,3-diyl group; a cyclopentanediyl group such as a cyclopentane-1,2-diyl group and a cyclopentane-1,3-diyl group; a cyclohexanediyl group such as a cyclohexane-1,2-diyl group, a cyclohexane-1,3-diyl group, and a cyclohexane-1,4-diyl group; a cycloheptanediyl group such as a cycloheptane-1,2-diyl group, a cycloheptane-1,3-diyl group, and a cycloheptane-1,4-diyl group; a cyclooctanediyl group such as a cyclooctane-1,2-diyl group, a cyclooctane-1,3-diyl group, a cyclooctane-1,4-diyl group, and a cyclooctane-1,5-diyl group; a cyclodecanediyl group such as a cyclodecane-1,2-diyl group, a cyclodecane-1,3-diyl group, a cyclodecane-1,4-diyl group, and a cyclodecane-1,5-diyl group; a cyclododecanediyl group such as a cyclododecane-1,2-diyl group, a cyclododecane-1,3-diyl group, a cyclododecane-1,4-diyl group, and a cyclododecane-1,5-diyl group; a cyclotetradecanediyl group such as a cyclotetradecane-1,2-diyl group, a cyclotetradecane-1,3-diyl group, a cyclotetradecane-1,4-diyl group, a cyclotetradecane-1,5-diyl group, and a cyclotetradecane-1,7-diyl group; a cycloeicosanediyl group such as a cycloeicosane-1,2-diyl group and a cycloeicosane-1,10-diyl group; and the like. 
     Examples of the divalent fused alicyclic group having 10 to 30 carbon atoms include a decalindiyl group such as a decalin-2,5-diyl group and a decalin-2,7-diyl group; an adamantanediyl group such as an adamantane-1,2-diyl group and an adamantane-1,3-diyl group; a bicyclo[2.2.1]heptanediyl group such as a bicyclo[2.2.1]heptane-2,3-diyl group, a bicyclo[2.2.1]heptane-2,5-diyl group, and a bicyclo[2.2.1]heptane-2,6-diyl group; and the like. 
     These divalent alicyclic hydrocarbon groups may be substituted with a substituent at an arbitrary position. Examples of the substituent include those mentioned above in connection with a substituent that may substitute the aromatic ring included in A x . 
     A 2  and A 3  are preferably a divalent alicyclic hydrocarbon group having 3 to 12 carbon atoms, more preferably a cycloalkanediyl group having 3 to 12 carbon atoms, still more preferably a group among the groups respectively represented by the following formulas (A31) to (A34), and particularly preferably the group represented by the formula (A32). 
     
       
                 
         
             
             
         
      
     
     The divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms is classified into a cis-stereoisomer and a trans-stereoisomer based on the difference in the steric configuration of the carbon atom bonded to Y 1  and Y 3  (or Y 2  and Y 4 ). For example, a cyclohexane-1,4-diyl group is classified into a cis-isomer (A32a) and a trans-isomer (A32b) (see below). 
     
       
                 
         
             
             
         
      
     
     The divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms may be a cis-isomer, a trans-isomer, or a mixture of a cis-isomer and a trans-isomer. Note that it is preferable that the divalent alicyclic hydrocarbon group having 3 to 30 carbon atoms be a trans-isomer or a cis-isomer, and more preferably a trans-isomer, since an excellent alignment capability can be obtained. 
     A 4  and A 5  are independently a substituted or unsubstituted divalent aromatic group having 4 to 30 carbon atoms. 
     The aromatic group represented by A 4  and A 5  may be a monocyclic aromatic group, or may be a polycyclic aromatic group. 
     Specific examples of A 4  and A 5  include, but are not limited to, the groups respectively represented by the following formulas. 
     
       
                 
         
             
             
         
      
     
     These aromatic groups (i.e., specific examples of A 4  and A 5 ) may be substituted with a substituent at an arbitrary position. Examples of the substituent include a halogen atom, a cyano group, a hydroxyl group, an alkyl group having 1 to 6 carbon atoms, an alkoxy group having 1 to 6 carbon atoms, a nitro group, a —C(═O)—OR group, and the like. Note that R is an alkyl group having 1 to 6 carbon atoms. Among these, a halogen atom, an alkyl group having 1 to 6 carbon atoms, and an alkoxy group having 1 to 6 carbon atoms are preferable as the substituent. A fluorine atom is preferable as the halogen atom. A methyl group, an ethyl group, and a propyl group are preferable as the alkyl group having 1 to 6 carbon atoms. A methoxy group and an ethoxy group are preferable as the alkoxy group having 1 to 6 carbon atoms. 
     It is preferable that A 4  and A 5  be independently a substituted or unsubstituted phenylene group, or a substituted or unsubstituted naphthylene group, more preferably a group among the groups respectively represented by the following formulas (A41), (A42), and (A43) that are optionally substituted with a substituent, and particularly preferably the group represented by the formula (A41) that is optionally substituted with a substituent, in order to ensure that the intended effects of the invention can be more advantageously achieved. 
     
       
                 
         
             
             
         
      
     
     Q 1  is a hydrogen atom, or a substituted or unsubstituted alkyl group having 1 to 6 carbon atoms. 
     Examples of the substituted or unsubstituted alkyl group having 1 to 6 carbon atoms include those mentioned above in connection with A x . 
     It is preferable that Q 1  be a hydrogen atom or an alkyl group having 1 to 6 carbon atoms, and more preferably a hydrogen atom or a methyl group. 
     m and n are independently 0 or 1. It is preferable that both m and n be 0. 
     Note that the polymerizable compound according to one embodiment of the invention may be a stereoisomer based on the carbon-nitrogen double bond. These stereoisomers are also intended to be included within the scope of the invention. 
     The polymerizable compound according to one embodiment of the invention may be produced by effecting the following reaction, for example. 
     (1) Production Method 1 
     The polymerizable compound according to one embodiment of the invention in which A y  is a hydrogen atom, and X included in A x  is a nitrogen atom (i.e., a compound represented by the following formula (Ia)) may be produced as described below. 
                                
wherein Y 1  to Y 8 , G 1 , G 2 , Z 1 , Z 2 , A x , A 1  to A 5 , Q 1 , R a , R b , m, and n are the same as defined above, A y′  is the same as A y , provided that a hydrogen atom is excluded, and L 1  and L 2  are independently a leaving group (e.g., halogen atom, methanesulfonyloxy group, or p-toluenesulfonyloxy group).
 
     Specifically, the thiosemicarbazide hydrochloride (1) (in an equimolar amount) is added to and reacted with the carbonyl compound represented by the formula (4) (carbonyl compound (4)) (reaction 1), and the compound represented by the formula (2) (compound (2)) (in an equimolar amount) is added to and reacted with the resulting product (reaction 2) to produce the target polymerizable compound according to one embodiment of the invention that is represented by the formula (Ia) (polymerizable compound (Ia)). 
     A solvent used for the above reaction is not particularly limited as long as the solvent is inert to the reaction. Examples of the solvent include an alcohol-based solvent such as methyl alcohol, ethyl alcohol, n-propyl alcohol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, and t-butyl alcohol; an ether-based solvent such as diethyl ether, tetrahydrofuran, 1,2-dimethoxyethane, 1,4-dioxane, and cyclopentyl methyl ether; an ester-based solvent such as ethyl acetate, propyl acetate, and methyl propionate; an aromatic hydrocarbon-based solvent such as benzene, toluene, and xylene; an aliphatic hydrocarbon-based solvent such as n-pentane, n-hexane, and n-heptane; an amide-based solvent such as N,N-dimethylformamide, N-methylpyrrolidone, and hexamethylphosphoric triamide; a sulfur-containing solvent such as dimethyl sulfoxide and sulfolane; a mixed solvent of two or more solvents among these solvents; and the like. 
     Among these, an alcohol-based solvent, an ether-based solvent, and a mixed solvent of an alcohol-based solvent and an ether-based solvent are preferable. 
     The solvent may be used in an appropriate amount taking account of the type of each compound, the reaction scale, and the like. The solvent is normally used in an amount of 1 to 100 g per gram of the carbonyl compound (4). 
     The reaction 1 and the reaction 2 proceed smoothly when the reaction temperature is within the range from −10° C. to the boiling point of the solvent. The reaction time is determined taking account of the reaction scale, but is normally several minutes to several hours. 
     The polymerizable compound according to one embodiment of the invention that is represented by the formula (Ib) (polymerizable compound (Ib)) can be obtained by reacting the compound represented by the formula (3) (compound (3)) (in an equimolar amount) with the polymerizable compound (Ia) under reaction conditions similar to those employed when effecting the above reactions. 
     (2) Production Method 2 
     The polymerizable compound (I) according to one embodiment of the invention may also be produced by effecting the following reaction. 
                                
wherein Y 1  to Y 8 , G 1 , G 2 , Z 1 , Z 2 , A x , A y , A 1  to A 5 , Q 1 , m, and n are the same as defined above.
 
     Specifically, the polymerizable compound according to one embodiment of the invention that is represented by the formula (I) can be produced with high selectivity in high yield by reacting the hydrazine compound represented by the formula (5) (hydrazine compound (5)) with the carbonyl compound represented by the formula (4) (carbonyl compound (4)) in a molar ratio (hydrazine compound (5):carbonyl compound (4)) of 1:2 to 2:1 (preferably 1:1.5 to 1.5:1). 
     The above reaction may be effected in the presence of an acid catalyst such as an organic acid (e.g., (±)-10-camphorsulfonic acid or p-toluenesulfonic acid), or an inorganic acid (e.g., hydrochloric acid or sulfuric acid). The addition of the acid catalyst may reduce the reaction time, and improve the yield. The acid catalyst is normally added in an amount of 0.001 to 1 mol based on 1 mol of the carbonyl compound (4). The acid catalyst may be added directly, or a solution prepared by dissolving the acid catalyst in an appropriate solvent may be added. 
     A solvent used for the above reaction is not particularly limited as long as the solvent is inert to the reaction. Examples of the solvent include an alcohol-based solvent such as methyl alcohol, ethyl alcohol, n-propyl alcohol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, and t-butyl alcohol; an ether-based solvent such as diethyl ether, tetrahydrofuran, 1,2-dimethoxyethane, 1,4-dioxane, and cyclopentyl methyl ether; an ester-based solvent such as ethyl acetate, propyl acetate, and methyl propionate; an aromatic hydrocarbon-based solvent such as benzene, toluene, and xylene; an aliphatic hydrocarbon-based solvent such as n-pentane, n-hexane, and n-heptane; an amide-based solvent such as N,N-dimethylformamide, N-methylpyrrolidone, and hexamethylphosphoric triamide; a sulfur-containing solvent such as dimethyl sulfoxide and sulfolane; a mixed solvent of two or more solvents among these solvents; and the like. 
     Among these, an alcohol-based solvent, an ether-based solvent, and a mixed solvent of an alcohol-based solvent and an ether-based solvent are preferable. 
     The solvent may be used in an appropriate amount taking account of the type of each compound, the reaction scale, and the like. The solvent is normally used in an amount of 1 to 100 g per gram of the hydrazine compound (3). 
     The reaction proceeds smoothly when the reaction temperature is within the range from −10° C. to the boiling point of the solvent. The reaction time is determined taking account of the reaction scale, but is normally several minutes to several hours. 
     The hydrazine compound (5) may be produced as described below. 
                                
wherein A x  and A y  are the same as defined above, and X is a leaving group (e.g., halogen atom, amino group, methylthio group, methanesulfonyloxy group, or p-toluenesulfonyloxy group).
 
     Specifically, the compound represented by the formula (7a) is reacted with hydrazine (6) in an appropriate solvent in a molar ratio (compound (7a):hydrazine (6)) of 1:1 to 1:20 (preferably 1:2 to 1:10) to obtain the corresponding hydrazine compound (5a), and the hydrazine compound (5a) is reacted with the compound represented by the formula (7b) to obtain the hydrazine compound (5). 
     Hydrazine monohydrate is normally used as the hydrazine (6). A commercially available product may be used directly as the hydrazine (6). 
     A solvent used for the above reaction is not particularly limited as long as the solvent is inert to the reaction. Examples of the solvent include an alcohol-based solvent such as methyl alcohol, ethyl alcohol, n-propyl alcohol, isopropyl alcohol, n-butyl alcohol, isobutyl alcohol, sec-butyl alcohol, and t-butyl alcohol; an ether-based solvent such as diethyl ether, tetrahydrofuran, 1,2-dimethoxyethane, 1,4-dioxane, and cyclopentyl methyl ether; an aromatic hydrocarbon-based solvent such as benzene, toluene, and xylene; an aliphatic hydrocarbon-based solvent such as n-pentane, n-hexane, and n-heptane; an amide-based solvent such as N,N-dimethylformamide, N-methylpyrrolidone, and hexamethylphosphoric triamide; a sulfur-containing solvent such as dimethyl sulfoxide and sulfolane; a mixed solvent of two or more solvents among these solvents; and the like. 
     Among these, an alcohol-based solvent, an ether-based solvent, and a mixed solvent of an alcohol-based solvent and an ether-based solvent are preferable. 
     The solvent may be used in an appropriate amount taking account of the type of each compound, the reaction scale, and the like. The solvent is normally used in an amount of 1 to 100 g per gram of hydrazine. 
     The reaction proceeds smoothly when the reaction temperature is within the range from −10° C. to the boiling point of the solvent. The reaction time is determined taking account of the reaction scale, but is normally several minutes to several hours. 
     The hydrazine compound (5) may also be produced by reducing a diazonium salt (8) (see below) using a known method. 
                                
wherein A x  and A y  are the same as defined above, and X −  is an anion that is a counter ion for diazonium. Examples of the anion represented by X −  include an inorganic anion such as a hexafluorophosphoric acid ion, a fluoroboric acid ion, a chloride ion, and a sulfuric acid ion; an organic anion such as a polyfluoroalkylcarboxylic acid ion, a polyfluoroalkylsulfonic acid ion, a tetraphenylboric acid ion, an aromatic carboxylic acid ion, and an aromatic sulfonic acid ion; and the like.
 
     Examples of a reducing agent used for the above reaction include a metal salt reducing agent. 
     The term “metal salt reducing agent” normally refers to a compound that includes a metal having a small valence, or a compound that includes a metal ion and a hydrido source (see “ Yuki Gosei Jikkenhou Handbook  (Handbook of Organic Synthesis Experiments)”, 1990, edited by The Society of Synthetic Organic Chemistry, Japan, published by Maruzen Co., Ltd., p. 810). 
     Examples of the metal salt reducing agent include NaAlH 4 , NaAlH p (Or) q  (wherein p and q are independently an integer from 1 to 3, provided that p+q=4, and r is an alkyl group having 1 to 6 carbon atoms), LiAlH 4 , iBu 2 AlH, LiBH 4 , NaBH 4 , SnCl 2 , CrCl 2 , TiCl 3 , and the like. 
     The reduction reaction may be effected under known reaction conditions. For example, the reduction reaction may be effected under the reaction conditions described in JP-A-2005-336103 , “Shin - Jikken Kagaku Koza  (New Experimental Chemistry Course)”, 1978, Vol. 14, published by Maruzen Co., Ltd., “ Jikken Kagaku Koza  (Experimental Chemistry Course)”, 1992, Vol. 20, published by Maruzen Co., Ltd., or the like. 
     The diazonium salt (8) may be produced from aniline or the like using a normal method. 
     The carbonyl compound (4) may be produced by appropriately bonding and modifying a plurality of known compounds having the desired structure by arbitrarily combining an ether linkage (—O—)-forming reaction, an ester linkage (—C(═O)—O— or —O—C(═O)—)-forming reaction, a carbonate linkage (—O—C(═O)—O—)-forming reaction, and an amide linkage (—C(═O)NH— or —NHC(═O)—)-forming reaction. 
     An ether linkage may be formed as described below.
     (i) A compound represented by D1-hal (wherein hal is a halogen atom; hereinafter the same) and a compound represented by D2-OMet (wherein Met is an alkali metal (mainly sodium); hereinafter the same) are mixed and condensed (Williamson synthesis). Note that D1 and D2 are an arbitrary organic group (hereinafter the same).   (ii) A compound represented by D1-hal and a compound represented by D2-OH are mixed and condensed in the presence of a base (e.g., sodium hydroxide or potassium hydroxide).   (iii) A compound represented by D1-J (wherein J is an epoxy group) and a compound represented by D2-OH are mixed and condensed in the presence of a base (e.g., sodium hydroxide or potassium hydroxide).   (iv) A compound represented by D1-OFN (wherein OFN is a group that includes an unsaturated bond) and a compound represented by D2-OMet are mixed and subjected to an addition reaction in the presence of a base (e.g., sodium hydroxide or potassium hydroxide).   (v) A compound represented by D1-hal and a compound represented by D2-OMet are mixed and condensed in the presence of copper or cuprous chloride (Ullmann condensation).   

     An ester linkage and an amide linkage may be formed as described below.
     (vi) A compound represented by D1-COOH and a compound represented by D2-OH or D2-NH 2  are subjected to dehydration and condensation in the presence of a dehydration-condensation agent (e.g., N,N-dicyclohexylcarbodiimide).   (vii) A compound represented by D1-COOH is reacted with a halogenating agent to obtain a compound represented by D1-CO-hal, and the compound represented by D1-CO-hal is reacted with a compound represented by D2-OH or D2-NH 2  in the presence of a base.   (viii) A compound represented by D1-COOH is reacted with an acid anhydride to obtain a mixed acid anhydride, and the mixed acid anhydride is reacted with a compound represented by D2-OH or D2-NH 2 .   (ix) A compound represented by D1-COOH and a compound represented by D2-OH or D2-NH 2  are subjected to dehydration and condensation in the presence of an acid catalyst or a base catalyst.   

     More specifically, the carbonyl compound (4) in which the group represented by Z 2 -Y 6 -G 2 -Y 4 -A 3 -Y 2 -is identical with the group represented by Z 1 -Y 5 -G 1 -Y 3 -A 2 -Y 1 —, and Y 1  is a group represented by Y 11 —C(═O)—O— (hereinafter referred to as “compound (4′)”) may be produced by effecting the following reaction. 
                                
wherein Y 3 , Y 5 , Y 7 , G 1 , Z 1 , A 1 , A 2 , A 4 , Q 1 , and m are the same as defined above, Y 11  is a group provided that Y 11 —C(═O)—O— is Y 1 , Y 1  is the same as defined above, and L is a leaving group (e.g., hydroxyl group, halogen atom, methanesulfonyloxy group, or p-toluenesulfonyloxy group).
 
     Specifically, the dihydroxy compound represented by the formula (9) (compound (9)) is reacted with the compound represented by the formula (10) (compound (10)) in a molar ratio (compound (9):compound (10)) of 1:2 to 1:4 (preferably 1:2 to 1:3) to produce the target compound (4′) with high selectivity in high yield. 
     When the compound (10) is a compound (carboxylic acid) represented by the formula (10) wherein L is a hydroxyl group, the target product may be obtained by effecting the reaction in the presence of a dehydration-condensation agent (e.g., 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride or dicyclohexylcarbodiimide). 
     The dehydration-condensation agent is normally used in an amount of 1 to 3 mol based on 1 mol of the compound (10). 
     When the compound (10) is a compound (acid halide) represented by the formula (10) wherein L is a halogen atom, the target product may be obtained by effecting the reaction in the presence of a base. 
     Examples of the base include an organic base such as triethylamine and pyridine; and an inorganic base such as sodium hydroxide, sodium carbonate, and sodium hydrogen carbonate. 
     The base is normally used in an amount of 1 to 3 mol based on 1 mol of the compound (10). 
     When the compound (10) is a compound (mixed acid anhydride) represented by the formula (10) wherein L is a methanesulfonyloxy group or a p-toluenesulfonyloxy group, the target product may be obtained in the same manner as in the case where L is a halogen atom. 
     Examples of the solvent used for the above reaction include a chlorine-based solvent such as chloroform and methylene chloride; an amide-based solvent such as N-methylpyrrolidone, N,N-dimethylformamide, N,N-dimethylacetamide, and hexamethylphosphoric triamide; an ether-based solvent such as 1,4-dioxane, cyclopentyl methyl ether, tetrahydrofuran, tetrahydropyran, and 1,3-dioxolane; a sulfur-containing solvent such as dimethyl sulfoxide and sulfolane; an aromatic hydrocarbon-based solvent such as benzene, toluene, and xylene; an aliphatic hydrocarbon-based solvent such as n-pentane, n-hexane, and n-octane; an alicyclic hydrocarbon-based solvent such as cyclopentane and cyclohexane; a mixed solvent of two or more solvents among these solvents; and the like. 
     The solvent may be used in an appropriate amount taking account of the type of each compound, the reaction scale, and the like. The solvent is normally used in an amount of 1 to 50 g per gram of the dihydroxy compound (9). 
     Many of the compounds (9) are known compounds, and may be produced using a known method. For example, the compound (demethylated product) represented by the formula (9) wherein A 1  is a trivalent benzene ring group, and Q 1  is a hydrogen atom, may be produced by sequentially adding an alkyllithium (e.g., n-butyllithium) and N,N-dimethylformamide to 1,4-dimethoxybenzene in the presence of a base (e.g., N,N,N′,N′-tetramethylethylenediamine), stirring the mixture to obtain a formyl product, and reacting boron tribromide with the product. A product commercially available as the compound (9) may be used after optional purification. 
     Many of the compounds (10) are known compounds, and may be produced by appropriately bonding and modifying a plurality of known compounds having a desired structure by arbitrarily combining an ether linkage (—O—)-forming reaction, an ester linkage (—C(═O)—O— or —O—C(═O)—)-forming reaction, a carbonate linkage (—O—C(═O)—O—)-forming reaction, and an amide linkage (—C(═O)NH— or —NHC(═O)—)-forming reaction. 
     After completion of the reaction, a post-treatment operation normally employed in synthetic organic chemistry is performed, optionally followed by a known separation/purification means such as column chromatography, recrystallization, or distillation to isolate the target product. 
     The structure of the target product may be identified by measurement (e.g., NMR spectrometry, IR spectrometry, or mass spectrometry), elemental analysis, and the like. 
     2) Polymerizable Composition 
     A polymerizable composition according to one embodiment of the invention includes the polymerizable compound according to one embodiment of the invention, and an initiator. The initiator is used in order to more efficiently polymerize the polymerizable composition according to one embodiment of the invention. 
     The initiator may be appropriately selected taking account of the type of the polymerizable group included in the polymerizable compound. For example, a radical initiator may be used when the polymerizable group is a radically polymerizable group. An anionic initiator may be used when the polymerizable group is an anionically polymerizable group. A cationic initiator may be used when the polymerizable group is a cationically polymerizable group. 
     Examples of the radical initiator include a thermal radical generator that is a compound that generates active species that initiate polymerization of the polymerizable compound upon heating, and a photo-radical generator that is a compound that generates active species that initiate polymerization of the polymerizable compound upon exposure to exposure light (e.g., visible rays, ultraviolet rays (e.g., i-line), deep ultraviolet rays, electron beams, or X-rays). It is preferable to use the photo-radical generator. 
     Examples of the photo-radical generator include an acetophenone-based compound, a biimidazole-based compound, a triazine-based compound, an O-acyloxime-based compound, an onium salt-based compound, a benzoin-based compound, a benzophenone-based compound, an α-diketone-based compound, a polynuclear quinone-based compound, a xanthone-based compound, a diazo-based compound, an imide sulfonate-based compound, and the like. These compounds generate active radicals, or an active acid, or both active radicals and an active acid, upon exposure. These photo-radical generators may be used either alone or in combination. 
     Specific examples of the acetophenone-based compound include
     2-hydroxy-2-methyl-1-phenylpropan-1-one,   2-methyl-1-[4-(methylthio)phenyl]-2-morpholinopropan-1-one,   2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)butan-1-one,   1-hydroxycyclohexyl phenyl ketone, 2,2-dimethoxy-1,2-diphenylethan-1-one,   1,2-octanedione, 2-benzyl-2-dimethylamino-4′-morpholinobutyrophenone, and the like.   

     Specific examples of the biimidazole-based compound include
     2,2′-bis(2-chlorophenyl)-4,4′,5,5′-tetrakis(4-ethoxycarbonylphenyl)-1,2′-biimidazole,   2,2′-bis(2-bromophenyl)-4,4′,5,5′-tetrakis(4-ethoxycarbonylphenyl)-1,2′-biimidazole,   2,2′-bis(2-chlorophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole,   2,2′-bis(2,4-dichlorophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole,   2,2′-bis(2,4,6-trichlorophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole,   2,2′-bis(2-bromophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole,   2,2′-bis(2,4-dibromophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole,   2,2′-bis(2,4,6-tribromophenyl)-4,4′,5,5′-tetraphenyl-1,2′-biimidazole, and the like.   

     When using a biimidazole-based compound as a photoinitiator, it is preferable to use a hydrogen donor in combination with the biimidazole-based compound since sensitivity can be further improved. 
     The term “hydrogen donor” used herein refers to a compound that can donate a hydrogen atom to radicals generated by the biimidazole-based compound upon exposure. A mercaptan-based compound, an amine-based compound, and the like are preferable as the hydrogen donor. 
     Examples of the mercaptan-based compound include 2-mercaptobenzothiazole, 2-mercaptobenzoxazole, 2-mercaptobenzimidazole, 2,5-dimercapto-1,3,4-thiadiazole, 2-mercapto-2,5-dimethylaminopyridine, and the like. Examples of the amine-based compound include 4,4′-bis(dimethylamino)benzophenone, 4,4′-bis(diethylamino)benzophenone, 4-diethylaminoacetophenone, 4-dimethylaminopropiophenone, ethyl-4-dimethylaminobenzoate, 4-dimethylaminobenzoic acid, 4-dimethylaminobenzonitrile, and the like. 
     Specific examples of the triazine-based compound include a triazine-based compound that includes a halomethyl group, such as
     2,4,6-tris(trichloromethyl)-s-triazine, 2-methyl-4,6-bis(trichloromethyl)-s-triazine,   2-[2-(5-methylfuran-2-yl)ethenyl]-4,6-bis(trichloromethyl)-s-triazine,   2-[2-(furan-2-yl)ethenyl]-4,6-bis(trichloromethyl)-s-triazine,   2-[2-(4-diethylamino-2-methylphenyl)ethenyl]-4,6-bis(trichloromethyl)-s-triazine,   2-[2-(3,4-dimethoxyphenyl)ethenyl]-4,6-bis(trichloromethyl)-s-triazine,   2-(4-methoxyphenyl)-4,6-bis(trichloromethyl)-s-triazine,   2-(4-ethoxystyryl)-4,6-bis(trichloromethyl)-s-triazine, and   2-(4-n-butoxyphenyl)-4,6-bis(trichloromethyl)-s-triazine.   

     Specific examples of the O-acyloxime-based compound include
     1-[4-(phenylthio)phenyl]-heptane-1,2-dione-2-(O-benzoyloxime),   1-[4-(phenylthio)phenyl]-octane-1,2-dione-2-(O-benzoyloxime),   1-[4-(benzoyl)phenyl]-octane-1,2-dione-2-(O-benzoyloxime),   1-[9-ethyl-6-(2-methylbenzoyl)-9H-carbazol-3-yl]-ethanone-1-(O-acetyloxime),   1-[9-ethyl-6-(3-methylbenzoyl)-9H-carbazol-3-yl]-ethanone-1-(O-acetyloxime),   1-(9-ethyl-6-benzoyl-9h-carbazol-3-yl)-ethanone-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-4-tetrahydrofuranylbenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-4-tetrahydropyranylbenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-5-tetrahydrofuranylbenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-5-tetrahydropyranylbenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-{2-methyl-4-(2,2-dimethyl-1,3-dioxolanyl)benzoyl}-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-4-tetrahydrofuranylmethoxybenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-4-tetrahydropyranylmethoxybenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-5-tetrahydrofuranylmethoxybenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methylbenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-(2-methyl-5-tetrahydropyranylmethoxybenzoyl)-9H-carbazol-3-yl]-1-(O-acetyloxime),   ethanone-1-[9-ethyl-6-{2-methyl-4-(2,2-dimethyl-1,3-dioxolanyl)methoxybenzoyl}-9H-carbazol-3-yl]-1-(O-acetyloxime), and the like.   

     A commercially available product may be used directly as the photo-radical generator. Specific examples of a commercially available product that may be used as the photo-radical generator include Irgacure 907, Irgacure 184, Irgacure 369, Irgacure 651, Irgacure 819, Irgacure 907, and Irgacure OXE02 (manufactured by BASF); Adekaoptomer N1919 (manufactured by Adeka Corporation); and the like. 
     Examples of the anionic initiator include an alkyllithium compound;
     a monolithium salt or a monosodium salt of biphenyl, naphthalene, pyrene, and the like;   a polyfunctional initiator such as a dilithium salt and a trilithium salt; and the like.   

     Examples of the cationic initiator include a proton acid such as sulfuric acid, phosphoric acid, perchloric acid, and trifluoromethanesulfonic acid; a Lewis acid such as boron trifluoride, aluminum chloride, titanium tetrachloride, and tin tetrachloride; an aromatic onium salt or a combination of an aromatic onium salt and a reducing agent; and the like. 
     These initiators may be used either alone or in combination. 
     The initiator is normally added to the polymerizable composition according to one embodiment of the invention in an amount of 0.1 to 30 parts by weight, and preferably 0.5 to 10 parts by weight, based on 100 parts by weight of the polymerizable compound. 
     It is preferable to add a surfactant to the polymerizable composition according to one embodiment of the invention in order to adjust surface tension. The surfactant is not particularly limited, but is preferably a nonionic surfactant. Examples of the nonionic surfactant include an oligomer having a molecular weight of about several thousand, such as KH-40 (manufactured by AGC Seimi Chemical Co., Ltd.). The surfactant is normally added to the polymerizable composition according to one embodiment of the invention in an amount of 0.01 to 10 parts by weight, and preferably 0.1 to 2 parts by weight, based on 100 parts by weight of the polymerizable compound. 
     The polymerizable composition according to one embodiment of the invention may further include an additional additive such as an additional copolymerizable monomer, a metal, a metal complex, a dye, a pigment, a fluorescent material, a phosphorescent material, a leveling agent, a thixotropic agent, a gelling agent, a polysaccharide, a UV absorber, an IR (infrared) absorber, an antioxidant, an ion-exchange resin, or a metal oxide (e.g., titanium oxide). Each additive is normally added to the polymerizable composition according to one embodiment of the invention in an amount of 0.1 to 20 parts by weight based on 100 parts by weight of the polymerizable compound. 
     The polymerizable composition according to one embodiment of the invention may be prepared by mixing and dissolving given amounts of the polymerizable compound according to one embodiment of the invention, the initiator, and an optional additive in an appropriate organic solvent. 
     Examples of the organic solvent include a ketone such as cyclopentanone, cyclohexanone, and methyl ethyl ketone; an acetate such as butyl acetate and amyl acetate; a halogenated hydrocarbon such as chloroform, dichloromethane, and dichloroethane; an ether such as 1,4-dioxane, cyclopentyl methyl ether, tetrahydrofuran, tetrahydropyran, and 1,3-dioxolane; and the like. 
     The polymerizable composition thus obtained is useful as a raw material for producing a polymer according to one embodiment of the invention, or an optically anisotropic article according to one embodiment of the invention (described below). 
     3) Polymer 
     A polymer according to one embodiment of the invention is (1) a polymer obtained by polymerizing the polymerizable compound according to one embodiment of the invention, or (2) a polymer obtained by polymerizing the polymerizable composition according to one embodiment of the invention. 
     The term “polymerization” used herein refers to a chemical reaction in a broad sense including a normal polymerization reaction and a crosslinking reaction. 
     (1) Polymer Obtained by Polymerizing Polymerizable Compound 
     The polymer obtained by polymerizing the polymerizable compound according to one embodiment of the invention may be a homopolymer of the polymerizable compound according to one embodiment of the invention, a copolymer of two or more types of the polymerizable compound according to one embodiment of the invention, or a copolymer of the polymerizable compound according to one embodiment of the invention and an additional copolymerizable monomer. 
     Examples of the additional copolymerizable monomer include, but are not limited to, 4′-methoxyphenyl 4-(2-methacryloyloxyethyloxyl)benzoate, biphenyl 4-(6-methacryloyloxyhexyloxyl)benzoate, 4′-cyanobiphenyl 4-(2-acryloyloxyethyloxyl)benzoate, 4′-cyanobiphenyl 4-(2-methacryloyloxyethyloxyl)benzoate, 3′,4′-difluorophenyl 4-(2-methacryloyloxyethyloxyl)benzoate, naphthyl 4-(2-methacryloyloxyethyloxyl)benzoate, 4-acryloyloxy-4′-decylbiphenyl, 4-acryloyloxy-4′-cyanobiphenyl, 4-(2-acryloyloxyethyloxy)-4′-cyanobiphenyl, 4-(2-methacryloyloxyethyloxy)-4′-methoxybiphenyl, 4-(2-methacryloyloxyethyloxy)-4′-(4″-fluorobenzyloxy)-biphenyl, 4-acryloyloxy-4′-propylcyclohexylphenyl, 4-methacryloyl-4′-butylbicyclohexyl, 4-acryloyl-4′-amyltolan, 4-acryloyl-4′-(3,4-difluorophenyl)bicyclohexyl, (4-amylphenyl) 4-(2-acryloyloxyethyl)benzoate, (4-(4′-propylcyclohexyl)phenyl) 4-(2-acryloyloxyethyl)benzoate, and the like. 
     Examples of a commercially available product that may be used as the additional copolymerizable monomer include LC-242 (manufactured by BASF) and the like. The compounds disclosed in JP-A-2007-002208, JP-A-2009-173893, 
     JP-A-2009-274984, JP-A-2010-030979, JP-A-2010-031223, JP-A-2011-006360, and the like may also be used as the additional copolymerizable monomer. 
     A polyfunctional monomer that includes a plurality of polymerizable unsaturated groups (e.g., acryloyl group, methacryloyl group, vinyl group, and allyl group) may also be used as the additional copolymerizable monomer. 
     Examples of such a polyfunctional monomer include an alkanediol diacrylate such as 1,2-butanediol diacrylate, 1,3-butanediol diacrylate, 1,4-butanediol diacrylate, neopentanediol diacrylate, and 1,6-hexanediol diacrylate, an alkanediol dimethacrylate such as 1,2-butanediol dimethacrylate, 1,3-butanediol dimethacrylate, 1,4-butanediol dimethacrylate, neopentanediol dimethacrylate, and 1,6-hexanediol dimethacrylate, a polyethylene glycol diacrylate such as ethylene glycol diacrylate, diethylene glycol diacrylate, triethylene glycol diacrylate, and tetraethylene glycol diacrylate, a polypropylene glycol diacrylate such as propylene glycol diacrylate, dipropylene glycol diacrylate, tripropylene glycol diacrylate, and tetrapropylene glycol diacrylate, a polyethylene glycol dimethacrylate such as ethylene glycol dimethacrylate, diethylene glycol dimethacrylate, triethylene glycol dimethacrylate, and tetraethylene glycol dimethacrylate, a polypropylene glycol dimethacrylate such as propylene glycol dimethacrylate, dipropylene glycol dimethacrylate, tripropylene glycol dimethacrylate, and tetrapropylene glycol dimethacrylate, a polyethylene glycol divinyl ether such as ethylene glycol divinyl ether, diethylene glycol divinyl ether, triethylene glycol divinyl ether, and tetraethylene glycol divinyl ether, a polyethylene glycol diallyl ether such as ethylene glycol diallyl ether, diethylene glycol diallyl ether, triethylene glycol diallyl ether, and tetraethylene glycol diallyl ether, bisphenol F ethoxylate diacrylate, bisphenol F ethoxylate dimethacrylate, bisphenol A ethoxylate diacrylate, bisphenol A ethoxylate dimethacrylate, trimethylolpropane triacrylate, trimethylolpropane trimethacrylate, trimethylolpropane ethoxylate triacrylate, trimethylolpropane ethoxylate trimethacrylate, trimethylolpropane propoxylate triacrylate, trimethylolpropane propoxylate trimethacrylate, isocyanuric acid ethoxylate triacrylate, glycerol ethoxylate triacrylate, glycerol propoxylate triacrylate, pentaerythritol ethoxylate tetraacrylate, ditrimethylolpropane ethoxylate tetraacrylate, dipentaerythritol ethoxylate hexacrylate, and the like. 
     The polymerizable compound according to one embodiment of the invention may be (co)polymerized optionally together with the additional copolymerizable monomer in the presence of an appropriate initiator. The initiator may be used in an amount similar to that of the initiator included in the polymerizable composition. 
     When the polymer according to one embodiment of the invention is a copolymer of the polymerizable compound according to one embodiment of the invention and the additional copolymerizable monomer, the content of structural units derived from the polymerizable compound according to one embodiment of the invention is not particularly limited, but is preferably 50 wt % or more, and more preferably 70 wt % or more, based on the total structural units. When the content of structural units derived from the polymerizable compound is within the above range, a polymer that has a high glass transition temperature (Tg) and high hardness can be obtained. 
     The polymer (1) may be produced by (A) (co)polymerizing the polymerizable compound optionally together with the additional copolymerizable monomer in an appropriate organic solvent in the presence of an appropriate initiator, isolating the target polymer, dissolving the polymer in an appropriate organic solvent to prepare a solution, applying the solution to an appropriate substrate to obtain a film, and drying the film, followed by optional heating, or (B) applying a solution prepared by dissolving the polymerizable compound and an initiator in an organic solvent optionally together with the additional copolymerizable monomer to a substrate using a known coating method, removing the solvent, and effecting polymerization by applying heat or activated energy rays, for example. 
     Examples of the initiator include those mentioned above in connection with the initiator included in the polymerizable composition. 
     The organic solvent used for polymerization when using the method (A) is not particularly limited as long as the organic solvent is inert. Examples of the organic solvent include an aromatic hydrocarbon such as toluene, xylene, and mesitylene; a ketone such as cyclohexanone, cyclopentanone, and methyl ethyl ketone; an acetate such as butyl acetate and amyl acetate; a halogenated hydrocarbon such as chloroform, dichloromethane, and dichloroethane; an ether such as cyclopentyl methyl ether, tetrahydrofuran, and tetrahydropyran; and the like. Among these, it is preferable to use a compound having a boiling point of 60 to 250° C., and preferably 60 to 150° C., from the viewpoint of handling capability. 
     Examples of the organic solvent used to dissolve the polymer when implementing the method (A), and the organic solvent used for the method (B), include a ketone-based solvent such as acetone, methyl ethyl ketone, methyl isobutyl ketone, cyclopentanone, and cyclohexanone; an ester-based solvent such as butyl acetate and amyl acetate; a halogenated hydrocarbon-based solvent such as dichloromethane, chloroform, and dichloroethane; an ether-based solvent such as tetrahydrofuran, tetrahydropyran, 1,2-dimethoxyethane, 1,4-dioxane, cyclopentyl methyl ether, 1,3-dioxolane; an aprotic polar solvent such as N,N-dimethylformamide, N,N-dimethylacetamide, dimethyl sulfoxide, gamma-butyrolactone, and N-methylpyrrolidone; and the like. Among these, it is preferable to use a compound having a boiling point of 60 to 200° C. from the viewpoint of handling capability. These solvents may be used either alone or in combination. 
     A substrate formed of a known organic or inorganic material may be used as the substrate. Examples of the organic material include a polycycloolefin (e.g., Zeonex and Zeonor (registered trademark; manufactured by Zeon Corporation); Afton (registered trademark; manufactured by JSR Corporation); and Apel (registered trademark; manufactured by Mitsui Chemicals Inc.)), polyethylene terephthalate, a polycarbonate, a polyimide, a polyamide, polymethyl methacrylate, polystyrene, polyvinyl chloride, polytetrafluoroethylene, cellulose, cellulose triacetate, polyethersulfone, and the like. Examples of the inorganic material include silicon, glass, calcite, and the like. It is preferable to use an organic material. 
     The substrate may be a single-layer substrate, or may be a laminate. 
     The substrate is preferably a substrate that is formed of an organic material, and more preferably a resin film that is formed of the organic material. 
     The polymer solution (method (A)) or the solution subjected to polymerization (method (B)) may be applied to the substrate using a known coating method. Examples of the coating method include a curtain coating method, an extrusion coating method, a roll coating method, a spin coating method, a dip coating method, a bar coating method, a spray coating method, a slide coating method, a print coating method, and the like. 
     (2) Polymer Obtained by Polymerizing Polymerizable Composition 
     The polymer according to one embodiment of the invention can be easily obtained by polymerizing the polymerizable composition according to one embodiment of the invention. It is preferable to use the polymerizable composition that includes the initiator (particularly a photoinitiator) in order to more efficiently effect polymerization. 
     Specifically, it is preferable to produce the polymer according to one embodiment of the invention using the method (B) that applies the polymerizable composition according to one embodiment of the invention to a substrate, and polymerizes the applied polymerizable composition. Examples of the substrate include a substrate used to produce an optically anisotropic article (described later), and the like. 
     The polymerizable composition according to one embodiment of the invention may be applied to the substrate using a known coating method (e.g., bar coating method, spin coating method, roll coating method, gravure coating method, spray coating method, die coating method, cap coating method, or dipping method). A known organic solvent may be added to the polymerizable composition according to one embodiment of the invention in order to improve the applicability of the polymerizable composition. In this case, it is preferable to remove the organic solvent by natural drying, drying by heating, drying under reduced pressure, drying by heating under reduced pressure, or the like, after applying the polymerizable composition to the substrate. 
     The polymerizable compound according to one embodiment of the invention, or the polymerizable composition according to one embodiment of the invention, may be polymerized by applying activated energy rays, or utilizing a thermal polymerization method, for example. It is preferable to polymerize the polymerizable compound or the polymerizable composition by applying activated energy rays since heating is unnecessary (i.e., the reaction can be effected at room temperature). It is preferable to apply light (e.g., ultraviolet rays) to the polymerizable compound or the polymerizable composition since the operation is simple. 
     The temperature during application (irradiation) is preferably set to 30° C. or less. The irradiance is normally 1 W/m 2  to 10 kW/m 2 , and preferably 5 W/m 2  to 2 kW/m 2 . 
     A polymer obtained by polymerizing the polymerizable compound according to one embodiment of the invention, or the polymerizable composition according to one embodiment of the invention, may be removed from the substrate, and used alone, or may be used directly as an optical film organic material or the like without removing the polymer from the substrate. 
     The number average molecular weight of the polymer according to one embodiment of the invention thus obtained is preferably 500 to 500,000, and more preferably 5000 to 300,000. When the number average molecular weight of the polymer is within the above range, the resulting film exhibits high hardness and an excellent handling capability. The number average molecular weight of the polymer may be determined by gel permeation chromatography (GPC) using monodisperse polystyrene as a standard (eluant: tetrahydrofuran). 
     It is considered that the polymer according to one embodiment of the invention has a structure in which crosslinking points are uniformly present within the molecule, and exhibits a high crosslinking efficiency and excellent hardness. 
     The polymer according to one embodiment of the invention makes it possible to inexpensively produce an optical film that achieves uniform conversion of polarized light over a wide wavelength band, and exhibits satisfactory performance. 
     4) Optically Anisotropic Article 
     An optically anisotropic article according to one embodiment of the invention includes the polymer according to one embodiment of the invention. 
     The optically anisotropic article according to one embodiment of the invention may be obtained by forming an alignment film on a substrate, and forming a liquid crystal layer on the alignment film using the polymer according to one embodiment of the invention. 
     The alignment film is formed on the surface of the substrate in order to achieve in-plane alignment of an organic semiconductor compound in one direction. 
     The alignment film may be obtained by applying a solution (alignment film composition) that includes a polymer (e.g., polyimide, polyvinyl alcohol, polyester, polyallylate, polyamideimide, or polyetherimide) to the substrate to form a film, drying the film, and subjecting the film to a rubbing treatment in one direction, for example. 
     The thickness of the alignment film is preferably 0.001 to 5 μm, and more preferably 0.001 to 1 μm. 
     The rubbing treatment may be performed on the alignment film or the substrate. The rubbing treatment may be implemented using an arbitrary method. For example, the alignment film may be rubbed in a given direction using a roll around which a cloth or felt formed of synthetic fibers (e.g., nylon) or natural fibers (e.g., cotton) is wound. It is preferable to wash the alignment film with isopropyl alcohol or the like after the rubbing treatment in order to remove a fine powder (foreign substance) formed during the rubbing treatment, and clean the surface of the alignment film. 
     The alignment film may be provided with a function of achieving in-plane alignment in one direction by applying polarized ultraviolet rays to the surface of the alignment film. 
     The liquid crystal layer may be formed on the alignment film using the polymer according to one embodiment of the invention by utilizing the method described above in connection with the polymer according to one embodiment of the invention. 
     Since the optically anisotropic article according to one embodiment of the invention is produced using the polymer according to one embodiment of the invention, the optically anisotropic article can be produced at low cost, achieves uniform conversion of polarized light over a wide wavelength band, and exhibits satisfactory performance. 
     Examples of the optically anisotropic article according to one embodiment of the invention include a retardation film, an alignment film for a liquid crystal display device (liquid crystal display), a polarizer, a viewing angle-improving film, a color filter, a low-pass filter, an optical polarization prism, an optical filter, and the like. 
     EXAMPLES 
     The invention is further described below by way of examples. Note that the invention is not limited to the following examples. 
     Example 1 
     Synthesis of Compound 1 
                                
Step 1: Synthesis of Intermediate A
 
     
       
                 
         
             
             
         
      
     
     A four-necked reactor equipped with a thermometer was charged with 20 g (144.8 mmol) of 2,5-dihydroxybenzaldehyde, 105.8 g (362.0 mmol) of 4-(6-acryloylhex-1-yloxy)benzoic acid (manufactured by DKSH Japan K.K.), 5.3 g (43.4 mmol) of 4-(dimethylamino)pyridine, and 200 ml of N-methylpyrrolidone under a nitrogen stream to prepare a homogeneous solution. After the addition of 83.3 g (434.4 mmol) of 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride (WSC) to the solution, the mixture was stirred at 25° C. for 12 hours. After completion of the reaction, the reaction mixture was added to 1.5 of water, followed by extraction with 500 ml of ethyl acetate. After drying the ethyl acetate layer over anhydrous sodium sulfate, sodium sulfate was filtered off. Ethyl acetate was evaporated from the filtrate under reduced pressure using a rotary evaporator to obtain a light yellow solid. The light yellow solid was purified by silica gel column chromatography (toluene:ethyl acetate=9:1 (volume ratio)) to obtain 75 g of an intermediate A as a white solid (yield: 75.4%). 
     The structure of the target product was identified by  1 H-NMR. 
       1 H-NMR (400 MHz, CDCl 3 , TMS, δ ppm): 10.20 (s, 1H), 8.18-8.12 (m, 4H), 7.78 (d, 1H, J=2.8 Hz), 7.52 (dd, 1H, J=2.8 Hz, 8.7 Hz), 7.38 (d, 1H, J=8.7 Hz), 7.00-6.96 (m, 4H), 6.40 (dd, 2H, J=1.4 Hz, 17.4 Hz), 6.12 (dd, 2H, J=10.6 Hz, 17.4 Hz), 5.82 (dd, 2H, J=1.4 Hz, 10.6 Hz), 4.18 (t, 4H, J=6.4 Hz), 4.08-4.04 (m, 4H), 1.88-1.81 (m, 4H), 1.76-1.69 (m, 4H), 1.58-1.42 (m, 8H). 
     Step 2: Synthesis of Compound 1 
     A three-necked reactor equipped with a thermometer was charged with 2.00 g (2.92 mmol) of the intermediate A synthesized in the step 1 and 20 ml of tetrahydrofuran (THF) under a nitrogen stream to prepare a homogeneous solution. After the addition of 60 ml of ethanol and 0.38 g (2.92 mmol) of thiosemicarbazide hydrochloride to the solution, the mixture was stirred at 25° C. for 1.5 hours. After the addition of 0.72 g (2.92 mmol) of 2-bromoacetylnaphthalene, the mixture was stirred at 25° C. for 2 hours. After completion of the reaction, 200 ml of distilled water, 100 ml of saturated sodium bicarbonate water, and 100 ml of a saturated sodium chloride solution were added to the reaction mixture, followed by extraction twice with 200 ml of ethyl acetate. The organic layer was collected, and dried over anhydrous sodium sulfate, and sodium sulfate was filtered off. The filtrate was concentrated under reduced pressure using a rotary evaporator, and the concentrate (residue) was purified by silica gel column chromatography (chloroform:THF=98:2 (volume ratio)) to obtain 1.44 g of a compound 1 as a light yellow solid (yield: 54%). 
     The structure of the target product was identified by  1 H-NMR. 
       1 H-NMR (500 MHz, DMSO-d 6 , TMS, δ ppm): 12.34 (s, 1H), 8.34 (s, 1H), 8.10-8.19 (m, 5H), 7.98 (dd, 1H, J=1.5 Hz, 8.5 Hz), 7.85-7.94 (m, 3H), 7.74 (d, 1H, J=3.0 Hz)7.34-7.56 (m, 5H), 7.17 (d, 2H, J=9.0 Hz), 7.14 (d, 2H, J=9.0 Hz), 6.33 (dd, 2H, J=1.5 Hz, 17.5 Hz), 6.18 (dd, 2H, J=10.5 Hz, 17.5 Hz), 5.94 (dd, 2H, J=1.5 Hz, 10.5 Hz), 4.07-4.17 (m, 8H), 1.72-1.83 (m, 4H), 1.57-1.71 (m, 4H), 1.34-1.53 (m, 8H). 
     Example 2 
     Synthesis of Compound 2 
                                
Step 2: Synthesis of Compound 2
 
     A three-necked reactor equipped with a thermometer was charged with 3.75 g (5.45 mmol) of the intermediate A synthesized in the step 1 of Example 1 and 30 ml of THF under a nitrogen stream to prepare a homogeneous solution. After the addition of 90 ml of ethanol and 0.7 g (5.45 mmol) of thiosemicarbazide hydrochloride to the solution, the mixture was stirred at 25° C. for 2 hours. After the addition of 1.25 g (5.45 mmol) of 2-chloro-2-phenylacetophenone, the mixture was stirred at 60° C. for 3 hours. After completion of the reaction, 200 ml of distilled water and 70 ml of a saturated sodium chloride solution were added to the reaction mixture, followed by extraction twice with 300 ml of ethyl acetate. The organic layer was collected, and dried over anhydrous sodium sulfate, and sodium sulfate was filtered off. The filtrate was concentrated under reduced pressure using a rotary evaporator, and the concentrate (residue) was purified by silica gel column chromatography (chloroform:THF=97:3) to obtain 1.15 g of a compound 2 as a light yellow solid (yield: 22%). 
     The structure of the target product was identified by  1 H-NMR. 
       1 H-NMR (500 MHz, DMSO-d, TMS, δ ppm): 10.28 (s, 1H), 8.15 (d, 2H, J=9.0 Hz), 8.12 (s, 1H), 8.11 (d, 2H, J=9.0 Hz), 7.69 (d, 1H, J=2.5 Hz), 7.34-7.45 (m, 4H), 7.23-7.32 (m, 6H), 7.19 (d, 2H, J=6.5 Hz), 7.13 (t, 4H, J=8.5 Hz), 6.33 (dd, 1H, J=1.5 Hz, 17.5 Hz), 6.33 (dd, 1H, J=1.5 Hz, 17.5 Hz), 6.18 (dd, 1H, J=10.5 Hz, 17.5 Hz), 6.18 (dd, 1H, J=10.5 Hz, 17.5 Hz), 5.94 (dd, 1H, J=1.5 Hz, 10.5 Hz), 5.94 (dd, 1H, J=1.5 Hz, 10.5 Hz), 4.03-4.16 (m, 8H), 1.72-1.82 (m, 4H), 1.60-1.70 (m, 4H), 1.35-1.52 (m, 8H). 
     Synthesis Example 1 
     Synthesis of Compound A 
                                
Step 2: Synthesis of Compound A
 
     A four-necked reactor equipped with a thermometer was charged with 10.5 g (15.3 mmol) of the intermediate A synthesized by the step 1 of Example 1, 3.0 g (18.3 mmol) of 2-hydrazinobenzothiazole, and 80 ml of tetrahydrofuran (THF) under a nitrogen stream to prepare a homogeneous solution. After the addition of 18 mg (0.08 mmol) of (±)-10-camphorsulfonic acid, the mixture was stirred at 25° C. for 3 hours. After completion of the reaction, the reaction mixture was added to 800 ml of 10% sodium bicarbonate water, followed by extraction twice with 100 ml of ethyl acetate. The ethyl acetate layer was collected, and dried over anhydrous sodium sulfate, and sodium sulfate was filtered off. Ethyl acetate was evaporated from the filtrate under reduced pressure using a rotary evaporator to obtain a light yellow solid. The light yellow solid was purified by silica gel column chromatography (toluene:ethyl acetate=8:2 (volume ratio)) to obtain 8.0 g of a compound A as a light yellow solid (yield: 62.7%). 
     The structure of the target product was identified by  1 H-NMR and mass spectroscopy. 
       1 H-NMR (500 MHz, DMSO-d 6 , TMS, δ ppm): 12.30 (br, 1H), 8.19 (s, 1H), 8.17-8.12 (m, 4H), 7.76 (d, 1H, J=3.0 Hz), 7.68 (d, 1H, J=7.5 Hz), 7.45-7.39 (m, 3H), 7.28 (t, 1H, J=8.0 Hz), 7.18-7.14 (m, 4H), 7.09 (t, 1H, J=8.0 Hz), 6.33 (dd, 2H, J=1.5 Hz, 17.5 Hz), 6.18 (dd, 2H, J=10.5 Hz, 17.5 Hz), 5.944 (dd, 1H, J=1.5 Hz, 10.5 Hz), 5.941 (dd, 1H, J=1.5 Hz, 10.5 Hz), 4.14-4.10 (m, 8H), 1.80-1.75 (m, 4H), 1.69-1.63 (m, 4H), 1.53-1.38 (m, 8H). 
     LCMS (APCI): calcd for C 46 H 47 N 3 O 10 S: 833[M + ]; Found: 833. 
     The phase transition temperature was measured as described below using the compounds 1 and 2 obtained in Examples 1 and 2, the compound 1r of Reference Example 1 that was used in Comparative Example 1 (“K35” manufactured by Zeon Corporation), and the compound 2r of Reference Example 2 that was used in Comparative Example 2 (“LC242” manufactured by BASF). 
                                
Measurement of Phase Transition Temperature
 
     10 mg of each compound (compounds 1, 2, 1r, and 2r) was weighed, and placed in a solid state between two glass substrates provided with a polyimide alignment film subjected to a rubbing treatment (manufactured by E.H.C. Co., Ltd.). The substrates were placed on a hot plate, heated from 40° C. to 200° C., and cooled to 40° C. A change in structure when the temperature changed was observed using a polarizing microscope (“ECLIPSE LV100 POL” manufactured by Nikon Corporation). The phase transition temperature measurement results are shown in Table 1. 
     In Table 1, “C” refers to “crystal”, “N” refers to “nematic”, “I” refers to “isotropic”, and “S A” refers to “smectic A”. The term “crystal” means that the test compound was in a solid phase, the term “nematic” means that the test compound was in a nematic liquid crystal phase, the term “isotropic” means that the test compound was in an isotropic liquid phase, and the term “smectic A” means that the test compound was in a smectic A phase. 
     
       
         
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Compound 
                 Phase transition temperature 
               
               
                   
               
             
             
               
                 Example 1 
                 Compound 1 
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 Example 2 
                 Compound 2 
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 Reference Example 1 
                 Compound 1r 
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
               
                 Reference Example 2 
                 Compound 2r 
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
     Example 3 
     0.5 g of the compound 1 obtained in Example 1, 0.5 g of the compound A obtained in Synthesis Example 1, 30 mg of Adekaoptomer N-1919 (manufactured by Adeka Corporation (hereinafter the same)) (photoinitiator), and 100 mg of a 1% cyclopentanone solution of KH-40 (manufactured by AGC Seimi Chemical Co., Ltd. (hereinafter the same)) (surfactant) were dissolved in 2.2 g of cyclopentanone. The solution was filtered through a disposable filter having a pore size of 0.45 μm to obtain a polymerizable composition 1. 
     Example 4 
     0.5 g of the compound 2 obtained in Example 2, 0.5 g of the compound A obtained in Synthesis Example 1, 30 mg of Adekaoptomer N-1919 (photoinitiator), and 100 mg of a 1% cyclopentanone solution of KH-40 (surfactant) were dissolved in 2.2 g of cyclopentanone. The solution was filtered through a disposable filter having a pore size of 0.45 μm to obtain a polymerizable composition 2. 
     Comparative Examples 1 and 2 
     1 g of the compound 1r of Reference Example 1 or the compound 2r of Reference Example 2, 30 mg of Adekaoptomer N-1919 (photoinitiator), and 100 mg of a 1% cyclopentanone solution of KH-40 (surfactant) were dissolved in 2.3 g of cyclopentanone. The solution was filtered through a disposable filter having a pore size of 0.45 μm to obtain a polymerizable composition 1r or 2r, respectively. 
     Measurement of Retardation and Evaluation of Wavelength Dispersion 
     
         
         (i) Formation of liquid crystal layer using polymerizable composition 
       
    
     Each polymerizable composition (polymerizable compositions 1, 2, 1r, and 2r) was applied to a transparent glass substrate provided with a polyimide alignment film subjected to a rubbing treatment (manufactured by E.H.C. Co., Ltd.) using a #4 wire bar. The resulting film was dried for 30 seconds at the temperature shown in Table 2, and subjected to an alignment treatment for 1 minute at the temperature shown in Table 2 to form a liquid crystal layer. Ultraviolet rays were applied to the liquid crystal layer at a dose of 2000 mJ/cm 2  to effect polymerization to prepare a wavelength dispersion measurement sample.
     (ii) Measurement of retardation   

     The retardation between 400 nm and 800 nm was measured using the sample utilizing an ellipsometer (“M2000U” manufactured by J. A. Woollam).
     (iii) Evaluation of wavelength dispersion   

     The wavelength dispersion was evaluated from the values α and β that were calculated by the following expressions using the measured retardation.
 
α=(retardation at 449.9 nm)/(retardation at 548.5 nm)
 
β=(retardation at 650.2 nm)/(retardation at 548.5 nm)
 
     The value α is smaller than 1, and the value β is larger than 1 when an ideal wideband wavelength dispersion (reverse wavelength dispersion) is achieved. The values α and β are almost identical when a flat wavelength dispersion is achieved. The value α is larger than 1, and the value β is smaller than 1 when a normal dispersion is achieved. 
     A flat wavelength dispersion that ensures that the values α and β are almost identical is preferable, and a reverse wavelength dispersion that ensures that the value α is smaller than 1, and the value β is larger than 1, is particularly preferable. 
     Table 2 shows the thickness (μm) of the liquid crystal polymer films obtained by polymerizing the polymerizable compositions, the retardation (Re) at a wavelength of 548.5 nm, and the values α and β. 
     
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
             
             
               
                   
                   
               
               
                   
                   
                 Polymerizable 
                 Polymerizable 
                 Drying 
                 Alignment 
                 Thick- 
                   
                   
               
               
                   
                 Polymerizable 
                 compound 1 
                 compound 2 
                 temperature 
                 temperature 
                 ness 
                 Re 
               
             
          
           
               
                   
                 composition 
                 Compound 
                 Ratio (%) 
                 Compound 
                 Ratio (%) 
                 (° C.) 
                 (° C.) 
                 (μm) 
                 (548.5 nm) 
                 α 
                 β 
               
               
                   
                   
               
             
          
           
               
                 Example 3 
                 1  
                 1  
                 50 
                 A 
                 50 
                 120 
                 23 
                 1.319 
                 160.55 
                 0.955 
                 0.994 
               
               
                 Example 4 
                 2  
                 2  
                 50 
                 A 
                 50 
                 160 
                 23 
                 1.800 
                 167.45 
                 0.987 
                 1.009 
               
               
                 Comparative 
                 1r 
                 1r 
                 100 
                 — 
                 — 
                 90 
                 23 
                 1.509 
                 355.97 
                 1.193 
                 0.918 
               
               
                 Example 1 
               
               
                 Comparative 
                 2r 
                 2r 
                 100 
                 — 
                 — 
                 80 
                 23 
                 1.479 
                 222.9 
                 1.086 
                 0.970 
               
               
                 Example 2 
               
               
                   
               
             
          
         
       
     
     As shown in Table 2, it was confirmed that the polymers obtained in Examples 1 and 2 according to the invention were optically anisotropic articles. The optically anisotropic articles had a reverse wavelength dispersion (i.e., a preferable wavelength dispersion) in which the values α and β are almost identical, and the value β was larger than the value α.