79  US 9,958,775 B2  80  [Chem.45]  In addition, in another embodiment, the repeating unit  represented by the general formula (A2) is also preferably a  repeating unit represented by the general formula (A3)  shown below.  [Chem.46]  (A3)  R  I  ----fCH2-Cr- H  I  I  C02-C-AR  I  Rn  In the general formula (A3),  AR represents an aryl group;  Rn represents an alkyl group, a cycloalkyl group, or an  ary I group. Rn and AR may be bonded to each other to  form a non-aromatic ring; and  R represents a hydrogen atom, an alkyl group, a  cycloalkyl group, a halogen atom, a cyano group, or an  alkyloxycarbonyl group.  The repeating unit represented by the general formula  (A3) will be described in detail.  AR represents an aryl group as described above. As the  aryl group of AR, those having 6 to 20 carbon atoms, such  as a phenyl group, a naphthyl group, an anthryl group, or a  fluorene group are preferred, and those having 6 to 15  carbon atoms are more preferred.  In the case where AR is a naphthyl group, an anthryl  group, or a fluorene group, the bonding position between the  carbon atom to which Rn is bonded and AR is not particu› larly limited. For example, when AR is a naphthyl group, the 45  carbon atom may be bonded to the a-position or the ~-po› sition of the naphthyl group. Or when AR is an anthryl  group, the carbon atom may be bonded to the I -position, the  2-position or the 9-position of the anthryl group.  The aryl group as AR may have one or more substituents.  Specific examples of such a substituent include a linear or  branched chain alky group having 1 to 20 carbon atoms,  such as a methyl group, an ethyl group, a propyl group, an  isopropyl group, an n-butyl group, an isobutyl group, a  t-butyl group, a pentyl group, a hexyl group, an octyl group,  and a dodecyl group, an alkoxy group containing such an  alkyl group moiety, a cycloalkyl group such as cyclopentyl  group and cyclohexyl group, a cycloalkoxy group contain› ing such a cycloalkyl group moiety, a hydroxyl group, a  halogen atom, an aryl group, a cyano group, a nitro group,  an acyl group, an acyloxy group, an acylamino group, a  sulfonylamino group, an alkylthio group, an arylthio group,  an aralkylthio group, a thiophenecarbonyloxy group, a thio› phenemethylcarbonyloxy group, and a heterocyclic residue  such as a pyrrolidone residue. The substituent is preferably  a linear or branched chain alkyl group having 1 to 5 carbon  atoms or an alkoxy group containing such an alkyl group  moiety, and more preferably a paramethyl group or a param› ethoxy group.  In a case where an aryl group as AR has a plurality of  substituents, at least two of a plurality of substituents may be  bonded to each other to form a ring. The ring is preferably  a 5- to 8-membered ring, and more preferably a 5- or  6-membered ring. The ring may be also a heterocycle  containing a heteroatom such as an oxygen atom, a nitrogen  atom and a sulfur atom in the ring members.  Furthermore, this ring may have a substituent. Examples  of the substituent include the same as those described later  for the further substituent which Rn may have.  In addition, from the viewpoint of the roughness perfor- mance, the repeating unit represented by the general formula  (A3) preferably contains two or more aromatic rings. The  number of aromatic rings contained in the repeating unit is  usually preferably 5 or less, and more preferably 3 or less.  In addition, from the viewpoint of the roughness perfor- mance, in the repeating unit represented by the general  formula (A3), AR preferably contains two or more aromatic  rings, and AR is more preferably a naphthyl group or a  biphenyl group. The number of the aromatic rings contained  in AR is usually preferably 5 or less, and more preferably 3  or less.  As described above, Rn represents an alkyl group, a  cycloalkyl group or an aryl group.  The alkyl group of Rn may be a linear alkyl group or a  branched-chain alkyl group. As the alkyl group, an alky  group having 1 to 20 carbon atoms, such as a methyl group,  an ethyl group, a propyl group, an isopropyl group, an  n-butyl group, an isobutyl group, at-butyl group, a pentyl  group, a hexyl group, a cyclohexyl group, an octyl group,  and a dodecyl group is preferably included. The alkyl group  of Rn is preferably an alkyl group having 1 to 5 carbon  atoms, and more preferably an alkyl group having 1 to 3  carbon atoms.  Examples of the cycloalkyl group of Rn include a  cycloalkyl group having 3 to 15 carbon atoms, such as a  cyclopentyl group and a cyclohexyl group.  As an aryl group of Rn, for example, an aryl group having  6 to 14 carbon atoms, such as a phenyl group, a xylyl group,  a tolyl group, a cumenyl group, a naphthyl group and an  anthryl group is preferred.  Each of the alkyl group, the cycloalkyl group, and the aryl  group as Rn may further have a substituent. Examples of the  substituent include an alkoxy group, a hydroxyl group, a  halogen atom, a nitro group, an acyl group, an acyloxy  group, an acylamino group, a sulfonylamino group, dialky- !amino group, an alkylthio group, an arylthio group, an  aralkylthio group, a thiophenecarbonyloxy group, a thio› phenemethylcarbonyloxy group, and heterocyclic residues  such as a pyrrolidone residue. Among these, an alkoxy  group, a hydroxyl group, a halogen atom, a nitro group, an  acyl group, an acyloxy group, an acylamino group, and a  sulfonyl amino group are particularly preferred.  As described above, R represents a hydrogen atom, an  alkyl group, a cycloalkyl group, a halogen atom, a cyano  group or an alkyloxycarbonyl group.  Examples of the alkyl group and the cycloalkyl group of  R include the same as those described above for Rn. Each of  these alkyl groups and cycloalkyl groups may have a sub› stituent. Examples of this substituent include the same as  those described above for Rn.  In the case where R is an alkyl group or a cycloalkyl group  having a substituent, particularly preferred examples of R  include a trifluoromethyl group, an alkyloxycarbonyl methyl 