TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Solvent: The polar solvent is at least one of N-methyl-2-pyrollidone, N,N'-dimethylacetoamide, dimethylformamide, dimethylsulfoxide, acetonitrile, butyrolactone, phenol, toluene, and cyclohexane.    TECHNOLOGY FOCUS - POLYMERS - Preparation (claimed): The polyimide is prepared by reacting a tetracarboxylic dianhydride compound of formula (viii), a diamine compound NH2-Y(OH)2-NH2 and a monoamine compound or monoanhydride compound having at least one carbon-carbon double bond in a polar solvent to form predetermined polyamic acid; curing the polyamic acid by heat in a polar solvent to prepare a soluble polyhydroxyimide; reacting the polyhydroxyimide with a compound of formula (ix) in a polar solvent to introduce a dendrimer structure into a side chain; and reacting the reaction product with a sulfonic acid compound to introduce a sulfonic acid group into a terminal of the side chain.Preferred Polyimide: The polyimide comprises (parts by weight) the monoamine compound or monoanhydride compound (5 - 50).Preferred Electrolyte: The curing step is performed by heating the polyimide under an inert gas or vacuum at 100 - 300degreesC for 0.5 - 5 hours. If a weight of the polyimide is represented by A and a weight of the polyamic acid or soluble polyhydroxyimide is represented by B, the polyimide and the polyamic acid or soluble polyhydroxyimide are mixed at a ratio A/(A+B) of 0.1 - 0.9. Preferred Definitions:    X1 - X8, Y1 - Y3, Y5 - Y7=H;    Y4 and Y8=H or CF3;    Q1=bond, O, C(O), C(CF3)2, S(O)2;    Q2=S(O)2, O, CH2, C(CF3)2, bond or (OTO)a;    T=1,3-phenylene or 1,4-phenylene;    a=1.    SPECIFIC COMPOUNDS - The monoamine compound or monoanhydride compound is at least one of 5-norbornene-2,3-dicarboxylic anhydride, 3,4,5,6-tetrahydrophthalic anhydride, cis-1,2,3,6-tetrahydrophthalic anhydride, maleic anhydride, 2,3-dimethylmaleic anhydride, citraconic anhydride, itaconic anhydride, maleic imide, and ethynyl aniline. The dianhydride compound is at least one of pyromellitic dianhydride, 3,3,4,4-biphenyl tetracarboxylic dianhydride, 4,4-oxydiphthalic dianhydride, 3,3',4,4'-benzophenone tetracarboxylic dianhydride, 2,2-bis(3,4-benzenedicarboxylic anhydride) perfluoropropane, and 4,4-sulfonyldiphthalic dianhydride. The diamine compound is at least one of 1,3-diamino-4-dihydroxybenzene, 1,3-diamino-5-dihydroxybenzene, 3,3'-diamino-4,4'-dihydroxybiphenyl, 4,4'-diamino-3,3'-dihydroxybiphenyl, 2,2-bis(3-amino-4-hydroxyphenyl)propane, bis(4-amino-3-hydroxyphenyl)propane, bis(3-amino-4-hydroxyphenyl)sulfone, bis(4-amino-3-hydroxyphenyl)sulfone, bis(3-amino-4-hydroxyphenyl)ether, bis(4-amino-3-hydroxyphenyl)ether, and 2,2-bis(3-amino-4-hydroxyphenyl)- hexafluoropropane.    EXAMPLE - No relevant example given.