TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The sulfonating agent is concentrated sulfuric acid, chlorosulfonic acid, fuming sulfuric acid or fuming sulfuric acid triethyl phosphate salt.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The solvent is dimethylacetamide, N-methylpyrrolidone, dimethylformamide, dimethyl sulfoxide, dichloromethane, chloroform, tetrahydrofuran, benzene, toluene and/or xylene.    TECHNOLOGY FOCUS - POLYMERS - Preparation (Claimed): The preparation of polyarylene polymer comprises coupling and polymerizing aromatic dihalide compounds of formulae (III) and (X-(Ar1-Y1-Ar2-Y1-Ar1)m-X) (IV) in presence of a catalyst.X = halo;Ar1 = bisphenylsulfone moiety of formula (V), bisphenylketone moiety of formula (VI), 2,3,5,6-tetrafluoro-1,4-phenylene, 2,3,5,6,2',3',5',6'-octafluoro-biphenyl-4,4'-diyl, cyanophenylene moiety of formula (VII) or 1,4-dibenzoylbenzene-4',4''-diyl;Ar2 = biphenyl-diyl of formula (VIII), diphenyl thioether moiety of formula (IX), (V), (VI), bisphenyl isopropane moiety of formula (X), bisphenyl hexafluoroisopropane moiety of formula (XI), 3,5,3',5'-tetramethyl-biphenyl-4,4'-diyl, 3,5,3',5'-tetramethylbis(phenyl)sulfone-4,4'-diyl, (3,5,3',5'-tetramethylbis(phenyl)isopropane)-4,4'-diyl, naphthylene moiety of formula (XII), 9,9-diphenylfluorene moiety of formula (XIII) or 1,1'-binaphthyl-diyl of formula (XIV);Y1 = O, S or chemical bond; andm = 1-100.Preferred Components: Polyarylene polymer has weight average molecular weight of 10000-1000000. Polyarylene polymer further comprises substituted arylene recurring units of formula (-(Ar1-Y1-Ar2-Y1-Ar1)m-) (II). In the method, the addition amount of (IV) is 0.01-1 equivalent, based on 1 equivalent of (III). The preparation of the polymer is carried out in presence of a solvent. The method further comprises sulfonating the polymer to introduce sulfonate group of formula (SO2R) to the polymer using a sulfonating agent; and introducing sulfonate group into dihalide monomer. The method further comprises removing one of R1-R4 of dihalide monomer by introducing sulfonate group, preferably sulfonic acid group prior to the polymerization step in presence of lithium bromide, pyridine hydrochloride, nitric acid or sodium nitrite. Preferred Definitions:    R1-R4 = H or SO3H (where at least one of R1-R4 is SO3 H).    EXAMPLE - No suitable example given.