TECHNOLOGY FOCUS - POLYMERS - Preferred Crosslinker: The crosslinker may bind to the polymer to form an imide group of formula (I):A = carbon, sulfur or phosphorus;n = 1 for carbon and 2 for sulfur or phosphorus;M+ = any cationic species including H+.Preferred crosslinkers are ammonia, ammonium compounds, compounds of formula (a), (b) and (c):R = alkyl, aryl or a heterocyclic group, all optionally substituted,The crosslinker may also have the formula (d):X = halogen.Preferred Method: The method may also comprise (1) forming a crosslinkable mixture of the polymer with pendent groups and its crosslinker then, in any order, forming a film of the mixture and crosslinking the polymer by exposing the mixture to an alkaline environment; or (2) forming a film of the polymer with pendent groups and crosslinking the polymer by applying the crosslinker under reactive conditions. Preferred Materials: The polymer has pendent groups of formula (II) and the crosslinker has the formula (III):Z = a polyvalent linker, e.g. a polymer, or an alkyl, aryl or heteroatomic function, all optionally substituted;A = = carbon, sulfur or phosphorus;n = 1 when A is carbonn = 2 when A is sulfur or phosphorus, where m more than 1;G = halide or amino;J = NH2 when G = halide and halide when G = NH2. EXAMPLE - PEEK (RTM: polyetheretherketone) (30 g) was dissolved with shaking at room temperature (10-190 hours) in concentrated (100-102%) sulfuric acid (400 ml). The sulfonated polymer was then poured into a stirred mixture of water and ice (4 l), collected, washed with water until the washings were pH-neutral and dried at 40 degreesC/0.1 Torr for 24 hours.    A polymer sulfonated for 190 hours (10 g) and thionyl chloride (80 ml) were refluxed under nitrogen for 12 hours, then poured into a stirred mixture of water and ice (500 ml). The polymer was washed with water as above then with methanol, and dried as above (yield 9.8 g, 93%). The sulfonyl chloride functional polymer was soluble in dimethyl formamide, N-methylpyrrolidone, cyclopentanone, dichloromethane and tetrahydrofuran and, unlike the sulfonated polymer, insoluble in water and alcohol. The polymer formed transparent, freestanding membranes which, in their hydrolyzed form, had a conductivity at room temperature of 0.60 S/cm but which swelled significantly in cold water and which were soluble in boiling water.    The polymer (1 g), cyclopentanone (9 ml) and compound of formula (V) (100 mg) were stirred while triisopropylamine (0.3 g) was added dropwise.    The solution was quickly cast on a flat glass dish and allowed to dry overnight. The membrane was hydrolyzed in 5% aqueous sodium hydroxide for 12 hours then exchanged twice in 20% nitric acid for 1 hour. A transparent film was obtained when it was immersed in 30% methanol and 70% water at 50 degreesC for 30 minutes. The membrane had an absorption capacity of 163% in boiling water and 40% in cold water, reduced from completely soluble and 5,000% respectively for the uncrosslinked polymer. The conductivity at room temperature was 0.6 S/cm.