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Polybenzimidazole (PBI) membranes doped with phosphoric acid are used as proton-conducting membrane in high-temperature polymer electrolyte fuel cells. There is no general model for the thermodynamics of the absorption process over the whole accessible doping range for all published data. The interactions between $$\hbox {H}_3\hbox {PO}_4$$ H 3 PO 4 and polymer chains, the polycondensation...