A crosslinked polymer composition comprising: (i) a base polymer containing a multiplicity of at least one type of functional group selected from amino, amido, thiol, carboxylic acid, carboxylic acid ester, and epoxy groups; (ii) a multiplicity of hydroxylated benzene rings covalently linked to the base polymer, wherein each hydroxylated benzene ring contains at least two hydroxy groups, and with at least two of the hydroxy groups on said hydroxylated benzene rings being free as OH groups; and (iii) a multiplicity of crosslinking groups that crosslink at least two of said functional groups in the base polymer. The invention is also directed to lithium-ion batteries in which the above-described composition is incorporated in an electrode of the battery, and also directed to methods of operating a lithium-ion battery in which the above-described crosslinked polymer composition is incorporated in an electrode thereof.