Crosslinked polymers and related compositions, electrochemical cells, batteries, methods and systems

A dendritic polymer represented by Formula (II)

• [D-LND-YNL-1NY-1]G Formula (II)
• wherein
• D is a dendritic core having a core multiplicity ND,
• L is a bidentate, tridentate, tetradentate, pentadentate or a hexadentate redox active monomeric moiety comprising a carbocyclic structure and at least one carbonyl group or a carboxyl group presented on the carbocyclic structure, L having a L-multiplicity NL and a redox potential of 0.5 V to 3.0 V with reference to Li/Li+ electrode potential under standard conditions or −2.54 V to −0.04 V with reference to SHE, and
• Y is a comonomeric moiety selected from a bidentate, tridentate, tetradentate, pentadentate and a hexadentate chemical moiety, Y having a Y-multiplicity NY,
• wherein
• ND number of L is covalently linked to D,
• (NL−1) number of Y is covalently linked to each L for each successive generation,
• NY number of L is covalently linked to Y,
• and wherein
• ND ranges from 3 to 6,
• NY and NL range independently from 2 to 6, with the proviso that at least one of NY and NL is at least 3, and
• G≥3.