•Synthesis and characterization of diblock-copolymer brushes aimed at cell-culture experiments.
•Diblock copolymers had a hydrophobic, substrate-bound layer and a hydrophilic interfacial brush.
•Effect of the hydrophobic block on biopassivity and stability in cell-culture medium was determined.
•Higher stiffness and the hydrophobicity of substrate-bound block improved stability of system compared to brush alone.
•Grafting density of the substrate-bound layer was the main factor determining biopassivity.