Principles and embodiments of the present invention relate generally to thermoplastic polyurethane materials having controlled and improved stiffness and/or flexibility, and methods to prepare them. The thermoplastic polyurethanes described herein having superior stiffness and softening properties may be fabricated into film, tubing, and other forms of medical devices. The thermoplastic polyurethanes comprise: an aromatic diisocyanate excluding non-aromatic diisocyanates; at least one polyglycol; and a chain extender comprising at least one side-chain branching diol and excluding linear diols.