Injection of aqueous fluids into reservoirs as an enhanced oil recovery (EOR) tool has been of great interest in petroleum engineering. EOR using viscous polymer solutions improves the volumetric sweep efficiency. However, significant polymer adsorption on reservoir rock surfaces is one of the greatest challenges in polymer-flooding EOR. We have synthesized and characterized five zwitterionic copolymers and studied their static adsorption on limestone surfaces in seawater at high temperatures and salinities. Our results indicate that polymer adsorption directly correlates to a small percentage of functional co-monomers on the polymer backbone. One particular copolymer shows negligible static adsorption on limestone surfaces.