This paper reports a facile synthesis of new water-soluble poly(ethylene oxide) (PEO)-based amphiphilic block copolymers showing pH sensitive phase transition behaviors. The copolymers were prepared by atom transfer radical polymerization (ATRP) of methacrylamide type of monomers carrying a sulfonamide group using a PEO-based macroinitiator and a Cu(I)Br/$Me_6TREN$ catalytic system in aqueous media. The resulting polymers were characterized by a combination of $^1H$-NMR, size exclusion chromatography, and UV/Visible spectrophotometeric analysis. The micellization of the block copolymers as a drug-loading mechanism in aqueous media using fluorescein salt was examined as a function of pH. The stable micelle formation and its loading efficacy suggest that the block copolymers can be used as precursors for drug-nanocontainers.