Null ellipsometry is used to obtain the adsorption isotherms for functionalized polystyrene-block-polybutadiene diblock copolymers, in which polar urazole groups, 4-(3,5-dioxo-1,2,4-triazolidin-4-yl)benz acid, are attached randomly to a short polybutadiene block. The block copolymer molecular weight and the number of functional groups are varied. Adsorption investigations are performed from very dilute solution of these copolymers in toluene, using silicon wafers as the substrate. Toluene is a good solvent for both blocks and a nonsolvent for the functional groups. The system largely behaves like a conventional block copolymer with selective adsorption of one block. The conformation of the adsorbed chains has "brush" character. The surface density scales with the size of the dangling, nonadsorbing blocks and is essentially independent of the number of functional groups of the adsorbing block. A model for this behavior is proposed based on largely independent adsorbing urazole groups connected via flexible nonadsorbing polybutadiene sequences. A "zipper" mechanism for desorption is envisaged. In a still better solvent, tetrahydrofuran, no adsorption takes place.