We have used Johnson-Kendall-Roberts contact mechanics methodology to study the sell adhesion of block copolymers. The block copolymers studied contain building blocks that have different physical states as well as different dynamic characteristics. The polymers chosen are poly(styrene)-poly(isoprene) (PS-PI), poly(styrene)-poly(ethylethylene) (PS-PEE) diblocks and PS-PI-PS, PS-PEE-PS triblocks that have the tail and looped chain surface architectures, respectively. Our results for unloading of the diblock/triblock mixtures, where two surfaces are separated by decreasing the amount of compression, show a maximum in adhesion vs mixture composition when the contact time is short. For contact times longer than 30 min, only unloading of triblock-dominated mixtures shows considerable buildup of adhesion with time. The surface energies obtained from loading experiments do not show any detectable influence of chain architecture on the thermodynamic work of adhesion.