Incorporating dirt-attracting polycationic polymers, such as polyethyleneimines, into cleaning wipes, mop pads, and similar substrates, improves dirt pick-up and retards redeposition of the dirt back onto the cleaned surface. The polymers can be incorporated directly into the non-woven substrates or they can be formulated with a cleaning composition for use with the substrate. The substrate containing the dirt-attracting polycationic polymers can be employed to clean hard and soft surfaces. The presence of the dirt-attracting polycationic polymers also facilitates biocide release from the substrates.