Articles can be provided with odor resistance by applying a dispersion of a halogenated heterocyclic N-halamine in an inert liquid carrier onto the surface of the article and allowing the inert liquid carrier to penetrate into it. The N-halamine accordingly becomes deposited on the surface of the article after the inert liquid carrier penetrates into the article. This method can be used to provide odor resistance to a variety of substrates, including garbage bags. It can also be used to deposit other functional particulates onto the surface of substrates having sufficient porosity to take up the vehicle. For instance, such functional particles can be oxidants that display antimicrobial and/or enzyme inhibitory efficacy or particles having toxin interaction potentials through oxidative degradation or adsorption of toxic substances in air and/or water, such as fluoride uptake by metal oxide microparticles.