Articles can be provided with a high level of odor resistance by applying a dispersion of a halogenated heterocyclic N-halamine in an inert liquid carrier to the surface of the article and allowing the inert liquid carrier to penetrate into the article. However, it is important for the inert liquid carried not to react with halogen atoms in the halogenated heterocyclic N-halamine, and for the halogenated heterocyclic N-halamine to become deposited on the surface of the article after the inert liquid carrier penetrates into the article. This method can be used to provide a high level of odor resistance to a wide variety of substrates. It is of particular value for use in manufacturing garbage bags having a high level of odor resistance. It can also be used to deposit other functional particulates onto the surface of substrates that have porosity sufficient to take up the vehicle, including oxidants that may display antimicrobial and enzyme inhibitory efficacy, including, but not limited to N-halamines, and tox
