Volatile substances such as fragrances, perfumes, deodorizers, room freshener compositions and the like are dispensed in vapor phase from a container holding the substance in liquid phase at room temperature and under atmospheric pressure. The container has a window covered with a microporous membrane with an active structure formed from a material having a critical surface tension that is below the surface tension of the liquid substance. Generally the active membrane material has a critical surface tension that is below 22 dynes/cm and preferably below 20 dynes/cm while the surface tension of the liquid is at least 22 dynes/cm. One example is an ultraviolet irradiated polymer composition with 0.2 microns nominal pore size. In all instances the volatile substance is first sorbed within a porous element and desorbed therefrom for transport through the membrane only in its vapor phase.