The present invention is concerned with the production and use of water-insoluble particulate heteropolymers made by sequential emulsion polymerization in dispersed particles of which a "core" of a polymeric acid is at least partially encased in a "sheath" polymer that is permeable to a volatile base, such as ammonia or an organic amine, adapted to cause swelling of the core by neutralization. The aqueous dispersion of the acid-containing core/sheath particles is useful in making water-base coating compositions wherein it may serve as an opacifying agent when a volatile base is used to at least partially (to a pH of at least 6) neutralize the heteropolymer, microvoids being formed in cores of the swollen particles in the film during the drying thereof. Thus, the heteropolymer dispersion can serve as an opacifying agent in coating compositions, such as water-base paints, as a supplement or replacement of part or all of the pigmentary material or extenders that would otherwise be used in such coating compositions.For convenience of description herein, the terms "core", "sheath", and "core/sheath polymr" are frequently used to refer to the distinct functional components of the individual polymer particles of the essential "mode" of the heteropolymers of the present invention even though in actuality, the components of the polymer particles thereof may not have the precise arrangement implied by this terminology.