Aims: We study the production of dust in Type II-P supernova by coupling the gas-phase chemistry to the dust nucleation and condensation phases. We consider two supernova progenitor masses with homogeneous and clumpy ejecta to assess the chemical type and quantity of dust that forms. Grain size distributions are derived as a function of post-explosion time. Methods: The chemistry of the gas phase and the simultaneous formation of dust clusters are described by a chemical network. The formation of key species (CO, SiO) and dust clusters of silicates, alumina, silica, metal carbides and sulphides, pure metals, and amorphous carbon is considered. The master equations describing the chemistry of the nucleation phase are coupled to a dust condensation formalism based on Brownian coagulation. Results: Type II-P supernovae produce dust grains of various chemical compositions and size distributions as a function of time. The grain size distributions gain in complexity with time, are slewed towards large grains, and differ from the usual MRN power-law distribution used for interstellar dust. Gas density enhancements in the form of clumps strongly affect the dust chemical composition and the grain size distributions. Silicates and pure metallic grains are highly dependent on clumpiness. Specifically, clumpy ejecta produce grains over 0.1 micron, and the final dust mass reaches 0.14 Msun. Conversely, carbon and alumina dust masses are controlled by the mass yields of alumina and carbon in the zones where the dust is produced. Several dust components form in the ejecta and the total dust mass gradually builds up over a time span of 3 to 5 years post-outburst. This gradual growth provides a possible explanation for the discrepancy between the small dust masses formed at early post-explosion times and the high dust masses derived from recent observations of supernova remnants.
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