We developed a model for the nucleation, growth and transport of carbon dust particles in a DC discharge. The carbon source comes from the sputtering of a graphite cathode resulting in the production of primary clusters and then of nanoparticles. We consider the ionic cluster growth as well as the particle growth and charging and the influence of both on the discharge equilibrium. We found that the discharge becomes electronegative for long duration when particle density reaches 10 9 cm-3 and particle size 45 nm. The corresponding transition modifies the electric field profile in the vicinity of the field reversal region in the negative glow. We then analyze the space and time evolution of the different discharge characteristics and the mechanisms involved in the discharge. We showed that particle density is governed by nucleation, coagulation and transport, while particle size is mainly governed by the deposition of the small neural clusters emitted at the cathode on the particle surface