A modeling study of carbon clusters and dust particles formation through carbon graphite sputtering in argon DC discharges is presented. The model combines the description of plasma discharge kinetics, molecular growth and transport of carbon clusters and aerosol dynamics for dust particles. Results show that field reversal is a key effect that ensures trapping and growth of negatively charged molecular carbon clusters, which are the precursors for dust particles. The model enables prediction of the space-time distributions of carbon clusters density as well as dust particle density, average charge and average diameter. Results especially show that dust particles and carbon clusters exhibit a pronounced density maximum in the vicinity of the field reversal position. A parametric study is presented in order to analyze the model sensitivity to some key parameters used in the physical model.