We present particle-in-cell dust models for kinetic simulation of interaction between dust and plasma in a capacitive radio frequency discharge and afterglow. We study the properties of a capacitive 13.56 MHz discharge in pure argon and in a mixture of with nanosize particles. For the first time it is found that at initial stage of growth the mobile nanoparticles are accumulated near the sheath-plasma boundaries. The transition between different modes of discharge operation is found to be associated with the growing nanoparticles. In discharge afterglow, it is shown that the electrons released from the dust surface contribute to the anomalous growth of the electron density. A hybrid model was developed to combine the kinetic description for electron motion and the fluid approach for negative and positive ion transports and plasmochemical processes. The growth of heavy hydrocarbons is studied in a capacitive 13.56 MHz discharge in a mixture of taking into account the plasmochemistry. The densities of negatively and positively charged heavy hydrocarbons are sufficiently large to be precursors for the formation of nanoparticles in the discharge volume. We study also the influence of the fraction of acetylene in the mixture of on the negative ion density.