The nonlinear modification to the Debye-Hückel potential of a dust grain depends on the thermodynamic properties of the background plasma. When the grain carries more than one electronic charge, the nonlinear self-interaction of the potential substantially modifies the ion-dust collision frequency. The electron-negatively charged dust collision frequency on the other hand remains largely unaffected by such a nonlinear modification. In the absence of nonlinear modification, collisions between the electrons and the negatively charged dust cease completely when the potential energy is four times the electron thermal energy. Thus once the dust acquires maximum charge, it will encounter electrons only because of its induced dipole field. Our electron-dust collision frequency agrees well with the previously known result whereas ion-dust collision frequency is always small compared with the known fitting formula.