Capacitively coupled radio frequency plasmas operated in an electronegative gas (CF 4 ) and driven by voltage waveforms composed of four consecutive harmonics are investigated for different fundamental driving frequencies using PIC/MCC simulations and an analytical model. As has been observed previously for electropositive gases, the application of peak-shaped waveforms (that are characterized by a strong amplitude asymmetry) results in the development of a DC self-bias due to the electrical asymmetry effect (EAE), which increases the energy of ions arriving at the powered electrode. In contrast to the electropositive case (Korolov et al 2012 J. Phys. D: Appl. Phys . 45 465202) the absolute value of the DC self-bias is found to increase as the fundamental frequency is reduced in this electronegative discharge, providing an increased range over which the DC self-bias can be controlled. The analytical model reveals that this increased DC self-bias is caused by changes in the spatial profile and the mean value of the net charge density in the grounded electrode sheath. The spatio-temporally resolved simulation data show that as the frequency is reduced the grounded electrode sheath region becomes electronegative. The presence of negative ions in this sheath leads to very different dynamics of the power absorption of electrons, which in turn enhances the local electronegativity and plasma density via ionization and attachment processes. The ion flux to the grounded electrode (where the ion energy is lowest) can be up to twice that to the powered electrode. At the same time, while the mean ion energies at both electrodes are quite different, their ratio remains approximately constant for all base frequencies studied here.