The cantilever is mechanically driven at two resonant frequencies in a bimodal atomic force microscope (AFM). To generate the feedback signal for topography measurement the deflection signal is demodulated at one frequency and for compositional surface mapping at the other. In particular, the second mode amplitude and phase signals are used to map surface forces such as the van der Waals interaction. On electrically charged surfaces both, van der Waals forces and electrostatic forces contribute to the second eigenmode signal. The higher eigenmode signal in bimodal AFM reflects the local distribution of electrical charges. Mechanically driven bimodal AFM thus also provides a valuable tool for compositional mapping based on surface charges.