Effects of Electric Fields on Forces between Dielectric Particles in Air

We developed a quantitative measurement technique using atomic force microscopy (AFM) to study the effects of both DC and AC external electric fields on the forces between two dielectric microspheres. In this work we measured the DC and AC electric field-induced forces and adhesion force between two barium titanate (BaTiO?) glass microspheres in a low humidity environment by this technique. The objective here is to find out the correlation between these measured forces and applied field strength, frequency, and the separation distance between the two spheres was studied. Since the spheres would oscillate under an AC field, the AC field-induced force was divided into dynamic component (i.e., time-varying term) and static component (i.e., time-averaged term) to investigate. The oscillatory response occurs at a frequency that is twice the drive frequency since the field-induced force is theoretically proportional to the square of the applied field. This behavior can be observed in the fast Fourier transformation (FFT) spectra of the time series of the deflection signal. The magnitude of the vibration response increases when the frequency of the drive force is near resonant frequency of the particle-cantilever probe. The amplitude of this vibration increases with proximity of the two particles, and ultimately causes the particles to repeatedly hit each other as in tapping mode AFM.

The effect of the Maxwell-Wagner interfacial relaxation on the DC electric field-induced force was discovered by monitoring the variation of the field-induced force with time. The static component of the AC electric field-induced force does not vary with the applied frequency in the range from 1 to 100 kHz, suggesting that the crossover frequency may equal to or less than 1 kHz and the permittivities of the BaTiO? glass microspheres and medium dominate the field-3 induced force. The AC field-induced force is proportional to the square of the applied electric field strength. This relationship persists even when the separation between the spheres is much smaller than the diameter of the microspheres. The large magnitude of the force at small separations suggests that the local field is distorted by the presence of a second particle, and the continued dependence on the square of the field but the measured force is much larger than the theoretical results, suggesting that the local electric field around the closely spaced spheres is distorted and enhanced but the effects of the local field distortion may have not much to with the applied electric field. Compared with the calculated results from different models, our results demonstrate that the field-induced force is much more long-range than expected in theory. In addition, the DC field-induced adhesion force is larger than the AC field-induced one due to the interfacial charge accumulation, agreeing with the discovery of the Maxwell-Wagner interfacial relaxation effect on the DC field-induced force. No obvious correlation between the field-induced adhesion and the applied frequency is found. However, both the DC and AC field-induced adhesion forces display the linearity with the square of the applied electric field strength as well.