Application of DT method to the nonlinear analysis of microcantilever-sample interaction in AFM

The atomic force microscope system has become a popular and useful instrument to measure the intermolecular forces with atomic-resolution that can be applied in electronics, biological analysis, materials, semiconductors etc. This paper studies the complex nonlinear dynamic behavior of the probe tip between the sample and cantilever of an atomic force microscope using the differential transformation method (DTM). The dynamic behavior of the probe tip is characterized by reference to bifurcation diagrams, and Poincare maps produced using the time-series data obtained from differential transformation method. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the probe tip motion changes from T-periodic to 3T-periodic, then from 6T-periodic to multi-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0 to 5.0. Furthermore, it is demonstrated that the differential transformation method is in good agreement for the considered system.