Browsing by Author "Hashemi, Nastaran"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Basins of attraction of tapping mode atomic force microscopy with capillary force interactions
    Hashemi, Nastaran; Montazami, Reza (AIP Publishing, 2009-06-01)
    We perform a large number of simulations over a wide range of system parameters to approximate the basins of attraction of steady oscillating solutions. We find that the basins of attraction vary as a function of system parameters and initial conditions. For large equilibrium separations, the basin of attraction is dominated by the low-amplitude solution. The location of the fixed point is shifted toward the higher values of instantaneous displacement and velocity for larger equilibrium separations. We show that the basin of attraction in the neighborhood of the fixed point is dominated by low-amplitude solutions as relative humidity is increased.
  • Thumbnail Image
    The dissipated power in atomic force microscopy due to interactions with a capillary fluid layer
    Hashemi, Nastaran; Paul, Mark R.; Dankowicz, Harry; Lee, M.; Jhe, W. (American Institute of Physics, 2008-09-15)
    We study the power dissipated by the tip of an oscillating micron-scale cantilever as it interacts with a sample using a nonlinear model of the tip-surface force interactions that includes attractive, adhesive, repulsive, and capillary contributions. The force interactions of the model are entirely conservative and the dissipated power is due to the hysteretic nature of the interaction with the capillary fluid layer. Using numerical techniques tailored for nonlinear and discontinuous dynamical systems we compute the exact dissipated power over a range of experimentally relevant conditions. This is accomplished by computing precisely the fraction of oscillations that break the fluid meniscus. We find that the dissipated power as a function of the equilibrium cantilever-surface separation has a characteristic shape that we directly relate to the cantilever dynamics. Even for regions where the cantilever dynamics are highly irregular the fraction of oscillations breaking the fluid meniscus exhibits a simple trend. Using our results we also explore the accuracy of the often used harmonic approximation in determining dissipated power. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2980057]
  • Thumbnail Image
    Exploring the Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy with Capillary Layer Interactions
    Hashemi, Nastaran (Virginia Tech, 2008-06-18)
    Central to tapping mode atomic force microscopy is an oscillating cantilever whose tip interacts with a sample surface. The tip-surface interactions are strongly nonlinear, rapidly changing, and hysteretic. We explore numerically a lumped-mass model that includes attractive, adhesive, and repulsive contributions as well as the interaction of the capillary fluid layers that cover both tip and sample in the ambient conditions common in experiment. To accomplish this, we have developed and used numerical techniques specifically tailored for discontinuous, nonlinear, and hysteretic dynamical systems. In particular, we use forward-time simulation with event handling and the numerical pseudo-arclength continuation of periodic solutions. We first use these numerical approaches to explore the nonlinear dynamics of the cantilever. We find the coexistence of three steady state oscillating solutions: (i) periodic with low-amplitude, (ii) periodic with high-amplitude, and (iii) high-periodic or irregular behavior. Furthermore, the branches of periodic solutions are found to end precisely where the cantilever comes into grazing contact with event surfaces in state space corresponding to the onset of capillary interactions and the onset of repulsive forces associated with surface contact. Also, the branches of periodic solutions are found to be separated by windows of irregular dynamics. These windows coexist with the periodic branches of solutions and exist beyond the termination of the periodic solution. We also explore the power dissipated through the interaction of the capillary fluid layers. The source of this dissipation is the hysteresis in the conservative capillary force interaction. We relate the power dissipation with the fraction of oscillations that break the fluid meniscus. Using forward-time simulation with event handling, this is done exactly and we explore the dissipated power over a range of experimentally relevant conditions. It is found that the dissipated power as a function of the equilibrium cantilever-surface separation has a characteristic shape that we directly relate to the cantilever dynamics. We also find that despite the highly irregular cantilever dynamics, the fraction of oscillations breaking the meniscus behaves in a fairly simple manner. We have also performed a large number of forward-time simulations over a wide range of initial conditions to approximate the basins of attraction of steady oscillating solutions. Overall, the simulations show a complex pattern of high and low amplitude periodic solutions over the range of initial conditions explored. We find that for large equilibrium separations, the basin of attraction is dominated by the low-amplitude periodic solution and for the small equilibrium separations by the high-amplitude periodic solution.
  • Thumbnail Image
    The nonlinear dynamics of tapping mode atomic force microscopy with capillary force interactions
    Hashemi, Nastaran; Dankowicz, Harry; Paul, Mark R. (American Institute of Physics, 2008-05-01)
    We study the nonlinear dynamics of a tapping mode atomic force microscope with tip-surface interactions that include attractive, repulsive, and capillary force contributions using numerical techniques tailored for hybrid or discontinuous dynamical systems that include forward-time simulation with event handling and numerical pseudo-arclength continuation. We find four branches of periodic solutions that are separated by windows of complex and irregular dynamics. The branches of periodic solutions end where the cantilever comes into grazing contact with event surfaces in state space, corresponding to the onset of capillary interactions and the onset of repulsive forces associated with contact. These windows of irregular dynamics are found to coexist with the periodic branches of solutions as well as exist beyond the termination of the periodic solution. Finally, we show that these details can be overlooked unless one is careful to sample the dynamics appropriately. (C) 2008 American Institute of Physics.