Dynamical modeling of manipulation process in Trolling-Mode AFM.

Dynamical lumped modeling of Trolling-mode AFM in manipulation of bio-samples is presented. The combination of high accuracy and compatibility with physiological conditions makes AFM a unique tool for studying biological materials in liquid medium. However, AFM microcantilever suffers from severe sensitivity degradation and noise intensification while operating in liquid; the large hydrodynamic drag between the cantilever and the surrounding liquid overwhelms the tip-sample interaction forces that are important in controlling the process. Therefore, an appropriate nanoneedle should be long enough to keep the cantilever out of liquid medium and short enough to be able to transmit the required force to push nanoparticle. Nonetheless, a long nanoneedle may deflect under the pushing force; therefore, its bending deflection should be accounted for in governing equations. Moreover, analytical and finite element stress analysis of nanoneedle and cantilever is performed to assure about their selected material and geometry. JKR theory is utilized to model contact mechanics between the needle/surface and the particle. Drag and meniscus forces are used to model the liquid media. Governing equations are solved using ODE45 and the system behavior is simulated. Critical conditions of sliding including critical time and force are obtained and changes of pushing force, needle deflection and indentation depths are illustrated. Also, effects of velocity variations are observed. Then, different heights for nanoneedle are tested and an appropriate one is selected for our purpose (to keep the needle out of liquid and transmit the force appropriately). The simulation is repeated for various biological particles and their behaviors are studied. At the end, the present simulation is validated through comparing the results with a previous work. This comparison shows that the simulation is reliable for the intended purpose.