Atomic force microscopy bending tests of a suspended rod-shaped object: Accounting for object fixing conditions

The technique of atomic force microscopy (AFM) bending tests of a suspended nano-object (scroll, tube, rod) makes it possible to calculate the Young's modulus of the material it is made of based on experimental data. However, the calculation results involve a large error due to uncertain conditions (console or bridge) of fixing the test object. One of the ways to reduce this error is based on the theoretical consideration of consoles or bridges as beams with one or two ends resting on Winkler elastic foundations. The beam bending problems have been solved in both cases using Krylov's functions. This has allowed for developing an approach to the analytical identification of fixing conditions and including them in the calculations. The application of the approach is illustrated by AFM measurements of the Young's modulus of MgNi_{2}Si_{2}O_{5}(OH)_{4} nanoscrolls.