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

Determining Young's and shear moduli of a rod-shaped object in an AFM bending test

“…When a rigid cylinder is pressed into a softer elastic base with Young's modulus E B , the Winkler coefficient in ( 8) is estimated to be k W ≈ E B [15].…”

“…As a result, for a bridge and console in each case of fixing conditions in Fig. 1, we obtained simultaneous systems of linear equations, which were solved analytically, Determination of elastic moduli in AFM bending tests 125 see, for example, the paper [15]. To speed up the calculations, we used computer algebra programs Mathematica (Wolfram Research, USA) and Mathcad (PTC, USA).…”

“…Then, for correct calculation, it is necessary to know the conditions for fixing the object to recess edges. This information can be obtained by comparing test data with model bending profiles [9][10][11][12][13][14][15]. In paper [15], analytical dependence was obtained for the bending profiles of model beams (consoles and bridges), supported, in particular, on elastic Winkler foundations [16].…”

“…In this paper, the problems of bending of model consoles and bridges are solved taking into account shear strains in the Timoshenko approximation [19]. As before [15], three types of conditions for fixing the ends of the beam were studied, Fig. 1: clamping, ring spring, and elastic Winkler foundation.…”

“…1: clamping, ring spring, and elastic Winkler foundation. The analytical dependence obtained for the bending profiles of consoles and bridges was used to process the data from AFM bending tests of MgNi 2 Si 2 O 5 (OH) 4 nanoscrolls [15].…”