Determination of Elastic Moduli of Thin Layers of Soft Material Using the Atomic Force Microscope

Abstract

We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.

Mechanical Criterion for the Rupture of a Cell Membrane under Compression

“…In our simulations of cell indentation, the endothelial cell is modeled as a nearly incompressible (14,27) hyperelastic neo-Hookean (13,28,29) material, with a Poisson's ratio of 0.49 and a Young's modulus of 1 kPa. The microindenter's spherical tip is considered infinitely rigid compared to the cell.…”

“…In AFM, forces are applied onto a cell through a cantilever ending at a sharp tip, with a typical radius at its extremity of~10 nm. Such a sharp tip induces high local strains that can exceed the linear regime, thus introducing artifacts in the determination of the cell's mechanical properties (14,15). To avoid such artifacts, an alternative technique is often used where a micrometric bead is attached to the tip of the AFM cantilever (16)(17)(18).…”

Basilar Membrane and Tectorial Membrane Stiffness in the CBA/CaJ Mouse

“…In order to compare the results with data in the literature, Young's modulus was extracted from the measurements using a model describing a sphere indenting an elastic material (Dimitriadis et al 2002;Shoelson et al 2004). The model is based on Hertz's description of a spherical sensor indenting an elastic isotrophic material.…”

“…The model is based on Hertz's description of a spherical sensor indenting an elastic isotrophic material. A detailed derivation of the model is given in Dimitriadis et al (2002). In the present study, it has been assumed that the sample (TM) is not bonded to the supporting substrate (reticular lamina).…”

Determination of work of adhesion of biological cell under AFM bead indentation

“…The maximum indentation depth of cell is approximately 0.7μm. Thus, the substrate effect is negligible since the indentation is smaller than 10% of the sample thickness (ISO14577-4; Dimitriadis et al, 2002;Jung et al, 2004).…”