Fig 1.
AFM indentation experiments on a thin PAAm sample.
a) Calculated Young’s moduli as a function of indentation depth show that a high enough indentation depth is necessary to reach a Young’s modulus value that is independent of indentation depth. This is important for the reliability and comparability of elasticity measurements. In order to enable the analysis of huge amounts of data (many measurements on different positions), we created an algorithm that detects the plateau region of the E-d curves automatically. The orange dots represent the plateau region of the Young’s modulus determined by our algorithm, whereas the green cross shows the Young’s modulus with the lowest error of the Hertzian fit detected by our algorithm. Furthermore, the used fit range and contact point are displayed in the corresponding force-distance curve (b).
Fig 2.
Effect of indenter size on the measured Young’s modulus for a PAAm sample.
A thin PAAm sample was indented with beads of 6.47 μm, 15.0 μm or 21.82 μm diameter. Each box represents the distribution of Young’s moduli calculated from 30 indentation curves, taken at 3 different sample positions. A decrease of Young’s modulus is clearly visible when increasing the indenter diameter from 15.0 μm to 21.82 μm, which might be due to the fact that the indentation strain is larger for smaller indenters, resulting in the Hertz model to not be applicable anymore.
Fig 3.
Influence of PAAm thickness on Young’s modulus.
A thin (a) as well as a 1 mm (b) and a 2 mm (c) thick PAAm sample indented with a bead of 21.82 μm diameter. Although indentation depths up to 10 μm were reached for the bulk PAAm samples, no plateau region was detected. Only the thin sample shows a plateau value for the Young’s modulus for indentation depths above 0.4 μm. Generally, Young’s moduli decrease with increasing sample thickness.
Fig 4.
Dependence of Young’s moduli on indentation speed for a thin PAAm sample.
For each of several indentation speeds ranging from 0.1 μm/s to 100 μm/s, 250 force-distance curves (10 curves at each of 25 positions) or 150 force-distance curves (10 curves at each of 15 positions) for 0.1 μm/s were measured and the distributions of Young’s moduli are presented as boxplots. The AFM measurements result in higher Young’s moduli for higher indentation speeds, except for 100 μm/s. The dependence of the Young’s modulus on the indentation speed is probably due to PAAm being viscoelastic [45]. Viscoelastic properties can be neglected on longer timescales [3] (i.e. for quasi-static indentation speeds such as 0.1 μm/s).
Fig 5.
Young’s modulus on different positions on a thin PAAm sample.
These measurements were carried out at an indentation speed of 1 μm/s using an indenter bead with a diameter of 21.82 μm and a setpoint force of 300 nN. The distributions of Young’s moduli are broad and mean values vary from one position to another. Measurements on different sample positions as well as several measurements at one position are necessary for reliably determining Young’s moduli.