Chapter 3 Methodology
3.2 in situ Nanomechanical Testing
3.2.5 Accuracy and Errors
As discussed in section 3.2.3, different laser positions on the AFM cantilever affects the outputting cantilever deflection signal and influences the accuracy of the force measurement. Therefore, in this section, the accuracy and errors of the
force measurements in the AFM system are discussed by considering the laser located at the back of AFM cantilever as shown at position d0 in Figure 3.11.
a. Accuracy
As defined in Equation 3.15, the force applied to the sample is calculated from the cantilever deflection in the test, which is equal to the cantilever displacement recorded in calibration as discussed in Equation 3.12 and Equation 3.13. Therefore, the force resolution of the AFM is defined as the product of the smallest recorded displacement of the cantilever and the spring constant of the cantilever. The Attocube AFM system used in this study has a smallest displacement of 0.36 nm at 300 K and 0.23 nm at 4 K for z axis piezo movement [210]. Mechanical tests were carried out at room temperature, which approximates to 300 K and therefore provides a cantilever deflection resolution of 0.36 nm. The AFM cantilever spring constants (K) used in nanofibre mechanical testing in this thesis are typically ranged between 0.01 Nm-1 to 0.2 Nm-1. Therefore, the smallest force that is measured by the AFM is equal to the product of the cantilever deflection resolution (0.36 nm) and K = 0.01 Nm-1, to give a minimum force of 3.6 pN. The nanomechanical tests produce the recorded forces by movement of the piezo positioner in order to provide displacement of the AFM cantilever. In this thesis, 2048 data points were sampled during each
tensile test during a 20 μm z axis piezo displacement. The accuracy of the smallest detectable piezo displacement is therefore 9.8 nm, which corresponds to a force resolution of around 100 pN when using a cantilever with a spring constant of 0.01 Nm-1. The forces and displacements used in the AFM setup are considerably smaller than micro electro mechanical systems (MEMS). In particular, MEMS devices measure forces in the range of tens of nano-Newtons up to hundreds of micro-Newtons [211-214].
Finally, the SEM used in this study has a spatial resolution of 1.0 nm in secondary electron imaging mode at 30 kV, 2.0nm at 2 to 3 kV and 3.0 nm at 1 kV under high vacuum operation mode [215].
b. Errors
The mechanical oscillation of the AFM cantilever is the major factor in the force measurement error and is dominated by the vibration of the SEM sample stage. In addition, the interference of electronic components in the AFM controller unit can also affect the stability of the signal output. All these effects will lead to a resultant “oscillating” signal as shown by the recorded variation in the laser intensity, in volts, over time as recorded in Figure 3.13. The average signal is shown in Figure 3.13 as being, on average, 5.455 V with a range from 5.45 V to
5.46 V. As shown in Figure 3.12 (A), the largest slope in the first period of the sine curve is recorded to be 0.52 μm/V at the point with Y value of round 5.4 V. The intensity-displacement relation is approximately linear near the largest slope point where the cantilever displacement can be calculated from the slope directly. Therefore, the 0.01 V noise in laser intensity signal corresponds to a displacement of approximately 0.01 V 0.52 μm/V = 5.2 nm. Hence, the general error of all the interferences on the force measurement was estimated to be about 0.1 nN from the noise level of the original signal in a 1 kHz bandwidth using a 0.02 Nm-1 cantilever as shown in Figure 3.13. AFM cantilever with lower spring constants of 0.01 Nm-1 have smaller measured force noise ranged between 0.05 to 0.08 nN. As the mechanical forces recorded using tensile testing of nanofibres range from 314 to 1413 nN, a force error of 0.1 nN represents a maximum 0.03 % error in the recorded forces.
0 1 2 3 4 5.44 5.45 5.46 5.47 Laser int ensit y (V) Time (s)
for the AFM integrated within SEM (1 kHz data sampling bandwidth, cantilever spring constant is 0.02Nm-1).
The accurate determination of the stress-strain behaviour when mechanically testing samples requires the reliable measurement of the sample’s dimension, especially the cross section area. As shown in Equation 3.12, the radius of the nano fibrous samples has a square dependence on their stress level. High magnification secondary electron images of sample were taken from different view angles in prior of testing to verify a circular cross-section. The radius of the nanofibre was carefully measured from SEM images by using pixel analysis software (ImageJ, NIH, USA). However, the samples tested in the experiment are made up of non-conductive polymeric materials. Hence, charging effects due to electrons from the SEM beam residing on the nanofibre surface influences the SEM image quality and causes distortion of the resultant image. The evaluation of the charging effect was carried out by measuring the radius of nylon-6 samples with and without gold sputter coating. The nanofibre radius was calculated by averaging 6 measured radius values at different random positions along the fibre length. The measured nanofibre radius for 20 individual non-coated nylon-6 nanfibres showed a larger standard deviation of 14 % compared to 8 % for nylon-6 nanofibres with a gold-coating, indicating a 6% error caused by the charging effect alone (non-coated sample are measured in images taken under 3
kV and gold-coated sample are imaged under 30 kV). The error in values of stress arising from inaccuracies in measuring the nanofibre radius from SEM images are calculated to be around 12% which is significantly higher than the measured force noise level of the AFM cantilever. Therefore, errors in values of stress are dominated by the fibrous sample radius measurement using SEM.