TY - JOUR
T1 - A model-based approach to compensate for the dynamics convolution effect on nanomechanical property measurement
AU - Xu, Zhonghua
AU - Zou, Qingze
N1 - Funding Information:
The financial support from NSF Grant No. CMMI-0626417 and NSF-CAREER Award No. CMMI-0846350 is gratefully acknowledged. The authors would also like to thank Professor Zhiqun Lin from Iowa State University for the preparation of the PDMS sample. Table I. The parameters of a third-order Prony series model obtained by curve fitting the total convoluted dynamics ratio, G c v ( j ω ) . Para. G 0 G 1 G 2 G 3 τ 1 (ms) τ 2 (ms) τ 3 (ms) Value 1.361 0.133 0.088 0.084 8.406 0.792 0.030 FIG. 1. (a) The force curve measurement scheme and (b) a schematic drawing of a force-distance curve. FIG. 2. Representation of dynamics that are involved in the nanomechanical property measurement using SPM. FIG. 3. The diagram of system dynamics. FIG. 4. Comparison of (a)(1) the force spectrum applied to the PDMS sample, (b)(1) the spectrum of the indentation in the PDMS sample, and (c)(1) the uncompensated complex compliance, all obtained by using the multiple-frequency method with those obtained by using the MIIC technique in (a)(2), (b)(2), and (c)(2), respectively. Note in (a)(2), the desired force spectrum is also shown. FIG. 5. The total deflection dynamics measured on the PDMS sample (blue solid line) and on the sapphire sample (red dotted line), and the ratio of them (black dashed line), i.e., the total convoluted dynamics ratio [see Eq. (10) ]. FIG. 6. (a) The total deflection dynamics from the piezoactuator to the deflection measured by using the same input voltage at five different contact points on the sapphire sample, and (b) the maximum difference between them. FIG. 7. Comparison of the uncompensated indentation in the PDMS sample obtained by using the MIIC-based method (red dashed line) with the total convoluted dynamics ratio (blue solid line). FIG. 8. The curve fitting result of (a) the real part and (b) the imaginary part of the total convoluted dynamics ratio G c v ( j ω ) by a third-order Prony series like model. FIG. 9. (a) The compensated indentation data obtained by using the multifrequency excitation and (b) the comparison of the uncompensated compliance of the PDMS sample (blue solid line) with the compensated compliance of the PDMS sample (red dashed line). FIG. 10. (a) The compensated indentation result obtained by using the MIIC-based method and (b) the comparison of the uncompensated compliance (blue solid line) of the PDMS sample with the compensated compliance of the PDMS sample (red dashed line).
PY - 2010
Y1 - 2010
N2 - A model-based approach to compensate for the dynamics convolution effect on the measurement of nanomechanical properties is proposed. In indentation-based approach to measure nanomechanical properties of soft materials, an excitation force consisting of multiple frequencies needs to be accurately exerted (from the probe) to the sample material, and the indentation generated in the sample needs to be accurately measured. However, when the measurement frequency range becomes close to the bandwidth of the instrument hardware, the instrument dynamics along with the probe-sample interaction can be convoluted with the mechanical behavior of the soft material, resulting in distortions in both the applied force and the measured indentation, which, in turn, directly lead to errors in the measured nanomechanical properties of the material (e.g., the creep compliance). In this article, the dynamics involved in indentation-based nanomechanical property measurement is investigated to reveal that the convoluted dynamics effect can be described as the difference between the lightly damped probe-sample interaction and the overdamped nanomechanical behavior of the soft sample. Thus, these two different dynamics effects can be decoupled via numerical fitting based on the viscoelastic model of the soft material. The proposed approach is illustrated by implementing it to compensate for the dynamics convolution effect on a broadband viscoelasticity measurement of a polydimethylsiloxane sample using a scanning probe microscope.
AB - A model-based approach to compensate for the dynamics convolution effect on the measurement of nanomechanical properties is proposed. In indentation-based approach to measure nanomechanical properties of soft materials, an excitation force consisting of multiple frequencies needs to be accurately exerted (from the probe) to the sample material, and the indentation generated in the sample needs to be accurately measured. However, when the measurement frequency range becomes close to the bandwidth of the instrument hardware, the instrument dynamics along with the probe-sample interaction can be convoluted with the mechanical behavior of the soft material, resulting in distortions in both the applied force and the measured indentation, which, in turn, directly lead to errors in the measured nanomechanical properties of the material (e.g., the creep compliance). In this article, the dynamics involved in indentation-based nanomechanical property measurement is investigated to reveal that the convoluted dynamics effect can be described as the difference between the lightly damped probe-sample interaction and the overdamped nanomechanical behavior of the soft sample. Thus, these two different dynamics effects can be decoupled via numerical fitting based on the viscoelastic model of the soft material. The proposed approach is illustrated by implementing it to compensate for the dynamics convolution effect on a broadband viscoelasticity measurement of a polydimethylsiloxane sample using a scanning probe microscope.
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U2 - 10.1063/1.3327450
DO - 10.1063/1.3327450
M3 - Article
AN - SCOPUS:77950568092
SN - 0021-8979
VL - 107
JO - Journal of Applied Physics
JF - Journal of Applied Physics
IS - 6
M1 - 064315
ER -