# Effect of Substrates on the Dynamic Properties of Inkjet-Printed Ag Thin Films
## 3 Measuring the Dynamic Properties of Ag Ink on Flexural Substrates
### Dynamic Properties of the Ag Films  
The wave propagations on the beam are dependent on the bending stiffness and mass per unit length of the beam. The combined bending stiffness was obtained from Equation (10). The mass per unit length of the bilayer was calculated as the simple sum of the values. Figure 4 shows the measured transfer functions of the bare substrates and the Ag-printed PI and glass beams. The predicted functions were plotted using the derived properties in Figure 5. The vibration transfers in Figure 4 showed evident variations due to the printing process. The vibration responses of PI shifted higher, and those of the silicon wafer and glass shifted to lower frequencies. The effects of Ag ink were determined by the stiffness and mass per length of the substrates. These variations definitely show that the properties of the Ag ink were correlated with the substrates.  
Figure 5 shows the bending stiffness and loss factor of the bare substrates and the bilayer beams. The obtained properties were calculated numerically through Equations (3) and (6). The averaged properties were used as representative values to minimize errors. The Young's modulus and loss  
Figure 4: Measured transfer function of Ag-printed beams on PI and glass substrates. The alterations of vibration responses due to the printing process showed different tendencies according to substrate.  
Figure 5: Measured bending stiffness and loss factor of the bare substrates and the Ag-printed beams.  
factor of the inkjet-printed Ag thin films were calculated by solving Equation (10). The results of the numerical calculation were shown in Figure 6. The acquired Young's modulus of the Ag thin films on the thin PI, the thick PI, the silicon wafer, and the glass were 38.5 GPa, 41.1 GPa, 55.2 GPa, and 75.4 GPa, respectively, and the acquired loss factors were 0.03, 0.036, 0.047, and 0.058, respectively. Even though the same ink was used, the Young's modulus of the ink, depending on the substrate, varied considerably. The loss factor tended to increase with increments of the modulus. Based on the measured properties of the thin PI and the thick PI, the modulus and loss factor depended on the type of substrate when the sintering process was identical. These trends suggest that the effect of the substrate should be considered to obtain the mechanical properties of the ink.  
The densification of the Ag film depends on the substrate due to differences in the coefficient of thermal expansion [19]. Densification is known to be affected by temperature, pressure, the number of overprints, and grain size [14; 15]. As densification reaches completion, the Young's modulus of the Ag film converges to that of silver. When nanoparticles of silver ink are formed during the sintering process, the geometric properties change. The surface roughness and thickness fluctuations may cause a systematic error in the measuring method. The wave approach allows accurate measuring of the properties because wave propagation on the printed substrates considers physical changes directly. In this study, the dynamic properties were obtained numerically as discussed earlier using the wave approach. The Young's modulus and loss factor were directly determined without any damage to the thin film due to the wave approach.