# Web Unevenness Due to Thermal Deformation in the Roll-to-Roll Manufacturing Process
## 3 Experiment
### Effects of Web Unveverenness on YSZ Layer Crack  
The YSZ electrolyte layers were fabricated at the four drying-temperature levels of 30, 60, 90, and 120 \({}^{\circ}\)C using the R2R slot-die coating process to analyze the effects of web unevenness on the crack developed in the YSZ layer. Table 5 presents the coating conditions according to drying conditions. Figure 7a,b present the dried YSZ layers coated at drying-temperature levels of 30 and 90 \({}^{\circ}\)C, respectively. Few coating defects were obtained in the YSZ layer at 30 \({}^{\circ}\)C; defects in the x direction were generated in the YSZ layer only at 90 \({}^{\circ}\)C. Figure 8 indicates the surface of the YSZ dried at (a-c) 30, (d-f) 60, (g-i) 90, and (j-l) 120 \({}^{\circ}\)C, measured by a microscope (LV100 ND, Nikon, Tokyo, Japan), a scanning electron microscope (FE-SEM, S-480, Hitachi Inc., Tokyo, Japan), and an interferometer (NS-E1000, NanoSystem Co. Ltd., Daejeon, Korea). Figure 8a,d,g,j, show more coating defects generated at higher drying-temperature levels. In particular, defect width also rose with the increase in drying temperature. The web unevenness generated in the dryer spread to the slot-die coating section, and the YSZ ink coated on the peak of web unevenness flowed down to the valley as the ink was deposited on the uneven web in the transverse direction, which generated the coating \begin{table}
\begin{tabular}{c c c} \hline  & **Properties** & **Value** \\ \hline \multirow{4}{*}{YSZ Ink} & Contact angle (\({}^{\circ}\)) & 61.91 \\  & Viscosity (cP) & 30 \\  & Solid contents (\%) & 35.91 \\ \hline \multirow{4}{*}{Substrate} & Thickness (mm) & 0.1 \\  & Width (mm) & 150 \\ \cline{1-1}  & Elastic modulus (GPa) & 5.5 \\ \cline{1-1}  & Poisson’s ratio & 0.37 \\ \hline \multirow{4}{*}{Process} & Operating tension (kgf) & 1 \\  & Flow rate (ml/min) & 20 \\ \cline{1-1}  & Web speed (mm/min) & 1000 \\ \cline{1-1}  & Coating gap (mm) & 0.35 \\ \cline{1-1}  & Drying temperature (\({}^{\circ}\)C) & 30 \\ \hline \end{tabular}
\end{table} 
Table 4: YSZ ink properties and processing condition of slot-die coating. Figure 6: (a) YSZ coating layer during tensile test; (b) stress–strain curve. The effects of the coating defects on SOFC performance were analyzed. SOFCs were fabricated using YSZ layers prepared at the different drying-temperature levels shown in Figure 8. Open-circuit voltage (OCV), which directly affects the internal resistance and performance of SOFCs, was measured. Equation (2) presents the mathematical model of OCV obtained using the Nernst equation [26]. \[E_{T}=E_{0}+\frac{RT}{2F}\ln\left(P_{H_{2}}\right)-\frac{RT}{2F}\ln\left(P_{H_{ 2}O}\right)+\frac{RT}{2F}\ln\left(P_{O2}\frac{1}{2}\right) \tag{2}\]  
where \(E_{T}\) represents OCV; \(R\) is the universal gas constant (8.314 JK\({}^{-1}\)mol\({}^{-1}\)); \(T\) and \(F\) are the temperature and Faraday constant (96,484 Cmol\({}^{-1}\)), respectively; and \(P_{H2}\), \(P_{H2O}\), and \(P_{O2}\) are the partial pressures of \(H_{2}\), \(H_{2}O\), and \(O_{2}\) at 1 atm, respectively. Figure 9 indicates the OCV measurement of SOFCs fabricated using the YSZ layer at 30, 60, 90, and 120 \({}^{\circ}\)C drying temperature. OCV using the YSZ layer fabricated at 60, 90, and 120 \({}^{\circ}\)C could clearly not be measured due to the coating defects. This means that the coating defects due to web unevenness could damage the SOFCs and decrease their yield in the R2R process. These results suggested that the effects of web unevenness on the coating defect due to convection and conduction heat from the dryer should be considered in fabricating the brittle electrolyte with the R2R process. For instance, the distance between slot-die coater and the inlet of the dryer can be determined by considering the minimum permissible distance at which web unevenness is not generated by considering web unevenness according to the distance between the position of the slot-die coater and dryer inlet at the drying temperature set by the user.