# Web Unevenness Due to Thermal Deformation in the Roll-to-Roll Manufacturing Process
## 1 Introduction  
The roll-to-roll manufacturing (R2R) process is ecofriendly and low-cost, and has the advantage of mass production, which makes it attractive in manufacturing flexible electronic devices such as thin film transistors and solid oxide fuel cells (SOFCs) [1; 2; 3; 4; 5]. Recently, a brittle electrolyte, which is a separator used in SOFCs to transmit oxygen ions, was coated using this R2R process [6]. Slot-die coating is one of the best methods for coating a large-area electrolyte using this process. In slot-die coating, ink is supplied at a constant flow rate to the reservoir of the slot-die coater, discharged through the coater lip while forming a coating bead, and then deposited on the web. The coating quality of the liquid varies according to the distance between coater lip and web (coating gap), ink viscosity, ink surface tension, and substrate surface energy [7]. Accordingly, many research groups studied the effects of ink properties and coating parameters on coating quality [8; 9]. One of the most important parameters in the R2R process is the uniformity of the web obtained in the transverse direction. Assuch, the material of the web used to coat the electrolyte should be a thin, flexible, nonbreakable plastic film such as polyethylene terephthalate (PET) or polyimide (PI) [10; 11; 12]. Moreover, the web can be easily deformed by external forces due to the roll eccentricity and temperature fluctuations of the heater in the dryer during the movement of the web, which could deteriorate coating quality. Therefore, numerous studies on the behavior of the web according to external forces were conducted. [PERSON] et al. [9] developed a mathematical model to express the behavior of tension applied to the web in the R2R process, and controlled web-tension disturbances using a load cell and passive dancer. [PERSON] et al. [13] proposed a web-tension control method based on a proportional-integral (PI) controller and analyzed the tension behavior according to different velocity variations of driven rollers using the developed model. [PERSON] et al. [14] proposed an efficient web-tension estimation method using a nonlinear model-based observer, followed by experimental verifications. [PERSON] et al. [15] analyzed web-tension behavior in the transverse direction. [PERSON] et al. [16] postulated that the surface roughness of the substrate depends on web-tension disturbances in the R2R process, which affect coating and printing qualities. [PERSON] et al. [17] analyzed the effects of temperature disturbance in the dryer on thermal characteristics of the web followed by experimental verifications. [PERSON] et al. [18] studied web behavior according to heat conducted by the heating rollers in the R2R process. As mentioned above, previous studies mainly considered tension fluctuation in the web due to the velocity variations of driven rollers and temperature disturbances in the dryer in the R2R process. However, few studies were conducted on web defects due to thermal deformation of the dryer inlet [7]. Thermal deformations of the web could generate sine-wave-shaped deformation of the web in the transverse direction (web unevenness). If such web unevenness occurs in the coating section, the coating bead may become unstable, and the thickness of the coating layer may become nonuniform even though the desired coating parameters are set. Moreover, a crack could be generated by the bending of the coating layer due to web unevenness if brittle material is coated on the uneven web. These coating defects can negatively affect the performance of devices constructed on the coated layer [19; 20]. Therefore, it is essential to study defects at the inlet of the dryer during the coating of a brittle material to obtain a high-quality electrolyte layer in the R2R process. In this study, we analyzed the effect of thermal deformation in the tensioned web and web unevenness near the inlet of the dryer on the coating quality of a brittle electrolytic layer.