## 3 Microstructure and Macroscopic Properties of Catalyst Ink
### Macroscopic Properties of the Catalyst Ink  
The macroscopic properties of the catalyst ink, including rheology (viscosity and thixotropy), surface tension, and stability (material stability and colloidal stability), are impacted by the catalyst ink composition or microstructure of catalyst ink. The macroscopic properties of the catalyst ink highly influence the coating process and the deposited ink film, hence the multiscale structure of CL (Figure 4). 1. Rheology: During the coating process, the ink with the desired viscosity is necessary for high-quality, continuous, and defect-free coating. Some coating techniques, e.g., slot die coating, doctor blade coating, brush coating, or print coating, usually need a relatively viscous ink, often called slurry or paste. A too viscous paste results in poor flowability, leading to a poor distribution of ink on the substrate or weak adhesion of CLs to the membrane [66]. Inkjet printing and spray coating generally need a low viscous ink (e.g., 4.9 mPa s) to avoid blocking the spraying nozzle and decrease the structural defects in the CLs, for example, the ink with a viscosity of 25.3 mPa s [67] may result in the nozzle clogging, making it hard to control the amount of ink sprayed. For spray coating, the viscosity has an influence on the atomization of the catalyst ink. When the viscosity is lower than a certain critical value (e.g., 15 mPa s [68]), increasing the viscosity of ink will decrease the number of large droplets and increase the uniformity of the formed droplets, enhancing spraying quality. The viscosity of catalyst ink is generally determined by temperature, the viscosity of solvent, the volume fraction of solids in the ink, and shear rate [53]. 1. Temperature, the viscosity of solvent, and the volume fraction of solids in the ink. The viscosity of a liquid always decreases with an increase in temperature. A viscous solvent or an increase in the solid volume in the ink lead to an increase in ink viscosity. Here, the solid refers to the catalyst, ionomer, and their formed agglomerates, as well as the solvent trapped in the loose agglomerates, which is equal to a pseudo-solid phase [52]. For a certain solid content, the ink viscosity usually increases with decreasing the size of agglomerates [28; 69]. Furthermore, the viscosity will decrease when the strength of the electrostatic repulsion force between agglomerates increases [53]. 2. Shear rate: When applying a shear force, e.g., during dispersing or coating of the catalyst ink, the fluid properties change, e.g., viscosity, different from the stationary case, which is commonly due to the change of the fluid microstructure caused by shear force [70]. The rheological behavior of fluid could be studied by measuring the change of viscosity or shear stress (\(\tau\)) with shear rate (\(\gamma\)). Fluid can be categorized into Newtonian fluids with shear-independent viscosity and non-Newtonian fluids. The non-Newtonian flow behavior could be further categorized in shear-thickening fluids and shear-thinning fluids. The Newtonian fluid exhibits a linear function between the applied \(\tau\) and the rate of strain (or \(\gamma\)). The non-Newtonian fluid could exhibit such a nonlinear function, called the Ostwald-de Waele model or Power Law model: \[\tau=\kappa\gamma^{n}=\left(\kappa\gamma^{n-1}\right)\gamma=\eta\gamma\] (1) where \(\kappa\) is the rheological consistency index, and \(\eta\) is the apparent viscosity; the exponent \(n\) can be determined if the applied \(\tau\) and the resulting \(\gamma\) are measured. For a Newtonian fluid, \(n=1\), and the apparent viscosity is independent on \(\gamma\). If \(n\
eq 1\), the fluid is termed non-Newtonian, or pseudo-plastic. The apparent viscosity increases with \(\gamma\) when \(n>1\), i.e., shear-thickening fluid, or decreases with the \(\gamma\) when \(n<1\), i.e., shear-thinning fluid [71]. The difference between n and 1 determines the degree of shear-thinning or shear-thickening. The larger the difference, the higher the shear-thinning or shear-thickening behavior.