## 3 Microstructure and Macroscopic Properties of Catalyst Ink
### Macroscopic Properties of the Catalyst Ink
There are several other visco-elastic models to describe shear-thinning flow behavior, e.g., the Carreau-Yasuda-Cross Model [72], or for fluids exhibiting a yield stress, the Herschel-Bulkley Model [73]. For non-Newtonian fluid, the microstructure variation will occur under shear force. For example, the large agglomerates are broken down to small agglomerates by shear force; the initially tangled polymer chains disentangle and stretch under shear force; the initially disordered particles align with flow [71]. The fluids exhibiting these structural variations will show a shear-thinning behavior. The fluids exhibiting the reversed structure variations will show a shear-thickening behavior. The catalyst ink is a multi-phase fluid system, likely exhibiting non-Newtonian fluid behavior when flowing. The commonly used water and alcohol mixed solvents are Newtonian fluids. When dispersing Nafion ionomer in the solvent with a weight ratio from 0.25 to 5.5 wt.%, the dispersion solution still approaches a Newtonian behavior for shear rates above 10 s\({}^{-1}\)[52; 53]. When dispersing Pt/HSC (high surface carbon) in the solvent, the fluid exhibits a shear-thinning behavior. When simultaneously dispersing Pt/HSC and Nafion ionomer in the solvent, i.e., the catalyst ink, it presents a shear-thinning nature [53] (Figure 5). To the best of our knowledge, most catalyst inks usually give a shear-thinning behavior [28; 52; 53; 74]; only a few cases exhibit a nearly Newtonian behavior for shear rate of about 1-1000 s\({}^{-1}\)[53; 75]. Under shear force, the primary or secondary agglomerates in the catalyst ink will align with the flow, or the large secondary agglomerates break down to small secondary agglomerates or primary agglomerates, resulting in a shear-thinning behavior. The degree of shear thinning increases with increasing the concentration of catalyst or ionomer due to the increased degree of agglomeration [53], as shown in Figure 5b,c. Badly dispersed carbon inks with dry agglomerates could exhibit shear thickening behavior at critical shear rates, whereas the overall flow behavior is shear thinning [76; 77]. When through a spray nozzle, doctor blade, or brush, the catalyst ink is subjected to the different shear environments, e.g., through a spray nozzle, a high shear environment (the shear rate at the ink film is ca. 10\({}^{4}\)-10\({}^{6}\) s\({}^{-1}\) in the spraying process [68]), through a brush, a low shear environment exists [35]. Especially, the flow behavior at high shear rates (>10\({}^{4}\) s\({}^{-1}\)) is hardly measurable with rotational rheometers due to edge fracture and spillage. Therefore, modeling the flow behavior could give an indication of the visco-elastic behavior at high shear rates during the coating process [78]. If the fluid approaches a Newtonian behavior, the catalyst ink would suffer nearly no microstructure variation during the coating process. The deposited ink film keeps a similar microstructure to that of the catalyst ink. However, in most cases, the catalyst ink is a shear-thinning fluid. During the coating process, the deposited ink film suffers deformation, showing a different microstructure from the catalyst ink. Such deformation complicates the relation between  
Figure 5: Viscosity of Nafion ionomer dispersions (**a**), Pt/HSC dispersions (**b**), Pt/HSC and ionomer dispersions with a fixed 3 wt.% carbon (**c**) in 1-propanol and aqueous solvent mixture (3:1 mass ratio) at different concentrations or I/C ratios (Reprinted with permission from ref. [53]. Copyright (2018) American Chemical Society). the catalyst ink microstructure and the CL structure as well as increase the difficulty in controlling the CL structure. However, the shear-thinning behavior will contribute to the uniformity of the coated CL and controlling the CL thickness during the coating process. The viscosity and rheology of catalyst ink are sensitive to its microstructure.