## 2 Multiscale Structure of CL in PEM Fuel Cell  
The CL is a three-dimensional intersecting network of catalyst, ionomer, and pore. The electrochemical reaction in the CL occurs at the TPB, as described earlier. Hence, this requires the mass transport pathways to/from the TPB in CLs and hence demands the ionomer or water for proton transport, Pt/C for catalyzing the electrochemical reaction and electron transport, and the pores next to the fully or partially covered Pt/C for the transport of reactant gas and water. This is schematically illustrated in Figure 2.  
Although typical CLs only have a thickness of 5-10 \(\upmu\)m [21], they have a complicated multiscale structure, i.e., micro-, meso-, and macro-structure, due to the catalyst particles  
Figure 2: Illustration of ionomer-coated catalyst agglomerate [21; 45].  
and ionomer, primary agglomerate particles, and secondary aggregation of primary agglomerates. The catalyst particles, 2-5 nm Pt nanoparticles supported on 10-50 nm carbon black with a pore diameter of a few nm, tend to strongly bond together and aggregate, forming primary catalyst agglomerates, which are commonly surrounded by absorbed ionomer films 3.5-20 nm thick [46], i.e., primary catalyst-ionomer agglomerates of a few hundred nm [47]. The primary catalyst-ionomer agglomerates usually aggregate into large secondary agglomerates of a few \(\upmu\)m through Van Der Waals force. Therefore, the secondary catalyst-ionomer agglomerates usually exhibit a bimodal pore size distribution, including 2-20 nm-sized pores within primary agglomerates and larger over 20 nm-sized pores between primary agglomerates in the secondary agglomerates--the former is often referred to as the primary pores, and the latter the secondary pores [47; 48]. Moreover, there also exist large irregular ionomer patches formed by non-absorbed ionomer agglomerates [49]. The distribution of ionomer in CLs is usually inhomogeneous, in the sense that the coverage of Pt nanoparticles can be categorized as (i) fully covered with a thick ionomer film, (ii) fully covered with a thin ionomer film, (iii) partially covered by ionomer, and (iv) completely uncovered by ionomer [45]. Hence, to meet the activity requirements for high current production, the ionomer film distribution needs to be optimized.  
Many advanced characterization techniques and simulation methods have been used to investigate the multiscale structure of CLs [44; 50]. The studies of the CLs structure generally include but are not limited to (i) CL: the uniformity of the individual constituents in CL, the uniformity of CL thickness, surface roughness, TPB, or the interfaces of CL and membrane or CL and GDL; (ii) pore: pore size distribution, porosity, and tortuosity; (iii) agglomerates: the size, shape, or fractal dimension; (iv) ionomer: the ionomer coverage on Pt and carbon, thickness of ionomer film, ionomer connectivity, distribution of ionomer through the CL, the interaction/interface between ionomer and Pt, non-absorbed ionomer agglomerates in the macropores; (v) Pt: distribution in/on carbon, or size and shape; (vi) carbon: pore size distribution, porosity, size and shape, or surface groups (Figure 1). These would impact the physicochemical and electrochemical properties of CL and thus influence the activation, ohmic, or concentration polarization and durability of PEM fuel cells (Figure 1). The physicochemical properties mainly include effective diffusion coefficient, local gas transport resistance, local interfacial resistance between ionomer and Pt, or permeability (gas transport), capillary pressure and contact angle (water management), effective electron/proton/thermal conductivity, as well as Young's modulus, which govern the transport or mechanical behaviors of CL [44]. The electrochemical properties primarily include electrochemical surface area, mass activity, exchange current density, charge transfer number [44].