# Structured Alumina Substrates for Environmental Catalysis Produced by Stereolithography
## 2 Materials and Methods  
### Design of the Structures and Geometrical Requirements  
The closed-walls lattices were generated via a purpose-built 3D numerical tool developed in MATLAB R2019a (MathWorks, Natick, MA, USA) for the generation of periodic architectures made up of struts elements. The selected unit cell, corresponding in this case to a rotated cube (i.e., main diagonal of the cube aligned with the flow direction), was replicated in the space, forming datasets containing positions of the nodes and the connections. The produced nodes and connections were then converted into a STEP file,  
Figure 1: Schematic representation of the scattering phenomenon occurring when a ceramic slurry is invested by photons. made up of spheres (for each node) and cylinders (for each connection) with adjustable diameters [23; 24]. The lattice was then cropped into the desired shape using a commercial CAD software. Finally, the outer walls were built to close the external faces of the lattice and form a tubular architecture. Prior to the 3D printing, the geometry was converted into STL file. One of the major advantages of additive manufacturing is the flexibility in choosing the dimensions of the structure to be manufactured and used. Main characteristics are the porosity \(\varepsilon\) and the strut diameter ds. By choosing these two parameters, the surface properties of the resulting catalyst are fixed in terms of specific as well as of wetted surface area. Figure 2 shows the wetted surface of a series of additively manufactured open lattice structures in respect to state-of-the-art honeycombs. The chosen dimensions are selected from the best performing ones in a preceding work [16] where different geometrical features were compared systematically in terms of reactivity as well as of pressure drop. Looking at Figure 2, it is clear that the structure with thinner struts and lower porosity leads to higher wetted surface area, which is, however, a factor of 2 below the conventional honeycombs. In terms of reactivity, the additively manufactured structure with porosity \(\varepsilon=80\%\) and ds = 0.5 mm shows the best performance (Figure 3), closely followed by the 600 cpsi honeycomb (HC600). Since this honeycomb has three times higher wetted surface area, it requires also three times higher precious metal quantity (assuming similar dispersion of the precious metals on the outside layer of the surfaces). Interestingly, higher porosities and/or larger strut diameters directly affect the surface reactions, resulting in deficits with respect to the honeycombs, particularly at high gas velocities. Thus, efforts in additive manufacturing should focus on delivering thin struts, with a diameter of 0.5 mm and a moderate porosity of about 80%. Figure 2: Wetted surface area (S\({}_{\text{w}}\)) by the gas flow of three additively manufactured structures based on a rotated cube elementary cell (cubic 45) for different struts diameter (ds), porosities (\(\varepsilon\)), and cell size (Ls) in comparison with two state-of-the-art honeycombs (HC) with different cpsi (i.e., 400 and 600). Data source [16]. Keeping in mind the optimal configuration, in terms of geometric specifications, provided by the previous results [16], the subsequent 3D printing trials allowed us to select the optimal lattice configuration (see Figure 4) from a manufacturing point of view. To guarantee a good result in terms of printing quality and repeatability, preliminary investigations were performed to determine the minimum diameter of the struts that can be reproduced with the SLA technique employing the selected Al\({}_{2}\)O\({}_{3}\)-based slurry. Very thin struts, with a diameter of 0.20 mm, can be 3D printed (see chapter \"Results and Discussion\"), but the final sintered component is very fragile and difficult to handle. In particular, the subsequent coating with precious metals is very challenging to perform without damaging the substrate.