## 2 Thin and Structured Coatings of Densely Packed \(\mathrm{CeO_{2}}\) Nanoparticles
### Microfluidic Pervaporation  
Microfluidic pervaporation is a templated self-assembly method [22] where a PDMS mould--the template--is used to guide the growth of a solid made of nanoparticles. In turn, the template also serves as a pump via the pervaporation mechanism described more in detail in Section 4.2. The process is self-powered: We fill the microfluidic template with a dilute dispersion and pervaporation extracts the solvent, which in turn concentrates the dispersion until a solid nucleates, which then progressively grows. It can be a long process as the growth velocity \(v_{g}\) can be understood on a simple volume conservation assumption, very similar to Equation (3): \(v_{g}\sim v_{e}\phi_{0}/(\phi_{c}-\phi_{0})\) where \(v_{e}\) is an evaporation velocity associated with the pervaporation mechanism [12; 23]. It offers little flexibility as it is mainly governed by the geometry of the template, i.e., surface exchange for pervaporation, yet the growth velocity is still largely tunable via \(\phi_{0}\). We typically see \(v_{g}\approx 0.2\,\upmu\)m.s\({}^{-1}\) which permits us to fill the entire length of the template in about one day. It is slow mostly because the stock solution is dilute, \(\phi_{0}\approx 1\%\), and much slower than CSA (\(v\approx 10^{1}-10^{2}\,\upmu\)m.s\({}^{-1}\), Figure 1) because the evaporation proceeds across the PDMS template, not directly in air.  
In general, the solid we obtain nicely replicates the shape of the mould [13]. However, we discovered fairly recently that there are cases where the solid significantly deforms the template during its growth [24]. It is likely due to a poro-elastic mechanism related to the depression generated inside the material, originating from the suction mechanism during the evaporation-induced growth [25].  
We deliver here the very same observation: Whereas the mould has a nominal thickness of \(\approx\)3 \(\upmu\)m, the final material barely reaches h \(\approx\) 300 nm, see Figure 3. We understand it on the basis of the small  
Figure 2: (**Top**): Representative optical microscopy images (bright field) for the coatings deposited at different deposition speeds using CeO\({}_{2}\) sols with nanoparticle size of 4 nm (first row) and 40 nm (second row); the morphologies of the coating are either with thickness oscillations and possible delamination, or flat (see also Figure 1 left). (**Bottom**): Scanning electron microscopy (SEM) (SEM-FEG HR JEOL 6700F) images of (**A**) the surface of coatings deposited at different speeds using CeO\({}_{2}\) sols with nanoparticle size of (top) 4 nm and (bottom) 40 nm and (**B**) of a cross-section of a coating deposited at 20 \(\upmu\)m.s\({}^{-1}\) (40 nm particles).  
size of particles, here \(\approx\)4 nm, which generates a massive pressure drop inside the material during the growth of the solid upon evaporation that tends to collapse the soft PDMS template. It is somewhat disappointing as we targeted thick deposits, but the final material turns out to be fairly flat (Figure 3). Altogether, this method mainly leads to arbitrarily structured coatings which are impossible to obtain with CSA only and where the structure could bring some additional function.