## 2 Thin and Structured Coatings of Densely Packed \(\mathrm{CeO_{2}}\) Nanoparticles
### Convective Self-Assembly  
CSA has been extensively used to deposit a variety of objects (from molecules [15] to large colloids [6]) into homogeneous thin coatings on relatively large scales (tens of cm\({}^{2}\)). It is possible to control the thickness and to some extent the morphology of the coating via process parameters such as the casting velocity, the concentration of the stock solution [16], temperature, humidity, etc., but also to couple the reaction to the deposition process, for instance for sol-gel coatings [17], and finally to stop and re-run the process (stop-and-go), in order to add more structure to the deposit [18]. Here, we use the simplest version of CSA, namely a continuous and slow deposition of a dispersion at constant volume fraction \(\phi_{0}\) at room temperature and with no specific control of the atmosphere (the room in which we work is nevertheless air-conditioned with a constant temperature 21 \({}^{\circ}\)C and relative humidity \(\approx\)0.5). The air flow over the evaporating zone is not controlled and is left to natural convection; it has been demonstrated that for the deposition colloids and unlike the case of polymers, it is _not_ a crucial parameter [7]. The only control parameter we use is the casting velocity \(v\); we deposit the same grade of \(\mathrm{CeO_{2}}\) nanoparticles with batches coming at two different typical sizes: \(\approx\)4 and \(\approx\)40 nm (average diameter, see Section 4.1). The overview of our deposition campaigns is summarized in Figure 1 with the coating thickness, the morphology of the coatings, and their optical appearance. In the velocity range of deposition we studied (\(v<100\,\mathrm{\SIUnitSymbolMicro m.s^{-1}}\)), the decreasing trend of \(h\) against \(v\) is a clear signature of the CSA regime and with a comparable behaviour for the two sizes of nanoparticles studied here; it contrasts with the Landau-Levich regime where \(h\) is expected to scale like \(h\sim v^{2/3}\)[15]. However, the coating is not always homogeneous and flat, see Figure 2 top and the grey and blue zones in Figure 1, bottom left. Instead, for the large particles and at low deposition velocity (\(\mathrm{v}\lesssim 40\,\mathrm{\SIUnitSymbolMicro m.s^{-1}}\)) the coating exhibits thickness oscillations. Notice this is definitely not stick-and-slip [19] but instead oscillations around a mean (non zero) thickness with no return to the bare substrate. At even lower velocity (\(\mathrm{v}\lesssim 10\,\mathrm{\SIUnitSymbolMicro m.s^{-1}}\)), the coating delaminates, probably because it becomes thick, tough and brittle [20]. For the small-size particles, we observe only thickness oscillations below \(\mathrm{v}\lesssim 10\,\mathrm{\SIUnitSymbolMicro m.s^{-1}}\) (blue zone in Figure 1, bottom left). The same data can be re-scaled using a simple mass-conservation assumption (Equation (3) simply states that all the particles coming from the bulk reservoir are accumulated into the final deposit via evaporation), that takes into account both the initial and final volume fractions, \(\phi_{0}\) and \(\phi_{c}\) respectively. Using \(\phi_{c}=0.61\) a value that we obtained from ellipsometry, which is in agreement with a close packing of a polydisperse hard-sphere [21], the data reasonably collapse and follow the expected trend \(h\sim v^{-1}\) indeed. In all cases but the ones where the coatings delaminate, the coated substrate appears perfectly transparent with no visible effect of surface undulations and no haze (upper inserts in Figure 1), even though optical microscopy reveals the defects (Figure 2 top). Low resolution scanning electron microscopy (SEM) of the surface of some samples may show evidence of the granulometry of the particles (Figure 2 bottom left) but a cross-section of a selected sample demonstrates a beautiful, flat, and large-scale structure (Figure 2 bottom right). Figure 1: (**Left**): Thickness of coatings of \(\mathrm{CeO_{2}}\) nanoparticles deposited at different coating speeds \(v\); each point averages at least seven independent experiments.