The drying of a drop of particle dispersion in open air on a solid substrate generates the formation of a solid deposit (i.e. dry pattern) which can take different morphologies. 1 These morphologies are influenced by several parameters such as particles concentration, particles and substrate wettability, temperature (i.e. atmospheric, substrate), relative humidity, particle "interactions" (i.e. particle/substrate, particle/particle, particle/liquid-gas interface) to name a few. [1] [2] [3] [4] Understanding the role of each parameter on pattern formation is important because this evaporative process is at the basis of a large number of coating applications 5 with a renewed activity linked, in part, to the development of inkjet printing methods that enable the fast elaboration of nanostructures over a wide variety of substrates. [6] [7] [8] The purpose of the present work is to reconsider the role of the particle/substrate interaction on the shape of final deposits when long distance repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) particle/particle interactions are maintained for most of the drying time. This aspect which has been little studied 1, [9] [10] [11] [12] [13] [14] [15] so far might become important with the emergence of (i) plasmonic applications requiring deposits with nanoscale resolution 16, 17 and no structural defects, such as cracks; and (ii) biomedical applications linking diagnosis to the shape of a deposit obtained by drying a sample of biofluid. [18] [19] [20] [21] The dynamic of particles self-assembly at the contact line during evaporation was studied at the local scale by Yan et al. 22 . They showed that attractive DLVO interaction between polystyrene microparticles (~ 800 nm in size) and a negatively charged glass substrate leads to a low mobility of the particles in the vicinity of the substrate resulting in disordered local packing, regardless of the overall shape of the final deposit. This observation shades previous results obtained by Denkov et al. 23 showing that the dynamic of two-dimensional ordering is governed by the capillary force and the convective flow, while the DLVO force between particles play no significant role. The role of the DLVO force on the macroscopic shape of the solid deposit was also studied experimentally and numerically. Bhardwaj et al. 11 considered dispersions of TiO2 nanoparticles (~ 25 nm in size) deposited on a glass substrate. They varied the particle/substrate and particle/particle DLVO forces by modifying the pH of the dispersions.
They concluded that the deposit shape is dictated by the competition among (i) the evaporationdriven flow favoring ring-shaped deposits; (ii) the DLVO interaction between particles and substrate favoring uniform deposits when attractive; and (iii) the Marangoni flow, favoring a central bump deposit with a diameter much smaller than the initial drop diameter. The respective influence of particle/particle and particle/substrate interactions on the morphology of the dry pattern was also studied theoretically by Zigelman and Manor in 2017. 24 Their model accounts for an irreversible particle adsorption onto the substrate by using the boundary-layer theory and for irreversible coagulation of particles in the bulk using the Smoluchowski relation.
They notably predict the formation of uniform deposits when the contribution of adsorption dominates that of coagulation. They underline the agreement with Bhardwaj et al.'s observations performed at low pH where coagulation is negligible due to repulsive particle/particle interactions. Overall, Anyfantakis and Baigl underline in their review, 10 that, regardless of their origin (i.e. DLVO or hydrophobic), most of existing experimental results agree on the fact that attractive particle/substrate forces promote the formation of uniform deposits. However, in the case of DLVO forces, we point out that this statement is based on few experimental studies 11,12 conducted on a single particle type at a fixed concentration using pH as a mean of controlling interactions. A disadvantage of this approach is that pH controls, at the same time, particle/substrate and particle/particle interactions, or even, the affinity of the particles for the liquid-gas interface. This multiple role complicates the analysis of one single contribution among others in the pH range around the particle isoelectric point.
Looking more generally at experiments conducted under particular drying conditions, or free-drying experiments where the role of the DLVO forces has also been described but indirectly without explicitly stating so, the effect of the DLVO forces seems unclear. For instance, Moraila-Martínez et al. 13 studied the role of particle/particle and particle/substrate interactions on the deposit formation without macroscopic evaporation using the "controlled shrinking sessile drop" method which enable to control the contact line dynamic. They considered different particles, substrates and pH for a fixed particle concentration. They observed ring-shaped deposits in all cases and they could not correlate the characteristic lengths of the deposits to the sign and magnitude of substrate/particle interactions. They concluded that the final morphology of the deposits would be driven by the particle/particle interaction rather than the particle/substrate interaction. Lee et al. studied the effects of particle size, concentrations of nanofluids and nature of the substrates on the residue patterns formed after drying Al2O3 and TiO2 aqueous nanofluid droplets. 25 They obtained ring-shaped patterns at low particle concentrations and uniform patterns at high concentrations whatever the systems except for substrates with low wettability.
In this context, we used an alternative strategy to further explore the potential role of particle/substrate DLVO forces for freely evaporating drops. It consisted in considering model substrates and particles of different nature, surface chemistry and size (in the case of particles), whereas long-distance repulsive interactions between particles were maintained at fixed pH.
This method enabled us to cover a range of DLVO forces 3 orders of magnitude higher than that investigated in previous studies. For each set of particles and substrate, we considered at least 8 particle concentrations, over 4 decades, to identify the effect of interactions in the different concentration domains.
Dry deposits were observed with a scanning electron microscope equipped with a field emission gun (i.e. SEM-FEG) to probe dry pattern shapes and structures on length scales ranging from macroscale to nanoscale. Our main result is that the different shapes of deposits obtained by modifying the particle concentration are the same in the different regimes of concentration regardless of particle/substrate interaction in the studied range of DLVO forces and particle concentrations. The second result is that, contrary to expectations, the dominant morphology of dry patterns at low particle concentration exhibits dot-like pattern for all the studied systems.
Materials. Gold (III) chloride trihydrate (HAuCl4.3H2O, > 99.99 %), trisodium citrate dihydrate (Na3C6H5O7·2H2O,  99 %), cysteamine (HS(CH2)2NH2, noted CEA, 95 %), 11-mercaptoundecanoic acid (HS(CH2)10CO2H, noted MUA, 98 %), α-lipoic acid (C8H14O2S2,  99 %) and silicon wafers ⟨111⟩ were purchased from Sigma-Aldrich and used as received without further purification. Aluminia coated silica nanoparticles Klebosol ® 30CAL50 (noted SiNP + in the following) were purchased from Merck. Silica nanoparticles Snowtex ® ST-OL (noted SiNPin the following) were a gift from Nissan Chemical Industries Ltd., Tokyo, Japan. All the content of a gold salt powder batch was used at the first opening to prepare, using a glass spatula, a mother solution at 10 g/L in milliQ water that was stocked for periods not exceeding 3 months in a dark area to minimize photo-induced oxidation. The same batch of trisodium citrate has been used for all syntheses; it has been stored in desiccators after first opening. All glassware and teflon-coated magnetic bars were washed thoroughly with freshly prepared aqua regia and rinsed with milliQ water after each synthesis. All solutions were prepared with milliQ water (R = 18.2 MΩ).
Synthesis of Gold Nanoparticles. The citrate stabilized gold nanoparticles were synthesized by Turkevich reaction, following a reported procedure. 26, 27 Briefly, 97 mg of trisodium citrate (0.33 mmol) were put in 150 mL of water (2.2 mM solution) and refluxed for 15 min, before adding 1mL of a 10 g/L solution of HAuCl4.3H2O. The solution was kept on reflux for 10 min, then the heating was stopped and the solution was slowly cooled down to 90 °C, leaving the reaction mixture in the oil bath. The seeds had their size increased by repeating several growing cycles as followed: 55 mL of the solution were withdrawn, followed by the addition of 53 mL of water and 1mL of a 60 mM citrate solution. As soon as the temperature reached 90 °C again, 1 mL of HAuCl4.3H2O were added and the solution was stirred for 30 min. Then, another portion of 1 mL of HAuCl4.3H2O was added and the solution was stirred again for 30 min.
These growing cycles were repeated up to the desired size of AuNPs. Typically, 3 cycles were required to obtain 25 nm (diameter) particles.
Citrate replacement by 11-mercaptoundecanoic acid (MUA) was achieved in two steps by adapting a protocol from literature. 28 The positively charged substrates were obtained by immersion of the surfaces in an ethanolic solution of cysteamine (10 mM) for 3h, whereas the negatively charged substrates were immerged in an aqueous solution of MUA (10 mM) for 12h. The positive (respectively negative) substrates were then sonicated in ethanol (resp. water) to desorb the non-grafted molecules and rinsed in ethanol then water before being dried under nitrogen flow. RMS roughness was typically of 1.6 nm for the gold surfaces, and 2.8 nm for MUA or CEA-gold surfaces (see AFM images 15x15µm² in Figure S3 ).
Drop Deposition and Drying. Deposition of the nanoparticles was done by careful dropping 0.5 µL of each solution on a horizontal substrate using a manual micropipette or an automated syringe pump (i.e. Krüss DSA 100 set-up). The deposition was carried out either in the cleanroom (25 °C, 40 % of relative humidity) or using the same device used for the contact angle measurements, giving identical deposited patterns and drop sizes with respect to the volume used.
Atomic force microscopy (AFM) images were recorded with an NT-MDT Solver proequipment. AFM topography was performed in the intermittent contact mode with standard silicon cantilevers. Image analysis was achieved with the free software WSxM. 32 Surface Profilometry. Height profile measurements of the dried patterns were performed using a mechanical profilometer Dektak 150.
Static contact angles were measured under ambient conditions (at 20°C and 40% relative humidity) analyzing the drop profile of sessile drops. A 10 μL droplet of milliQ water was deposited on the sample surface using a Krüss DSA100 apparatus (Germany) equipped with a CCD camera and an image analysis processor. Three droplets were analyzed on different locations on each sample.
The reported values are the averages of these measurements for each kind of surface (see Table S1 -S5, Figure S4 ). 
images of the deposited nanoparticles were obtained using a SEM-FEG Zeiss Merlin Compact with a resolution of  2 nm at 10 kV. All images are displayed without any post processing.
Calculation of the DLVO force between a nanoparticle and the substrate. The electrostatic double layer force ( . ) between a spherical particle (radius and surface potential ) and a flat substrate (surface potential ), separated by a layer of electrolyte aqueous solution (Debye length − ), of thickness , has been estimated using the expression 33 :
where Z (in J.m -1 ) stands for the interaction constant defined for monovalent electrolyte at 25 °C by:
Where 0 is the total permittivity of the water, is the Boltzmann constant, is the temperature, the electronic unit charge. All of the suspensions under scrutiny contained a small amount of ionic additives (i.e. Na + for SiNPand AuNP -, Clfor SiNP + ) at  35 mM in the stock solutions. In our experiments the stock solutions were diluted with milliQ water so that the initial concentration of ions varies together with the initial concentration of particles:
, mM ≲ 11 for 10 -2 ≲ [NP], g/L ≲ 100. As a consequence, −1 varied between 300 nm and 3 nm, before drying, in the investigated range of particle concentration assuming that these ions are the only contributors to −1 . For the calculation we considered that −1 ( ) ≈ 0.304 √[ions] ⁄ for 1:1 electrolytes at 298 K. 33 The van der Waals force ( . ) between a spherical particle (radius ) and a flat substrate, separated by a layer of thickness , has been calculated using the expression:
With H, the non retarded Hamaker constant for a particle interacting with the substrate across water at room temperature. Negative force implies attraction.
The particle/substrate DLVO force is the algebraic sum of the van der Waals and the electrostatic forces:
= . + . . The evolution of κ -1 and , calculated at t0 for D = κ -1 , with the initial particle concentration is plotted in the Figure 1 . We underline that the expression (1) used for the calculation of . is obtained with the weak overlap approximation which is accurate for surface separations beyond about κ -1 . 33 The choice to work at the limit of 
+1.410 -3 /+0.14 -0.710 -7 /-0.06 +1.410 -3 /+0.08 53 Table 1 . Nanoparticles (NP) and Substrates (Sub) used in this study with their acronym and main characteristics: particle radius measured by SEM-FEG (R, see figure S1 and S2), particle surface potential (ΨP.) assumed to be equal to the zeta potential knowing that this is an underestimation, substrate surface potential (ΨS.), Hamaker constant Particle/Water/Gold (Hin water), electrostatic double layer force (FEl.), van der Waals force (FvdW.), DLVO force (FDLVO) and equilibrium contact angle averaged on the different concentrations (Θ, see Table S1 -S5 and Figure S4 ). We indicate the minimum/maximum forces that have been calculated before drying (t0) for D = κ -1 at the initial minimum/maximum particle concentrations respectively. The evolution of κ -1 and with the initial particle concentration is plotted in the Figure 1 . For comparison, FDLVO considered in reference [9] , calculated in the same way, ranged between -0.02 nN and + 0.13 nN. Negative force implies attraction. The energies corresponding to the potentials of interaction and Hamaker constants used for calculations are given in the table S13 and S14 respectively of S.I.. 
Influence of particles concentration and FDLVO on the dry pattern for SiNP + /AuSub + .
We first investigated dry patterns obtained with cationic gold substrates (AuSub + ) and
cationic silica particles (SiNP + ) with initial concentrations varying over 4 decades between 0.01 g/L and 100 g/L (i.e. 4.10 -4 ≤ Φvol. (%) ≤ 4). We placed 0.5 μL of the drops on the gold substrates, and we observed the patterns after complete drying with tdrying ≈ 15 min. In this case study, the particle/substrate interaction is always repulsive with FDLVO ranging between +4.7×10 -3 and +0.44 nN with the initial particle concentration at a separation distance corresponding to the Debye length (Table 1, Figure 1 ). For clarity, in this part, we will mainly discuss the observed effects with reference to the concentration. The effect of FDLVO will be more specifically discussed in the following section where we will consider the different particle/substrate associations. (Table S11 ) and the deposition height from the surface (Table S12 ). This model predicts a square root dependence of w with the initial volume fraction, as ⁄ ∝ ( ⁄ ) 0.5 with ρ the particle packing fraction. 41 We underline that the width of the ring does not respect the power law evolution at the beginning of the intermediate domain and sometimes also in the dilute domain. Qualitatively, the power law evolution indicates that NPs accumulate in greater quantities near the triple contact line during the first 80% of the evaporation time when the initial particle concentration is increased. When the height of the external ring is large enough, for [SiNP + ]t0 ≥ 0.5 g/L, we observe cracks at fairly regular intervals with a radial orientation (Figure 4c ). This radial orientation agrees with our low charge screening condition. 43 We underline the presence of secondary ortho-radial cracks connected to the main radial crack pattern at the two lowest concentrations for which the system must relax stress more frequently. The crack spacing measured on the outside circumference line (noted d, see Figure 4c ) increases with the particle concentration and, as a consequence with w, in a linear manner (Figure 4b ). This result agrees with previous w d studies 44, 45 assuming that the height and the width scale in the same manner with concentration. 41, 42 Overall, this first part of the study allowed us to identify original patterns (i.e. dot-like patterns and a central thick ring with fine satellite rings) in the dilute domain and to retrieve several known results at higher concentrations, which assures us of the method robustness.
We continued by examining more specifically the influence of NP/Sub DLVO force on the dry pattern morphology in the different concentration regimes identified in the previous section. This work was carried out considering three types of particles and three types of substrates (see Table 1 dominates the pattern formation. Moreover, we observed that the addition of salt, as low as 10 mM ( Figure S10 and S13), induced the formation of uniform deposits mixing particles and salt crystals instead of ring patterns whatever the system. This shows that the pattern morphology can be easily modified by a screening of NP/NP interactions. A study taking into account the contribution of this dimension would be relevant in the future given the screening conditions encountered in biofluids or just in buffered media.
We then conducted a more quantitative study on certain characteristic lengths of the structures formed. We first considered the relation between the width (w) of the thick ring, observed in the intermediate domain of concentration, and the particles concentration ( Figure   7a ). In all cases, w increases as power law with an exponent close to the expected square root dependence. From this figure it is also clear that the power laws are identical for a given type of particle whatever the substrate and thus, whatever the NP/Sub DLVO force. Interestingly, slight variations were observed between the different set of particles suggesting that the power law could be influenced by the particle size as illustrated in Figure 7a where data from Deegan 41 and Brutin 36 were added for comparison. It may reflect the influence of NP/NP interaction and/or polydispersity on the particle packing (i.e. heterogeneity between the layers). These effects appear credible in the light of past studies. 40, 46 We then studied the cracks for the different combinations of particles and substrates with the exception of the gold particles for which we were unable to probe regimes sufficiently concentrated in particles to have outer rings of sufficient thickness for the cracks to appear. At high concentrations, typically for [SiNP]t0 ≥ 0.5 g/L, the external rings have cracks similar to those described in the previous section whatever the combination of particle and substrate ( Figure S14 ). We did not observe a significant difference in the shape of the cracks from one system to the other with predominantly radial patterns and an increasing proportion of secondary orthoradial patterns moving towards low concentrations (i.e. low thicknesses). In all cases, a linear relation exists between the crack spacing, d, and the width, w, of the external ring ( Figure 7b ). The relations are clearly different for the same type of particle depending on the substrate. Nevertheless, this effect does not seem to be correlated to the NP/Sub DLVO force but more to the nature of the substrate. Thus, films deposited on the anionic substrates must relax stress less frequently than films deposited on the cationic substrates (i.e. lower d for same w for films on AuSubthan for films on AuSub + ). We do not have a clear explanation for this result since the equilibrium contact angles are globally the same on these two surfaces.
Finally, we also considered the drying of aqueous drops containing cationic or anionic gold nanoparticles (see Table 1 ) on different substrates. In general, the contrast of the images (i.e. gold on gold) and the small size of the particles complicate the observations as shown in Figure S15 . Nevertheless, it appears that the succession of the different deposit morphologies with particle concentration is roughly the same as for silica. A particularity of gold particles is that, in diluted or even semi-diluted regime, they are deposited in the form of small clusters of nanoparticles forming monolayer islands and rarely in the form of a single dot. This may reflect an eventual contribution of the van der Walls force which is greater for gold particles compared to silica particles (see Table 1 ). Overall, the most striking feature of this second part is that, contrarily to expectations from previous studies dedicated to DLVO interaction, the different shapes of deposits obtained by modifying the particle concentration are the same in the different regimes of concentration regardless of particle/substrate DLVO interaction in the studied range of forces and particle concentrations. Slight effects could be detected on characteristic lengths (i.e. w/r, d) from one system to another but without a clear relation with DLVO force. These results are consistent with the observation of Anyfantakis et al. 47 that the morphology of the dry deposit is mainly determined by interactions between particles in the mass, whereas, in their case, they studied the influence of particle wettability and concentration on the shape of the deposit.
In this last part, we focus on the mechanism of pattern formation at low and high particle Our main result is that the different shapes of deposits obtained by modifying the particles concentration are the same regardless of particle/substrate interaction in the studied range of DLVO forces and particle concentrations.
The second result is that, contrary to expectations, the dominant shapes of deposits at low particles concentration is dot-like patterns for all the studied systems. Zooming into the dot, it appears that they are a continuous domain of particles compacted in a monolayer. We show that this structure results from a stick-slip evaporation process.
We believe that our results and methodology pave the way toward a better understanding of 