# Rheology and Structure of Ceramic Stereolithography Slurries: Role of Powder Nature, Dispersant and Orthogonal Strain

Sylvain Fournier, Jérôme Chevalier, Helen Reveron, William Chèvremont, Guilhem Baeza

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Sylvain Fournier, Jérôme Chevalier, Helen Reveron, William Chèvremont, Guilhem Baeza. Rheology and Structure of Ceramic Stereolithography Slurries: Role of Powder Nature, Dispersant and Orthogonal Strain. Journal of the American Ceramic Society, In press, 10.1111/jace.20304. hal-04849714

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# Rheology and Structure of Ceramic Stereolithography Slurries: Role of Powder Nature, Dispersant and Orthogonal Strain

Sylvain Fournier<fnref n="1" /> | Jérôme Chevalier<fnref n="1" /> | Helen Reveron<fnref n="1" /> | William Chèvremont<fnref n="2" /> | Guilhem P. Baeza*<fnref n="1" />

## Correspondence

Guilhem Baeza, INSA Lyon, Université Claude Bernard Lyon 1, CNRS, MATEIS, UMR5510, Villeurbanne, 69621, France.
*current address is : Université Jean Monnet, CNRS, UMR 5223, Ingénierie des Matériaux Polymeres, F-42023 Saint-Etienne Cedex
Email: guilhem.baeza@univ-st-etienne.fr

## Funding information

This work results from a PhD thesis founded by the French Ministry of Higher Education and Research. This work has also been partly funded by a public grant from the French National Research Agency (ANR) under the "France 2030" investment plan, which has the reference EUR MANUTECH SLEIGHT - ANR-17-EURE-0026.

We investigate the rheological properties of ceramic slurries designed for laser stereolithography manufacturing in relation to their formulation, including the powder morphology, their volume fraction and the concentration of dispersing agent. By combining dynamic strain sweep and Small-Angle X-ray Scattering (SAXS) experiments, we first illustrate that slurry viscosity follows an exponential trend with increasing particles content, with steeper increase observed for more aggregated particles. We then show that increasing the dispersant concentration up to an optimal value decreases slurry viscosity, as SAXS measurements reveal a reduction and homogenization in agglomerate size. Finally, we evidence that applying vertical oscillatory deformation during steady shear flow induces fluidization of the slurry. The shear viscosity exhibits a time-strain rate equivalence, enabling the generalization of this effect across a wide range of formulations. This methodology holds potential for industrial applications, where introducing vibration perpendicular to the scraping blade motion could improve the surface quality of the spread slurry prior to polymerization.

## KEYWORDS

Stereolithography, Rheology, Dispersant, Slurry, Zirconia

<footnote n="1">¹INSA Lyon, Université Claude Bernard Lyon 1, CNRS, MATEIS, UMR5510, Villeurbanne, 69621, France</footnote>

<footnote n="2">²ESRF, The European Synchrotron, 71 Avenue des Martyrs, CS40220, 38043 Grenoble Cedex 9, France</footnote>
# 1 | INTRODUCTION

The challenge of printing structural ceramics consists of producing objects of complex geometries endowed with a high final density implying a limited number of as small as possible defects¹:² ensuring good mechanical properties and long-term reliability. Among the wide variety of ceramic Additive Manufacturing (AM) processes, photopolymerization-based techniques can achieve a dimensional accuracy comparable to those obtained through more traditional processes (e.g., pressing and subtractive machining), while satisfying the high density requirement. Currently, the industrially most developed photopolymerization printing methods are Digital Light Processing (DLP) and Stereolithography (SLA), which are based on layerwise recoating and pattern polymerization of the ink using near-UV radiation. The recent availability of commercial lab-scale handy SLA and DLP printers opens opportunities to develop lab-madeprintable ceramic inks from any powder³. Yet, because of the long processing duration and cost of these AM processes, as well as the amount of parameters impacting the final result, optimizing an ink formulation remains quite challenging.

In particular, the ink formulation must be adapted to the recoating step settings of the printing process, which consists of stacking ink layers while limiting the presence of defects inbetween. The layer height is usually set at 20 µm to 100 µm³:⁴ to maximize spatial resolution while optimising the printing time that also depends on the scraper blade speed resulting in shear rates up to $\dot{\gamma}_{SLA} = 10^2 s^{-1}$ for paste printers⁵:⁶, and $\dot{\gamma}_{DLP} = 10^3 s^{-1}$ for liquid-like slurries printers⁷. The process geometry is sketched in Fig.1.

<figure><img src="image_3.png" /><figcaption>**FIGURE 1** Schematic representation of a scraper blade on a typical photopolymerization-based printer</figcaption></figure>

To ensure the accurate spreading of the ink, a rheological optimisation study is generally conducted on several formulations, but is often limited to finding a tradeoff between the viscosity measured at the processing shear rate, the solid loading and the amount of dispersant⁸:⁹:¹⁰:¹¹. However, single viscosity measurements do not provide information about crucial phenomena like shear-thinning that helps to form homogeneous ink layers or shear-thickening that conversely leads to major spreading defects. Hence, a more complete rheological characterization is required, including: 1) flow curves providing the slurry viscosity on a range of shear rates¹²:⁶, 2) steady shear tests that are truly representative of the scraping that occurs during SLA and DLP printing⁶:¹³, and 3) oscillatory shear measurements that enable a deep characterization of energy storage and dissipation mechanisms both at equilibrium and under large amplitude deformation¹⁴. It is to note that while flow curves tend to mask potential flow inhomogeneity causing de-
fects, oscillatory rheometry is efficient to measure shear-thickening severity and the strain amplitude range at which it occurs<sup>15</sup>. Systematic rheological characterization notably demonstrated that shear-thickening was highly dependent on inorganic particles features such as solid loading<sup>16</sup>, size distribution<sup>17</sup>, shape<sup>18</sup>, roughness<sup>19</sup> and dispersion state,<sup>8,20</sup> further emphasizing the importance of structural characterization. Beyond inorganic particles and dispersing molecules, photopolymerizable inks also contain fast branching monomers (usually multifunctional acrylates)<sup>3,21</sup> and a low concentration of photoinitiators<sup>22</sup> that however have a limited impact on the ink rheology. Conversely, additives such as plasticizers can more significantly alter the slurry rheology<sup>23:24</sup>. For instance, converting a liquid slurry into a viscoelastic solid can better align with printer specifications, as is the case with thick suspensions required for ADMATEC systems<sup>25</sup> or paste formulations suited for various 3DCERAM Sinto printers.

While the majority of recent studies dealing with rheological characterizations of SLA-relevant slurries focus on the optimization of viscosity at the maximal process shear rate<sup>26:27</sup>, the aim of the present work is to systematically correlate their rheological properties with their microstructure and their processing conditions to enhance our fundamental understanding of the phenomena at stake. The first section is dedicated to the influence of the ceramic particles' size, shape, roughness and maximal solid loading on the slurry viscosity where a deep morphological characterization of two yttria-stabilized zirconia powders is conducted by combining Scanning Electron Microscopy (SEM) and Small-Angle X-ray Scattering (SAXS). The second section focuses on the role of dispersing molecules on the particles aggregation occurring in high solid loading slurries and its direct consequences on their rheological properties. The third section addresses the peculiar case of a multiaxial strain, allowing to evaluate the *fluidization* effect implied by the addition of an oscillatory deformation in the orthogonal direction during a steady shear experiment. This approach reveals a time-orthogonal strain rate equivalence of the viscosity, possibly helping to further improve the SLA process.

## 2 | EXPERIMENTAL PROCEDURES

### 2.1 | Materials

A commercially available yttria-stabilized zirconia powder (ZrO₂ with 3 mol.% of Y₂O₃) TZ-3YSE (TOSOH, Japan), denoted TOSOH hereafter, was used as a starting raw material. It exhibits a low specific surface area (SSA = 6.7 m²·g⁻¹)²⁸, which optimizes its flowability, and contains a small fraction of alumina (Al₂O₃) to facilitate sintering²⁹. These characteristics make it a good candidate for photopolymerization printing as reported in refs ³⁰;³¹;³²;³³. A second zirconia-based powder extracted from a commercial stereolithography paste (3Y-F01, 3DCERAM Sinto, France) by pyrolisis at 600 °C was also used for comparison. This powder is denoted YZCP, standing for Yttria doped Zirconia from Commercial Paste, hereafter. It is also made of ZrO₂ with 3 mol.% of Y₂O₃. Both the powders characteristic dimensions provided by TOSOH and the ones determined by us are reported in Table 2.

A dispersant adapted to non-aqueous media, namely Disperbyk-111 (BYK-Chemie GmbH, Germany), denoted BYK hereafter, was added to the pastes formulation. It is a phosphoric acid ester that can bind to the -OH groups present onto zirconia particles surface through its phosphate anchoring head, while its polymer tail works as a steric repelling agent<sup>34;35</sup>. Its effect on the rheological behavior of slurries comes from its ability to decrease the dimension of agglomerates and to limit frictional contacts between adjacent nanoparticles and aggregates.

Acrylate monomers: 1,6-Hexanediol Diacrylate (HDDA) and Pentaerythritol Tetraacrylate (PPTTA) (Sigma Aldrich, UK), represent most of the organic phase of the slurries. The plasticizer used in this work was PolyEthylene Glycol
(PEG) with a molecular weight of 400 g.mol⁻¹ (Sigma Aldrich, UK) denoted PEG400 hereafter.

2-Benzyl-2-(dimethylamino)-1-[4-(morpholinyl) phenyl]-1-butanone (also called Irgacure 369 or PI369) was chosen as a photoinitiator. Because we demonstrated that 1 wt.% of PI369 had no effect on the rheological behavior of the slurry³⁶, all the rheology experiments were conducted with PI-free slurries to simplify the pastes preparation and avoid any risk of dark polymerization.

## 2.2 | Methods

### 2.2.1 | Slurry preparation

The preparation of stereolithography inks included powder functionalization with dispersant molecules, the preparation of the organic phase, and their mixing. All the slurries were made of 70 wt.% HDDA, 10 wt.% PPTTA and 20 wt.% PEG400. They differed by their solid loading, powder nature, amount of dispersant and dispersion technique, as reported in Table 1. The BYK content, is expressed as the mass of dispersant per unit area of particle surface (mg.m⁻²), BYKload = wBYKSSA, where SSA is the specific surface of the powder, and wBYK is the weight fraction of dispersant with respect to the powder.

<table><caption>TABLE 1 Composition of the slurries and processing conditions.</caption><thead><tr><td>Φ (vol.%)</td><td>Powder</td><td>BYK<sub>load</sub> (mg.m<sup>-2</sup>)</td><td>Dispersion technique</td><td>Relevant section</td></tr></thead><tbody><tr><td>45</td><td>TOSOH</td><td>3.0</td><td>regular</td><td>Reference (all sections)</td></tr><tr><td>40 to 50</td><td>TOSOH</td><td>3.0</td><td>regular</td><td>Section 3.2</td></tr><tr><td>40 to 52</td><td>YZCP</td><td>3.0</td><td>regular</td><td>Section 3.2</td></tr><tr><td>40</td><td>TOSOH</td><td>0 to 6.0</td><td>asymmetrical</td><td>Section 3.3</td></tr><tr><td>40</td><td>TOSOH</td><td>0.6</td><td>asymmetrical</td><td>Section 3.4</td></tr></tbody></table>

To maximize the particle functionalization, two different methods of dispersion were tested, see Fig.2 and Supplementary Information section S-1 for more details. For asymmetrical and regular planetary ball-milling procedures, the same mass of ethanol, milling media (2 mm diameter zirconia Mg - PSZ balls), and powder were used. Fast asymmetrical planetary ball milling was conducted with a Speedmixer (Hauschild GmbH & Co.KG, Hamm, Germany) at 1750 rpm for 2 min using polypropylene grinding jars. Regular planetary ball milling consisted of a more classical mixing step with two parallel axes. Rotation speed was set to 250 rpm for 20 min with a direction change every minute. A zirconia jar was used in a ball milling Retsch S100 equipment (Retsch GmbH, Germany). Following the dispersion procedure, the obtained suspension were centrifugated at 7000 rpm for 10 min in a Rotina 380 equipment (Hettich GmbH, Germany). The particles sediment was retrieved at the bottom of the centrifugation tubes and dried in an oven at 70 °C for 1 h until no ethanol remained. Manual grinding was then performed with a mortar to reduce the size of the largest agglomerates.

The organic compounds of the slurry were first mixed by magnetic stirring for 10 min. Subsequently, the organic mix was agitated by the fast asymmetrical planetary device at 2000 rpm for 2 min to obtain a homogeneous organic phase. The functionalized, dried, and ground powder was then added to the organic blend and mixed in a polypropylene jar at 1500 rpm for 2 min using the fast asymmetrical planetary device. For slurries with high solid loading or low
dispersant concentration, the powder was incorporated to the organic mix in two steps, each followed by a 2 min mixing period to ensure homogeneity while minimizing temperature increase. This precaution was taken to prevent damage to the jar, which could lead to the formation of polypropylene debris, and to limit the degradation of the organic compounds. Note that prior to their functionalization, a pre-processing step of pyrolysis at 600 °C was conducted to extract the YZCP powder from the commercial paste. We detail this process in Supplementary Information S-2 where a comparison with an alternative extraction method based on centrifugation is included.

<figure><img src="image_4.png" /><figcaption>**FIGURE 2** Preparation route of stereolithography slurries. The top and bottom rows respectively refer to the separated preparation of the powder and the organic phase before their mixing.</figcaption></figure>

### 2.2.2 | Rheometry

A stress-controlled MCR-301 rheometer (Anton Paar, Austria) equipped with a stainless-steel cone-plate geometry (diameter 25 mm, angle: 1°, truncation: 51 µm) was used for all the shear tests not requiring orthogonal superposition. The sample temperature was controlled by a Peltier plate system ensuring 20.0 °C ± 0.1 °C. The experiments and pre-conditioning steps conducted with this rheometer were either oscillatory shear measurements consisting of *Dynamic Strain Sweeps* (DSS) or steady shear measurements. In the latter case, we either used a constant shear rate (*Start-up*) or varied it in a progressive way to obtain *Flow Curves*.

After loading the slurry, a preconditioning shear step was applied either through 1) a DSS from $\gamma = 10^{-5}$ to $10^1$ at $\omega = 10 \text{ rd.s}^{-1}$, bringing the sample to the *oscillatory sheared state*, or 2) a steady shear of 15 s at $\dot{\gamma} = 130 \text{ s}^{-1}$, which approximates the shear rate experienced by the paste in our SLA process ($\dot{\gamma}_{SLA}$), followed by a relaxation period of 300 s, bringing the sample to the *steady sheared state*, as established in our previous work$^6$. DSS measurements were performed with increasing the strain amplitude for samples tested from the *steady sheared state* whereas they were performed with decreasing the strain amplitude when starting from the *oscillatory sheared state*. Flow curves were performed from $\dot{\gamma} = 10^1 \text{ s}^{-1}$ to $10^{-3} \text{ s}^{-1}$.

A strain-controlled ARES-G2 rheometer (TA Instruments, USA) equipped with an open bottom double-wall concentric Couette geometry was used for Orthogonal SuperPosition (OSP) rheology experiments. The geometry was thoroughly described by Tao *et al.*$^{37}$. The measurements were operated at the classical distance of 8 mm between the bottom of
the bob and the bottom of the cup. The preconditioning step performed with the OSP device consisted of measuring a flow curve from $\dot{y} = 3.2 \text{ s}^{-1}$ to $10^{-4} \text{ s}^{-1}$. Flow curve experiments with constant orthogonal Vibration (FCV) were performed from $\dot{y} = 1 \text{ s}^{-1}$ to $10^{-3} \text{ s}^{-1}$. The impact of the vertical strain amplitude $\epsilon$ and the vertical pulsation $\omega_{\perp}$ were respectively explored from $5 \times 10^{-3}$ to $5 \times 10^{-2}$ and from $1 \text{ rd. s}^{-1}$ to $10^2 \text{ rd. s}^{-1}$. The OSP geometry induces a non-uniform shear rate distribution over its annular cross-section, which tends to overestimate the shear viscosity of our inks. Therefore, the shear viscosity measured in the rotational direction was corrected through the primary end-effect factor $c_L^{FC}$ such as $\eta_{OSP\parallel} = \eta_{OSP\parallel(recorded)} / c_L^{FC}$. The Flow Curves recorded with the OSP setup overlapped the ones recorded with the cone-plate geometry for $c_L^{FC} = 2.19$. We refer the reader to our previous article$^6$ for a more in-depth description of the device, preparation, and testing procedure, and to Supplementary Information S-3 for symbols definition.

### 2.2.3 | Microstructural and chemical characterization

(Ultra) Small Angle X-ray Scattering (U)SAXS measurements were conducted on the Time Resolved Ultra Small Angle X-ray Scattering (TRUSAXS) Instrument of ESRF (The European Synchrotron - Grenoble, France; beamline ID02). 70 µm thick layers of ($\Phi = 40$ vol.% of TOSOH powders) slurries sandwiched between Kapton tape sheets were analysed at three sample-detector distances (1 m, 10 m and 31 m), resulting in a scattering vector modulus range spanning $3 \times 10^{-3} \text{ nm}^{-1} < ||\vec{q}|| < 3.5 \text{ nm}^{-1}$. Beam energy had to be high enough to overcome the zirconia X-ray absorption while avoiding its absorption bands, which led to choose a photon energy of 17 keV, just below the adsorption edge of Zr. Sets of ten scattering acquisitions of 200 ms separated by 100 ms were averaged for each measurement. The same beam settings were applied to characterize 1 vol.% dispersions of TOSOH and YZCP powders functionalized with $3.0 \text{ mg.m}^{-2}$ dispersant in ethanol. In this case, 1 mm diameter capillary tubes were used to conduct the experiments.

Ceramic particles were observed with a SEM (Zeiss SUPRA VP55, Switzerland) at $5 \times 10^4$ magnification and a ca. 5 mm working distance. These non-conducting particles were observed in low voltage conditions with 2 kV. Particles' "equivalent spherical diameter" $d_A$ distribution was obtained from image analysis performed with ImageJ (National Institutes of Health, USA) through the measurement of the apparent particles contours on at least 200 particles. $d_{50}$ is the median value of $d_A$$^{38}$ (see Supplementary Information S-4).

# 3 | RESULTS AND DISCUSSION

## 3.1 | Powders characterization

Fig.3a presents SEM micrographs of TOSOH and YZCP powders. The TOSOH powder exhibits a quite wide particle size distribution (Fig.S4.1), comprising equivalent diameters ranging from 30 nm to 170 nm and a $d_{50} = 95$ nm, in good agreement with the value provided by the supplier (Table 2). Identifying individual particles is however challenging because most of them are merged into larger aggregates (circled by red or blue ellipses in Fig.3a), with equivalent diameters in the 100-4000 nm interval according to the supplier (Table 2). The YZCP powder SEM analysis also reveals a wide particle size distribution ranging from 30 nm to 210 nm with a $d_{50} = 93$ nm. At first sight, YZCP particles appear to have sharper edges and look less aggregated than their TOSOH counterparts.

To complement the SEM analysis, SAXS measurement of 1 vol.% TOSOH and YZCP powders dispersed (Disperbyk-111 at $3.0 \text{ mg.m}^{-2}$) in ethanol are presented in Fig.3b. These signals represent the apparent form factors of the powders
(with negligible structural interferences), revealing fundamental features of the two powders on a statistically reliable number of particles. At first sight, no oscillation of the intensity can be detected at high *q* (*q* > 0.1 nm⁻¹), being typical of the high polydispersity in particles diameter, confirming SEM micrographs and image analysis for both types of powders. Also, the corresponding Porod regimes are characterized by a *I* ~ *q*⁻³.⁸⁵±⁰.⁰⁵ dependency, indicating that both types of particles present a moderated surface roughness³⁹:⁴⁰ (*I* ~ *q*⁻⁴ is expected for smooth colloids⁴¹).

<figure><img src="image_5.png" /></figure>

**FIGURE 3** a) SEM micrographs of TOSOH and YZCP powders. Captions and corresponding ellipses highlight the multiscale structures. b) SAXS intensity of 1 vol.% TOSOH and YZCP particles suspensions dispersed with 3.0 mg.m⁻² in ethanol. TOSOH curve is shifted up with a ×10 coefficient for clarity. TOSOH and YZCP signals were respectively fitted with a "guinier_porod" model (dark red line) and a polydisperse sphere model (light blue line). The inset represents the lognormal size distribution determined from the polydisperse sphere form factor fit of the YZCP signal.

The TOSOH signal was fitted with the "guinier-porod" model proposed by Hammouda⁴² where the Porod (high *q*) and Guinier (low *q*) power-law exponents were found to be -3.8 and -2.0 respectively. The latter parameter is an estimation of the average fractal dimension (*D*<sub>f</sub>) of the agglomerates larger than *d*<sub>aggr</sub><sup>TOSOH</sup> ≈ 208 nm (fit parameter), being in good agreement with the typical diameter of red-circled dense aggregates in Fig. 3a. Interestingly, the SAXS intensity also contains the signature of the single crystallites that appear around *d*<sub>cry</sub><sup>TOSOH</sup> = 29 nm, as expected from the supplier data (Table 2).

On the other hand, the YZCP data exhibits a quasi-plateau at low *q*, which evidences that for a similar dispersing agent concentration, YZCP particles can be seen as isolated objects in the suspension rather than forming superstructures. This important result is confirmed by the fact that a polydisperse sphere form factor can be used to fit the YZCP data. At large *q*, the moderate fit quality emphasizes the slight particles roughness, while the shoulder and the
low-q plateau are well captured by the model. The corresponding (arbitrarily chosen) lognormal size distribution is reported in the inset (Fig.3b), pointing that the shoulder position of the SAXS intensity matches rather well $q_z = 2\pi/d_z$, where $d_z = 183$ nm is the third moment of the distribution. Indeed, the fact that the intensity prefactor of each object depends on its volume gives more weight to the largest objects in the suspension resulting in an overestimation of the actual size of the elementary scatterer when compared to SEM results (see Table 2 where $d_{part} = 93$ nm $<d_z$). Nevertheless, it is noteworthy that by using SAXS, we estimated an equivalent diameter of 195 nm⁶ in a highly loaded commercial paste composed of the same powder ($\Phi \approx 49$ vol%), in excellent agreement with the present estimation obtained from a diluted environment.

<table><caption>**TABLE 2** TOSOH and YZCP powders multiscale characteristic dimensions provided by the supplier and extracted from SEM and SAXS experiments. The corresponding measurement techniques are reported under the numerical values.</caption><thead><tr><th rowspan="2"></th><th colspan="2">TOSOH</th><th>YZCP</th></tr><tr><th>from<sup>28;43;29</sup></th><th>measured</th><th>measured</th></tr></thead><tbody><tr><td><strong>crystallite</strong><br>size<br>$d_{cry}$ (nm)</td><td><strong>39</strong></td><td><strong>29</strong><br>(SAXS)</td><td>-</td></tr><tr><td><strong>particle</strong><br>size<br>$d_{part}$ (nm)</td><td><strong>90</strong></td><td><strong>95*</strong><br>[30;170]<br>(SEM)</td><td><strong>93*</strong><br>[20;210]<br>(SEM)</td></tr><tr><td><strong>aggregate</strong><br>size<br>$d_{aggr}$ (nm)</td><td><strong>600</strong><br>[100;4000]<br>before dispersion</td><td><strong>208</strong><br>1 vol.% in ethanol<br>(SAXS)</td><td><strong>183</strong> 1 vol.% in ethanol (SAXS)<br><strong>195</strong> in commercial paste<br>(SAXS<sup>6</sup>)</td></tr></tbody></table>

The key findings from the structural analysis of these two industrially relevant powders are as follows: 1) Both TOSOH and YZCP powders exhibit significant polydispersity in terms of size and shape, as observed in SEM micrographs of a limited number of particles. This high polydispersity is confirmed by the absence of intensity oscillations at high *q* in SAXS measurements, which were performed on a statistically significant number of particles, 2) Surface roughness is comparable between the two powders, though slightly more pronounced for TOSOH particles, which also display smoother edges, and 3) The TOSOH particles tend to form very dense aggregates of ca. 200 nm in diameter made of strongly merged particles that organize into relatively open agglomerates ($D_f = 2$) on a larger lengthscale. Conversely, the YZCP powder is made of particles and small aggregates that can be isolated in suspension, indicating a less constrained structure that is likely to impact the slurry's rheology in a significant way. We remind the reader that both 3Y-TZP zirconia powders can be used to build dense structural ceramics by SLA as their particles and crystallite sizes ($\approx 100$ nm and $\approx 30$ nm respectively) allow long thermal cycles while ensuring a well-controlled grain size growth during sintering and good final mechanical properties⁴⁴. In the following discussion about rheology, crystallites, particles, and aggregates are all defined as compact objects that cannot be broken by shear (during blade scraping or in a rheometer), making the aggregates the smallest relevant object dictating rheological properties.

<footnote>*When SEM and image analysis are used, the value of $d_{50}$ and of the whole diameter interval are reported.</footnote>
## 3.2 | Effect of particles morphology and solid loading on slurries rheology

To investigate the effect of solid loading on YZCP and TOSOH slurries under comparable conditions, we prepared identical slurry formulations using TOSOH and YZCP powders with an equivalent concentration of dispersant. Prior to slurry preparation, the YZCP powder needed to be extracted from a commercial paste. Various extraction methods were tested, before to conclude that pyrolysis was the most effective to ensure that only Disperbyk-111 was grafted onto the particles surface, thereby allowing a fair comparison between slurries based on YZCP and TOSOH powders (see Supplementary Information S-2).

Fig.4 shows DSS experiments $|η^*| = f(γ)$ performed on TOSOH slurries with solid loadings of 40, 45, 48 and 50 vol.% (Fig.4a), and on YZCP ones with 40, 45, 50 and 52 vol.% (Fig.4b). TOSOH slurries with $Φ$ from 40 vol.% to 48 vol.% exhibit a Newtonian behavior up to $γ = 10^{-1}$ where a slight shear-thinning effect is detected prior to a more severe shear-thickening, which amplitude is increased with the particles volume fraction. This global trend is also observed at 50 vol.% with the sole difference being an anticipated shear thinning starting from $γ = 10^{-4}$. Overall and as expected, a higher solid loading causes an increase of the slurry viscosity on the whole strain amplitude range and enhances shear-thickening at large strain amplitude. Interestingly, Fig.4b displays comparable results for the YZCP slurries with the striking difference that the shear-thickening effect observed at large strain amplitude is almost inexistant. Considering both the structural analysis reported in the previous section and this rheological characterization suggests that larger agglomerates in the TOSOH slurries not only increase the viscosity through hydrodynamic effects ($|η^*|_{TOSOH} > |η^*|_{YZCP}$) but also lead to further frictional contacts at high strain amplitude, increasing both the strain amplitude onset of the shear-thickening regime and its amplitude.

<figure><img src="image_6.png" /><figcaption>**FIGURE 4** DSS ($ω = 10 \text{rd.s}^{-1}$) slurries composed of a) TOSOH powders and b) YZCP powders for various solid loadings and a fixed dispersant concentration of 3.0 mg m$^{-2}$. Storage and shear moduli representation is provided in Supplementary Information Fig.S6.1.</figcaption></figure>

Beyond oscillatory rheology, we performed steady shear experiments to compare YZCP and TOSOH slurries in conditions closer to the actual scraping step involved in SLA or DLP printing. We present in Fig.5 the corresponding evolution of the reduced steady-state viscosity, defined as the ratio between the slurry steady state viscosity and the viscosity of the slurry without ceramic particles $η_r = η_{SS}/η_{organic}$, measured at $γ̇ = 130 \text{ s}^{-1}$ for the same set of samples
investigated in Fig.4. Both series of experiments show a pronounced increase of the viscosity with the solid loading as expected from the close packing of the particles. Yet, the TOSOH slurries exhibit a viscosity divergence at a significantly lower solid loading than their YZCP counterparts, being reminiscent of the branched nature of the TOSOH agglomerates, which limits their rotational and translational degree of freedom in the flow. More quantitatively, we fit the (popular) Krieger-Dougherty (KD) model$^{8,9,45}$ (see Eq.1) on $\eta_r(\dot{\gamma})$ data for both types of slurries, which provided the values of the maximum packing fraction $\Phi_M$ and the intrinsic viscosity [$\eta$].

$$ \eta_r = \left(1 - \frac{\Phi}{\Phi_M}\right)^{-\Phi_M[\eta]} \qquad (1) $$

As anticipated, $\Phi_M$ is significantly higher for YZCP slurries than for TOSOH ones (57 vol.% vs. 53 vol.%) while remaining far from the monodisperse sphere random close packing asymptotic value of 64 vol.%$^{46}$. The latter observation is in line with the fact that both TOSOH and YZCP slurries contain repulsive aggregates made of polyhedral and rough particles overall promoting free volume. On the other hand, the ("low filling fraction") intrinsic viscosity [$\eta$] for TOSOH and YZCP slurries are found to be 5.7 and 5.0, respectively. As clearly shown in the Fig.5 inset (representing the same data in a semi-logarithmic scale), a higher value of $\eta_r$ is synonymous of a shift-up of the data together with a steeper increase at high $\Phi$ indicating a higher propensity to cause frictional contacts, typically increasing with the anisotropy of the particles$^{45,47,48}$. Here again, these values are significantly higher than [$\eta$] =2.5, corresponding to the canonical case of monodisperse rigid spheres$^{45}$, because particles aggregation cause frictional effects on top of the hydrodynamic interactions from moderate particles solid loading.

<figure><img src="image_7.png" /><figcaption>**FIGURE 5** Relative viscosity $\eta_r$ measured from steady shear experiments of TOSOH and YZCP slurries vs. the particles solid loading $\Phi$. Solid lines are KD fits (Eq. 1)$^{16}$. Inset: analog data and fits in a semi-logarithmic representation. Fit parameters are $\Phi_M$ = 53 vol.% ; [$\eta$] = 5.7 and $\Phi_M$ = 57 vol.% ; [$\eta$] = 5.0 for TOSOH and YZCP slurries, respectively.</figcaption></figure>

Interestingly, for similar photosensitive ceramic slurries, Zhang et al.$^8$ reported $\Phi_M$ = 48 vol.% but did not provide the [$\eta$] value. Also, Tovar-Vargas et al.$^9$ obtained $\Phi_M$ from 47 vol.% to 51 vol.% and corresponding [$\eta$] from 4.3 to 4.9. These low $\Phi_M$ values attest of the difficulty to disperse efficiently a high volume fraction of hard particles into a complex slurry, requiring an improved preparation process. Yet, we remark that corresponding [$\eta$] values are close to ours, suggesting a similar nature of the particles in terms of size, shape and roughness. Conversely, Yang et al.$^{49}$ re-
ported $\Phi_M = 61$ vol.%, which is a surprisingly large value for a high intrinsic viscosity [$\eta$] = 7.1, most likely originating from a high particle shape anisotropy. In all of these articles, the lack of information about particles features however limits the interpretation of the results.

Moreover, Ermakova et al.¹¹ prepared slurries using the same TOSOH zirconia particles as us and obtained slightly higher $\Phi_M$ values (≈ 57 vol.%) and lower [$\eta$] values (≈ 4.5) in average, compared to those shown in Fig.5. This study also emphasizes that even if $\eta$ is normalized by the solvent viscosity in the KD formula, the solvent acts on the dispersant efficiency and thus on the overall behavior of the slurry. Therefore, the use of multiple organic compounds to control polymerization kinetics or debinding (like in the SLA or DLP slurries recipes) further complexifies the rheological behavior. It is also worth reminding that the $\eta_r = f(\Phi)$ data significantly depend on the type of measurement, i.e., on whether the viscosity is measured from a start-up, a flow curve or an oscillatory shear experiment, and on the absolute value of the shear rate⁵⁰;⁵¹.

To go further, a series of Flow Curve tests was conducted and analysed according to the methodology proposed by Zhou et al.⁵², consisting of the following steps: 1) The Flow Curve experiments results are displayed as viscosity in function of shear stress ($\eta = f(\sigma)$) (see e.g., Fig.6a for YZCP slurries), 2) From this graph, the values of $\eta(\sigma_i, \Phi)$ were collected for several values of $\sigma_i$, 3) For each $\sigma_i$, a KD fit was performed on the set of $\eta(\sigma_i, \Phi)$, providing a value of $\Phi_M$ as a result. As proposed by Zhou et al.⁵², the value of the exponential KD factor ($n = -\Phi_M[\eta]$) was fixed to 4.93 (determined as the median for 2-parameter KD fits), which provides rather accurate fits for every $\sigma_i$. Note that this value of $n$ is different than the ones obtained from KD fits in Fig.5 because [$\eta$] slightly depends on the measuring conditions⁵²;⁵⁰;⁵¹, and 4) The values of maximum packing fraction obtained from each KD fit are traced as $\Phi_M(\sigma_i)$ (see Fig.6b for both types of slurries). These data are fitted with the Zhou equation (Eq. 2), which not only allows to evaluate the maximal fraction of particles (like KD fits), but also characterize the ability of the agglomerates to resist to shear. For simplicity, the $p$ exponent was set to 1 as TOSOH and YZCP slurries provided meaningful values of $\Phi_0$ and $\sigma_{adh}$ together with good fitting accuracy in this case.

$$ \frac{1}{\Phi_M} = \frac{1}{\Phi_0} \left( 1 + \left( \frac{\sigma}{\sigma_{adh}} \right)^p \right)^{-1} + 1 - \frac{1}{\Phi_\infty} \left( 1 + \left( \frac{\sigma}{\sigma_{adh}} \right)^p \right)^{-1} \quad (2) $$

The Zhou model allows to frame the concentrated suspension domain where $\Phi_0$ defines the maximum packing fractions corresponding to the liquid-like state⁵², $\Phi_\infty$ is the ultimate packing fraction for solid-like state⁵²;⁵³, and $\sigma_{adh}$, which corresponds to the inflexion point of the curve, can be seen as the stress required to trigger the deagglomeration of aggregates. Interestingly, Fig.6b emphasizes that TOSOH slurries leave the liquid-like regime for lower solid loading than YZCP ones ($\Phi_0^{TOSOH} < \Phi_0^{YZCP}$). In other words, it indicates that TOSOH slurries may form spreading defects (resulting from solid-like features) for lower solid content than the YZCP ones, as anticipated from Figs.4 and 5. Moreover, TOSOH slurries exhibit a lower ultimate packing fraction than YZCP ones ($\Phi_\infty^{TOSOH} < \Phi_\infty^{YZCP}$) most likely caused by their higher degree of aggregation (i.e., higher $D_r$) limiting the interpenetration of the agglomerates hydrodynamic volumes. Finally, comparing the adhesion stresses results in $\sigma_{adh}^{TOSOH} > \sigma_{adh}^{YZCP}$, which indicate that TOSOH agglomerates are slightly harder to break than YZCP ones, promoting an easier reorganization of the particles structure and fewer frictional contacts in the latter material, in agreement with the above-mentioned lower proficiency to shear-thicken at high shear amplitude.
<figure><img src="image_8.png" /><figcaption>**FIGURE 6** a) Viscosity vs. shear stress representation of the Flow Curves of YZCP powder-based slurries. For a given $\sigma_i$ (vertical line), the values of $\eta_{\Phi}(\sigma_i)$ are collected on each Flow Curve (star symbols) and fit with a 1-free-parameter KD equation. b) Resulting $\Phi_M$ vs. $\sigma_i$ for YZCP and TOSOH based slurries. Solid lines are fits of the data with the Zhou equation (see text). Fit parameters are reported on the graph.</figcaption></figure>

## 3.3 | Effect of dispersing agent

In this section, we investigate a 40 vol.% TOSOH powder based slurry containing different amounts of dispersant with the aim to emphasize deagglomeration in purpose-made formulations. In Fig.7, we present SAXS (a) and DSS experiments (b) demonstrating the impact of Disperbyk-111 when its concentration is increased from 0 mg.m⁻² to 6.0 mg.m⁻².

Fig.7a strikingly evidences the effect of the dispersing agent on the slurry structure through an overall decrease of the low-q intensity and the emergence of a structure peak at $q^*$ that can clearly be identified for $BYK_{load} > 1.5$ mg.m⁻² in the $q = 3 \times 10^{-3}$ nm⁻¹ to $10^{-1}$ nm⁻¹ range. This effect is typical of the more pronounced structural periodicity appearing in the sample, which results from the increasingly repulsive potential generated by the addition of dispersant⁵⁴. While the most probable center-to-center inter-objects distance $d^* = 2\pi/q^*$ can be easily calculated for high concentration of dispersant, its extraction is not trivial for low concentrations - we refer the reader to Supplementary Information S-5 for more details.

Remarkably, while $d^*$ decreases from 160 nm to 90 nm for dispersant concentration ranging from 0 mg.m⁻² to $1.5 \times 10^{-2}$ mg.m⁻², it tends to saturate for $3.0 \times 10^{-2}$ mg.m⁻² prior to increase above this limit (inset Fig.7a). While the pronounced initial decrease of $d^*$ corresponds to the fragmentation of large agglomerates into smaller and isolated aggregates (see Fig.7c), the saturation and the more surprising $d^*$ upturn (together with a higher SAXS intensity) at high dispersant concentration unambiguously indicates their partial re-agglomeration. We therefore conclude that the optimal dispersant concentration is reached for $3.0$ mg.m⁻². At this concentration, we hypothesize that the dispersant adsorption state onto the ceramic surfaces is complete, i.e., that all the available adsorption sites are presumably occupied, and that dispersant chains are free to extend into the organic phase. In contrast, a lower concentration of dispersant only partially covers the particle surface, whereas an excessive concentration causes the dispersant layers to collapse, leading to flocculation⁵⁵.
<figure><img src="image_9.png" /><figcaption>**FIGURE 7** a) Normalized SAXS intensity measured on TOSOH-powder based slurries containing $\Phi = 40$ vol.% of particles for various dispersing agent concentrations. The scattering intensity was rescaled at high q to compensate thickness discrepancies ensuring a perfect overlap of the data. Inset: characteristic inter-particles distance $d^* = \frac{2\pi}{q^*}$ extracted from the apparent structure factor (see Supplementary Information S-5) vs. dispersant concentration. b) DSS experiments displayed as $|\eta^*|(\gamma)$ for analog samples. (Dynamic moduli representation is provided in Supplementary Information Fig.S6.2). c) Schematic representation of particles structures for low (top) and optimal dispersant concentration (bottom). Purple arrows represent the center-to-center distances between scattering objects.</figcaption></figure>

The parallel observation of Fig.7a and Fig.7b evidences the strong correlation existing between the morphology of the aggregates and the rheological properties of the corresponding slurries. We observe that the two slurries containing the lowest concentration of dispersant exhibit a similar and quite high value of the "zero-shear" viscosity modulus ($|\eta_0^*| \approx 3 \times 10^4$ Pa.s) together with a massive shear-thinning behavior starting from very low strain amplitude, reminiscent of a yield-stress fluid (i.e., paste) rheological behavior. After an intermediate behavior observed for a dispersant concentration of 0.6 mg.m⁻², the highly dispersed slurries all exhibit a nearly-constant $|\eta^*|$ between $7 \times 10^{-1}$ Pa.s and 5 Pa.s accompanied with minor variations at higher strain amplitude. Remarkably, the non-monotonic $d^*$ trend observed in SAXS for a "too high" dispersant concentration (6.0 mg.m⁻²) is also detectable with rheometry through a slight increase of the complex viscosity modulus on the whole strain amplitude range, strongly supporting the structural interpretation. To sum up, the slurry containing 3.0 mg.m⁻² of dispersant exhibits the most dispersed structure and the minimum complex viscosity modulus with no important shear-thickening event at high $\gamma$ making it a good candidate for vat-photopolymerization printing techniques³.

## 3.4 | Orthogonal superposition rheology

In line with our goal to tailor rheological properties through various approaches, this section is dedicated to the effect of an additional vibration on the steady shear viscosity of a viscous slurry. The investigated sample has a low dispersant concentration (0.6 mg.m⁻²), which provides it with a high zero-shear viscosity and a pronounced shear-thinning, resulting from the presence of large agglomerates that progressively break upon increasing the shear rate. In Fig.8a, we present flow curves performed in presence of a vertical vibration causing a constant strain amplitude ($\epsilon = 10^{-2}$) in the slurry at various pulsations ($\omega_\perp$). The results are compared to a reference flow curve, where no vibration is applied ($\eta_{ref} = \eta(\omega_\perp = 0 \text{ rd.s}^{-1})$). Similarly to the observations made on a commercial paste⁶, increasing $\omega_\perp$ is seen to reduce the shear viscosity at low shear rates and increase the value of the upper shear rate limit at which viscosity reduction occurs.
In addition, the flow curves reported in Fig.8a seem to overlap when shifted "diagonally" up-left, along the reference experiment. We thus propose to evaluate the effect of both vertical vibration parameters ($\epsilon$ and $\omega_{\perp}$) on the normalized viscosity ($\frac{\eta}{\eta_{ref}}$) by renormalizing the shear rate $\dot{\gamma}$ by the vibration equivalent strain rate $\dot{\epsilon}_{max} = \epsilon\omega_{\perp}$ (Fig.8b). The resulting data well overlap, which confirms that the samples measured at various vertical strain amplitudes have self-similar properties that are driven by $\dot{\epsilon}_{max}$. It is worth noting that the commercial paste in ref. 6 did not exhibit such $\dot{\epsilon}_{max}$ dependency because the strain amplitude $\epsilon$ was too small to induce yielding in the paste, which was reinforced by a gelling agent, contrarily to the present case.

Fig.8b indicates that the material viscosity is reduced by the vertical vibration for $\dot{\gamma}/\dot{\epsilon}_{max} < \dot{c} \approx 3$ only, where $\dot{c}$ is the "critical strain rate ratio" defining this limit. The sensitivity of slurries and other inks to this type of test could be evaluated by comparing the value of $\dot{c}$ and the slope of their mastercurve for $\dot{\gamma}/\dot{\epsilon}_{max} < \dot{c}$ to the present one (the slope is $\approx 0.5$ in Fig.8b).

<figure><img src="image_10.png" /><figcaption>**FIGURE 8** Flow curves measured under orthogonal oscillatory vibration for various sets of parameters ($\omega_{\perp}$, $\epsilon$) on a slurry loaded with 40 vol.% of particles functionnalized with 0.6 mg.m$^{-2}$ of dispersant. a) Effect of vibration frequency on flow curves for $\epsilon = 10^{-2}$. b) Master curve of normalized viscosity vs. the strain rate ratio $\frac{\dot{\gamma}}{\dot{\epsilon}_{max}}$.</figcaption></figure>

An important conclusion drawn from the mastercurve is that even at high shear rates, close to $\dot{\gamma}_{SLA}$, viscosity can be decreased by applying vibration of high $\dot{\epsilon}_{max}$. This suggests that material fluidization could enhance layer spreading in printing processes, which aligns with the systematic observations of Lin et al.⁵⁶ and the recent development of Pateloup et al.⁵⁷ who used a vibrating blade on their stereolithography printer. While the application of vibrations alone may not prevent all types of defects reported by Xing et al.⁵⁸, real-time monitoring could further provide a more practical solution to address spreading issues. Notably, the work of Zhao et al.⁵⁹ introduces an integrated tool within a printing system that applies an additional recoating step before lasing whenever a surface defect is detected in the spreaded layer.
4 | CONCLUSIONS/SUMMARY

The rheology of ceramic stereolithography slurries is primarily governed by their solid loading, which should be max-
imized to produce dense structural ceramic objects. By carefully selecting powder characteristics, it is possible to
mitigate viscosity increases and delay the onset of shear-thickening as solid loading rises. The size, shape, and struc-
ture of particles, from the nanometer to micrometer scale, have a significant impact on rheological behavior. SAXS
and SEM analyses show that non-spherical, rough particles with a broad size distribution enhance frictional contacts
and agglomeration within the slurry. Optimizing the dispersant quantity and refining dispersion techniques reduce
particle agglomeration, thereby lowering slurry viscosity across a broad shear rate range. This effect correlates closely
with a reduction in agglomerate size, as indicated by SAXS measurements of inter-object distance, and reduced shear-
thickening at high shear rates due to the dispersant's repulsive effect, as revealed by rheometry. Furthermore, orthog-
onal superposition rheometry indicates that adding vibration to a steady sheared slurry improves its spreadability. A
general relationship between shear rate and vibration parameters has been identified, offering potential for predicting
the effects of vibration at specific shear rates and thus tuning the rheological behavior of SLA slurries. Our findings
suggest that future advancements incorporating vibration during the spreading step could further enhance spreaded
layers quality by improving homogeneity and reducing defect size and frequency in photopolymerized ceramic prod-
ucts.

Acknowledgements

We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities under proposal number MA-5093. We also thank the CLyM platform (Lyon, France) for the use of their facilities. Special thanks are addressed to Pr. Minale team at University of Campania “Luigi Vanvitelli”, Department of Engineering, where Orthogonal Superposition Rheology measurements were conducted. The authors thank IMCD France for providing a free sample of Disperbyk-111. This work has been partly funded by a public grant from the French National Research Agency (ANR) under the “France 2030” investment plan, which has the reference EUR MANUTECH SLEIGHT - ANR-17-EURE-0026. SF is grateful to the French Ministry of Higher studies and Research for his PhD grant. This work benefited from the use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed with funding from the European Union's Horizon 2020 research and innovation programme under the SINE2020 project, grant agreement No 654000.

Other information

Experimental data from ESRF can be found online at https://data.esrf.fr/doi/10.15151/ESRF-ES-651037210.

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# Supporting Information

## S-1 | Dispersion method

The parameters of the dispersion method can have a strong influence on the adhesion of the dispersant to the particles surface. For example, Charbonnier et al.¹ discuss the influence of the grinding time and the grinding rate on the specific surface of the powder, and the viscosity of a slurry, in order to find the optimal grinding process. The aim of this section is to evaluate the relevance of comparing slurries dispersed with an asymmetrical fast milling process (section 3.3 & 3.4) to slurries based on regular milling process (section 3.2).

In the literature, a large range of milling parameters have been tested for oxide powders, including long procedures at low rate for zirconia tape casting slurries (40 rpm from 1 h to 24 h)², to more energetic processes (70 min at 250 rpm to 350 rpm) for a photopolymerizable alumina dispersion³. For our slurries preparation, the milling was conducted at a rather fast and energetic method (250 rpm for 20 min) because the rheology of slurries could not be improved when increasing the time of the milling process. Studying Sun et al. work²⁰ helped to guide the powder preparation procedure, making sure no dispersant was lost before mixing with the rest of the organic mix. The strategy of mixing directly the dispersant with the organic media and particles has produced interesting results⁵ but the lack of pre-dispersion step with milling balls (impossible to incorporate in the full mix for SLA pastes contrarily to liquid slurries) rises the risk of agglomerates remaining and causing printing defects.

The impact of the dispersion method on the grafting of the dispersant to the powder was controlled by different characterization methods. First, the DSS of Φ = 40 vol.% slurries dispersed with 3.0 mg.m⁻² of BYK (Fig.S1.1a) exhibits very similar *G'* and *G''* curves. It supports the idea that for the given dispersant amount (i.e. 3.0 mg.m⁻²), the maximal functionalization was reached for both powders.

To compare the quantity of dispersants that were bonded to the particles after functionnalization, Fourier Transform InfraRed spectroscopy measurements of samples of raw powder, raw dispersant and functionnalized (with 3.0 mg.m⁻² and 6.0 mg.m⁻² of BYK) were measured. The spectra were acquired by transmission method with an IS50 spectrometer (Thermo Fisher Scientific, USA) on disk samples made of 300 mg of KBr and 3 mg of the powder or the dispersant sample. The acquisition was done from 4000 to 400 cm⁻¹, with a spectral resolution of 4 (digital step of 0.5 cm⁻¹) and averaged on 32 scans. The spectra baseline was corrected with the OMNIC software (ThermoFisher, USA) to determine reliably the area of each peak. Fig.S1.1b displays the characteristic zone (1450 cm⁻¹ to 1800 cm⁻¹) of the dispersant peaks, along with the spectra of raw powder and raw dispersant. The 1636 cm⁻¹ peak appears on the raw powder spectrum and on functionalized powders too but with a reduced area. This peak is characteristic of the stretching vibration of the –OH group, which is located on the oxide powders surfaces, even more visible when no dispersant is bonded. The peak at 1733 cm⁻¹ corresponds to the C=O stretching vibration of the acid group, which is visible on the dispersant itself (Disperbyk-111 contains acid groups) and on the dispersed powders, proving that dispersant molecules attached to powders during the dispersion procedure. The dispersant has an effect as long as it is attached to particles but saturation of every adsorption site (–OH group on the surface of the powder) is not achievable nor desirable for a good dispersion.

For the acid group peaks, a regular growth trend between 0 and 3.0 mg.m⁻² can be reported for both dispersion methods. The number of attached dispersing agents is doubled when the initial dispersant amount is doubled. Powders with 6.0 mg.m⁻² projected dispersant load attest of a higher grafting than 3.0 mg.m⁻² ones. However, SAXS
and DSS results (Fig.7a-b) proved that $BYK_{load} = 6.0 mg.m^{-2}$ slurries were more aggregated and had higher viscosity. Therefore, a detrimental effect of a too high amount of dispersant can be expected for these high solid loading slurries, as discussed in section 3.3. Also, the slope on Fig.S1.1c between $3.0 mg.m^{-2}$ and $6.0 mg.m^{-2}$ clearly declined compared to previous points, showing the grafting saturation on powder surfaces.

<figure><img src="image_11.png" /></figure>

**FIGURE S1.1** DSS of a) 40 vol.% slurries dispersed with $3.0 mg.m^{-2}$ Disperbyk-111 with different techniques b) Transmission FTIR normalized peaks of $ZrO_2$ powder, dispersant and different functionalized powders c) Area of the $1730 cm^{-1}$ peak of the dispersant in FTIR spectra of powder samples. These samples were functionalized with different amounts of dispersant and different techniques.

Now comparing the different dispersion techniques, the FTIR results revealed more variability for asymmetrical planetary dispersion, with even one value notably lower than the others for $1.5 mg.m^{-2}$ and $3.0 mg.m^{-2}$. As no rheological behavior difference on the slurries of Fig.S1.1a was observed, we can think that the outliers prove that the asymmetrical planetary resulted in a less homogeneous dispersion than with regular ball milling. It explains that slurry DSS are almost identical, but the dispersion inhomogeneity could leave large agglomerates that could induce defects in the final ceramic part. This result may be caused by the smaller ball milling time of asymmetrical planetary method compared to regular planetary, although it is conducted at higher speed.

Fast asymmetrical milling for dispersion of photocurable slurries can be of interest in the printing material development stage, when many dispersion trials are necessary, making it a valuable option for reducing milling time. This procedure could also be improved by solving the issue of damaging the container by changing its material, to allow faster milling.
## S-2 | YZCP particles extraction and functionalization

<table><caption>TABLE S2.1 Slurries and powders pre-processing for dispersion study.</caption><thead><tr><th>Φ (vol.%)</th><th>Powder (pre-processing)</th><th>BY K<sub>load</sub> (mg.m<sup>-2</sup>)</th><th>Dispersion technique</th><th>PEG (M<sub>w</sub>)</th></tr></thead><tbody><tr><td rowspan="2">45</td><td rowspan="2">YZCP centrifugated</td><td>0</td><td>none</td><td>none</td></tr><tr><td>3.0</td><td>regular</td><td>400</td></tr><tr><td rowspan="2">45</td><td rowspan="2">YZCP pyrolized</td><td>0</td><td>none</td><td>none</td></tr><tr><td>3.0</td><td>regular</td><td>400</td></tr><tr><td>Powder</td><td>TOSOH centrifugated</td><td>3.0</td><td>regular</td><td>400</td></tr><tr><td>Powder</td><td>TOSOH pyrolized</td><td>3.0</td><td>regular</td><td>400</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>FIGURE S2.1 Schematic representation of the two pre-processing routes tested for YZCP powders extraction from the commercial paste, also applied on TOSOH powders for comparison.</figcaption></figure>

Fig.S2.1 describes the two pre-processing routes tested on the commercial paste to extract the YZCP powders before to functionalize and use them in slurries.

The "so-called" centrifugation method comprehends the centrifugation of the commercial paste with ethanol, with the same device and parameters than the ones used for the preparation of slurries described in section 2.2.1. Then, the powder at the bottom of the tube can be collected, rinsed with ethanol, dried in an oven at 70°C for 1 h to remove the remaining ethanol, and finally grinded. The pyrolisis procedure consisted of heating the paste up to 600°C (1°C.min⁻¹), with a 1 h dwell and an equivalent cooling ramp, before to grind it. The powders obtained by both procedures were subjected to a transmission FTIR analysis at that point of the process.

Followingly, the powders were prepared according to the procedure of section 2.2.1 (including powder functionalization with the dispersant) before to be analysed again by transmission FTIR, and then mixed in slurries for rheological testing.

The FTIR spectra of YZCP powders show that extracting the powders from paste through centrifugation did not
remove the functionalizing molecules used in the paste, as numerous peaks associated to the stretching vibration of carbon and oxygen bonds are still visible compared to the spectra of pyrolized powders (Fig.S2.2a). After powder dispersion, FTIR peaks of priorly centrifugated or pyrolized powders are very similar and present vibration peaks at 1100 and 1730 cm⁻¹ corresponding to COC and C = O dispersant bonds. Indeed, these peaks are not present in the solely pyrolized YZCP powder.

The DSS of the YZCP slurries display a lower overall complex viscosity η* when powders were centrifugated rather than pyrolized before dispersion (Fig.S2.2b). Pyrolisis completely removed the dispersant used in the commercial paste from the surface of YZCP powders. Pyrolisis may have had an effect on powder surface and aggregation because TOSOH slurries also report a slightly higher η* when their particles were pyrolized before dispersion. Pyrolisis is still the best pre-processing option to make sure that only the Disperbyk-111 is grafted on particles surface, and to allow a fair comparison with TOSOH particles.

<figure><img src="image_13.png" /><figcaption>**FIGURE S2.2** a) FTIR spectra of centrifugated and pyrolized YZCP powders with and without dispersant. Non-dispersed powders are shifted up to help the readability. Pure Disperbyk-111 is also represented shifted up with its signal divided by 20 to facilitate its representation. b) DSS of slurries made with TOSOH and YZCP powders. For both graphs, purple curves indicate that the slurry's powders were centrifugated prior to dispersion while blue ones concern powders that were pyrolized before dispersion.</figcaption></figure>
S-3 | Symbols definition

<table><thead><tr><th>Symbol</th><th>Meaning</th><th>Unit</th></tr></thead><tbody><tr><td colspan="3">Materials</td></tr><tr><td>Ink</td><td>Feedstock for printing ceramics designating here both pastes and slurries</td><td></td></tr><tr><td>Slurry</td><td>Ink that is self-levelling and liquid-like at rest</td><td></td></tr><tr><td>Paste</td><td>Ink for top-down SLA, self-supporting and solid-like at rest</td><td></td></tr><tr><td>TZ-3YSE</td><td>Commercial 3Y-TZP powder for facilitated sintering and shaping called TOSOH in this publication</td><td></td></tr><tr><td>YZCP</td><td>Powder extracted from commercial 3Y-F01 SLA paste standing for Yttria doped Zirconia from Commercial Paste</td><td></td></tr><tr><td>Φ</td><td>Solid loading</td><td>vol.%</td></tr><tr><td>BYK</td><td>Disperbyk-111 dispersant</td><td></td></tr><tr><td>BY K<sub>load</sub></td><td>Amount of dispersant per unit area of the powder</td><td>mg.m<sup>-2</sup></td></tr><tr><td>w<sub>BYK</sub></td><td>Weight fraction of dispersant compared to the powder</td><td>wt.%</td></tr><tr><td>SSA</td><td>Specific surface area</td><td>m<sup>2</sup>.g<sup>-1</sup></td></tr></tbody></table>

<table><thead><tr><th colspan="3">SAXS and Microscopy</th></tr></thead><tbody><tr><td>q = ||q||</td><td>Momentum transfer norm</td><td>nm<sup>-1</sup></td></tr><tr><td>q*</td><td>Momentum transfer value at the ink structure peak</td><td>nm<sup>-1</sup></td></tr><tr><td>I</td><td>Scattering intensity</td><td>a.u.</td></tr><tr><td>S<sub>app</sub></td><td>Apparent structure factor</td><td>a.u.</td></tr><tr><td>d<sub>A</sub></td><td>Projected area diameter</td><td>nm</td></tr><tr><td>d50</td><td>Median diameter</td><td>nm</td></tr><tr><td>d<sub>cry</sub></td><td>Crystallite equivalent diameter</td><td>nm</td></tr><tr><td>d<sub>part</sub></td><td>Particle equivalent diameter</td><td>nm</td></tr><tr><td>d<sub>aggr</sub></td><td>Aggregate equivalent diameter</td><td>nm</td></tr><tr><td>d*</td><td>Inter-aggregates center-to-center distance in 40 vol.% homemade slurries</td><td>nm</td></tr><tr><td>d<sub>1</sub></td><td>Characteristic diameter of dense objects in TOSOH powder</td><td>nm</td></tr><tr><td>Q<sub>1</sub></td><td>Characteristic inflexion point between Guinier and Porod regime</td><td>nm<sup>-1</sup></td></tr><tr><td>d<sub>z</sub></td><td>Third moment of the lognormal distribution determined by fitting of the YZCP powder SAXS signal</td><td>nm</td></tr><tr><td>q<sub>z</sub></td><td>Momentum transfer associated to d<sub>z</sub><br>Fit parameter of polydisperse spheres model for YZCP powder</td><td>nm<sup>-1</sup></td></tr></tbody></table>
<table><thead><tr><th>Symbol</th><th>Meaning</th><th>Unit</th></tr></thead><tbody><tr><td colspan="3" style="text-align: center; font-weight: bold;">Strain rate</td></tr><tr><td>γ̇</td><td>Shear rate</td><td>s<sup>-1</sup></td></tr><tr><td>γ̇<sub>SLA</sub></td><td>Maximal shear rate during scraping of stereolithography process</td><td>s<sup>-1</sup></td></tr><tr><td>γ̇<sub>DLP</sub></td><td>Maximal shear rate during scraping of Digital Light Processing process</td><td>s<sup>-1</sup></td></tr><tr><td>γ̇<sub>max</sub></td><td>Maximal shear rate during oscillatory experiment</td><td>s<sup>-1</sup></td></tr><tr><td>ε̇<sub>max</sub> = εω<sub>⊥</sub></td><td>Maximal strain rate in the vertical direction</td><td>s<sup>-1</sup></td></tr><tr><td>γ̇</td><td>Value of ε̇<sub>max</sub> separating the two regimes of the FCV mastercurve such as γ̇/ε̇<sub>max</sub> &lt; γ̇ the "critical strain rate ratio"</td><td>(-)</td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">Strain</td></tr><tr><td>γ</td><td>Shear strain</td><td>(-)</td></tr><tr><td>ε</td><td>OSP orthogonal strain</td><td>(-)</td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">Viscosity</td></tr><tr><td>η<sub>0</sub></td><td>Zero-shear viscosity</td><td>Pa.s</td></tr><tr><td>η</td><td>Steady-shear viscosity</td><td>Pa.s</td></tr><tr><td>η<sub>SS</sub></td><td>Steady-state viscosity</td><td>Pa.s</td></tr><tr><td>|η<sup>*</sup>|</td><td>Complex viscosity modulus</td><td>Pa.s</td></tr><tr><td>|η<sub>0</sub><sup>*</sup>|</td><td>Complex viscosity in the linear regime</td><td>Pa.s</td></tr><tr><td>η<sub>r</sub> = η<sub>SS</sub>/η<sub>organic</sub></td><td>Steady state relative viscosity</td><td>Pa.s</td></tr><tr><td>η<sub>organic</sub></td><td>Viscosity of the organic binders</td><td>Pa.s</td></tr><tr><td>η<sub>ref</sub></td><td>η measured in OSP without orthogonal vibration</td><td>Pa.s</td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">Stress</td></tr><tr><td>σ</td><td>Shear stress</td><td>Pa</td></tr><tr><td colspan="3" style="text-align: center; font-weight: bold;">Krieger-Dougherty</td></tr><tr><td>KD</td><td>Krieger-Dougherty</td><td></td></tr><tr><td>Φ<sub>M</sub></td><td>Maximum packing fraction</td><td>%</td></tr><tr><td>[η]</td><td>Intrinsic viscosity</td><td>Pa.s</td></tr><tr><td>n = Φ<sub>M</sub>[η]</td><td>Exponential KD factor</td><td>Pa.s</td></tr><tr><td>σ<sub>i</sub></td><td>i<sup>th</sup> value of stress chosen to collect values of η(Φ) for Zhou procedure</td><td>Pa</td></tr><tr><td>η(σ<sub>i</sub>, Φ)</td><td>Viscosity at σ = σ<sub>i</sub> from Flow curve measurement of a printing material with a given solid loading Φ</td><td>Pa.s</td></tr><tr><td>Φ<sub>M</sub>(σ<sub>i</sub>)</td><td>Φ<sub>M</sub> obtained from 1-parameter KD fits of the gathered η(σ<sub>i</sub>, Φ) values</td><td>%</td></tr><tr><td>σ<sub>adh</sub></td><td>Inter-aggregates cohesion stress</td><td>Pa</td></tr><tr><td>Φ<sub>0</sub></td><td>Maximal solid loading for a liquid-like slurry, obtained from Zhou equation</td><td>%</td></tr><tr><td>Φ<sub>∞</sub></td><td>Ultimate packing fraction obtained from Zhou equation</td><td>%</td></tr><tr><td>p</td><td>Exponential Zhou fit parameter</td><td></td></tr></tbody></table>
Oscillation frequencies

<table><tr><td>ω</td><td>Oscillation Frequency</td><td>rd.s<sup>-1</sup></td></tr><tr><td>ω<sub>⊥</sub></td><td>OSP orthogonal frequency</td><td>rd.s<sup>-1</sup></td></tr></table>

Shear Moduli

<table><tr><td>G'</td><td>Storage modulus</td><td>Pa</td></tr><tr><td>G''</td><td>Loss modulus</td><td>Pa</td></tr></table>

Orthogonal

<table><tr><td>R<sub>1</sub></td><td>Inside cup radius</td><td>mm</td></tr><tr><td>R<sub>2</sub></td><td>Inside bob radius</td><td>mm</td></tr><tr><td>R<sub>3</sub></td><td>Outside bob radius</td><td>mm</td></tr><tr><td>R<sub>4</sub></td><td>Inside cup radius</td><td>mm</td></tr><tr><td>h</td><td>Immersed height or the bob effective length</td><td>mm</td></tr><tr><td>l</td><td>Inner cylinder height</td><td>mm</td></tr><tr><td>dL</td><td>OSP orthogonal displacement</td><td>mm</td></tr><tr><td>c<sup>FC</sup><sub>L</sub></td><td>Primary end-effect factor applied for Flow Curve</td><td>(-)</td></tr></table>

Acronyms

<table><tr><td>OSP</td><td>Orthogonal SuperPosition</td><td></td></tr><tr><td>3Y-F01</td><td>Commercial stereolithography paste for 3Y-TZP ceramic</td><td></td></tr><tr><td>DSS</td><td>Dynamic Strain Sweep</td><td></td></tr><tr><td>SAXS</td><td>Small Angle X-ray Scattering</td><td></td></tr><tr><td>FTIR</td><td>Fourier Transform InfraRed spectroscopy</td><td></td></tr></table>
S-4 | Particles size

Fig.S4.1 gathers the results of particle size distributions measured on SEM micrographs of YZCP and TOSOH powders. The distributions are both lognormal and their width and *d*50 are very close. The *d*50 value is reported in table 2 for both powders.

<figure><img src="image_14.png" /></figure>

**FIGURE S4.1** Particle size distribution of TOSOH and YZCP powders. Histograms on the left axis and cumulative curves related to the right axis.
S-5 | SAXS apparent structure factors for dispersant quantity effect on slurry structure

The apparent structure factors S<sub>app</sub>(q) (see Fig.S5.1) are obtained by dividing the slurries SAXS intensity (Fig.7a) by the form factor signal on Fig.3b. The break-in slope of S<sub>app</sub>(q) (that corresponds to the beginning of the peak inflexion on I(q)) is related to the most probable distance between the center of mass of neighbouring objects. Precisely, it is the index q* of the inflexion point that provides the inter-objects distance d* = 2π/q*. For each S<sub>app</sub> curve, the q* index was determined from the intersection of the tangents of the left and right part of the curve and is reported with a star of the corresponding color. The corresponding equivalent dimensions d* are reported on the inset of Fig.7a versus the dispersant quantity.

<figure><img src="image_15.png" /></figure>

**FIGURE S5.1** SAXS apparent structure factor of slurries containing TOSOH particles with different amount of dispersant. The *q* range of the graph is restricted to the zone in which for all composition, *S*<sub>app</sub> diverges from 1 and may even show a structure peak. The *q*<sup>*</sup> indexes are indicated with star symbols.
## S-6 | DSS for different particles and solid loadings: Storage and shear moduli representation

The results of Fig.4 are displayed in another representation providing more details in Fig.S6.1. The elastic moduli versus strain amplitude given in Fig.4 allows to see that TOSOH slurries have a more viscous than elastic behavior, while YZCP ones have an elastic dominance before to crossover after yielding.

<figure><img src="image_16.png" /><figcaption>FIGURE S6.1 Storage and shear moduli representation of Fig.4.</figcaption></figure>

Similarly, the results of Fig.7b are given in moduli vs strain amplitude in Fig.S6.2. However, the main information of this graph is to compare the value of moduli between the different formulations, which is already observable from the main graph (Fig.7b).

<figure><img src="image_17.png" /><figcaption>FIGURE S6.2 Storage and shear moduli representation of Fig.7b.</figcaption></figure>
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