# Direct Ink Writing of metakaolin-based geopolymers: Rheology and printability control using PEG and inorganic fillers

Xavier Lacambra-Andreu, Mario Scheel, Arnaud Poulesquen

► To cite this version:

Xavier Lacambra-Andreu, Mario Scheel, Arnaud Poulesquen. Direct Ink Writing of metakaolin-based
geopolymers: Rheology and printability control using PEG and inorganic fillers. Additive Manufac-
turing, 2025, 117, pp.105086. 10.1016/j.addma.2026.105086. cea-05501577

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Research paper

# Direct Ink Writing of metakaolin-based geopolymers: Rheology and printability control using PEG and inorganic fillers

Xavier Lacambra-Andreu<sup>a,†</sup>, Mario Scheel<sup>b</sup>, Arnaud Poulesquen<sup>a,*</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

MSC:

0000

1111

Keywords:

Geopolymer

Rheology

Direct Ink Writing

Yield stress

Synchrotron X-ray microtomography

## ABSTRACT

This study aims to optimize the rheological properties of metakaolin (MK) based geopolymers for Direct Ink Writing (DIW) applications. The research explores the effects of Polyethylene Glycol (PEG) and calcite (HP) as rheological modifiers, focusing on their impact on yield stress, shear modulus, the time-dependent evolution of viscosity and structural stability. Through rheological analysis, we identify the formulation with the optimal balance between buildability and extrudability. Results demonstrate that PEG significantly decreases geopolymerization kinetics, increasing the printability window, while HP enhances the mechanical stiffness and yield stress of geopolymer paste. A comprehensive rheological evaluation, including stress growth, oscillatory tests, and creep experiments, highlights the importance of following long-term behavior. A case study on column printing demonstrates the importance of rheological controlling by predicting and confirming critical failure heights (sagging and buckling). X-ray tomography confirms the internal porosity and structural integrity of the printed filters. This work establishes the potential for geopolymer formulations in innovative applications like 3D-printed filtration systems by offering an approach to create formulations that combine printability, shape stability, and mechanical integrity.

## 1. Introduction

Direct Ink Writing (DIW) is a layer-by-layer fabrication technique that involves the precise deposition of a viscoelastic paste through a nozzle. Rheological characterization is crucial in DIW, as it enables the prediction and control of paste behavior during extrusion, solidification, and the stacking of layers, under conditions that simulate the DIW process [1]. Such rheological experiments and models minimize the cost of iterative testing, reducing the amount of trial and error needed to achieve a correct 3D printing. The optimal rheological behavior for a DIW paste is typically that of a Herschel-Bulkley pseudoplastic fluid, characterized by an initial yield stress and a viscosity that decreases with increasing shear rate [2]. This behavior enables the paste to be easily extruded at low pressure while maintaining its shape after deposition.

Geopolymers are inorganic materials with a three-dimensional network structure formed as a result of alkaline- or alkali-silicate activation of aluminosilicate precursors at ambient or elevated temperature [3]. While additive manufacturing (AM) with cement-based materials has been widely studied during the pasts years the use of metakaolin-based geopolymers for AM is relatively new [4,5]. Moreover, the early-age setting mechanisms of geopolymers are completely

different from those of cement paste, especially in terms of rheological behavior. Indeed, Geopolymers are obtained through the alkaline dissolution of metakaolin (calcinated aluminosilicate clay), followed by polycondensation reactions between aluminate and silicate species, leading to the formation of an amorphous three-dimensional aluminosilicate network. In contrast, the hydration of Ordinary Portland Cement (OPC) is based on dissolution-precipitation reactions. The rheological behavior of geopolymers is mainly driven by hydrodynamic interactions, resulting in a non-zero viscous modulus G", whereas OPC hydration induces colloidal interactions responsible to elasticity and a viscous dissipation that tends to zero [6–8]. These differences allow geopolymers better control over yield stress evolution, shape retention after extrusion, and printability windows, which are important parameters for successful DIW processes. In addition, geopolymers offer several intrinsic benefits over OPC for specific applications especially in nuclear fields that further justify their use in additive manufacturing. Indeed due to their properties of ionic exchange and emulsification properties, they could be used to decontaminate liquid (aqueous or organic effluents) [9,10] or condition contaminated oil [11] respectively. Furthermore, geopolymers present significant potential for

<footnote><sup>a</sup> CEA, DES, ISEC, DPME, Univ. Montpellier, Bagnols sur Ceze, F 30207, France</footnote>

<footnote><sup>b</sup> Synchrotron SOLEIL, Saint-Aubin, F 91190, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: arnaud.poulesquen@cea.fr (A. Poulesquen).</footnote>
diverse applications such as lightweight construction [12], water filtration [13], lunar infrastructure [14,15], thermal insulation [16], artificial reefs [17] and sorption [18,19]. The alkali activators used in the literature are mainly sodium-based chemicals, and the geopolymer precursors include fly ash, silica fume, or metakaolin.

Recent studies have investigated admixtures like polyethylene glycol (PEG), fiber reinforcements, and inorganic fillers as rheological modifiers to enhance paste consistency and printability [20–22]. Furthermore, the use of retarders [23] or modifications in the sodium content of the activated solution [24] have been employed to enhance the printability time window, allowing for better control of the material’s workability during the printing process.

However, additive manufacturing with geopolymers remains an emerging field, particularly in understanding how rheological properties influence print performance [5]. Rigorous rheological characterization is essential to avoid structural collapse and maintain the final geometry of printed objects throughout the process [6].

Previous studies have extensively explored the use of PEG and inorganic fillers to improve viscosity, yield stress, and mechanical properties of geopolymers. For example, PEG has been employed to enhance mechanical performance [25,26], to improve recovery of storage modulus after shear deformation [21] and to introduce shear-thinning behavior [12]. Additionally, PEG increases water retention, lubrication, and thermal cracking resistance [27,28]. Regarding the effect of inorganic fillers, Scanferla et al. increased yield stress with 20 vol% filler additions [22], while Zhong et al. showed increased storage modulus upon adding graphene oxide particles [29]. Nanoclay was also found effective for improving geopolymer thixotropic behavior [30]. In our previous study [9], we enhanced the 3D printability of metakaolin-based geopolymers by incorporating PEG and inorganic fillers, observing stable rheological properties during the first 5 h of paste preparation with PEG.

However, most of these studies were limited to short-term rheological tests (typically less than 3 h), and focused primarily on immediate effects on yield stress or viscosity. To our knowledge, two significant aspects remain to explore: PEG’s retarding effect and quantitative modeling with inorganic fillers. First, while PEG’s viscosity-increasing and yield-stress-enhancing properties are well documented, its role in slowing geopolymerization kinetics—thereby significantly extending the printability window—has not been thoroughly investigated. Second, previous research on inorganic fillers has shown qualitative improvements in rheological parameters, but there is a lack of predictive quantitative modeling capable of tailoring geopolymer rheology.

Moreover, although yield stress measurements have been conducted at various intervals after paste preparation, the rheological tests typically used (oscillatory shear and stress growth tests) are based on short-duration measurements. Consequently, these methods do not adequately capture the effects of prolonged stress on paste behavior, a critical factor for ensuring long-term structural stability in DIW applications.

In this study, we specifically explored these aspects by conducting a comprehensive investigation into the long-term evolution of geopolymer paste rheology, highlighting the retarding effect of PEG and quantitatively modeling the rheological impact of inorganic fillers using the modified Eilers model. We employ long-duration creep tests to explore the paste’s deformation behavior and the effect of PEG’s hygroscopic behavior under constant stress.

To validate our approach, we present a detailed case study calculating critical heights to prevent structural buckling in printed columns, corroborating theoretical predictions with experimental observations. Additionally, X-ray tomography was used to evaluate the porosity, interconnectivity, and channel size of the printed structures, providing critical insights into their suitability for filtration applications.

This study provides new insights and quantitative methods in order to control and predict the long-term rheological behavior and structural stability of geopolymer pastes for DIW applications.

## 2. Materials & methods

### 2.1. Raw materials and sample preparation

Geopolymer (GP) paste was synthesized with the molar composition $SiO_2/Al_2O_3/Na_2O/H_2O = 3.8/1/1/11$. This formulation was specifically designed to ensure a slow geopolymerisation and viscous paste, particularly suitable for Direct Ink Writing (DIW) applications. Sodium hydroxide (NaOH) was selected as the alkaline activator due to its slower reaction kinetics compared to potassium-based activators. A high $SiO_2/Na_2O$ ratio was employed in the alkali-silicate solution to further slow down the geopolymerization kinetics. Additionally, the formulation presented a low water content, resulting in a high solid-to-liquid ratio and therefore higher viscosity. Polyethylene glycol (PEG, Thermo Scientific Acros), with an average molecular weight of 1500 g mol$^{-1}$, was used to increase the viscosity and promote the shear-thinning behavior required for printing. The activating solution consisted of a commercial sodium silicate solution (Betol 52 T, Woellner) and sodium hydroxide pellets (Fisher Scientific, UK). Betol 52 T presented the following composition: 30.2 wt% $SiO_2$, 14.7 wt% $Na_2O$ and 55.1 wt% $H_2O$. Metakaolin (M 1000, Imerys) with a $d_{50}$ = 6 µm, was used as aluminosilicate source. M1000 consists of approximately 83% amorphous phase. The amorphous phase, which is the reactive part, is composed of 54.4 wt% $SiO_2$, 38.4 wt% $Al_2O_3$, 1.3 wt% $Fe_2O_3$, 0.6 wt% $K_2O$, 1.6 wt% $TiO_2$. Additionally, M1000 contains mineral phases such as quartz (8.0 wt%), anatase (2.0 wt%), kaolinite (3.0 wt%), and illite (4.0 wt%). Calcite particles (Betocarb HP, Omya) with a similar particle size to metakaolin particles ($d_{50}$ = 8 µm), referred to as HP, were used to increase the elastic modulus and, consequently, the yield stress.

The preparation of the GP paste followed the protocol established in our previous studies [31,32]. Initially, the activating solution was prepared by dissolving sodium hydroxide pellets and, as required by the composition, polyethylene glycol flakes into the sodium silicate solution. The solution was mixed using magnetic stirring at 150 rpm at room temperature until all solids were fully dissolved. Subsequently, metakaolin particles were gradually added, followed by 5 min of mechanical stirring at 1000 rpm. The HP was then introduced and mixed mechanically for an additional 5 min at 1000 rpm at room temperature. To minimize the air trapped in geopolymer paste, the freshly mixed geopolymer was subjected to a vibration step immediately after preparation. The cartridges used in DIW holding the paste was placed on a vibrating table for one minute to enhance compaction and enables air bubbles to rise to the surface.

The concentrations of organic additives and inorganic fillers are expressed as weight percentage, wt%, and volume percentage, vol%. The GP formulations studied in this article are designated using the following nomenclature: xPEG-yHP, where: - xPEG represents the amount of polyethylene glycol (PEG) in weight percent (between 0 and 3 wt%) - yHP represents the amount of $CaCO_3$ (HP, Betocarb) in weight percent (between 0 and 35 wt%)

### 2.2. Direct Ink Writing (DIW)

The DIW process was conducted using a LUTUM5 (VormVrij, Netherland) 3D clay printer with a nozzle diameter of 0.8 mm. This hybrid printer consists of a screw and pneumatic piston system. The pneumatic piston provides the primary pressure (2 bars), while a rotating helical screw regulates the paste flow rate. This screw pushes the material towards the nozzle, ensuring continuous extrusion and precise control of the flow rate. Column filters were printed with a -45°/45° orientation layer, a layer thickness of 0.4 mm, and a printing speed of 20 mm/s. After printing, the column filters were cured in a 99% humidity chamber at 25°C for 28 days to achieve a firm structure. For the clarity of this study, only results with 2PEG-25HP composition will be presented.
## 2.3. Characterization techniques/ samples characterization

### 2.3.1. Calorimetry

The geopolymerization process was monitored using a TAM Air conduction microcalorimeter (TA Instruments, New Castle, USA) under isothermal conditions at 25°C during 10 days. The metakaolin particles and activating solution were mixed outside the calorimeter. Approximately 6 g of the geopolymer paste was cast into a glass ampoule and introduced into the calorimeter. Heat flow was recorded as a function of time and compared to control sample maintained at 25°C, consisting of water with an adjusted volume to match the same calorific capacity of the paste sample.

### 2.3.2. Compressive strength

The compressive strengths of geopolymers samples were measured using a hydraulic press (3R RP 40/400 N) in accordance with the European EN 196-1 standard. The specimens were 4 × 4 ×4 cm cubes.

## 2.4. Rheological analysis

Rheological tests were performed using a rotational rheometer (Discovery HR-2, TA Instruments, New Castle, USA) equipped with parallel plates of 10 mm (10PP) and 20 mm (20PP) diameter. For all rheological experiments, a fresh sample was used to ensure the accuracy of the measurements and avoid any potential influence of prior tests. The geopolymer paste was prepared no more than 30 min prior to rheological characterization. To accurately characterize the intrinsic properties of the geopolymer paste, we prevented surface drying by applying hexadecane to the edges of the samples during rheological tests. Our previous studies have shown that hexadecane does not interfere with the geopolymerization process [11].

### 2.4.1. Oscillatory rheology

Oscillatory shear strain sweeps were performed at a constant angular frequency of 10 rad/s at 25°C. Each strain sweep test was completed in less than 10 minutes Oscillatory time sweeps were carried out at a fixed shear strain of 0.02% and an angular frequency of 10 rad/s to follow the evolution of the viscoelastic properties over time. These measurements were performed over 24 h to monitor the geopolymerization process.

### 2.4.2. Shear rheology

For stress growth tests, a constant shear rate ($\dot{\gamma}$) was applied, ranging from $10^{-3}$ to $10^{-1}$ s$^{-1}$, and the stress ($\sigma$) was recorded as a function of time. Depending on the applied shear rate, the duration of stress growth tests ranged from approximately 20 min at $10^{-3}$ s$^{-1}$ to 2 min at $15^{-1}$ s$^{-1}$. During the creep tests, a constant shear stress (between 600 Pa and 4000 Pa) was applied, and the resulting shear strain ($\gamma$) was measured as a function of time to evaluate the material's long-term deformation under sustained loads. The duration of creep tests varied from 2 min to 24 h, depending on the applied stress, until either flow occurred or network hardening was observed. Before each experiment, a preconditioning shear step was applied with $\dot{\gamma} = 1^{-1}$ s$^{-1}$ during 5 s to homogenize the sample and eliminate any initial memory effects. Subsequently, an oscillatory time sweep test was performed with $\gamma = 0.01^{-1}$ at 10 rad/s for 200 s to ensure that the geopolymer paste was fully relaxed prior the test.

## 2.5. Microstructural analysis

X-ray tomography experiments were run on ANATOMIX [33] beamline of Synchrotron SOLEIL, located in Saint-Aubin, France. The undulator (U18) gap was set to 7.7 mm, the white X-ray beam was filtered by a 0.2 mm Cu filter, and the mean X-ray energy was 35 keV. The indirect detector optics provides a pixel size of 3.07 µm and the sample/detector distance set at 0.3 m. A Hamamatsu Orca Flash 4.0 V2 camera was used

to acquire 2000 projections over a 180° rotation, with an exposure time of 30 ms per projection, resulting in a total scan time of about one minute.

The samples used for tomography were cylindrical columns produced by Direct Ink Writing (DIW), with a diameter of 2 cm and a height of 4 cm. The images were acquired directly from the core of printed samples. To enhance visualization along the Z-axis, a superposition of three tomography scans was performed for each sample. This approach enabled the reconstruction of a larger volume by carefully aligning and merging the scans.

Volumes were reconstructed with PyHST2 [34] (ESRF, Grenoble, France) and a Paganin filter was applied during the data reconstruction. For 3D quantitative analysis, we followed the protocol described by Petlitckaia et al. [35]. The reconstructed 3D views were visualized using the Paraview software.

# 3. Results & discussion

## 3.1. Quantifying the yield stress of GP pastes

When studying the rheological properties of geopolymers, the yield stress is a critical parameter, as it defines the stress level required for the material to transition from a solid-like state to a flowable state. Several methods are used to determine yield stress, each offering insights into different aspects of the material's behavior:

**Dynamic Rheological Tests:** These tests involve applying oscillatory shear stress or strain to the material and measuring the storage modulus (G') and loss modulus (G''). The yield stress ($\tau_y$) can be calculated from G' and G'' intersection.

**Stress Growth Tests:** These tests involve applying a very low shear rate and observing the stress response over time. The yield stress is often identified at the onset point, where the shear stress begins to increase rapidly, indicating the material's transition from an elastic solid to a flowing state.

**Creep Tests:** In creep experiments, a constant shear stress is applied to the material, and the resulting shear strain is monitored over time. Yield stress is identified when the shear strain starts to diverge, indicating that the material is no longer able to resist the applied stress and begins to flow.

The long-term behavior of yield-stress materials under stress close to the yield stress remains an open question. These materials exhibit a transition from elastic solid-like behavior at low stresses and short times to slow relaxation or “aging” at intermediate times, and finally to flow under stresses higher than the yield stress [36].

In this study we first characterized the yield stress by a dynamic rheological test and then, for a chosen GP formulation, we carried out a deeper characterization with the other rheological tests (stress growth and creep). This approach allows us to provide a more accurate estimation of the yield stress. Finally, we model the printable height limits as a function of yield stress and the shear strain at the yield point. Fig. 1a shows the results of the Dynamic Stress Sweep test conducted on geopolymer (GP) pastes containing 2 wt% PEG and varying amounts of HP filler, ranging from 0 to 35 wt%. The data reveal significant changes in the materials' viscoelastic properties. As observed in our previous study, the incorporation of PEG increases the elastic modulus of GP by two orders of magnitude [9]. Additionally, PEG introduces a yielding point, which is necessary to ensure the elastic-behavior of GP paste.

As suggested by Bessaies-Bey et al. [37] for cement paste, this behavior can be attributed to depletion-induced flocculation mechanisms, where PEG acts as a non-adsorbing polymer with respect to the mineral particle surfaces. The absence of PEG chains from the vicinity of particles results in polymer-depleted zones, which overlap and create effective attractive forces. These interactions promote the formation of a weakly flocculated, percolated network, which is responsible for the solid-like response observed in the linear viscoelastic regime.
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) Evolution of the Storage (G') and Loss modulus (G'') versus the Oscillation Shear Strain at 25°C for GP with 2 wt% PEG and 0 to 35 wt% of HP particles. (b) Evolution of the shear stress at the flow point versus the volume fraction of particles at 25°C for GP with 0 to 35 wt% of HP particles. The fitting parameters for the Eilers model are τ<sub>EM</sub> = 374 Pa and φ<sub>m</sub> = 0.73.</figcaption></figure>

The analysis of the storage modulus (G') and loss modulus (G") shows a gradual increase in the yield stress with rising HP content, as evidenced by the shift to higher stress values at the point where G' equals G" (referred to as the yield stress). This point marks the transition of the material from predominantly elastic behavior to viscous behavior. This evolution follows the classical behavior of concentrated suspensions, where increasing the solid volume fraction enhances particle-particle contacts and the formation of load-bearing force chains, leading to higher elastic modulus and yield stress [38]. In this context, HP particles act as inert mechanical reinforcements within the geopolymer matrix. Furthermore, the extension of the G' plateau at low stress levels, observed with the addition of HP, indicates a more pronounced elastic response and increased stability of the internal network of the paste under low stress. These observations suggest that the addition of HP enhances the rigidity and stability of geopolymer pastes, making them more resistant to deformation under stress. This is particularly beneficial for applications that require a rigid and stable structure. For the GP-2PEG-25HP formulation, the yield stress (τ<sub>y</sub> = 910 Pa) and shear strain at yield stress (γ<sub>y</sub> = 0.029) were extracted from Fig. C.12 in Appendix C.

Fig. 1b presents the stress at the yield point (corresponding to the intersection of G' and Gε from Fig. 1a) is plotted as a function of the total particle volume fraction (metakaolin and calcite combined). To highlight the effect of calcite particles, different calcite loadings (ranging from 0 wt% to 35 wt%) are marked with arrows. In this study, the evolution of yield stress τ<sub>y</sub> as a function of HP particle loading was modeled using a modified Eilers model (EM):

$$ \tau_y = \tau_{EM} \left( \frac{1.25\phi}{1 - \phi/\phi_m} \right)^2 \quad (1) $$

where τ<sub>y</sub> is the yield stress, τ<sub>EM</sub> is the reference yield stress that scales the model, φ is the current particle volume fraction and φ<sub>m</sub> is the maximum packing fraction. For spherical particles, φ<sub>m</sub> typically ranges from 0.52 (random loose packing) to 0.74 (random close packing or ordered packing). The exponent, 2 amplifies the rapid increase in yield stress as φ approaches to φ<sub>m</sub>. Unlike Eilers or Krieger-Dougherty models, Eq. (1) emphasize that yield stress is entirely dominated by particle interactions as φ increases.

As φ approaches φ<sub>m</sub>, the yield stress increases significantly, reflecting stronger particle-particle interactions that resist flow. The modified Eilers model provided a good fit to the data, demonstrating that the rheological behavior of GP pastes with HP particles can be effectively described using classical suspension models. A critical threshold for particle loading was observed at a volume fraction of approximately 0.45 (corresponding to 25 wt% HP), beyond which the paste exhibited a sharp increase in τ<sub>y</sub> and became too rigid to flow.

The geopolymer (GP) paste used in this study (SiO<sub>2</sub>/Al<sub>2</sub>O<sub>3</sub>/Na<sub>2</sub>O/H<sub>2</sub>O = 3.8/1/1/11) contains 33 vol.% of metakaolin particles, was further reinforced with HP particles to increase the yield stress. The addition of HP enhanced the paste's buildability, but formulations with HP levels exceeding 30 wt% displayed discontinuous flow and poor extrusion consistency, making them unsuitable for 3D printing using our screw extrusion system (Lutum5, VormVrij, Netherlands). Conversely, while formulations with lower filler levels maintained good extrudability, they lacked sufficient buildability for stable printing. The GP-2PEG-25HP formulation achieved an optimal balance between extrudability and buildability, making it highly suitable for Direct Ink Writing (DIW) applications. The case study section will provide a more detailed explanation.

## 3.2. Time stability

As shown in Fig. 2a, the complex viscosity of geopolymers increases over time, with significant variations depending on the composition. The geopolymer sample without PEG exhibits a sharper increase in viscosity compared to the samples containing PEG. In contrast, the samples with PEG (2PEG-0HP and 2PEG-25HP) display a more gradual increase in viscosity (from 0 to 5 h), emphasizing the role of PEG in modulating the flow properties during the geopolymerization process. Indeed, PEG acts both as a shear-thinning agent and a retarder. This retarding effect is primarily attributed to PEG's strong affinity for water molecules through hydrogen bonding, which reduces the fraction of free water available for metakaolin dissolution and subsequent polycondensation reactions. It absorbs water and maintains a liquid-like state under conditions of high humidity. PEG slows down the early dissolution-polycondensation mechanisms by reducing the amount of water available. This phenomenon contributes significantly to stabilizing paste viscosity, delaying the stiffening induced by the geopolymerization process. Based on these observations, we define a practical printability window of approximately 5 h. Beyond this period, the reaction between aluminate and silicate species becomes predominant over the dissolution mechanism. The subsequent polycondensation of these monomers results in the formation of oligomers that continuously connect with each other, contributing to the formation of the geopolymer gel phase [39].

Tan(δ) represents the ratio between the loss modulus (G") and the storage modulus (G'). The presence of a peak is often associated with the gelation point of GP [40], hereafter referred as setting time (t<sub>s</sub>). This peak reflects the acceleration of polycondensation reactions throughout the entire volume of the paste, and consequently the formation of an interconected gel phase around metakaolin grains, which are still dissolving. Interestingly, the setting times (t<sub>s</sub>) vary between samples,
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) Time evolution of the complex viscosity (empty marks) and tan(δ) (full marks) of GP, GP containing 2 wt% of PEG and 25 wt% of CaCO₃. (b) Heat evolution (empty marks) and cumulative heat release (full marks) of GP with 0%, 2% of PEG and 25% of CaCO₃ at 25°C.</figcaption></figure>

<figure><img src="image_6.png" /></figure>

with 2PEG-0HP reaching $t_s$ around 14 h, 0PEG-0HP around 10 h, and 2PEG-25HP around 12 h. These findings suggest that PEG reduces the geopolymerization kinetics, delaying the $t_s$.

The calorimetry results of Fig. 2b support these observations, showing the exothermic behavior associated with the geopolymerization process. Indeed, using calorimetry to follow geopolymerization kinetics is well-documented in literature. For example, previous studies have demonstrated that increasing alkali concentration or curing temperature significantly accelerates reaction rates and increases cumulative heat release [41]. Calorimetry analysis has also been employed on geopolymer formulations for DIW applications to investigate reaction kinetics. For instance, Chen et al. [42] used calorimetry to compare the impact of different precursors (blast-furnace slag, fly ash, and silica fume) on geopolymerization kinetics, while Yan et al. [43] demonstrated that calcium carbonate whiskers can improve interlayer bonding strength in 3D-printed geopolymer structures.

In our study, the initial peak in heat flow of Fig. 2b, observed within the first few hours, represents the exothermic nature of the early geopolymerization reactions. This peak aligns with the increase in viscosity observed in the rheological analysis. For the sample without PEG (0PEG-0HP), the higher cumulative heat release over time corresponds to a more rapid increase in viscosity, indicating a more rapid geopolymer network formation. In contrast, samples containing PEG (2PEG-0HP and 2PEG-25HP) exhibit lower heat flow and a slower cumulative heat release. This observation supports the hypothesis that PEG slows down the geopolymerization kinetics, estabilising the rheological behavior and extending the printability window.

Additionally, an exothermic peak is observed around 24 h for all formulations, corresponding to the continued progression of polycondensation. The cumulative heat release confirms that PEG reduces reactivity by approximately 10%, while the combined addition of 2% PEG and 25% calcite (2PEG-25HP) results in a total reduction of about 25% compared to the 2PEG-0HP.

In addition to PEG's retarding effect, calcite also influences by significantly reducing cumulative heat release. As calcite particles are inert and non-reactive, their addition reduces the proportion of the reactive geopolymer phase, consequently lowering overall exothermic activity. At 25 wt%, calcite significantly reduces the percentages of reactive geopolymer phase, which lowers total exothermic activity. For applications requiring long-term stability and reduced heat evolution, PEG and/or calcite addition could be advantageous.

### 3.3. Mechanical properties

Fig. 3 presents the maximum compressive strength values for the different formulations studied. The pure geopolymer (GP) paste exhibited a maximum compressive strength of 68 MPa. When adding 2 wt% of PEG, the compressive strength decreased by approximately 12%, dropping to 60 MPa. This reduction in strength can likely be attributed

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Maximum compressive strength obtained from compression tests performed on cubic samples (4 cm × 4 cm × 4 cm). Bars represent standard deviation. Three samples were tested for each composition. After preparation, the samples were cured for 28 days at 99% relative humidity and 25°C before testing.</figcaption></figure>

to the plasticizing effect of PEG, which interferes with the geopolymer network formation, reducing the overall structural rigidity.

During geopolymerization, PEG remains homogeneously distributed within the paste and leads to the formation of a secondary organic-rich phase after hardening. This second phase exhibits significantly lower stiffness and strength than the inorganic aluminosilicate network thus, reducing the overall structural rigidity and compressive strength of the material.

Additionally, previous studies have shown that PEG can increase the porosity of the geopolymer matrix. This increase in porosity is caused by the formation of cavities left by the PEG particles, which can contribute to a reduction in mechanical strength [44].

Interestingly, GP-2PEG-25HP displayed a significant recovery in strength, with a maximum value of 74 MPa, representing an 8% increase compared to the pure GP and an increase of 18% compared to GP-2PEG-0HP. The increase in strength when using HP fillers may be explained by the calcite's role as a structural filler agent. Calcite particles act as filler materials that enhance the packing density of the paste, resulting in a more compact and cohesive microstructure that reduces the presence of voids and defects. This densification compensates for the loss of mechanical strength caused by PEG.

Despite the slight decrease in strength observed in GP-2PEG-0HP, all tested formulations exhibited sufficient mechanical properties for use in decontamination applications, particularly as column filters.

### 3.4. Buildability by rheological analysis

#### 3.4.1. Stress growth and flow behavior

When a constant shear rate is applied to a yield stress material from $t = 0$, the material initially responds elastically, with stress increasing
<figure><img src="image_8.png" /><figcaption>Fig. 4. (a) Stress growth curves for GP at different constant shear rates, ranging from $\dot{\gamma} = 10^{-3}$ s$^{-1}$ to $15$ s$^{-1}$. (b) Zoom of stress growth curves for $\dot{\gamma} = 10^{-3}$ s$^{-1}$.</figcaption></figure>

linearly with strain. This linear elastic response transitions to a non-linear regime where, under certain conditions, the stress reaches a maximum (a stress overshoot) before relaxing to a steady-state value. At low shear rates (e.g., $10^{-3}$ s$^{-1}$), this peak stress is often used as an estimate of the material's yield stress [45].

As shown in Fig. 4a, stress growth tests were conducted on the GP-2PEG-25HP geopolymer paste across a range of shear rates ($\dot{\gamma} = 10^{-3}$ to $15$ s$^{-1}$) to investigate the yielding and flow behavior. These results show that GP pastes exhibit typical yield-stress fluid behavior, characterized by an initial viscoelastic response, followed by plastic deformation and eventual shear strain softening. At low shear rates, the stress increases nearly linearly with strain, indicating that the material response is dominated by elastic deformation of a percolated particle network. The subsequent stress peak is due to the progressive rupture of this network, marking the transition from a solid-like to a flowing state. The peak stress at low shear rates corresponds to yield stress. In this condition, geopolymer paste can be described using Herschel-Bulkley model [46], and yield stress can be accurately calculated from stress growth tests at very low shear rates [47]. Fig. 4b provides a zoomed-in view of the stress growth test, showing stress growth at $10^{-3}$ s$^{-1}$. Using this approach, a $\tau_y$ of 1200 Pa and $\gamma_y$ of 0.1 was determined from the stress and shear strain on the onset point.

At high deformations, edge fracture and material ejection were visually observed. This edge fracture causes the sample to lose homogeneity, resulting in the stress no longer reflecting the true bulk rheological response of the material. Once this regime is reached, the assumption of homogeneous shear flow is no longer valid. As seen in Fig. 4a, this phenomenon is observed after a pseudo-plateau at lower shear strain values, followed by a continuous stress decrease after the overshoot. These observations suggest that the material no longer behaves as a uniform yield-stress fluid due to localized failure near the sample edges. Only the stress growth experiments at low shear rates provide a reliable estimate of the yield stress. As a result, applying conventional rheological models, such as the Herschel-Bulkley model, to flow curves becomes challenging. This highlights the limitations of using stress growth tests alone to characterize yield stress in these materials.

### 3.4.2. Qualitative creep behavior

Creep experiments are essential for understanding the rheological behavior of geopolymer pastes used in 3D printing, particularly to estimate yield stress and flow dynamics. In these experiments, a constant shear stress is applied at $t = 0$, and the resulting shear strain $\gamma(t)$ is monitored over time. Fig. 5a shows the compliance ($\gamma/\sigma$) of GP-2PEG-25HP as a function of time under applied stress between 600 to 4000 Pa. For each measurement, a fresh batch of geopolymer paste was used to minimize any time-dependent effects of geopolymerization

prior to the test. From $\sigma = 600$ Pa to $800$ Pa, the measurements were stopped after the setting time was exceeded (12 h). The geopolymer paste exhibits time-dependent flow behavior that persists well beyond the typical measurement durations of standard rheological tests. This prolonged test highlights that the yield stress of these materials depends on the duration of the experiment, indicating that the yield stress is meaningful only within the context of a specific experimental timescale [36,48].

For Herschel-Bulkley materials, the application of a constant shear stress in a creep test may not always induce flow; the material may remain in a solid-like state, exhibiting different qualitative behaviors. Observing these behaviors in creep tests is essential for identifying the yield stress.

Fig. 5a illustrates that when the applied stress exceeds $\tau_y$, the GP paste begins to flow, as evidenced by a sharp increase in compliance. On the other hand, if the applied stress remains below the yield stress, the material retains its solid-like character, with the shear strain reaching an almost constant value over time, showing only a slight increase due to wall slip. This behavior is also reflected in the shear rate $\dot{\gamma}$, as shown in Fig. 5(b). When the stress is above $\tau_y$, $\dot{\gamma}$ reaches a nonzero value, whereas, below the yield stress, it drops to zero. These observations reinforce the utility of creep tests for accurately determining the static yield stress, complementing other rheological analyses.

As shown in Fig. 5b, GP paste undergoes several stages during creep. Initially, a short elastic response is observed, followed by a phase where $\dot{\gamma}$ decreases according to a power-law, with a slope around -1 [49,50]. This behavior marks the first stage of creep, during which the material deforms under stress but does not yet transition to flow. Afterwards, if the applied stress exceeds $\gamma_y$, $\dot{\gamma}$ reaches a minimum, referred to as the critical strain, and then increases rapidly. This rapid increase indicates a shift to a flowing state, eventually leading to edge failure of the sample.

Moreover, Fig. 6a shows that this transition time corresponds to a specific shear strain, denoted as $\gamma_c$. This observation indicates that the solid-to-fluid transition during creep is governed by strain accumulation rather than by stress alone. Such strain-controlled yielding is characteristic of soft yield-stress materials undergoing structural reorganization under prolonged loading.

The presence of PEG, which modifies the viscosity profile and water retention, is an important element that impact creep behavior. As previously observed, PEG can absorb water and remain liquid within the geopolymer matrix under high humidity conditions [51], which may induce a lubrication effect This phenomenon induces a progressive deformation and reduces the resistance to long-term strain accumulation, thereby lowering the effective yield stress. As a consequence, the critical strain $\gamma_c$ is reached earlier for lower values of stress, causing
<figure><img src="image_9.png" /><figcaption>Fig. 5. Temporal evolution of the (a) compliance (J) and (b) shear rate (γ̇) for GP-2PEG-25HP paste at 25°C. A fresh batch of geopolymer paste was used for each measurement. From σ = 600 Pa to 800 Pa, the measurements were stopped after the setting time was exceeded (12 h).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. (a) Evolution of the shear rate γ̇ as a function of shear strain γ. Each curve represents the response of the material at different stress levels and the black dots represent the transition time strain points. (b) Transition time Tᵢ as a function of the inverse of the applied stress 1/σ for GP-2PEG-25HP paste at 25°C. The red line represents the linear fit described by the equation log(Tᵢ) = 3287.21/σ - 0.35. The critical yield stress is indicated by the orange star marker.</figcaption></figure>

an earlier transitions from solid-like to fluid-like behavior during creep tests.

As previously observed by Caton and Baravian [36], a key observation from these experiments is the relationship between the applied stress and the transition time Tᵢ, which corresponds to reaching γ_c (Fig. 6b). This study indicates that Tᵢ follows a power-law relationship with the applied stress, as described by the model:

$$T_i/T_0 = 10^{\sigma_0/\sigma} \qquad (2)$$

where T₀ and σ₀ are the fitting parameters and are specific to GP paste. This exponential dependence implies that the creep behavior of the GP paste is governed more significantly by strain than by applied stress. Additionally, the transition time Tᵢ correlates with the setting time of the geopolymer. As aluminosilicate condensation progresses and geopolymer paste stiffens, deviations from the exponential relationship are observed, reflecting the increase of yield stress with reaction advancement. The consistent transition shear strain observed across varying stress levels further supports the idea that shear strain plays a dominant role in the material's response.

The yield stress values obtained from different tests (Table 1) highlight the variability in measurement approaches. The stress growth test gave the highest yield stress (1200 Pa), while the creep test showed the lowest yield stress (714 Pa), indicating that geopolymer pastes may deform under constant stress, which is relevant for long-term stability. This behavior suggests that selecting the appropriate test is essential

<table><caption>Table 1
Yield stress values for different tests.</caption><thead><tr><td>Test</td><td>τ<sub>y</sub> (Pa)</td></tr></thead><tbody><tr><td>Oscillation stress test</td><td>910</td></tr><tr><td>Stress growth test</td><td>1200</td></tr><tr><td>Creep test</td><td>714</td></tr></tbody></table>

to accurately capture the most relevant yield stress behavior for DIW applications.

The different values of yield stress calculated in this section are resumed in Table 1.

### 3.4.3. Case study

During the 3D printing of geopolymers, different types of structural failure may occur. In the case of cylinders, two primary failure mechanisms are typically observed: strength failure and buckling.

As successive layers are deposited, gravity-induced stress accumulates within the structure. To maintain the desired geometry, the printed object's height must stay below a critical threshold to prevent creep in the initial layers. When the printed height reaches a critical value, denoted as H_c, the stress in the bottom layer matches the yield stress, resulting in yielding. This critical height, derived in Eq. (3), represents the maximum height for structural stability under
gravity-induced stress [6,52].

$$H_c = \frac{\sqrt{3}\tau_y}{\rho_e g} \qquad (3)$$

where $\rho_e = (1 - \varphi)\rho$ is the effective density, and $\varphi$ represents the theoretical porosity of printed part.

Buckling does not originate from the bottom layer but is instead influenced by the geometry of the printed object. For a cylinder with a rectilinear infill pattern, assuming vertical isotropy and uniformly distributed pores, self-buckling under its own weight can occur beyond a critical height, calculated as:

$$H_c = \left( \frac{9E_z I_z}{16\rho_e g R^2} \right)^{1/3} \qquad (4)$$

Here $E_z$ is the effective elastic modulus reduced by porosity ($\varphi$) following the Gibson–Ashby relationship [53]:

$$E_z = E(1 - \varphi) \qquad (5)$$

where $E = 2G_0(1 + v)$, $v \approx 0.3$ [54] and $G_0 = 547.76\tau_y - 10728$ (See Appendix C). $I_z$ is the effective moment of inertia, adjusted for porosity as:

$$I_z = (1 - \varphi) \frac{\pi}{4} R^4 \qquad (6)$$

This approach assumes that the porosity uniformly reduces stiffness and density, allowing the vertically axisymmetric structure to be approximated as an equivalent homogeneous system. These assumptions provide a practical estimation to predict $H_c$ of 3D-printed cylindrical structures.

Fig. 7 compares the required yield stress to avoid strength failure (full line) and buckling failure (dashed lines) as a function of object height. The red colored area indicates the region where strength failure occurs due to excessive stress in the lower layers. The colored regions left of buckling failure line represents the printable zone for each diameter, where both failure modes are avoided. For example, according to Eq. (3), strength failure may occur above 15.2 cm with a yield stress of 1000 Pa. On the other hand, Eq. (4) predicts buckling for a cylinder of 2 cm diameter once the height exceeds 12.5 cm. These results emphasize the importance of balancing both yield stress and stiffness during 3D printing.

However, the applicability of these analytical models assumes simplified conditions: regular filament cross-sections, homogeneous adhesion between layers, and minimal geometric deformation. In practice, extrusion parameters such as nozzle diameter (D) and layer thickness (h) have a direct influence on filament geometry. In our study, we used a layer height of 0.4 mm and a nozzle diameter of 0.8 mm, with a D/h ratio of 2.0. This value was chosen based on previous studies, which indicate that $D/h \ge 1.5$ provides a good balance between printing speed and interlayer bond strength [55,56]. Flattened filaments increase interfacial contact, improving structural integrity and reducing the risk of failure.

Based on our previous rheological characterization, the GP-2PEG-25HP composition was selected to test the printability and structural stability of column filters with a 2 cm diameter and an 8 cm height. Mixtures with filler ratios exceeding 25 wt% faced challenges during extrusion, including discontinuous flow and poor extrusion consistency. In contrast, GP-2PEG-25HP demonstrated an optimal balance of extrudability and build stability, enabling the columns to maintain their geometry throughout the Direct Ink Writing (DIW) process without sagging or buckling.

For GP-2PEG-25HP composition, we observed in rheological study $\tau_y$ between 714 Pa and 1200 Pa, $\gamma_y = 0.02$ and from printing parameters $\varphi = 0.4$. When printing a 2 cm diameter cylinder, buckling failure is expected if $H_c > 11$ cm, while strength-based failure could occur above 12 cm. Increasing the paste's rigidity, increasing porosity, or enabling timed evolution of these parameters is necessary for printing higher structures. Fig. 8a shows 3D printed column filters of 2, 4,

6, 8 and 10 cm height. The height variation remained below 1%, even for the 8 cm column. However, the 10 cm column exhibited buckling failure, occurring slightly earlier than predicted by critical height calculations. This deviation may be attributed to slight nozzle movements during the 3D printing process, which may have introduced localized stress concentrations or minor structural imperfections. Additionally, the presence of PEG may have further contributed to this deformation by absorbing moisture and remaining in a liquid state under curing conditions. Fig. 8b provides a cross-section and a 3D tomography reconstruction of 8 cm column, revealing a well-defined porous structure that enhances both mechanical stability and filtration efficiency, essential for preventing preferential flow paths. From 3D tomography image analysis, several key structural parameters were quantified. Fig. 9 shows a XY and a vertical cross-section example of morphological analysis performed on a measurement of samples. The solid fraction was determined to be 62.5% while the porosity is divided into interconnected macropores (35.4%) and internal macropores trapped within the extruded GP filaments (2.15%), having an average pore size of 20 µm. This total porosity value is close to the target value of 40%. Variations may originate from differences in the extrusion flow rate, filament swelling at the nozzle exit, or the degree of filament flattening during deposition. This intrinsic macroporosity is characteristic of yield stress inks. Despite applying vibration to the paste before cartridge loading into 3D printer to remove most air trapped, residual microbubbles often remain in geopolymer paste due to its high viscosity. Similar levels of internal porosity have been reported in the literature [57]. The relatively low internal porosity confirms the effectiveness of our compaction method and helps to guarantee the structural integrity of the printed parts. The rectangular channels created using a rectilinear infill pattern measured 1.43 mm × 1.83 mm with a wall thicknesses of 1.2 mm. The average layer thickness was 1.06 mm. Using the BoneJ plugin in ImageJ [58], the interconnected surface-specific area ($S/V$) was calculated as $4.5 \text{ mm}^{-1}$, approximately three times higher than the value predicted for an equivalent geometry of rectangular channels. This increase is attributed to the additional tortuosity and surface roughness introduced by additive manufacturing, which enhances the specific surface area. These characteristics improve the filter's capacity for fluid interaction and exchange. Additionally, image analysis confirmed a continuous and interconnected macroporosity (Fig. 8b), aligned with the design objectives for filtration. The interlayer connections were uniform across all layers, ensuring mechanical integrity and homogeneity. These structural characteristics, coupled with the increased $S/V$, highlight the potential of this 3D-printed filter for efficient liquid filtration and decontamination applications.

These observations confirm that the PEG and HP additives substantially improved the paste's rheological properties, ensuring precise filament extrusion and stable layer stacking. The presence of PEG not only enhances the extrudability and structural integrity of the deposited layers but also ensures a gradual evolution of viscosity over time, which is particularly beneficial for maintaining the paste's printability during the entire printing process. Based on the rheological characterization of our geopolymer paste, we established the printable limits for our filter designs. The tomography results validated the interconnected porosity and structural stability of each printed layer.

## 4. Conclusions

The optimization of yield stress in geopolymer pastes is essential for successful 3D printing. This study demonstrates that PEG additions stabilize the rheological profile by extending the printability window and buildability.

Yield stress is a critical for ensuring the structural integrity of printed parts during and immediately after extrusion. In this work, multiple rheological characterization techniques were employed to determine yield stress, including dynamic rheology, stress growth test, and creep test. These complementary approaches revealed that yield
<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Required Yield Stress as function of the object height scale. The red solid line represents the critical yield stress threshold to avoid strength failure. The dashed lines correspond to the buckling failure criteria. The scatter points highlight the intersection with yield stress for the GP-2PEG-25HP formulation and both failure criteria. The red colored region indicates the zone where strength failure occurs, while the colored areas to the left of the buckling lines represent the printable regions for different cylinder diameters.</figcaption></figure>

stress is not a single intrinsic material constant, but a time- and strain- dependent parameter. Among these techniques, stress growth tests provided the highest apparent yield stress values, reflecting short-time elastic resistance, while creep tests showed lower values associated with long-term deformation under constant stress.

Based on the combined analysis of all rheological tests, an effective yield stress range between approximately 700 and 1200 Pa was identified for geopolymer pastes filled with PEG and inorganic fillers. Within this range, the lower bound (≈700 Pa), obtained from creep experiments, is the most relevant for assessing long-term stability and structural integrity of printed objects, while the upper bound (≈1200 Pa), calculated from stress growth tests, characterizes resistance to short-term deformation after filament extrusion. This multi-scale definition of yield stress provides a more realistic criterion for designing printable geopolymer formulations.

Creep tests proved particularly effective for long-term stability analysis of geopolymer pastes, capturing the transition from solid-like to fluid-like behavior governed by strain accumulation. This time- dependent yield stress aligns well with earlier studies on shear-strain- driven creep in yield-stress materials, confirming that creep testing as a reliable technique for predicting deformation and collapse in 3D-printed geopolymer structures.

The yield stress values obtained were used to predict the maximum printable height of geopolymer columns by considering both strength-based failure and buckling under self-weight. This case study demonstrated that formulations combining 2 wt% PEG with up to 25 wt% hard particles (HP) achieve an optimal equilibrium between extrudability, shape retention, and resistance to long-term creep deformation for DIW using an hybrid screw and pneumatic piston system. Even if PEG improves rheological behavior of geopolymer paste, its hygroscopic nature may enhance time-dependent deformation, particularly for structures approaching $H_c$, highlighting the importance of yield stress selection based on creep behavior. In summary, the control of rheological properties, particularly yield stress and creep behavior, is essential for 3D printing of geopolymers. This work provides a framework for designing geopolymer pastes that achieve a balance of extrudability and buildability, for future applications in construction, filtration, and waste management.

### CRediT authorship contribution statement

**Xavier Lacambra-Andreu:** Writing – original draft, Investigation, Conceptualization.
**Mario Scheel:** Writing – review & editing, Software.
**Arnaud Poulesquen:** Writing – review & editing, Validation, Conceptualization.

<table><caption>**Table B.2**
Phase composition by Rietveld for GP-2PEG-25HP powders.</caption><thead><tr><td>Type</td><td>Formulation (wt%)</td><td>XRD (wt%)</td></tr></thead><tbody><tr><td>Anatase</td><td>2.00</td><td>3.1</td></tr><tr><td>Illite</td><td>4.00</td><td>2.59</td></tr><tr><td>Quartz</td><td>8.00</td><td>5.77</td></tr><tr><td>Calcite</td><td>25.00</td><td>25.02</td></tr><tr><td>Geopolymer</td><td>66.554</td><td>66.531</td></tr></tbody></table>

### Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT, an AI-powered language model developed by OpenAI, in order to assist with language refinement and grammar corrections of the text. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

### Declaration of competing interest

The authors declare no conflict of interest.

### Acknowledgments

This research was supported by the ECCLOR project, funded by the R&D A&D program of the French Directorate of Nuclear Safety (DDSD). Beamtime on ANATOMIX was provided via SOLEIL proposal no. 202303487. ANATOMIX is an Equipment of Excellence (EQUIPEX) funded by the Investments for the Future program of the French National Research Agency (ANR), project NanoimagesX, grant no. ANR-11-EQPX-0031.

### Appendix A. Particle size

Particle size analysis was carried out using the Malvern Mastersizer 2000 (Scirocco, 2000, Malvern, UK) laser diffractometer using a dry sampling system with a refractive index = 1.52. The particle size distribution was characterized by the mass median diameter ($d_{50}$). Fig. A.10 shows the particle size distribution of HP particles used as inorganic filler for this study.

### Appendix B. Effect of activating solution on calcite

As mentioned in the main text, the calcite was chosen as an inert inorganic filler. In the following section we present the results of XRD. X-ray Diffraction (XRD) measurements were carried out using a device mounted on a high-gloss rotating copper anode, Rigaku RU-200BH. A reflective focusing optics, OSMIC, mainly transmits the Cu $K_\alpha$ radiation ($\lambda$ = 1.5418 Å) and a very small part of the $K_\beta$, the latter being completely absorbed by a Ni filter. A 2D detector, flat image type, model Mar345 is used. XRD patterns were collected from quartz capillaries containing crushed samples and experimental settings were a working power of 50 kV, an intensity of 50 mA and a beam size of 0.5x0.5 mm². Previous studies shown a reaction when calcite particles are diluted in NaOH solution forming Portlandite and Thermonatrite phases [59]. However, when Calcite particles are mixed with activated solution or with geopolymer, XRD does not show any new formation of crystalline phase (see Fig. B.11). Finally, the composition of the geopolymer from the Rietveld analysis given in B.2 confirms that the weight percentage of Calcite phase still the same after 14 days of geopolymer preparation, no reaction with calcite fillers and NaOH of activated solution.
<figure><img src="image_12.png" /><figcaption>Fig. 8. (a) 3D printed columns and (b) cross-section of 8 cm column with the corresponding 3D reconstruction of micro-tomography of GP-2PEG-25HP composition.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9. Cross-sectional views of the 3D-printed filter obtained from X-ray tomography. (Left) Cross-section of the cylindrical filter showing the regular arrangement of the rectangular channels and their distribution within the structure. The red arrow indicates the (Right) zoomed-in view of the vertical section (highlighted by the red box), revealing the well-defined channels with interconnected macroporosity and roughened internal surfaces. The grayscale contrast highlights the macropores (black), solid matrix (gray), and filler particles (white)</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. B.11. XRD analysis of GP-0PEG-0HP, GP-2PEG-0HP and GP-2PEG-25HP.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. A.10. Particle size distribution of CaCO3.</figcaption></figure>

## Appendix C. Supporting rheological analysis

Fig. C.12 shows the results of the Dynamic Stress Sweep (DSS) test performed on the GP-2PEG-25HP formulation. The DSS test was

conducted to determine the yield stress ($\tau_y$) and the shear strain at yield ($\gamma_y$), which are critical parameters to characterize the paste's printability and structural stability.

Fig. C.13 illustrates the linear relationship between the storage modulus in the linear viscoelastic regime ($G_0$) and the yield stress ($\tau_y$) for a geopolymer paste containing 2 wt% of PEG and 0 to 30 wt% of HP. This data is extracted from Oscillatory shear strain sweep tests at small deformations where the material exhibits predominantly elastic behavior. The linear fit shown on the graph is described by the equation:

$$G_0 = 547.76\tau_y - 10727.79 \quad (C.1)$$

The coefficient of determination ($R^2 = 0.9972$) indicates an excellent correlation between the two parameters, suggesting a strong linear dependence of the modulus on the yield stress within the tested range. This suggests that $G_0$ can be reliably predicted from $\tau_y$ for similar geopolymer formulations.

## Data availability

Data will be made available on request.
<figure><img src="image_16.png" /><figcaption>Fig. C.12. Evolution of the Storage, Loss modulus and Oscillation Shear Stress versus the Oscillation Shear Strain at 25°C for GP with 25 wt% of HP particles.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. C.13. Linear relationship between the yield stress ($\tau_y$) and the modulus ($G_0$) for 2PEG-25HP formulation. The experimental data points are represented by orange squares, while the dashed green line represents the linear fit.</figcaption></figure>

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