Introduction

As an extensively used ceramic additive, polyelectrolyte species play an essential role in colloidal processing. Polyelectrolytes are a kind of long-chain structure polymers containing at least one type of ionizable group (e.g. amino, carboxyl and sulfonic acid groups). According to their molecular weight, molecular architectures and functional groups, polyelectrolytes can be widely used as dispersants, thickeners, flocculating agents, adhesives, and so forth. Compared with inorganic and nonionic polymers, polyelectrolyte species exhibit incomparable superiority, including the multiplicity of structures, more significant powder coating effect, and most importantly, flexibility for tailoring rheological properties. It is favourable to meet the varying demands of rheological properties proposed by various colloidal processing methods. Furthermore, this regulation process can be realized merely through modulating the adsorption behaviour or conformation of polyelectrolytes [1, 2].

If the solvent conditions (e.g. pH, temperature and ionic strength) are precisely controlled, ionized polyelectrolytes can firmly anchor on the powder surface with a stretched configuration, imparting electrostatic and steric repulsion to a colloidal dispersion system. Thus, a stable suspension can be obtained. Also, by reducing the surface charge or transmitting polyelectrolyte conformation towards a compact coil, the repulsion force can be considerably weakened. Therefore, a weakly flocculated or strongly flocculated suspension can be achieved [3, 4].

Several forming methods have been developed based on the above theory, such as direct coagulation casting [5, 6], gel casting [7], temperature-induced gelation [8,9,10], and robocasting [11,12,13]. Although the specific processing substantially differs, these methods all begin with a well-dispersed suspension of reasonably low viscosity. The suspension was subsequently transformed into a stiff gel for the first three methods. The gel should have sufficient strength to support its own weight and be handled without shape distortion [14]. In recent years, a substantial amount of research has been conducted and the transforming mechanisms that relate to the formation of either physical or chemical bonds between particles have been deeply explored. However, for the forming method of robocasting, which relies on transmission from a well-dispersed suspension towards a viscoelastic gel, relatively little attention has been given to the regulatory mechanism, especially the relationship between the adsorption behaviour and viscoelastic properties.

As a novel rapid prototyping technique, robocasting has put forward much higher requirements for the rheological properties of colloidal gel inks [15]. The gel inks should possess low viscosity at high shear rate (arise from the severe friction between the inks and nozzle inner wall) to ensure smooth extrusion from the nozzle. After depositing on the substrate, the gel inks should be rigid enough with sufficient shear yield stress (τy) and storage modulus (G′), thus guaranteeing only minor elastic deformation (rather than plastic deformation) occurring during assembly of spanning structures [16, 17]. And the elastic properties (shear yield stress and storage modulus) can be tailored according to the following scaling relationship [18]:

$$y=k{\left(\frac{\phi }{{\phi }_{\mathrm{gel}}}-1\right)}^{x}$$
(1)

where y is the elastic property, k is a constant, \(\phi\) is the volume fraction, \({\phi }_{\mathrm{gel}}\) is the colloid volume fraction at the gel point, and x is the scaling exponent. As \(\phi\) remains constant, the elastic properties of the gel are only controlled by \({\phi }_{\mathrm{gel}}\). Since \({\phi }_{\mathrm{gel}}\) scales inversely with bond strength, the elastic properties increase significantly if the interparticle interaction becomes more attractive [11, 19]. So far, several efforts have been done towards adjusting the interparticle interaction, such as through adjusting solid content [19], pH values [12], and ionic strength [13], etc. However, the adjustment via tailoring adsorption behaviour of polyelectrolyte was rarely involved in the previous study.

In this study, SiC colloidal gel inks with viscoelastic property were prepared using a common two-step method, creating a well-dispersed suspension followed by inducing gelation by altering the pH values towards isoelectric points (IEPs). The effect of PEI adsorption behaviour, a commonly used cationic polyelectrolyte, on the rheological properties was systematically investigated for both steps. Particular attention was given to the relationship between adsorption behaviour and viscoelastic properties. Consequently, 3D SiC lattice structures were fabricated by robocasting using the optimum colloidal gel ink.

Experimental procedures

Colloidal gel inks preparation

Hongxin Grinding Material Co., LTD provided commercially available α-SiC powders with a mean particle size of 0.5 μm and a specific surface area of 15.36 m2/g. B4C (d50 = 0.5 μm, Jinma Industry, Dalian, China) and water-soluble nano-Carbon Black (CB) (d50 = 22 nm, Jinma Industry, Dalian, China) were used as sintering aids. 100 g SiC, 1.47 g B4C and 1.47 g CB were attrition milled in 200 ml proof ethanol for 6 h with 12.7 mm diameter spherical SiC milling media to obtain homogenized powder mixture without large agglomerates. After attrition milling, the slurry was poured through a 400 mesh sieve to remove milling media, followed by drying process in an 80 °C even for 24 h. The dried paste was crushed with an agate mortar and pestle. The powder mixture was sieved another time to eliminate undesired large agglomerates caused by ethanol evaporation.

Stable suspensions (52.4 vol.%) were firstly prepared by adding powder mixture in a stepwise manner to aqueous PEI (M.W. = 10,000, Aladdin Industrial Co. Shanghai, China) solutions of varying concentrations (0.8–2wt.%, corresponding to the total mass of SiC, B4C, and CB) under high-shear stirring. After powder addition, these suspensions were stirred continuously for 2 h at 600 rpm and ultrasonicated for 10 min to achieve uniform dispersion. Next, methylcellulose (1500 mPa s, Aladdin Industrial Co. Shanghai, China), acting as a thickening agent, was introduced to the suspensions to a final concentration of 5.9 mg/ml (refer to final suspensions), which were once again homogenized by agitation for 2 h at 600 rpm. Subsequently, gelation was induced by adjusting the pH values towards IEPs (pH ~ 10.4) with 5 mol/L NaOH (Aladdin Industrial Co. Shanghai, China). Notably, the IEPs referred to here are not the isoelectric point of a particular powder, but an intermediate pH between their respective IEPs. All the pH values were measured by a pH meter (AZ Instrument, AZ-8692, Taiwan). Prior to each measurement, the pH meter was calibrated using pH buffer solution (Reagecon Diagnostics Ltd. CC10405, USA). Each ink's ionic strength was fixed with 1 mol/L KCl (Aladdin Industrial Co. Shanghai, China) solution. The colloidal gel inks with a final solid content of 51 vol.% were homogenized by planetary ball milling for 12 h at 750 rpm.

Zeta potential tests

The Zeta potential of six suspensions (as-received SiC, B4C, and CB suspensions including and excluding 1 wt.% PEI) as a function of pH values were measured with a Zeta potential analyser (Dispersion Technology, Inc. Bedford Hills, NY USA), respectively. The effect of dispersant content on the Zeta potential of SiC suspensions was also tested to evaluate the PEI saturation adsorption capacity. In preparation for each measurement, powders with a solid content of 1 vol.% were suspended in aqueous solution and sonicated for 10 min. The pH values were adjusted with 1 mol/L NaOH and the ionic strength was tailored using 0.001 mol/L KCl solution.

Potentiometric titration

A 0.5 wt.% PEI solution (100 g) and a blank solution (100 g) without PEI were firstly alkalized towards pH value of 11.5 using 3 mol/L HCl. Subsequently, 1 mol/L KCl solution was added to the blank solution, so that both solutions possessed the same ion concentration. Next, the two solutions were gradually titrated with 1 mol/L HCl solution towards a final pH of 2.5. The amount of HCl solution was added each time and the corresponding pH values were recorded. Both titration curves were plotted and fitted with an 8-order polynomial function. The difference between these two functions (namely the blank titration curve was subtracted from the sample curve) can be treated as the net consumption of OH− as a function of pH values.

Adsorption measurements

10 vol.% suspensions at pH 10.4 were prepared with varying amounts of PEI and ball milled for 12 h to measure the adsorption amount of PEI on the surface of SiC, B4C, and CB particles. After centrifugation at 4000 rpm for 20 min, the sediments were collected and characterized by Thermogravimetric Analysers (TA Instrument, Q600, USA). The tests were conducted in an N2 atmosphere from room temperature to 750 °C at a heating rate of 5 °C/min. According to the test results, the adsorption isotherm was plotted and fitted with the Langmuir monolayer adsorption equation, as shown below.

$$\frac{C_{\rm e}}{A_{\rm s}}= \frac{C_{\rm e}}{C_{\rm m}} + \frac{K}{C_{\rm m}}$$
(2)

where Ce is the equilibrium concentration of PEI, As is the adsorption capacity of PEI to SiC surface when the adsorption process reaches equilibrium, Cm is monolayer saturated adsorption capacity of PEI, and K is a constant.

Rheological properties tests

Rheological properties were measured using a Rotational Rheometer (TA Instrument, DHR-2, USA) with 25 mm diameter parallel plates. Before each testing, the plates were roughened with 200-grit abrasive paper to avoid undesired wall-slip effect. A wet sponge was used to wrap the parallel plates without contacting them to minimize water evaporation during the testing.

Steady-state flow mode and oscillatory mode were employed. For both modes, a pre-shear of 60 s−1 was applied for 120 s followed by a quiescent time of 60 s before each test.

Flow curves were obtained by measuring shear stress (τ) as a function of ascending shear rate ranging from 0.1 s−1 to 100 s−1 with a frequency of 1 Hz. Each curve was fitted to the Herschel–Bulkley model [20], as presented in the following equation:

$${\tau ={\tau }_{y}+k\cdot }^{ n}$$
(3)

where τ is the applied shear stress, τy is the shear yield stress, k is the consistency index, Σ is the applied shear rate, and n is the flow index.

The viscosity versus shear rate curves for both suspensions (ceramic powders mixture dispersed with PEI without containing methylcellulose) and colloidal gel inks with varying PEI content were acquired using the same test parameters as steady flow curves.

The equilibrium storage modulus (G′) was tested with oscillatory mode. The shear stress increased logarithmically from 0.1 to 100 Pa with a frequency of 1 Hz. All rheological measurements were performed at 20 °C.

Fabrication of 3D periodic lattice structures

3D periodic lattice structures were fabricated using a homemade deposition apparatus, consisting of a 3-axis motion system, a high-pressure gas-assisted extruder, and a deposition platform. The extruder moves in the horizontal direction, while the platform travels along the z-axis. The platform was precoated with nonwetting oil to ease non-uniform shrinkage during the drying process [21]. A 5-ml syringe with a cylindrical tip (internal diameter = 0.2 mm, length = 2 cm) and a rubber plunger was used to load the gel inks. After driving the plunger into the syringe, the gel ink was extruded smoothly through the nozzle tip with a constant extrusion speed of 7 mm/s. The extruder and platform's motion was independently controlled by STL files, prepared using SolidWorks 2016 software. Other extra parameters are shown in Table S1. All samples were deposited under atmospheric conditions. The as-printed samples were continuously placed at the platform under atmospheric conditions (RH ~ 30%) for 24 h to remove the residual water. At last, the dried samples were pressureless sintered at 2000 °C for 1 h under an Ar atmosphere and freely cooled down to ambient temperature.

The sintered samples were observed by a scanning electron microscope (Hitachi, s4800, Japan). The apparent density (ρapp) was measured by water immersion method:

$${\rho }_{{\rm app}}=\frac{{m}_{1}}{{m}_{1}-{m}_{2}}{\rho }_{w}$$
(4)

where m1is the dried weight, m2 is the submerged weight. ρw is the density of distilled water. The porosity (P) in the filament was calculated as:

$$P=\left(1-\frac{{\rho }_{\mathrm{app}}}{{\rho }_{th}}\right)\cdot 100\%$$
(5)

where ρth is the theoretical density (ρth = 3.19), which was calculated by the composition and theoretical densities of the original powders.

Results and discussion

For the first step, well-dispersed suspensions with a solid content of 52.4 vol.% were generated. Zeta potential measurements were used to characterize the PEI effect (acting as the dispersant) on the surface charges, and therefore the dispersibility of SiC, B4C and CB, respectively. As displayed in Fig. 1a, all the particles are negatively charged under neutral and alkaline conditions in the absence of PEI. However, as 1.25 wt.% PEI was added to the suspensions, positively charged PEI chains could adsorb onto powders surface by electrostatic adsorption with an extended conformation, resulting in charge reversal.

Figure 1
figure 1

Zeta potential as a function of pH values for (a) as-received SiC, B4C, CB and powder mixture (named as PM) including and excluding 1.25 wt.% PEI, and (b) SiC particles with varying PEI content. The isoelectric points (IEPs) of SiC, B4C, CB and powder mixture were measured to be 10.45, 10.18, 10.38 and 10.01, respectively

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The effect of PEI content on the Zeta potential of SiC suspensions is revealed in Fig. 1b. All the curves followed the same trend. As pH < IEPs, the curve of 1.25 wt.% PEI always has a maximum value at the same pH compared with other curves. That’s likely because SiC particles had been saturated adsorbed with 1.25 wt.% PEI. Further increasing PEI merely elevates the ionic concentration, thus resulting in an aggravation of the screening effect [20, 22]. Hence, as the PEI content was greater than 1.25 wt.%, the resulting Zeta potential had relatively lower values. As for the suspensions containing 0.5 and 1 wt.% PEI, there was no sufficient adsorption of PEI on SiC particles surface, thus resulting in fewer net positive charges [23].

The rheological performance of 52.4 vol.% SiC suspensions with varying PEI content was studied since differences in PEI levels may drastically affect interparticle electrostatic repulsion. As illustrated in Fig. 2, the suspension dispersed with 1.25 wt.% PEI showed optimal fluidity with a low shear viscosity (η0) of 27.86 Pa s. By contrast, the 1.5 wt.% PEI curve displayed a relatively higher viscosity. In addition to a weaker electrostatic repulsion, polymer chain entanglement and/or particle bridging may also lead to a viscosity increment displayed in this suspension. The suspension dispersed with 1 wt.% PEI had the highest viscosity, which could be attributed to intense interparticle collisions under shear stress. Ultimately, suspension dispersed with 1.25 wt.% PEI was suggested as the optimum amount to produce SiC aqueous suspensions at high concentrations.

Figure 2
figure 2

Viscosity as a function of shear rate for 52.4 vol.%, as-received SiC suspensions with varying PEI content

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For the second step, a fluid-to-gel transition was induced by adjusting the pH values towards IEPs (pH 10.4). This process was accompanied by a PEI conformational change from an extended chain towards a compact coil [3], thus leading to a sharp reduction in electrostatic and steric repulsion forces. As the total interaction became attractive, an obvious viscoelastic response was generated [11]. Before viscoelasticity analysis, PEI adsorption experiments conducive to explaining viscoelastic behaviour were initially conducted.

Figure 3a shows the adsorption isotherm of PEI chains on the SiC surface at the pH of IEPs. At a low PEI content (< 1 wt.%), almost all the PEI added could adsorb on the surface without appreciable free polymer that remains in the solution. As PEI is higher than 1 wt.%, free PEI chains began to appear. With the increase in PEI, the adsorption amount increases continuously. The growth rate, however, slowed down, until the saturation adsorption reached 1.25 wt.%. The saturated adsorption capacity of PEI on B4C and CB particles was also measured to be 0.84 and 0.36 wt.%, respectively. The addition of B4C and CB (acting as sintering aids) hardly influenced the adsorption quantity on SiC, given their relatively small dosage.

Figure 3
figure 3

(a) PEI adsorption isotherm on the SiC surface at the pH of IEPs. The black line indicates the actual adsorption capacity. The red line represents an ideal condition that all the PEI added could adsorb (for comparison). (b) The fitting curve of the Langmuir monolayer adsorption model

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Due to the steep onset that presents at the adsorption isotherm, the adsorption mechanism could be classified as a high-affinity type [24], which has been widely reported [25,26,27]. Similar adsorption experiments had been reported by Zhang [25], and the findings proved that PEI chains could adsorb onto SiC surface at pH = 11 ± 0.1 through a few of the (C2H4)2NH2+ ions remaining at that pH range.

Next, the adsorption curve was reanalysed using the Langmuir monolayer adsorption equation, as displayed in Fig. 3b. The discrete data points fit well with the Langmuir model (correlation factor R2 = 0.998), indicating a monolayer adsorption type.

Based on the results of adsorption tests, PEI additions of 1, 1.25, and 1.5 wt.% were selected as three key variables (corresponding to unsaturated adsorption, saturated adsorption and excess PEI, respectively) for the follow-up experiments. In fact, we have tested the rheological properties of the gel inks with a wide range of PEI content (from 0.5 wt.% toward 3 wt.%). However, as PEI was lower than 1 wt.% or greater than 1.5 wt.%, the corresponding rheological curve exhibited irregular fluctuation (see Fig. S1 and S2). Thus, the corresponding gel inks behaved in a heterogeneous yield-pseudoplastic manner, which were not fitted for robocasting.

Figure 4a and b shows the shear stress versus shear rate and storage modulus (G′) versus oscillation stress relationships for the inks as a function of PEI content, respectively. Each flow curve in Fig. 4a accorded well with the Herschel–Bulkley model (R2 > 0.99) with the fitting parameters listed in Table 1, signifying that all the inks behaved in a yield-pseudoplastic manner.

Figure 4
figure 4

Elastic properties ((a) Shear stress versus shear rate and (b) log Storage modulus (G′) versus log Oscillation stress) of the gel inks with varying PEI content

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Table 1 Fitting parameters of Langmuir monolayer adsorption equation and Herschel–Bulkley model. Adsorption tyre and Storage modulus (G′) were also provided. It’s to note that K and Ra2 are for Langmuir monolayer adsorption equation, while k and Rb2 are for Herschel–Bulkley model
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According to Eq. (1), as the solid content remains constant (51 vol.%), the elastic properties (τy and G′) of the inks depend entirely on the bond strength. It was found that the ink containing 1.25 wt.% PEI displayed the highest storage modulus of 13,381.87 Pa and shear yield stress of 355.89 Pa, indicating a maximum bond strength. However, the ink containing 1 wt.% PEI presented the lowest elastic property (τy = 46.77 Pa and G′ = 1464.86 Pa), suggesting a minimum bond strength. This phenomenon could be ascribed to the difference in the adsorption amount of PEI on the SiC surface.

At the pH of IEPs, although only ~ 5% amine groups were protonated (see Fig. 5), the PEI chains could still adsorb onto the SiC surface through a few protonated amine groups via electrostatic force. However, the uncharged segments of the chains were hydrophobic and displayed a conformation of suppressed loops [3]. Since compactly covered with hydrophobic chains, SiC powders could attract each other via long-range hydrophobic forces and the attractive interaction became stronger with increasing adsorption amount [28]. For the steric repulsion force, however, adsorption amount contributes little to it, because increasing PEI content could not significantly thicken the adlayer, given the monolayer adsorption type and the compact coil configuration of PEI chains. Therefore, the increase in adsorption amount of PEI could remarkably enhance hydrophobic interactions and thus lead to higher elastic properties.

Figure 5
figure 5

Degree of ionization as a function of pH values. The insert is a magnified image (degree of ionization ≈5% at the pH of 10.4)

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As 1.5 wt.% PEI was added, 1.16 wt.% of which attached onto the SiC surface with 0.34 wt.% that dissociated in the solution (see Fig. 4a). The corresponding gel ink exhibited medium elastic properties. Thus, we could conclude that the nonadsorbed polymers only weaken elastic properties. Similar phenomena were reported by Ogden [4], who found that nonadsorbed poly-(methyl methacrylate) (PMMA) could improve the stability of weakly flocculated Al2O3 suspensions over a broad concentration range. Although having a negligible influence on the long-range van der Waals and steric interactions, the nonadsorbed PMMA that existed at gap region could introduce a depletion interaction with a repulsive barrier of a few kT or higher, thus dramatically weakening the attractive interaction between Al2O3 particles.

Figure 6 shows the viscosity versus shear rate relationships with varying PEI contents. It was found that all the gel inks revealed uniform shear thinning behaviour. The gel with 1.25 wt.% PEI always exhibits the highest viscosity at the same shear rate, followed by the 1.5 and 1 wt.% samples.

Figure 6
figure 6

Viscosity versus shear rate of the gel inks with varying PEI content

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At the pH of IEPs, attractive forces (including long-range hydrophobic force and van der Waals force) dominated the colloidal interaction. The particles were driven to be held together, thus forming a space-filling gel network. The gel strength, which is determined by the magnitude of attractive force, could be reflected by the low shear viscosity (η0) [29]. As shown in Fig. 6, the gel with 1.25 wt.% PEI exhibited the highest η0, followed by PEI concentrations of 1.5 and 1 wt.%, indicating a declining trend of attractive interaction, which is in accordance with the results shown in Fig. 4. As the shear rate increased to a certain level that the applied stress surpassed the yield stress (τy), the gelled structure was broken into smaller units. Flow was more facilitated under high shear rate, and therefore a noticeable shear-thinning phenomenon was observed.

Above all, we can conclude that as saturated coated with PEI, the SiC suspension exhibited the optimum dispersibility, and the corresponding gel displayed the strongest elastic properties. Since higher elastic properties facilitate the retaining of the initial shapes during the assembly of spanning structure, the gel ink with 1.25 wt.% PEI was suggested as the best composition for the process of robocasting.

The optimal gel with 1.25 wt.% PEI was utilized in fabricating a microsized 3-D lattice structure to assess its printability. Figure 7 shows images of the sintered 3D lattice structure fabricated with the optimum colloidal gel. The structure was composed of 16 layers with a boundary dimension of 19.12 mm (x-axis) × 18.98 mm (y-axis) × 2.65 mm (z-axis). Thus, the total linear shrinkage by 5.35%, 6.04% and 7.67% of the originally designed model was calculated. The structure was densified up to 97.2% of the theoretical density. The relatively lower shrinkage and higher density compared with previous reports [17, 30,31,32] could be attributed to its high solid content (51 vol.%). The separation distance between two adjacent filaments was set as 1 mm, as presented in Fig. 7a.

Figure 7
figure 7

Images of sintered 3D lattice structures fabricated with the optimal colloidal gel: (a) top view, (b, c) magnified images of top view, (d, e) magnified images of cross section

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Figure 7b and c gives the local magnified images of Fig. 7a. As was extruded from the nozzle, the filament could maintain its initial cylindrical shape with a diameter of 240 μm. The knots at the connection points are slightly thicker than the filaments, indicating a great lap joint between two adjacent layers.

Figure 7d and e shows the vertical section of the specimen. Owing to its outstanding elastic properties, no obvious deformation was detected, even at the centre of the lower support points.

Figure 8 illustrates SEM micrographs of the sintered sample. It was shown that the specimen was almost entirely dense without noticeable pores after sintering at 2000 °C for 1 h. The rod-like grains (diameter 1.7–3.2 μm, length 4.3–9.1 μm) were already completely grown with a uniform size.

Figure 8
figure 8

SEM micrographs of sintered sample surface. (a) The outer surface; (b) the fracture surface

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In summary, high solid loading (ϕ = 51 vol.%) SiC colloidal gel inks, which were applied in the novel forming method of robocasting, were prepared with a two-step method. The effect of PEI adsorption behaviour on the rheological properties of both steps was investigated separately. As was saturated coated with 1.25 wt.% PEI, the corresponding suspension presented the optimum dispersibility, and the colloidal gel displayed the strongest elastic properties, which was best fitted for robocasting. A microsized 3D lattice structure was fabricated with the developed ink. The sintered sample could maintain its initial shape without deformation and cracking.