Additive Manufacturing of Porous Silicon Nitride Inspired by Triply Periodic Minimal Surface

Abstract

Triply periodic minimal surface (TPMS) has been widely used in biology due to its excellent biological, controllable mechanical, and material transport properties. In this study, four types of TPMS structures with silicon nitride (Si₃N₄) ceramic were successfully prepared using digital light processing (DLP) with different minimal surface equations. The influence of different TPMS structures on the mechanical and biological properties of Si₃N₄ ceramic was systematically investigated. Results indicated a better cell proliferation ability in the D structure compared with three other structures, with favorable compressive strength and Young's modulus of 51.84 ± 8.85 MPa and 3.33 ± 0.08 GPa, respectively.

Introduction

Silicon nitride (Si₃N₄) is a structural ceramic well known for its robust flexural strength, good fracture toughness, high hardness, and self-lubrication. It has been widely used in mechanical, aerospace, automotive, and structural applications.^1–3 Research on biomedical materials has demonstrated that Si₃N₄ ceramics not only have good biocompatibility and bone conduction properties but also have excellent imaging performance, making them suitable as an artificial substitute for bone.^4–6

Considering the excellent compressive strength and mechanical and biological properties, Si₃N₄ has become an ideal material for fabricating bone. The porous structure is the key characteristic of bone tissue, which is amenable to cell infiltration, angiogenesis, nutrient transport, and metabolic waste removal.^7–9 Additionally, the porous structure of bone tissue is uneven. This porosity decreases gradually from the inside to the outside, changing in gradient.^10,11

The external layer of bone is compact bone and its central area is cancellous bone. Therefore, the structure and shape of an artificial scaffold must be very complicated. The high hardness and strength of Si₃N₄ are obstacles to fabricating Si₃N₄ bone, leading to time-consuming and labor-intensive processing using traditional methods with low yield. This has become a limiting factor for the application of Si₃N₄ in the field of bioceramics.

In recent years, additive manufacturing (AM) has attracted considerable attention in industry and academia due to its characteristic form-free fabrication method,^12–15 which can produce a complex structure by adding materials layer by layer. In addition, complex shapes and structures can be fabricated easily and cost-effectively. Moreover, the shape and structure prepared by AM have remarkable precision and surface quality. It has also been described as a net shape-forming process.

Digital light processing (DLP), as a forming method in 3D printing, has the advantages of high efficiency in the printing process, high dimensional accuracy, and the ability to produce more complex models or parts.^16–18 Hence, DLP is a viable method for preparing complex Si₃N₄ structures. Many simple porous structures have been successfully fabricated using DLP.^19–21 However, considering the complex structure and biological properties of bone tissue, the simple porous structure cannot meet the unique needs of implant materials.

Triply periodic minimal surface (TPMS) has been widely used in biology due to its excellent biological, controllable mechanical, and material transport properties.^22–27 Unlike traditional lattice or foam structures, TPMS has a smooth surface that allows cells to adhere and grow better.^27–29 In addition, TPMS has a high volume-to-surface area ratio and a highly interconnected porous structure that provides sufficient space for nutrient and waste transport.²⁹

Researchers have compared the effects of TPMS scaffolds and traditional salt-leached scaffolds on cell implantation and cultivation to verify the advantages of TPMS structures in biological applications.³⁰ TPMS scaffolds have ten-fold higher permeability through interconnecting pores than salt-leached scaffolds, making them suitable for cell attachment and growth.

After static cultivation for 5 days, many cell clusters could be observed in the central area of the TPMS scaffold, while only a small number of cells could be observed outside the salt-leached scaffold. Subsequently, Li et al.³¹ further discussed early bone integration of Ti-6Al-4V porous scaffolds designed based on TPMS, demonstrating that TPMS scaffolds could stimulate bone ingrowth and form stable interfaces with surrounding bone tissues.

Hsieh et al.³² compared the mechanical and biological properties of TPMS and traditional lattice structures, reporting more bone growth and a higher fatigue failure threshold in TPMS scaffolds. In summary, TPMS structures are very suitable for biological structures. To date, most materials used on TPMS structures have been metal alloys. For example, Alabort et al.²⁸ demonstrated the feasibility of employing 3D printing to create a Ti-6Al-4V metallic bone using submillimeter TPMS lattices.

Barba et al.²⁹ used TPMS to fabricate porous Ti-6Al-4V structures, effectively addressing the critical aspects of the existing porous implant materials. These aspects included (1) enhancing the feasibility and precision of the manufacturing process, (2) tailoring the design to match the elastic properties of bone, and (3) optimizing pore sizes conducive to osseointegration.

Liu et al.³³ prepared a graded, porous Ti-6Al-4V scaffold through selective laser melting (SLM) based on TPMS. The TPMS method proved effective for implementing multiple modes of gradient structure, comparable with natural bone tissue in terms of continuous topology and interconnections. Nevertheless, there are few reports about the TPMS structure with Si₃N₄ ceramic. Considering the excellent biological and mechanical properties of the Si₃N₄ ceramic, it is significant to research the TPMS structure with Si₃N₄ ceramic using DLP.

In this study, high-performance porous Si₃N₄ with TPMS structures were successfully prepared using DLP. The effects of different TPMS structures on the porosity, microstructure, and mechanical properties of porous Si₃N₄ were systematically analyzed. In addition, the cell viability in different structures was evaluated using the Cell Counting Kit-8 (CCK-8) method, and the cell morphology was observed under a confocal laser scanning microscope (CLSM).

Experimental Procedure

Raw materials

In this study, Si₃N₄ powder was used as the original material (CX-N03, α-phase >91 wt%, D₅₀ = 2.7 μm; Cixing New Material, Ltd.). Al₂O₃ powder (purity >99.99%; Taimicron) and Y₂O₃ powder (purity >99.99%; Shanghai Macklin Biochemical Co., Ltd.) were used as sintering additives. The sintering additives accounted for 10 wt% of the total powder (Si₃N₄ + Al₂O₃ + Y₂O₃).

TPMS design

A porous structure is designed to meet clinical needs; therefore, it is necessary to design the mechanical (compressive strength and Young's modulus, etc.) and biological (porosity connectivity, cell adhesion, and cell proliferation, etc.) properties of the implant to meet the requirements of the human body.

Therefore, this study systematically analyzed the influence of porous Si₃N₄ with different surface structure models on mechanical properties and biocompatibility, compared them with the microscopic structure of the human skeleton, and selected four models suitable for research on the human skeleton.

The TPMS parameterization model (Weierstrass formula) can be expressed by Equation (1)³⁴:

$$\left\{\begin{array}{c}x=Re{\int }_{w_0}^{w_1}{e}^{i\theta }\left(1-w^2\right)R\left(\omega \right)dw\\ y=Re{\int }_{w_0}^{w_1}{e}^{i\theta }\left(1+w^2\right)R\left(\omega \right)dw\\ z=Re{\int }_{w_0}^{w_1}{e}^{i\theta }\left(2w\right)R\left(\omega \right)dw\\ \end{array}\right.$$ (1)

where R(ω) is a complex variable and θ is the Bonnet angle.

Due to the difficulty in determining Weierstrass values, the TPMS is usually expressed approximately by an implicit surface, as shown in Equation (2)³⁴:

where A_k is the magnitude factor; λ_k is the wavelength of periods, r is the location vector in the Euclidean space, h_k is the kth lattice vector in the reciprocal space, P_k is the phase shift, and C is a constant.

In Equation (2), the surface is a TPMS when φ(r) = 0. Many methods are used to generate minimal surfaces, which are usually expressed using implicit trigonometric functions. The four minimal surface equations used in this experiment are shown below³⁵:

$$G:cos\left(x\right)sin\left(y\right)+cos\left(y\right)sin\left(z\right)+sin\left(x\right)cos\left(z\right)=0$$ (3)

$$\begin{array}{cc}& CY:-sin\left(x\right)sin\left(y\right)sin\left(z\right)+sin\left(2x\right)sin\left(y\right)+sin\left(2y\right)sin\left(z\right)+sin\left(2z\right)sin\left(x\right)-\\ & cos\left(x\right)cos\left(y\right)cos\left(z\right)+sin\left(2x\right)cos\left(z\right)+cos\left(x\right)sin\left(2y\right)+cos\left(y\right)sin\left(2z\right)=0\\ \end{array}$$ (4)

$$\begin{array}{cc}& D:sin\left(x\right)sin\left(y\right)sin\left(z\right)+sin\left(x\right)cos\left(y\right)cos\left(z\right)+\\ & cos\left(x\right)sin\left(y\right)cos\left(z\right)+cos\left(x\right)cos\left(y\right)sin\left(z\right)=0\\ \end{array}$$ (5)

$$\begin{array}{cc}& IWP:2\left(cos\left(x\right)cos\left(y\right)+cos\left(y\right)cos\left(z\right)+cos\left(z\right)cos\left(x\right)\right)\\ & -\left(cos\left(2x\right)+cos\left(2y\right)+cos\left(2z\right)\right)=0.3\\ \end{array}$$ (6)

Figure 1a shows the preparation process of porous ceramics. TPMS models were constructed based on Rhino software, and the Grasshopper visual programming language was used for implicit surface parameterization control. Figure 1b shows the four generated types of minimal surface unit cells with a dimension of 4 × 4 × 4 mm. As shown in Figure 1, a single-cell solid structure was prepared based on the skeletal method.

FIG. 1.

Schematic illustration of the fabrication process of porous Si₃N₄. (a) The preparation process of porous ceramics; (b) the four types of minimal surface unit cells. Si₃N₄, silicon nitride.

By modifying parameters in the main program, the minimal surface unit cells can be arrayed to obtain a 16 × 16 × 16-mm minimal surface structure. Similarly, corresponding solid models can be obtained, as shown in Figure 1b. The porosity of the designed TPMS porous model was 50% in this study.

Preparation of the suspension and sample

A ceramic suspension with a solid content of 38 vol% was prepared. The resins and powders were mixed uniformly using a centrifuge at 2500 rpm. First, the single-layer curing depth and single-layer excess curing width of the ceramic suspension were tested to improve the single-layer curing depth as much as possible while ensuring printing accuracy, which is beneficial to improve printing efficiency and the bond strength between the layers of the green body.

After testing, a curing time of 4 s at an energy level of 30 mJ/cm² was found to meet printing requirements. The STL file of the model in Figure 1b is imported into the printer, and Dolphin software was used to convert it into BMP, the image format that the printer can recognize. Finally, the printer's exposure power, exposure time, and X and Y axis motion parameters were designed, and printing was started.

Debinding and sintering of printed green bodies

Green bodies were manufactured through a two-step debinding process: vacuum and air debinding. Figure 2a shows the debinding process, and the air debinding process was the same as the vacuum debinding process. After debinding, the samples were sintered under an N₂ atmosphere and held at 1700°C for 2 h. Figure 2b shows the sintering process. Figure 4 shows the sintered samples, indicating that they were crack free and deformation free and had well-defined contours.

FIG. 2.

The vacuum/air pyrolysis debinding and the sintering schedule of green bodies. (a) Vacuum/air debinding; (b) pressureless sintering.

FIG. 4.

Printed and sintered porous structures with different TPMSs. (a) G; (b) CY; (c) D; (d) IWP. TPMS, triply periodic minimal surface; IWP, I-graph and Wrapped Package-graph; D, Diamond; G, Gyroid; CY, Fischer-Koch C(Y).

Material characterization

The density of Si₃N₄ ceramics was measured using the Archimedes method after sintering. The phase analysis of Si₃N₄ samples after sintering was carried out by X-ray diffraction (XRD; D8 ADVANCE; Bruker), with a scanning range of 2–10° and scanning speed of 90°/min. The surface and microstructure of the sample were observed under a scanning electron microscope (SEM; SU8220; Hitachi).

The porous structure was tested for compressive strength using a universal testing machine (Inspekt Table Blue 20; Hegewald & Peschke). Grid models were printed to evaluate the curing properties of ceramic suspensions.

The porosity of porous structures

$$q_2=1-\frac{{\rho }_1}{{\rho }_2}$$ (7)

$${\rho }_1=\frac{m_1}{V}$$ (8)

The total porosity of the sample is indicated in Equation (7), where q₂ is the total porosity of the porous structure, ρ₁ is the actual density of the porous structure, and ρ₂ is the theoretical density of the porous structure. In Equation (8), $m_1$ is the dry mass of the porous structure and V is the volume of the porous structure.³⁶

Cytotoxicity of porous Si₃N₄ ceramics

Rat bone marrow mesenchymal stem cells (rBMSCs; PriMed-iCell-012; iCell Bioscience, Ltd.) were used for in vitro cytotoxicity tests through direct contact. The CCK-8 method was used to determine cell viability after coculturing the cells with samples for 24, 96, and 168 h. Each experiment was repeated three times to confirm the accuracy of the results.

Afterward, absorbance was measured at a wavelength of 450 nm using a microplate reader (SpectraMax M5; Molecular Devices). Cells were stained using calcein-AM (Solarbio) and PI (Solarbio). The cells were imaged under a fluorescence microscope (DM2000; Leica).

The morphological changes of rBMSCs were observed under a CLSM after culturing with samples for 168 h. The nucleus and cytoskeleton stained blue and red, respectively. First, rBMSCs were cultured in a constant temperature incubator at 37°C under 5% CO₂. Then, samples were sterilized using high-temperature and high-pressure steam at 121°C for 20 min.

The cells were cultured continuously in a constant temperature incubator at 37°C under 5% CO₂ for 168 h. The culture medium was removed, and cells were washed twice with phosphate-buffered saline (PBS). Then, 4% paraformaldehyde was added at room temperature and fixed for 10 min. The cells were washed twice with PBS and then permeabilized with 0.5% Triton X-100 solution for 5 min.

Subsequently, cells were washed twice with PBS. Then, 1 mL/cell of SF633-labeled phalloidin (far red) and DAPI working solution were added to cover the cells and they were incubated at room temperature in the dark for 30 min. Finally, cells were washed three times with PBS and imaged.

Results and Discussion

Influence of curing energy on the photocuring performance

Figure 3 illustrates the influence of incident energy on the curing depth and excess width of the Si₃N₄ suspension. Figure 3a shows that the curing depth increased with increasing incident energy; when the incident energy increased from 4.1 to 5.2 mJ·cm², the curing depth of the Si₃N₄ suspension increased from 27 to 44 μm. Figure 3b shows that the additional curing width increased with increasing incident energy.

FIG. 3.

Influence of molding energy on curing depth and excess width of Si₃N₄ suspension. (a) Cure depth; (b) excess width.

When the incident energy increased from 4.1 to 5.2 mJ·cm², the excess width of the Si₃N₄ suspension increased from 72 to 761 μm. The curing depth reflects the printing efficiency and bonding strength between layers of the printed body, while the excess width reflects the accuracy of the printed model. A suitable curing performance of the suspension should simultaneously have a high curing depth and low excess width.

As shown in Figure 3, the incident energy value of 4.8 mJ·cm² was appropriate for this experiment since the suspension had a relatively high curing depth and relatively low excess width at this energy.

Phase analysis and microstructural characterization of porous structures

Figure 4 shows the printed porous structures, measuring 16 mm in diameter and 16 mm in height. The diameter and height of the sample used for compressive strength testing were 13 and 10 mm, respectively. Six samples were used for testing. Figure 4 shows the SEM images of different porous structures after pressureless sintering at 1700°C. Figure 4 shows that the sintered porous structures remained interconnected without significant blockage and exhibited a smooth surface. In addition to the designed macroscopic pores, the surfaces of the porous structures exhibited micropores measuring ∼1.4 μm.

Figure 5 illustrates the XRD pattern of the porous Si₃N₄ ceramic sample sintered at 1700°C. All the obtained sample phases were identified as β-Si₃N₄, indicating completion of the phase transformation from α-phase to β-phase during the pressureless sintering process. No crystalline phases containing Al₂O₃ and Y₂O₃ were detected, suggesting the formation of a glassy phase that XRD could not detect.

FIG. 5.

XRD pattern of the sintered porous structure. XRD, X-ray diffraction.

Porosity and linear shrinkage of porous structures

Table 1 shows the relative density and linear shrinkage of porous structures, indicating that the relative density of the porous structures after sintering at 1700°C was around 70%. Several factors, such as the content and variety of sintering aids, sintering temperature, and sintering method, influence densification of the samples. In this study, incomplete densification could be attributed to the low sintering temperature.

Table 1.

Density and Line Shrinkage of Different Structures

Samples	G	CY	D	IWP
Relative density (%)	70.89 ± 0.53	69.92 ± 0.08	70.40 ± 0.11	70.9 ± 0.48
Line shrinkage (diameter; %)	16.82 ± 0.02	17.68 ± 0.05	17.54 ± 0.03	16.5 ± 0.08
Line shrinkage (high; %)	17.76 ± 0.16	18.02 ± 0.18	18.15 ± 0.12	17.4 ± 0.05
Total porosity	52.88 ± 0.12	51.27 ± 0.54	52.67 ± 0.92	52.09 ± 1.2
Compressive strength	75.94 ± 8.44	81.27 ± 8.74	51.84 ± 8.85	172.58 ± 24.93
Young's modulus (GPa)	3.44 ± 0.05	3.78 ± 0.19	3.33 ± 0.08	4.8 ± 0.17

IWP, I-graph and Wrapped Package-graph; D, Diamond; G, Gyroid; CY, Fischer-Koch C(Y).

Typically, the temperature required for full densification of Si₃N₄ through pressureless sintering is around 1800°C. Linear shrinkage in the Z direction of the four structures is higher than that in the diameter direction since gravity promotes rearrangement of particles along the Z axis and densification during the sintering process.

In addition, as shown in Table 1, the total porosity of four different porous structures is slightly higher than the porosity we designed (50%) because the porous structure was not densely sintered, and many microscopic pores can be seen in Figure 4.

Mechanical performance analysis of porous structures

Figure 6a shows the compressive strength of different structures after sintering at 1700°C. Although the four structures had similar porosity characteristics, their compressive strengths differed. As shown in Figure 6a, the I-graph and Wrapped Package-graph (IWP) structure exhibited the highest compressive strength (172.58 ± 24.93 MPa). In contrast, the Diamond (D) structure exhibited the lowest compressive strength (51.84 ± 8.85 MPa).

FIG. 6.

Compressive strength and Young's modulus of different structures. (a) Compressive strength; (b) Stress-strain curve; (c) Young's modulus.

In compressive testing, the support columns of the IWP structure are parallel to the load direction. In contrast, the support columns of the Gyroid (G), D, and Fischer-Koch C(Y) (CY) structures exhibit a tilt relative to the direction of the applied load, resulting in torque in the walls of the structure, stress concentration, and lower compressive strength.^26,37

Figure 6b presents the compressive stress–strain curves of structures with different configurations. It can be observed that all four structures underwent a distinct linear elastic region phase until the peak stress, followed by sudden collapse. During this elastic stage, stress was directly proportional to the strain of the sample, and the deformation disappeared when the stress was removed.

Young's modulus is determined by the maximum slope of the stress–strain curve during the compression test.^38,39 According to Table 1, the IWP structure had the highest Young's modulus, reaching 4.8 ± 0.17 GPa, while the D structure had the lowest Young's modulus (3.33 ± 0.08 GPa). The compressive strength of human trabecular bone ranges from 5 to 12 MPa,^40–42 with Young's modulus range of 2–8 GPa.^43–45

The compressive strength and Young's modulus of the four structures presented in this study meet the requirements for human bone.

rBMSC proliferation on different structures

Proliferation of rBMSCs on the porous structure was evaluated using the CCK-8 method. Figure 7a shows the cell absorbance values of rBMSCs on different structures. As demonstrated by the graph, the optical density values of all the samples increased over time and reached a maximum on the 7th day, reflecting the favorable cell proliferation ability of cells on porous structures.

FIG. 7.

(a) CCK-8 detection. Proliferation of rBMSCs on different structures 1, 3, and 7 days after culture (**p < 0.01); (b) proliferative live/dead fluorescence staining of rBMSCs on porous Si₃N₄. (a), (d), (g), and (j) represent cells cultured for one day; (b), (e), (h), and (k) for three days; and (c), (f), (i), and (m) for seven days. CCK-8, Cell Counting Kit-8; rBMSC, rat bone marrow mesenchymal stem cell.

In addition, a comparison of absorbance values of different structures on the 7th day showed that the absorbance value of structure D was much higher than the other three structures, indicating that structure D had a better cell proliferation ability. This phenomenon demonstrates that different structures significantly impact cell proliferation. Relevant studies have shown inconsistent cellular activity on different structures.^46,47

In this study, the D structure showed the best cell proliferation at the same porosity compared with other structures, which might be due to their different permeability. Blanquer et al.⁴⁸ prepared eight different porous structures based on TPMS, and their porosity was exactly the same. The results showed that eight different structures had different permeability.

The high permeability of scaffolds can provide an environment where nutrients and metabolic waste can be diffused, a prerequisite for uniform tissue growth. The permeability of porous structures is determined by many parameters, such as pore size, orientation, and connectivity. In addition, permeability is also related to fluid flow within the porous structure. Shear stress during fluid flow strongly affects cell function and cell distribution after inoculation.

Ma et al.⁴⁹ showed that scaffolds with higher permeability can stimulate cell proliferation due to their better oxygen and nutrient supply capacity. Furthermore, live/dead staining was performed to visualize cell viability. Figure 7b displays the fluorescent images of rBMSCs on a porous, curved silicon nitride surface stained with live/dead dyes, where the green and red colors represent live and dead cells, respectively.

Figure 7 shows the typical time-dependent proliferation behavior of cells in the culture medium; as the cultivation time increased, the cells continued to grow, indicating the good proliferation ability of rBMSCs on the surface of porous Si₃N₄.^50–52

Adhesion of rBMSCs on different structures

Fluorescence staining was performed on rBMSCs cultured on porous structures for 7 days to observe cell adhesion and morphology on the porous structures. TRITC-phalloidin and DAPI were used for fluorescence labeling of rBMSCs to stain the cell cytoskeleton and nucleus, respectively. After staining, cells were observed under a CLSM, as shown in Figure 8.

FIG. 8.

CLSM images were captured to visualize the nucleoli and cytoskeletons of rBMSCs after 7 days of culture on various porous structures. (a) Surfaces; (b) planes. CLSM, confocal laser scanning microscope.

In staining the cell cytoskeleton, the TRITC-phalloidin fluorescent dye binds to F-actin in the cells. F-actin can regulate cell proliferation, apoptosis, and invasion and provide stiffness to the cell. In staining the cell nucleus, the DAPI fluorescent dye can strongly bind to DNA after penetrating the intact cell membrane.

Figure 8a shows effective adhesion of cells to the surface of the porous structure. Moreover, Figure 8b shows clear filamentous pseudopodia, lamellipodia, and average spreading area of the cells.⁵³ In summary, the D structure demonstrated superior cell proliferation capability and suitable mechanical properties compared with the other three structures. Hence, the D structure could be optimal for human implant structures.

Conclusions

The effects of four different minimal surfaces on the porosity, compressive strength, Young's modulus of porous structures, and proliferation and adhesion of rBMSCs on different structures were investigated. The main conclusions are as follows:

• (1)After sintering at 1700°C, there was no significant difference in porosity between the four different structures, but there were significant differences in compressive strength and Young's modulus. The compressive strength and Young's modulus of the IWP structure were the highest (172.58 ± 24.93 MPa and 4.8 ± 0.17 GPa, respectively); the compressive strength and Young's modulus of the D structure were the lowest (51.84 ± 8.85 MPa and 3.33 ± 0.08 GPa, respectively).
• (2)rBMSCs were incubated on the porous structure for 1, 3, and 7 days, and the cell absorbance values were tested. A comparison of the absorbance values of different structures on day 7 showed that the D structure had higher absorbance values, reflecting the better cell proliferation ability of the D structure. In addition, cell imaging was performed using the live/dead double staining method, and the number of cells increased over time. By staining, cell adhesion was found on the surfaces of all structures, with good morphology.

Authors' Contributions

S.H. was involved in writing—original draft; P.Y. was involved in writing—review and editing, and conceptualization; S.W. was involved in supervision; and H.W. was involved in investigation. All authors have read and agreed to the published version of the article.

Author Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Funding Information

This work was supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019B1515130005), Key Area Research and Development Program of Guangdong Province (Grant No. 2020B090923002), Foshan Science and Technology Innovation Team Project (Grant No. FS0AA-KJ919-4402-0023), Xijiang Innovation Team Introduction Program of Zhaoqing, and Science and Technology Program of Yunnan Precious Metals Laboratory (Grant Nos. YPML-2022050219 and YPML-2022050205).