Fabrication of Novel 316L Stainless Steel Scaffolds by Combining Freeze-casting and

3D-printed Gyroid Templating Techniques

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Kuan-Cheng Lai 1, Cheng Tsai 1, Shih-Yao Yen 1, Ko-Kai Tseng 1, Jien-Wei Yeh 1, 2,
Po-Yu Chen* 1, 2
1 Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu,

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300044, Taiwan
2 High Entropy Materials Center, National Tsing Hua University, Hsinchu, 300044, Taiwan
*Corresponding author. E-mail: poyuchen@mx.nthu.edu.tw

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Abstract
Porous metals have been widely investigated to develop advanced applications such as

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lightweight materials, catalyst carriers, electrodes, damping materials, impact energy
absorption materials, interconnected composites, and bioimplants. Porous bioimplants are often
used to repair cancellous bone defects. Nevertheless, how to endure extreme stress and strike a
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balance between load-bearing performance, elastic modulus, and permeability are important
issues. Freeze-casting is a novel technique for manufacturing micro-scale open-cellular lamellar
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porous materials. However, the pore size is relatively small, which allows for efficient
permeability for the transport efficiency of oxygen and nutrients throughout the scaffolds. On
the other hand, the scaffold with gyroid pore structures has been proven to have higher
permeability due to its larger and smoother channels. To combine the advantages of both porous
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structures, the present study is to develop dual-scale porous structures by incorporating the 3D-
printed gyroid templates into the freeze-casting for further improving the lightweight, specific
strength, toughness, and permeability of the porous structures for versatile advanced
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applications. In particular, 316L stainless steel (316L SS) was first selected to produce the dual-
scale scaffolds, considering its better strengths, ductility, wear resistance, corrosion resistance,
non-toxicity, biocompatibility, and cost-effectiveness. The results showed that macro-scale
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gyroid channels were successfully built into the micro-scale open-cellular lamellar porous
scaffolds. The porosity of dual-scale scaffolds was 70.1 % - 74.4 %, which was higher than that
of 53.1 % - 66.5 % in the single-scale scaffolds. The elastic moduli of the single-scale scaffolds
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were higher than that of the dual-scale scaffolds; both were within the range of human
cancellous bone, demonstrating their mechanical compatibility. Furthermore, the dual-scale
scaffolds presented a prominent rise in permeability compared to the single-scale scaffolds.
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Notably, the permeability of the 3G series scaffolds was comparable to human cancellous bone.

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 In summary, the hierarchical 316L SS scaffolds with controllable macro-scale gyroid channels
exhibit great potential for biomedical applications.

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Keywords: 316L stainless steel, freeze-casting, 3D printing, hierarchical scaffolds, gyroid channels.

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1. Introduction
Bioinspired structural designs have been developed across various research areas. Notably,
the hierarchical porous structure stands out as the most crucial feature. These multi-scale porous
structures exhibit superior characteristics, such as lightweight, high specific surface area,

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excellent fluid transport efficiency, and proper mechanical strength [1]. Bone is a hierarchical

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tissue consisting of open-cellular and three-dimensional interconnected porous structures. Bone
defects that arise from severe trauma, degenerative disease, infection, or tumor excision
typically demand surgical treatments for the reconstruction of bone morphology and
physiological function. Tissue engineering treatment strategies often introduce porous scaffolds
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to mimic the properties of native bone to promote bone healing [2, 3]. Porous metals have been
extensively used as orthopedic implants for their lightweight and highly strong characteristics.
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Porosity, pore size, pore geometry, and pore interconnectivity are essential for developing
porous implants [4]. Among these parameters, porosity is considered the dominant factor
influencing the mechanical properties and biological responses of the implant. High porosity
diminishes the elastic modulus mismatch between bone and implant, mitigating the stress-
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shielding effect and reducing the risk of aseptic loosening and osteolysis. Moreover, high
porosity offers an expanded specific surface area to improve oxygen and nutrient transportation,
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promoting bone tissue regeneration and osteointegration [5, 6]. To enhance the reliability of
porous implants for long-term clinical applications, the impact of porosity on mechanical and
biological performance needs to be systematically studied.
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316L stainless steel (316L SS) is an extensively utilized biomedical implant due to its
adequate wear resistance, biocompatibility, and significantly lower cost than other medical-
grade metals like CoCrMo and Ti6Al4V alloys [7-9]. 316L SS also can be used as the base
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material for further applications. Diverse surface modification techniques have been employed
to deposit bioactive ceramic on the surface of 316L SS to adjust properties for better biological
responses [10-12]. Moreover, as additive manufacturing progresses, porous 316 SS with a high
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surface area can be fabricated, which enhances corrosion resistance and supports osteoblast
adherence and differentiation [13, 14]. However, the long-term stability remains challenging,
and researchers are exploring solutions to address these issues.

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 The freeze-casting technique adopts a unidirectional cooling source, utilizing frozen liquid
as a template to fabricate the anisotropic lamellar porous materials with controllable porosity,

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pore size, and pore morphology. The fabrication procedure includes four steps: slurry
preparation, solidification, sublimation, and sintering. The fundamental principle of freeze-
casting depends on the phase transformation of solvent in the slurry. During solidification, the

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particles in the slurry are rejected by the growing ice front and entrapped between ice dendrites.
Adjusting the cooling rate, cooling direction, and other external forces can influence the
scaffolds' microstructure or overall porosity [15]. After sublimation to remove the frozen
dendrites, the green body experiences sintering to achieve the desired mechanical strength.

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Unlike the traditional freeze-casting technique, introducing an extra sacrificial template

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with a different scale into the freeze-casting process can develop a hierarchical porous structure
to meet specific applications. Several characteristics of porous materials, such as porosity,
permeability, and interconnectivity, can be adjusted and optimized. Polymeric materials can be
efficiently created as well-defined pore structures by 3D printing, which can be used as
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sacrificial templates in freeze-casting. These templates can be decomposed and removed during
sintering, leaving the expected porous structure [16]. Recent studies have incorporated extrinsic
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3D-printed sacrificial templates into freeze-casting to develop biomimetic hierarchical
structures [15]. The osteoblast-like cells cultured in the hydroxyapatite scaffolds with multiple
length scales presented better biocompatibility than the nonporous and microporous samples
without 3D-printed templates. The distribution of cells throughout the macro-micro scaffold
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penetrated deep into its core networks [17]. However, the pore structure of hydroxyapatite
scaffolds was very brittle, even under low-stress loading. Furthermore, the biomimetic 3D
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poly(𝜖-caprolactone) (PCL)/gelatin nanofiber aerogels with patterned macro-channels and

anisotropic micro-channels were fabricated by combining freeze-casting and solvent
suspension. The pore structure demonstrated remarkably improved cellular infiltration,
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angiogenesis, and host tissue integration than those without macro-channels [18]. Nevertheless,
the strength of PCL/gelatin nanofiber aerogels was deficient when applied as cancellous bone.
Triply Periodic Minimal Surfaces (TPMS) are periodic infinite surfaces with zero mean
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curvature, exhibiting distinctive geometric properties, mechanical behavior, and mass transfer
[19]. The gyroid structure is one of the TPMS structures characterized by its continuous and
intersecting network of interconnected channels [20]. It provides remarkable mechanical
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stability, enabling efficient load distribution and improving structural integrity [21, 22]. The
distinct geometry supplies high specific strength, making it advantageous for developing
lightweight and high-strength materials [23, 24]. Additionally, the gyroid structure could

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 significantly enhance fluid transport capabilities for mass transportation. The permeability of
the gyroid scaffolds was ten times higher than that of the scaffolds with random pore

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architecture. This much higher permeability could effectively transport oxygen and nutrients
throughout the scaffolds. After culturing, the cells were homogeneously distributed in the center
of the gyroid scaffolds [25]. For the histological analysis, the gyroid scaffolds exhibited more

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than twice the amount of bone tissue formation within the defect compared to the grid scaffolds.
Thus, the gyroid structure showed the capability to promote bone regeneration [26].
To further improve the specific strength, toughness, modulus compatibility, and
permeability of the pore structures for bone implant application, this study first chose the 316L

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SS to develop novel hierarchical 316L SS scaffolds with macro-scale TPMS gyroid channels

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and micro-scale lamellar structures by incorporating the 3D-printed sacrificial gyroid template
during unidirectional freeze-casting and then sintered at 1100 °C. The microstructure, phase
composition, elemental distribution, process-structure correlation, mechanical property, and
permeability were discussed in detail. We hypothesized that introducing the macro-scale gyroid
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channels could effectively improve the permeability of the 316L SS scaffolds and extend the
applicability for future biomedical, functional, and structural applications.
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2. Materials and methods
2.1 Design and fabrication of additive-manufactured sacrificial templates
Within the dual-templating process, the sacrificial templates created by additive
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manufacturing techniques served as the framework for generating the larger-scale porous
structure, which was generated by computer-aided design (CAD) and produced through 3D-
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printed based on the stereolithography apparatus technology (SLA). The initial generation of
structures involved mathematical formula-based design. This process entailed discretizing
continuous space into independent units and applying specific mathematical formulas to each
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unit. Gyroids with solid networks derived from triply periodic minimal surface (TPMS)
structures were selected, with 3 and 4 as the number of unit cells in all three directions, creating
3 x 3 x 3 and 4 x 4 x 4 gyroids, respectively. Dimensions of the templates were defined as a
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cylinder with a height of 20 mm and a diameter of 19.5 mm. The volume ratios of the templates
were 10 vol.%, 15 vol.%, and 20 vol.%, respectively. The produced structure was subsequently
optimized through the Netfabb software (Autodesk, Inc., U.S.A) to ensure the realization of the
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intended geometrical features and structural integrity. The gyroid template structure and the
supposed 2D cross-section view of the channel distribution on the dual-scale scaffold are shown
in Fig. 1(a) and (b), respectively. In the following sections of the article, templates with various

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 parameters will be denoted using the format "XG-Y". In this context, X represents the repeating
unit in all three axes, whereas Y represents the relative volume of the template. For example, a

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3 x 3 x 3 and 15 vol.% template will be labeled "3G-15", while a 4 x 4 x 4 and 20 vol.% template
will be named "4G-20".

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Fig. 1. The original cubic gyroid solid structure model and the conceptual channel
distribution after removing the sacrificial template of: (a) 3G and (b) 4G series.
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This study used Form 3 (Formlabs, Somerville, U.S.A.) as an SLA 3D printer and castable
wax resin (Castable Wax V1, RS-F2-CWPU, FormLabs) as the printed slurry. An ultraviolet
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laser was adopted to scan through the photosensitive resin in a precise pattern that led to the
formation of a cured layer. The layer-by-layer scanning process was iterated until the entire
model was constructed. Afterward, the printed components were rinsed with isopropanol to
remove excess resin and cured at 60 °C in the Form Cure apparatus (Formlabs, Somerville,
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U.S.A.) for 1 h.
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2.2 Materials selection and slurry preparation

Commercial 316L SS powders (Elecmat Technology, USA) with an average size of 5 μm
were used in this study. The polyethylene oxide (PEO, M.W. 300,000, Thermo Fisher Scientific,
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USA) was dissolved in deionized water with a concentration of 6 vol.% and used as the organic
binder. Then, a small amount of anionic dispersant (DARVAN® 811, R. T. Vanderbilt Co.,
Norwalk, CT) and 316L SS powders were dispersed in the PEO solution. The slurry was stirred
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for 30 min until the powders were suspended uniformly. For the single-scale scaffold
fabrication, the solid content of the slurry was controlled at 15, 20, and 25 vol.%, respectively.
Furthermore, for the dual-scale scaffold preparation, the solid content of the slurry was
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controlled at 20 vol.%.

2.3 Freeze-casting and sintering of 316L SS scaffolds

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 2.3.1 Single-scale scaffolds
The well-dispersed slurry was poured into the hollow PTFE mold. The mold was placed

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on the copper rod held at 10 ℃. It used liquid nitrogen as the cooling source, initiating a
unidirectional freezing process to the final temperature of -140 ℃ at a cooling rate of 2, 5, and
10 ℃ min-1, respectively. A stirring device was used to avoid powder precipitation during the

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freezing process. After the freeze-casting process, the frozen sample was removed from the
PTFE mold and transferred to a freeze dryer (FD-8530, Panchum Scientific Corp., Taiwan) for
48 h to sublimate ice crystals and preserve the laminar porous structure. Afterward, the green
body was sintered in a tube furnace. First, the polyethylene oxide and anionic dispersant were

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burned out at 400 ℃ for 1 h. Then, continuously heat it to 1100 °C and hold it for 1 h. The

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heating rate was kept at 4 °C min-1 during sintering. Finally, the sample was cooled to room
temperature at 2 °C min-1 to prevent crack formation. The sintering process was carried out
under vacuum conditions below 400 °C. However, when the temperature was higher than 400
°C, a reducing atmosphere of argon with 10 % hydrogen was introduced to reduce the sample
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and prevent the sample from reacting with the residual oxygen.
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2.3.2 Dual-scale scaffolds
The dual-templating process incorporated the initial ice template formed via freeze-casting
and a specifically designed 3D-printed sacrificial template. Dual-scale scaffolds could be
created by selectively removing different scale templates using distinct methods. The uniformly
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distributed slurry at 20 vol.% was poured into the hollow PTFE mold. The mold was placed on
the copper rod maintained at 10 ℃ and employed liquid nitrogen as the cooling source,
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initiating a unidirectional freezing process to reach the final temperature of -140 ℃ at a cooling
rate of 5 ℃ min-1. As the temperature of the copper rod approached approximately -5 °C, the
3D-printed sacrificial template was gradually introduced into the slurry. This step aimed to
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prevent contact between the 3D-printed sacrificial template and the dense zone. Following the
freeze-casting process, the frozen sample was removed from the PTFE mold and moved to a
freeze dryer (FD-8530, Panchum Scientific Corp., Taiwan) for 48 h to sublimate ice crystals
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and retain the laminar porous structure. Subsequently, the green body underwent sintering in a
tube furnace. This study developed a new heat treatment profile by incorporating the
recommended castable wax resin removal temperature into the initial sintering process of
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single-scale 316L SS scaffolds. First, the temperature was initially raised to 400 °C at a heating
rate of 4 °C min-1. The castable wax resin started to soften and flow out of the sample at this
temperature. The hold time was extended to 6 h to ensure resin removal. Then, the temperature

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 was further enhanced to 800°C at a heating rate of 2°C min-1 and held for 1 h to eliminate the
remaining resin. After removing the 3D-printed sacrificial template, continuously heated it to

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1100 °C and held it for 1 h. Finally, the sample was cooled to room temperature at 2 °C min-1
to prevent crack formation. The sintering process was conducted under vacuum conditions
below 400 °C. However, as the temperature exceeded 400 °C, a reducing atmosphere composed

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of argon with 10 % hydrogen was introduced to reduce the sample and prevent it from reacting
with the residual oxygen.

2.4 Porosity measurement

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The porosity of the scaffolds was determined using Archimedes' method and assessed by

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the MatsuHaKu porous solid density tester (TWS-214K, Group Prospers Enterprise Co.,
Taiwan). The specimen was first weighed after complete drying. Afterward, the test sample
was immersed in absolute ethanol and evacuated until all the air trapped in the pores was
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eliminated. The saturated sample's mass was measured in air and immersed in absolute ethanol,
and porosity could be calculated according to the following equation:
(𝒎𝐬𝐚𝐭𝐮𝐚𝐫𝐚𝐭𝐞𝐝 ― 𝒎𝐝𝐫𝐲) × 𝝆𝒆𝒕𝒉𝒂𝒏𝒐𝒍
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𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚 (%) = 𝒎𝐬𝐨𝐚𝐤𝐞𝐝 ― 𝒎𝐬𝐚𝐭𝐮𝐫𝐚𝐭𝐞𝐝
× 𝟏𝟎𝟎% (1)
𝝆𝒆𝒕𝒉𝒂𝒏𝒐𝒍

where 𝑚𝑑𝑟𝑦 is the mass of the dry scaffold in the air, 𝑚𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 is the mass of the saturated
scaffold filled with absolute ethanol in the air, 𝑚𝑠𝑜𝑎𝑘𝑒𝑑 is the mass of the saturated scaffold
immersed in the absolute ethanol, and 𝜌𝑒𝑡ℎ𝑎𝑛𝑜𝑙 is the density of absolute ethanol (0.79 g cm-3).
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2.5 Microstructure characterization

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The crystal structure and phase change of commercial 316L SS powders and freeze-casting
316L SS scaffolds were analyzed by X-ray diffraction (XRD-D2 PHASER, Bruker, Germany)
with Cu (Kα = 1.5405 Å) radiation at the 2θ scanning range from 40º to 80º with a constant
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increment of 0.03º and scanning speed of 9º min-1. A field emission electron probe
microanalyzer (FE-EPMA, JXA-iHP200F, JEOL, Japan) characterized the qualitative
(mapping) and quantitative analysis of elemental composition distributions. Optical
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(Stereomicroscope System, SZX7, OLYMPUS, Japan) and 3D laser confocal microscopy (VK-
X1000, KEYENCE, Japan) identified the surface topography and macro-scale porous structure.
The powder morphology and microstructure of scaffolds were observed by cold field-emission
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scanning electron microscopy (SU-8010, Hitachi, Japan). ImageJ software (Image J, U.S.
National Institutes of Health, LOCI, University of Wisconsin) measured scaffolds' pore and
wall widths on the SEM images. The three-dimensional structure of scaffolds was examined

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 and visualized by a micro-computed tomography system (multi-functional 3D XCT, SkyScan
2211, Bruker, U.S.A). The 3D image reconstruction was done by GPUNRecon, CTAn 1.20.8,

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and Dataviewer 1.5.6 software (Bruker micro-CT, Kontich, Belgium).

2.6 Mechanical properties test

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The uniaxial compressive tests were conducted by the universal testing machine (Instron
3367, Illinois Tool Works Inc., USA) equipped with a 30kN load cell to evaluate the
compressive properties of the scaffolds along the ice growth direction. The specimens used in
the compressive tests were cuboid with a length and width of 4 mm and a height of 6 mm, and

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the strain rate was controlled at 10-3 S-1. Five samples were tested for each group. The elastic

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modulus, yield strength, and energy absorption were discussed in this study. Elastic modulus
can be measured as the slope of the elastic region of the stress-strain curve. Yield strength can
be calculated using the 0.2 % strain offset method. Energy absorption can be evaluated by
calculating the area below a compressive stress-strain curve [27], which relates to how much
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energy the material can absorb per unit volume during material deformation before a specific
strain. This study integrated the stress-strain curve from 0 % up to the beginning of the
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densification strain. We employed the "energy absorption efficiency" to determine the
densification strain. "Efficiency" represents the ratio of the energy absorbed by a real foam
under maximum compressive strain to the energy absorbed by an ideal foam that transfers the
identical maximum constant stress to the product when fully compressed [28]. The formula for
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the energy absorption efficiency is shown as follows:

𝛆 𝛆
𝑨𝒉 ∫𝟎 𝒎 𝛔 𝐝𝛆 ∫𝟎 𝒎 𝛔𝐝𝛆
𝑬= = (2)
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𝑨𝒉𝛔𝒎 ∗ 𝟏 𝛔𝒎
where A is the contact area on the compressive material, εm is the maximum strain, σm is the
stress when the compressive procedure is in the maximum strain, and h is the thickness of the
porous material. The efficiency exhibits a maximum value at a particular strain [29], which is
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consistent with the densification strain.

2.7 Constant head permeability test

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The permeability of the scaffold was assessed by conducting a constant head permeability
test, which verified the scaffold's capacity for fluid flow under steady pressure. The specimen
was secured at a funnel, and the average fluid flow rate through the specimen was determined
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by measuring the time needed for every 10 mL of deionized water to pass through. The

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 permeability of the scaffolds was analyzed based on Darcy's law [30, 31]. The equation is
shown as follows:

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𝒌𝑨
𝑸 = 𝝁𝑳∆𝒑 (3)
The equation demonstrates that the discharge rate (Q, cm sec-1) of fluid flow through the porous
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medium is proportional to the permeability of the medium (k, cm2), the cross-sectional area (A,

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cm2) of the specimen, and the pressure drop (∆p, Pa), while inversely proportional to the length
(L, cm) of the specimen and the viscosity (μ, Pa·s) of the fluid. The theoretical viscosity value
of deionized water is 8.9×10-4 Pa·s. The pressure drop (∆p) represents the reduction in pressure
along the flow direction within a system. When fluid flows through porous media, the pressure

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drop means the pressure difference between the top and bottom of the specimen. It can be

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expressed by the following equation [32]:
∆𝒑 = 𝑷𝒕 ―𝑷𝒃 = 𝝆 × 𝒈 × 𝑯 (4)
Pt and Pb represent the pressure on the specimen's top and bottom, respectively. The pressure
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difference is estimated based on the theoretical pressure of the column, computed by
multiplying the fluid density (ρ, g cm-3), gravitational acceleration (g, m s-2), and the height of
the liquid column (H, mm). The theoretical value of water density (ρ) is 103 kg m-3, gravitational
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acceleration (g) is 9.81 m s-2, and the constant fluid height in the funnel (H) is 0.58 m.

3. Results and discussion

3.1 Microstructure, phase composition, and processing-structure correlations of the
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single-scale 316L SS scaffolds

3.1.1 Pore structure observation
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Fig. 2 (a) shows an SEM image of 316L SS powders with spherical shape and an average
particle size of 5 μm. The spherical-shaped alloy powders possess good flowability and uniform
size distribution, which is suitable for freeze-casted processes. The conventional freeze-casting
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method fabricated the single-scale 316L SS scaffolds. Scaffolds with a solid content of 15 vol.%,
20 vol.%, and 25 vol.% were synthesized, and the overall structures and porosities were further
analyzed. Fig. 2 (b-c) displays SEM images of single-scale 316L SS scaffolds fabricated with
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20 vol.% solid content at the cooling rate of 5 °C min-1 in the transverse and longitudinal
directions. The transverse section refers to the plane perpendicular to the temperature gradient,
while the longitudinal section is parallel to the temperature gradient. The scaffolds present
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aligned lamellar porous structure in the transverse and longitudinal sections. The advancing ice
crystals repelled the alloy powders and accumulated between the alloy powders during the
freezing process. Following the sublimation and sintering, the scaffolds preserved the lamellar

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 structure, which resembled human cancellous bone. Table 1 depicts detailed results of
porosities and volume shrinkages. The green body underwent shrinkage during the sintering

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process. The porosities of the scaffolds with 15 vol.%, 20 vol.%, and 25 vol.% solid contents
were 65.3 ± 1.0 %, 65.8 ± 1.9 %, and 53.1 ± 3.8 %, respectively. Similarly, the volume
shrinkage of the scaffolds with 15 vol.%, 20 vol.%, and 25 vol.% solid contents were 46.8 ±

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2.6 %, 45.4 ± 0.6 %, and 49.5 ± 5.4 %, respectively. In theory, higher solid contents typically
reduce the porosity and enhance the volume shrinkage. The results for 20 vol.% and 25 vol.%
were in line with the theory. However, due to the uneven shrinkages, the porosities increased
when the solid content increased from 15 vol.% to 20 vol.%. Insufficient powder for the lower

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solid content scaffolds hindered proper fusion, making them unable to support themselves,

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resulting in severe collapse after sintering. Therefore, the 15 vol.% scaffold exhibited higher
volume shrinkage than the 20 vol.% scaffold. The uneven shrinkages of the scaffolds may affect
not only the porosities and volume changes but also the microstructures and the mechanical
properties, which will be further analyzed in the following section. Conversely, the scaffolds
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with higher solid content (25 vol%) showed uniform shrinkage, but the porosities were
excessively low, limiting the potential applications. To develop scaffolds with higher porosities
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and adequate mechanical properties for better applications, we tried to balance porosities and
mechanical properties. The single-scale 316L SS scaffolds with a solid content of 20 vol.%
illustrate controllable structure and uniform shrinkage, as shown in Fig. 2 and Table 1, and
were chosen as the optimal condition for subsequent investigations.
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Fig. 2. SEM images of (a) 316L SS powders and single-scale 316L SS scaffolds with 20
vol.% solid content at the cooling rate of 5 °C min-1 in the (b) transverse and (c) longitudinal
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directions.

Table 1 Porosities and volume shrinkages of single-scale 316L SS scaffolds

with 20 vol.% solid content.
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Solid content [vol.%] 15 20 25

Porosity [%] 65.3 ± 1.0 65.8 ± 1.9 53.1 ± 3.8
Volume shrinkage [%] 46.8 ± 2.6 45.4 ± 0.6 49.5 ± 5.4

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 3.1.2 XRD analysis
Fig. 3 shows the XRD patterns of the 316L SS powder and freeze-casted 316L SS scaffold

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post-sintering. The results indicated that the crystal structure of the raw powder was composed
of a face-centered cubic (FCC) austenite phase with an additional body-centered cubic (BCC)
NiCrFe phase. The BCC phase's presence in the XRD profile might be associated with cold

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working and welding during powder preparation. After the sintering process, the crystal
structure of the freeze-casted 316L SS scaffold transformed into a single FCC austenite phase.
Hence, the 316L SS powders bonded together and experienced phase transformation during the
sintering process. For austenitic stainless steels, chromium carbide (Cr23C6) precipitation at

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grain boundaries may reduce the corrosion resistance along the chromium depletion region,

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resulting in sensitization of the stainless steel. Nevertheless, the extra peak corresponding to
chromium carbide was not detected in the XRD patterns.

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Fig. 3. XRD patterns of 316L SS powder and freeze-casted 316L SS scaffold.

3.1.3 Elemental distribution analysis

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The elemental composition distribution of the freeze-casted 316L SS scaffold post-

sintering was verified by a field emission electron probe microanalyzer (FE-EPMA). The
quantitative results are shown in Table 2, demonstrating that the chemical composition of the
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scaffolds corresponds to the theoretical values, except for some slight deviations in the
distribution of silicon and carbon. Fig. 4 illustrates the qualitative mapping results of the
scaffolds, revealing that the compositions of the 316L SS are homogeneously distributed in the
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specimens, consistent with the quantitative analysis displayed in Table 2. Nevertheless, the
elemental mappings indicated that the concentrations of silicon and carbon distributed in the

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 pore region were higher than in the scaffold region. This difference could be attributed to silicon
carbide particles detaching from the SiC abrasive papers used during the sample preparation

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process. The particles might accumulate in the pore regions, which could explain the reason for
higher values of Si and C in the quantitative analysis.

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Table 2 Elemental composition ratio (wt.%) of 316L SS scaffold evaluated by FE-EPMA.
Composition ratio Cr Ni Mo Mn Si C Fe
Theoretical 16.0 ~ 18.0 10.0 ~ 14.0 2.0 ~ 3.0 2.0 < 0.75 < 0.03 Bal.
FE-EPMA 17.23 ± 0.54 11.33 ± 0.45 2.34 ± 0.15 1.85 ± 0.07 0.98 ± 0.02 0.10 ± 0.01 66.17 ± 0.52

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Fig. 4. Elemental mapping of freeze-casted 316L SS scaffold by FE-EPMA analysis.

3.1.4 The correlation between processing and porous structure

The freeze-casted scaffolds typically exhibit aligned lamellar porous structures along the
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temperature gradient [33, 34], and various experimental parameters, such as solid contents,
cooling rate, sintering conditions, and other driving forces, influence the microstructural
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features. This study systematically discusses the impact of solid content and cooling rate on the
microstructure. SEM micrographs of scaffolds with different controlled parameters are
presented and analyzed as follows.
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This study compared the differences in the microstructure of single-scale 316L SS

scaffolds with 15 vol.%, 20 vol.%, and 25 vol.% solid contents. These scaffolds were
synthesized at a fixed sintering temperature of 1100 °C for 1 h, and the cooling rate was at 5 °C
ep

min-1. The SEM images of sintered products with different solid contents and the
microstructural characteristics in terms of pore and wall widths are shown in Fig. 5 and Table
3. Generally, the pore and wall widths will increase as the solid contents decrease. However,
Pr

the pore and wall widths of the scaffolds with 15 vol.% solid content were lower than those
with 20 vol.% due to the severe shrinkage at the macroscopic scale, as shown in Table 1. On
the other hand, higher solid contents will impede particle motion, making the particles not

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 separate well from the suspension, thus reducing the pore and wall widths. Consequently, the
pore and wall widths of the 25 vol.% scaffolds were lower than that of the 20 vol.% scaffolds.

ed
Moreover, the porous structure may be filled by excessive particles, thereby restricting its
applicability. In summary, the pore widths of the 20 vol.% scaffolds (11.6 ± 1.6 μm) were
higher than those of 15 vol.% (8.3 ± 1.3 μm) and 25 vol.% (9.5 ± 2.1 μm) scaffolds.

v iew
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Fig. 5. SEM images of single-scale 316L SS scaffolds with different solid contents: (a) 15
vol.%; (b) 20 vol.%; and (c) 25 vol.%. er
Table 3 Pore and wall widths of single-scale 316L SS scaffolds with various
solid contents.
Solid content [vol.%] 15 20 25
pe
Pore width [μm] 8.3 ± 1.3 11.6 ± 1.6 9.5 ± 2.1
Wall width [μm] 7.4 ± 1.1 8.4 ± 1.4 7.6 ± 0.9

The cooling rate is a crucial factor affecting the pore width within the lamellar structure.
ot

Higher cooling rates will accelerate the growth of ice crystals, thereby reducing the widths
between neighboring lamellae. This study utilized three cooling rates during the freeze-casting
process, including 2 °C min-1, 5 °C min-1, and 10 °C min-1. The solid content was maintained
tn

at 20 vol.%, and the scaffolds were sintered at 1100°C for 1 h. Fig. 6 shows three structures
with different cooling rates observed by SEM. From the SEM images, the scaffolds with a
cooling rate of 10 °C min-1 exhibited the smallest pore widths (7.4 ± 1.5 μm), and some pores
rin

were stuck by particles. For the unidirectional freeze-casting process, the velocity of ice crystal
growth is significantly affected by the cooling rate. If the cooling rate is too fast, ice dendrites
will not have sufficient time to grow into lamellae with adequate widths, and particles will be
ep

trapped within ice crystals during the freezing process. Furthermore, as shown in Fig. 6 (c), the
lamellar structures were distorted and connected in the scaffolds with a cooling rate of 10 °C
min-1. On the other hand, coarser ice dendrites and larger pores will form with a lower cooling
Pr

rate, and planar ice dendrite growth will occur. Fig. 6 (a) reveals that the scaffolds with a
cooling rate of 2 °C min-1 possessed the most significant pore widths (13.1 ± 1.9 μm). In

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 summary, the pore widths of the scaffolds with a cooling rate of 2 °C min-1 (13.1 ± 1.9 μm)
were higher than those of the scaffolds with a cooling rate of 5 °C min-1 (11.6 ± 1.6 μm) and 10

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°C min-1 (7.4 ± 1.5 μm).

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Fig. 6. SEM images of single-scale 316L SS scaffolds with different cooling rates: (a) 2 °C

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min-1; (b) 5 °C min-1; and (c) 10 °C min-1.

Table 4 Pore and wall widths of single-scale 316L SS scaffolds at various

cooling rates. er
Cooling rate [°C min-1] 2 5 10
Pore width [μm] 13.1 ± 1.9 11.6 ± 1.6 7.4 ± 1.5
Wall width [μm] 8.9 ± 0.9 8.4 ± 1.4 8.4 ± 1.3
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3.1.5 Three-dimensional structure characterization
As the SEM micrographs only illustrated localized two-dimensional observations, the
detailed three-dimensional internal structure evolution (from the bottom to the top) of single-
ot

scale 316L SS scaffolds was assessed by the micro-CT technique. Fig. 7 shows the cross
sections parallel and perpendicular to the scaffold's freezing direction. Images (1) to (6) shown
tn

in Fig. 7 (b) represent cross sections at various heights, and the positions of these cross sections
are indicated in Fig. 7 (a). In the cross section perpendicular to the cooling rate, the sample's
microstructures changed as the ice crystals grew upward. When the ice crystals initiated to grow
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from the cooling source, they would engulf the 316L SS particles. This process continued until
the ice crystals reached a height of approximately 300 μm, forming lamellar structures. As the
ice crystals gradually moved away from the cooling source, the layered structures gradually
ep

increased, and the disordered porous structure gradually decreased. Until the ice crystals at a
height of approximately 1 mm, the disordered structures were entirely converted into lamellar
channels. Compared with Fig. 7 (a), Fig. 7 (b) illustrates that the microstructural evolution
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extends from the dense region to the lamellar region with paralleled elongated lamellae. The
transition structure formation occurs due to the supercooling phenomenon at the freezing front,
transforming the structure from disorder to lamellar. The initial ice crystals form in a

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 supercooled suspension, resulting in the initial growth rate of ice crystals being fast. It can reach
an equilibrium point rapidly where the slurry temperature equals the temperature of the cooling

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source. Consequently, the initial frozen zone shows a planar ice front at which the particles
become engulfed (V >> Vc). As the degree of supercooling increases (with a higher cooling
rate), the freezing front solidifies more rapidly. Therefore, the initial solidification region

iew
exhibits high density without distinct lamellar structures. When the speed of the ice-freezing
front surpasses the critical rate, leading to the engulfment of the powders in this region. As the
ice crystals gradually move away from the cooling source, the freezing front's speed gradually
reduces, and the interface progressively transforms into a cellular structure (V > Vc). When the

v
speed is below the critical rate (V < Vc), the particles will be pushed by the freezing front,

re
causing the redistribution of ice crystals and particles to form a lamellar structure [35]. The
micro-CT scan results revealed that while it was challenging to distinguish the differences
between the dense and honeycomb regions, the transition from the honeycomb to lamellae
regions was observable.
er
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ot
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Fig. 7. 3D structure of the single-scale 316L SS scaffold reconstructed by micro-CT

technique. The cross sections are (a) parallel and (b) perpendicular to the scaffold’s freezing
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direction. The images shown in (b) are the cross sections at (1) 100, (2) 600, (3) 2000, (4)
3000, (5) 4000, and (6) 5000 μm height, corresponding to the regions displayed in image (a).
The tears near some edges are due to the tension force induced by the cutting operation.
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3.2 Microstructure and template geometry-structure correlations of the dual-scale

316L SS scaffolds
3.2.1 Printing quality and topology structure of the sacrificial templates
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The 3D-printed sacrificial templates were introduced into the freeze-casted process to
develop dual-scale scaffolds. The original ice template contributes to micro-porosity at the
micrometer scale, while the additional polymeric template provides macro-porosity at the

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 millimeter scale. It was essential to employ precise and high-resolution printing methods for
fabricating polymeric sacrificial templates to ensure the structural integrity of the scaffolds.

ed
Any defects in the sacrificial templates could cause uneven shrinkage or stress accumulation
during heat treatment, leading to structural instability or collapse of the scaffolds. The structure
topology of the polymeric sacrificial template in the transverse and longitudinal directions, as

iew
shown in Fig. 8 (a-b), demonstrates that the printed structural topology closely matched the
CAD model design. Furthermore, Fig. 8 (c) illustrates the enlarged optical microscopic image
of the printed template, which possesses a smooth surface and high precision. No apparent
layered structure was observed on the curved surface, even at a micrometer scale. These results

v
exhibited that stereolithographic 3D printing could effectively build intricate templates with

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outstanding surface quality and prevent defect formation of the freeze-casted scaffolds.

er
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Fig. 8. Structure topology of the CAD model and 3D-printed gyroid template: (a) transverse
plane view, (b) longitudinal plane view, and (c) the enlarged view of the curved region.

3.2.2 Pore structure observation

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Since the single-scale scaffolds with a solid content of 20 vol.% and a cooling rate of 5 °C
min-1 exhibited controllable structure and uniform shrinkage, they were selected as the basis for
developing dual-scale scaffolds. This section chose the dual-scale scaffolds with template
tn

settings 4G-15 to demonstrate the structural characterization. The macroscopic appearance and
the microstructure of the dual-scale scaffold are illustrated in Fig. 9. In Fig. 9 (b), the optical
microscope image illustrates the presence of micro-scale lamellae-structured pores alongside
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the larger gyroid channels. The SEM image in Fig. 9 (c) emphasizes the well-sintered powders
after the scaffolds underwent sintering at 1100 °C for 1 h. This powder fusion contributes to
strengthening the mechanical strength of the scaffolds. The macro-scale pore of the dual-scale
ep

scaffolds presented a gyroid structure featuring an average pore size of approximately 669 ±
134 µm. Concurrently, the micro-scale pore was structured in a lamella pattern, with an average
pore size of 13.6 ± 2.3 µm. With the same solid content of 20 vol.% in the slurry, the porosity
Pr

of the single-scale scaffolds was approximately 65.8 ± 1.9 %. Remarkably, the porosity of the
dual-scale scaffolds was around 72.3 ± 1.7 %. The higher value demonstrated a noticeable

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 increase compared to the single-scale scaffolds.

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Fig. 9. (a) Macroscopic appearance of the gyroid structured dual-scale 316L SS scaffold; (b)

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transverse viewed microstructure observed by optical microscope; (c) SEM image of sintered
powders.

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SEM images in Fig. 10 display the morphology of the macro-scale and micro-scale pore
structure of the dual-scale scaffold in both the transverse and longitudinal sections. Among the
macro-scale gyroid channels, anisotropic micro-scale lamellar pores were observed. Even with
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the introduction of macro-scale gyroid channels, the micro-scale lamellar pores preserved
anisotropic structure and resembled the pores of the single-scale scaffolds. This phenomenon
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meant that the 3D-printed templates did not significantly affect the growth of ice dendrites
during the ice template formation. For the macro-scale gyroid channels, the structure hybridized
with the micro-scale lamellar pores in both the transverse and longitudinal directions. For the
micro-scale lamellar pore structure, the transverse plane perpendicular to the freezing direction
ot

showed elongated pores with diverse orientations, and some pores presented round or oval
cross-sections. On the contrary, the longitudinal plane parallel to the freezing direction depicted
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well-aligned and elongated columnar pores, indicating solute particle alignment during the
freeze-casting process.
rin
ep
Pr

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 ed
v iew
Fig. 10. Macro-scale gyroid channel and micro-scale lamellar structure of the dual-scale

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316L SS scaffold were observed by SEM in both the transverse and longitudinal directions.

3.2.3 The correlation between template geometry and porous structure

The macro-scale porous structure in the dual-scale scaffold is modified by altering the
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volume ratios and the repeating units of the gyroid solid network templates. This section
discusses the effects of different volume ratios and repeating units on the porous structure.
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The template volume ratio is the volume percent relative to the cylindrical space of the
freeze-casting mold. In this section, the 4 x 4 x 4 gyroid structure was generated in the
cylindrical space. The volume ratios of the templates were 10 %, 15 %, and 20 %, respectively
(denoted as 4G-10, 4G-15, and 4G-20). As shown in Table 5, following sintering and complete
ot

removal of the template, the corresponding porosities of the dual-scale scaffolds with the
template volume ratios of 10 vol.%, 15 vol.%, and 20 vol.% were 70.1 ± 2.0 %, 72.3 ± 1.7 %,
tn

74.3 ± 1.3 %, respectively. Furthermore, the macro-scale pore sizes of the dual-scale scaffolds
with 4G-10, 4G-15, and 4G-20 gyroid templates were 472 ± 93 μm, 669 ± 134 μm, and 882
±145 μm, respectively. The results indicated that with the increase of template volume ratios,
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the dual-scale scaffolds' porosities and macro-scale pore sizes would also enhance after
sintering.
The repeating unit is the essential element to construct the TPMS structures. In this study,
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3 and 4 repeating units were chosen to establish the 3 x 3 x 3 and 4 x 4 x 4 gyroid structures,
respectively. These configurations enabled a comparative investigation of the dual-scale
scaffolds' structural variations. Regarding the influence of different repeating units on the pore
Pr

structure, taking 3G-15 and 4G-15 as examples, the porosities were 72.9 ± 1.7 % and 72.3 ±
1.7 %, respectively. It was demonstrated that the gyroid pore structures with the same volume
ratio but possessing different repeating units had no impact on the overall porosities of the dual-

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4809398
 scale scaffolds. Additionally, the macro-scale pore sizes of the 3G-15 and 4G-15 dual-scale
scaffolds were 861 ± 121 µm and 669 ± 134 µm, respectively. The results revealed that the

ed
repeating units of the gyroid pore structures increased, reducing the macro-scale pore sizes of
the dual-scale scaffolds. Compared with the single-scale scaffolds fabricated using the same
process parameters, the porosity was 65.8 ± 1.9 %. It meant that the porosities of the dual-scale

iew
scaffolds increased significantly due to the additional channels provided by the gyroid
templates. On the other hand, as shown in Table 5, the average micro-scale pore size
distribution of the dual-scale scaffolds was within the range between 13 and 15 µm, independent
of the presence of gyroid templates. It confirmed that the sizes of macro-scale and micro-scale

v
pores could be adjusted independently by modifying the design of the sacrificial templates. In

re
summary, adjusting the volume ratios of the sacrificial templates will affect the porosities of
the dual-scale scaffolds, while altering the repeating units will not. However, varying the
repeating units of the sacrificial templates can control the macro-scale pore sizes of the dual-
scale scaffolds with the same porosities.
er
Table 5 Porosities, volume shrinkages, and pore sizes of dual-scale 316L SS scaffolds with
various polymeric templates.
pe
10 vol.% 15 vol.% 20 vol.%
Polymeric template
3x3x3 4x4x4 3x3x3 4x4x4 3x3x3 4x4x4
Porosity [%] 70.5 ± 1.4 70.1 ± 2.0 72.9 ± 1.7 72.3 ± 1.7 74.4 ± 1.2 74.3 ± 1.3
Volume shrinkage [%] 42.5 ± 2.3 41.5 ± 2.5 39.5 ± 3.5 39.4 ± 4.2 34.9 ± 3.2 35.7 ± 2.2
Macro-pore size [μm] 599 ± 104 472 ± 93 861 ± 121 669 ± 134 1156 ± 165 882 ± 145
Micro-pore size [μm] 13.9 ± 2.7 14.2 ± 1.7 13.8 ± 2.1 13.6 ± 2.3 14.1 ± 1.8 14.2 ± 1.2
ot

3.2.4 Three-dimensional structure characterization

The three-dimensional image of the scaffold was sliced into multiple planes in all three
directions to reconstruct the internal structure evolution of the scaffold. Fig. 11 (a) illustrates a
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cube selected for observation. The slices of the dual-scale scaffolds were obtained by cutting a
cubic according to the normal direction of X-Y, Y-Z, and Z-X planes. The cooling direction
was set as the z direction, which was parallel to the orientation of the lamellae structure. When
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viewed from these distinct orientations, the periodic characteristics of the macro-scale gyroid
structure become more apparent, as shown in Fig. 11 (b). Additionally, Fig. 11 (c) depicts
micro-scale lamellar patterns with various orientations from the X-Y view. This transverse
ep

plane provided an image of the structure perpendicular to the freezing direction, presenting the
layered feature of the scaffold. In the longitudinal Y-Z and Z-X planes, the lamellar structure
appeared as elongated, parallel striations extending continuously throughout the scaffold. These
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striations aligned with the freezing direction, emphasizing the anisotropic feature of the freeze-
casting process.

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 ed
v iew
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Fig. 11. (a) 3D structure of the dual-scale 316L SS scaffold reconstructed by micro-CT
technique, sliced in different directions to observe the (b) macro-scale gyroid structure
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(resolution = 5 µm) and (c) micro-scale lamellar structure (resolution = 1 µm).

3.3 Compressive mechanical properties

3.3.1 Single-scale 316L SS scaffolds
Fig. 12 (a) shows the representative compressive stress-strain curves of single-scale
ot

scaffolds with 15 vol.%, 20 vol.%, and 25 vol.% solid contents were sintered at 1100 °C for 1
h with a cooling rate of 5 °C min-1 during the freezing process. The curves all display a
tn

considerable strain without any fracture. Three stages are observed: a linear elastic region, a
plateau region, and a densification region. The initial elastic deformation involves slight
bending or stretching of the metal walls. As the plastic deformations occur, the metal walls
rin

collapse. When the cells collapse almost completely, opposing metal walls crush each other,
and a further increase leads to densification. The influence of solid content on the compressive
mechanical properties is primarily associated with the porosity. Despite the uneven shrinkages
ep

resulting in higher porosities for 20 vol.% single-scale scaffolds than 15 vol.% single-scale
scaffolds, all mechanical properties improved as the solid contents enhanced from 15 vol.% to
25 vol.%. As shown in Table 6, the elastic modulus increased from 699 to 2029 MPa, the yield
Pr

strength raised from 18 to 47 MPa, and the energy absorption strengthened from 30 to 126 MJ
m-3, respectively.

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 The compressive results of single-scale scaffolds with various cooling rates are shown in
Fig. 12 (b) and Table 6. The single-scale scaffolds with 20 vol.% solid content were sintered

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at 1100 °C for 1 h. The results revealed that the elastic modulus of single-scale scaffolds with
cooling rates of 2 °C min-1, 5 °C min-1, and 10 °C min-1 was 805, 1140, and 1406 MPa, the yield
strength was 24, 25, and 28 MPa, and the increment in energy absorption was 30, 49, and 78

iew
MJ m-3, respectively. The mechanical properties of the scaffolds with varying cooling rates are
associated with the ratio of pore and wall widths [33, 36, 37]. The scaffolds are fabricated with
a lower cooling rate, leading to the ratio of the pore width to the wall width being greater than
the scaffolds solidified with a higher cooling rate. The lower wall ratio will decrease the

v
supporting forces during the compressive test. However, with an increase in the cooling rate,

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inadequate time for ice crystal growth reduces the channel size [38]. The higher wall ratio will
raise the sustaining forces during the compressive test. Although the single-scale scaffolds with
a cooling rate of 10 °C min-1 possessed better mechanical strengths, their distorted and non-
uniform structures limited further applications.
er
pe
ot
tn

Fig. 12. Representative compressive stress-strain curves of single-scale 316L SS scaffolds

fabricated with various (a) solid contents and (b) cooling rates.
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Table 6 Mechanical properties of single-scale 316L SS scaffolds with various solid

contents and cooling rates.
Process parameter Porosity [%] Elastic modulus [MPa] Yield strength [MPa] Energy absorption [MJ m-3]
15 vol.%, 5 °C min-1 65.3 ± 1.0 699 ± 189 18 ± 3 30 ± 3
ep

20 vol.%, 5 °C min-1 65.8 ± 1.9 1140 ± 161 25 ± 5 49 ± 7

25 vol.%, 5 °C min-1 53.1 ± 3.8 2029 ± 483 47 ± 9 126 ± 6
20 vol.%, 2 °C min-1 66.5 ± 1.6 805 ± 260 24 ± 3 30 ± 1
20 vol.%, 5 °C min-1 65.8 ± 1.9 1140 ± 161 25 ± 5 49 ± 7
20 vol.%, 10 °C min-1 62.2 ± 0.9 1406 ± 177 28 ± 6 78 ± 10
Pr

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 3.3.2 Dual-scale 316L SS scaffolds
Fig. 13 shows the representative compressive stress-strain curves of the dual-scale

ed
scaffolds with various template volume ratios and repeating units. The curves exhibited a
similar tendency corresponding to the elastic-plastic mechanical behaviors of typical cellular
foams [39]. The compressive test results were evaluated through the stress-strain curves and

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summarized in Table 7. Among the 4G series scaffolds, the 4G-10 dual-scale scaffolds
exhibited superior elastic modulus, yield strength, and energy absorption values than the 4G-
15 and 4G-20 dual-scale scaffolds. The mechanical properties of the scaffolds are related to
their pore size and porosity. Adjusting the sacrificial templates' volume ratio, as described in

v
Section 3.2.3, might affect both characteristics. As the template volume ratio increased, the

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macro-scale pore size and porosity of the dual-scale scaffold also increased. This relationship
is crucial because its pore size significantly influences the scaffold's mechanical strength,
reflecting the balance between structural integrity and load-bearing capabilities. Scaffolds with
lower porosities and smaller pore sizes exhibit a densely interconnected structure, enhancing
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the scaffold's ability to resist and distribute mechanical stresses. In addition, the 3G series dual-
scale scaffolds showed a similar trend in the influence of pore sizes and porosities on
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mechanical properties. As the template volume ratio increased, pore size enlarged, and the
porosity escalated, the dual-scale scaffolds revealed a diminishment in their mechanical
stability. These results demonstrated the significance of optimizing pore structure in dual-scale
scaffolds, especially for better mechanical performance.
ot

Differences emerged in the mechanical performance when comparing the dual-scale

scaffolds with the same volume ratio but various repeating units. For the 10 vol.% dual-scale
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scaffolds, the elastic modulus of the 3G-10 samples was 506 ± 10 MPa, whereas the 4G-10
samples showed a slightly elevated value of 511 ± 21 MPa. The yield strength and energy
absorption variations in all pairs of the samples (e.g., 3G-10 vs. 4G-10, 3G-15 vs. 4G-15, and
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3G-20 vs. 4G-20) demonstrated a similar tendency, as depicted in Table 7. Despite the
differences in mechanical performance, the porosities of the 3G-15 and 4G-15 samples were
very similar. Examining the complexities of the gyroid structure, a more significant number of
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repeating units means more junction points or nodal intersections, potentially enhancing the
structural rigidity of the scaffold [40]. This intricate network can improve the scaffold's
capabilities to distribute applied mechanical loads throughout its structure, thus influencing its
Pr

overall mechanical properties. Based on these findings, while porosities are vital, increasing the
number of repeating units in the template structure significantly improves the dual-scale
scaffolds' mechanical properties.

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 ed
v iew
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Fig. 13. Representative compressive stress-strain curves of (a) 3G and (b) 4G series dual-
scale 316L SS scaffolds.

Table 7 Mechanical properties of dual-scale 316L SS scaffolds with different sacrificial

templates.
Sacrificial template
3 x 3 x 3, 10 vol.%
Porosity [%]
70.5 ± 1.4
er
Elastic modulus [MPa]
506 ± 10
Yield strength [MPa]
28 ± 2
Energy absorption [MJ m-3]
60 ± 6
3 x 3 x 3, 15 vol.% 72.9 ± 1.7 405 ± 7 25 ± 3 38 ± 4
3 x 3 x 3, 20 vol.% 74.4 ± 1.2 299 ± 11 17 ± 3 22 ± 8
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4 x 4 x 4, 10 vol.% 70.1 ± 2.0 511 ± 21 29 ± 3 72 ± 4
4 x 4 x 4, 15 vol.% 72.3 ± 1.7 454 ± 8 28 ± 3 40 ± 4
4 x 4 x 4, 20 vol.% 74.3 ± 1.3 382 ± 11 19 ± 3 30 ± 4

3.3.3 Comparative of single-scale and dual-scale 316L SS scaffolds

Fig. 14 shows the representative compressive stress-strain curves of single-scale and dual-
ot

scale scaffolds with a constant solid content of slurry of 20 vol.% and a cooling rate of 5 °C
min-1. The slope of the elastic region of the single-scale scaffolds was significantly higher than
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that of the dual-scale scaffolds, signifying a more rigid structure in the former. However, the
elastic moduli of the single-scale and dual-scale scaffolds was within the range of human
cancellous bone (10 - 3000 MPa) [41]. Owing to their mechanical properties being close to that
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of human cancellous bone, they could reduce the stress shielding effect and improve
osteointegration. On the other hand, the energy absorption of the dual-scale scaffolds was lower
than that of the single-scale scaffolds, except for the 3G-10 and 4G-10 samples (e.g., 60 MJ m-3
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for 3G-10, 72 MJ m-3 for 4G-10, and 49 MJ m-3 for the single-scale scaffolds). The improved
energy absorption in the dual-scale scaffolds might be associated with its gyroid structure. In
contrast to the lamellar structure of the single-scale scaffolds, the unique geometry of the gyroid
Pr

structure presented a superior performance in energy dissipation even with higher porosity.
The insert graphs in Fig. 14 illustrate the corresponding SEM images of the micro-scale
lamellar structure of the dual-scale scaffold at the strain of 5 % and 40 %. At a compression

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 strain of 5 %, minor perturbations in the structure became noticeable. However, the lamellae
still retained their inherent shape but exhibited a marginal deformation. When the compression

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strain reached 40 %, the SEM image revealed a considerably transformed microstructure. The
initial parallel alignment of the lamellae was disrupted, and multiple layers of the lamellar
structure collapsed onto each other, resulting in a relatively dense structure.

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Fig. 14. Representative compressive stress-strain curves of single-scale and dual-scale
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scaffolds (3G-15 and 4G-15). The insert graphs are the corresponding SEM images of the
micro-scale lamellar structure of the dual-scale scaffold at the strain of 5 % and 40 %.

3.4 Permeability of single-scale and dual-scale 316L SS scaffolds

The permeability test results are shown in Fig. 15. For every scaffold tested, the constant
ot

solid content of the slurry and the cooling rate during the freezing process were set at 20 vol.%
and 5 °C min-1. A camera recorded the distinct water flow behaviors of single-scale and dual-
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scale scaffolds during the tests, as shown in Fig. 15 (a). In the single-scale scaffolds featuring
exclusively micro-porosity, water presented a slow flow, initially gathering at the center of the
bottom of the scaffolds and then dropping off. In the dual-scale scaffolds with macro-porosity,
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water flowed continuously throughout the process. For the 4G-15 scaffolds, several water
outlets with smaller flows were visible, while the 3G-15 scaffolds displayed a more significant
continuous water stream. The permeability of the single-scale scaffolds was 0.2 ± 0.1 x 10-12
ep

m2, as depicted in Fig. 15 (b). For the dual-scale scaffolds, the permeability was notably
modulated by both porosity and pore size. Specifically, the 3G and 4G series of dual-scale
scaffolds demonstrated a substantial increase in permeability compared to the single-scale
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scaffolds. The improved permeability in the dual-scale designs could be attributed to the
complicity of interconnected pore structures at both micro and macro-scales, providing

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 optimized fluid flow pathways. When comparing the permeability of dual-scale scaffolds, Fig.
15 (c) illustrates that as the volume ratio increases, leading to higher porosity, corresponding to

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better permeability. Additionally, the permeability of the 3G series scaffolds was consistently
notably higher than that of the 4G series scaffolds. Due to the 4G series scaffolds having more
frequent repeating units of their gyroid structure, they possessed a higher surface area than the

iew
3G series scaffolds. Although this network of channels supplied a higher surface area, it might
also create greater drag forces on the fluid flow, limiting overall permeability [42]. On the
contrary, the larger macro-scale pores in the 3G series scaffolds could reduce fluid flow
obstruction, contributing to its superior permeability. The design of the gyroid structure in both

v
series of dual-scale scaffolds ensured consistent pore interconnectivity. Thus, the primary

re
determinants in permeability could be ascribed to the size and distribution of the macro-scale
pore structure within the scaffold.
To assess the applicability of single-scale and dual-scale scaffolds in the field of tissue
engineering, a comparative analysis was listed in Table 8. The implant with appropriate
er
permeability is crucial for osteogenesis and angiogenesis during bone regeneration. The
desirable permeability of the implant should be comparable to or greater than the permeability
pe
of human cancellous bone. Previous studies have indicated that the permeability above the 3 x
10-11 m2 threshold value was necessary for mineralization and vascularisation within the porous
grafts [43]. The fluid permeability of the single-scale scaffolds was 0.2 ± 0.1 x 10-12 m2, much
lower than the range of human cancellous bone. Additionally, the dual-scale design effectively
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improved the permeability of the scaffolds, making them within the range of human cancellous
bone and even surpassing some other scaffolds [40, 44-46]. The TPMS-based scaffolds of
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previous research summarized in Table 8 were that of the single-scale porous variants. These
scaffolds featured more prominent and uniformly porous structures than multi-scale or
hierarchical designs, contributing to enhanced permeability. In comparison, although the
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porosities of the dual-scale scaffolds in this study exceeded 70 %, their microstructure mainly
consisted of a hierarchical porous structure. This meant that only a fraction of the total porosities
was that of the macro-scale channels; hence, they exhibited lower permeabilities than others.
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However, the hierarchical freeze-casted scaffolds have been shown to help cell penetration. The
results indicated that the osteocytes could migrate through the macro-scale channels and adhere
within the micro-scale pores. The cells were well distributed in the interior pore networks [17].
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Consequently, dual-scale scaffolds with controllable combinations of macro-porosity and

micro-porosity have considerable potential for biomedical application.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4809398
 ed
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Fig. 15. (a) The water flow behaviors of single-scale and dual-scale scaffolds. Yellow frames
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highlighted the process of water flowing from the scaffolds. (b) The comparison of
permeability between single-scale and dual-scale scaffolds. (c) The permeability of dual-
scale scaffolds with various gyroid templates.
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Table 8 Comparison of permeability for human cancellous bone and other porous
scaffolds.
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Porous scaffold Fabrication method Porosity [%] Permeability [× 10-12 m2] Ref.
Human cancellous bone - 50-90 120-8050 [46]
Titanium scaffold Powder metallurgy 45-75 16.3-1370 [44]
Diamond scaffold Selective Laser Melting 57-80 52-3610 [45]
Gyroid scaffold Selective Laser Melting 75-89 290-3910 [40]
Single-scale scaffold Freeze-casting 66 0.2 This study
Dual-scale scaffold Freeze-casting 70-74 18.8-385 This study
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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4809398
 4. Conclusions
The integration of the freeze-casting and 3D-printed sacrificial templating techniques

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could be used to develop the hierarchical 316L SS scaffolds with dual-scale porosities. The
freeze-casting process produced anisotropic micro-scale lamellar porous structures, while the
3D-printed sacrificial templates were employed to offer the macro-scale gyroid channels. The

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solid contents and cooling rates could adjust the single-scale scaffolds' porosities and micro-
scale pore sizes to optimize the performance. The compressive properties of the hierarchical
316L SS scaffolds showed a typical elasto-plastic mechanical behavior up to a considerable
strain of 0.6 without any fracture. Due to increased overall porosities, the dual-scale scaffolds'

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mechanical properties decreased as the macro-scale gyroid channels were introduced into the

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single-scale scaffolds. An inverse correlation existed between template volume ratio and
mechanical strength. The 4G dual-scale scaffolds exhibited superior compressive properties
compared to the 3G series at the same gyroid volume. The improved structural interconnectivity
and more nodal intersections generated better stress distribution and enhanced scaffold rigidity.
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In addition, the dual-scale scaffolds presented a notable rise in permeability only by introducing
a small amount of porosities into the single-scale scaffolds, effectively combining the function
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of the main channels and its surrounding fine network channels. With the escalation of the
template volume ratio, permeability values were significantly amplified. The 3G series
scaffolds revealed significantly better permeability than the 4G series scaffolds since the 4G
series scaffolds had more repeating units and higher surface area to give larger drag forces on
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the fluid flow. In particular, the permeability of the 3G dual-scale scaffolds was close to the
range of human cancellous bone. The present hierarchically porous 316L SS scaffolds with
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tunable macro-scale and micro-scale porosities have considerable potential for application in
bone tissue engineering.

Acknowledgements
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This work was financially supported by the “High Entropy Materials Center” from The
Featured Areas Research Center Program within the framework of the Higher Education Sprout
Project by the Ministry of Education (MOE) in Taiwan. We gratefully acknowledge research
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funding from the National Science and Technology Council (NSTC) in Taiwan under Grant
111-2221-E-007-084-MY3. We especially thank Ms. Su-Yueh Tsai (The Instrumentation
Center at National Tsing Hua University) for the High Resolution Field Emission-Electron
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Probe Micro-Analyser (JXA-iHP200F) sponsored by NSTC under Grant 111-2731-M-007-001.

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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4809398
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This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4809398