Direct 4D printing of functionally graded hydrogel networks for biodegradable, untethered, and multimorphic soft robots

Recent advances in functionally graded additive manufacturing (FGAM) technology have enabled the seamless hybridization of multiple functionalities in a single structure. Soft robotics can become one of the largest beneficiaries of these advances, through the design of a facile four-dimensional (4D) FGAM process that can grant an intelligent stimuli-responsive mechanical functionality to the printed objects. Herein, we present a simple binder jetting approach for the 4D printing of functionally graded porous multi-materials (FGMM) by introducing rationally designed graded multiphase feeder beds. Compositionally graded cross-linking agents gradually form stable porous network structures within aqueous polymer particles, enabling programmable hygroscopic deformation without complex mechanical designs. Furthermore, a systematic bed design incorporating additional functional agents enables a multi-stimuli-responsive and untethered soft robot with stark stimulus selectivity. The biodegradability of the proposed 4D-printed soft robot further ensures the sustainability of our approach, with immediate degradation rates of 96.6% within 72 h. The proposed 4D printing concept for FGMMs can create new opportunities for intelligent and sustainable additive manufacturing in soft robotics.

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Introduction
Soft robotics embodies the artificial design of flexibility, adaptability, and resilience of living organisms, which thus has become a rapidly growing field encompassing a wide range of potential applications.In specific, they are frequently designed to mimic the movements and behaviors of living organisms that can adapt to the environment, such as a gecko lizard robot that can adhere to uneven walls [1], an octopus leg robot that can grab complex shapes [2], hygrobot that morphs under the ambient humidity [3].Based on their versatile applicability and adaptability, the field has a great potential to revolutionize a wide range of industries, including healthcare, manufacturing, and transportation.Currently, the aim of such developments is to enable soft robotic systems to selectively adapt to the designated environments and maximize their functionality.Accordingly, additive manufacturing (also known as 3D printing), a technology that can incorporate the intelligence of things into a single object from the design of the process, is rapidly developing [4].Owing to rigorous investigations, 3D printing can currently be used in various technological fields, including robotics [5][6][7], bioelectronics [8][9][10], biomedical engineering [11,12], and meta-materials science [13].In particular, 3D printing technology has been recently employed as a 4D printing technology for intelligent soft robotics, which is used to demonstrate prototypes of untethered mechanical manipulations of the printed objects [14].Accordingly, various new paradigms for realizing selforganizing structures have been created through the adoption of new printing schemes [15][16][17][18][19][20][21], investigation of the functionalities of printable materials [22][23][24], and design of specifically targeted geometrical structures [25][26][27][28].S far, most 3D printing technologies for soft robotics have focused on realizing a homogeneous structure that can perform a single targeted function.However, it is imperative to expand the technological horizon and implement multiple, discrete, and adaptable functionalities into the printed objects in order to ultimately meet the criteria for a truly intelligent 3D printing technology [29].In this regard, Niino et al [30] recently proposed the concept of functionally graded materials (FGMs) that mimic natural structures, such as the bones and tissues of living organisms, as a feasible candidate for providing advancements in such aspects [31][32][33].
Functionally graded additive manufacturing (FGAM) is a promising technology that enables the fabrication of FGMs with locally tailored and multifunctional properties (e.g.light, magnetic, and humidity responses) by gradually changing the composition, microstructure or printing condition of the materials during structural design [34][35][36].For example, a recent report demonstrated a fused-deposition-modeling 4D printing of thermo-responsive shape memory polymers with volumetric pre-strain distributions, which enables thermomechanical programming of directional actuations [36].As such, although various printing methods (polyjet, fusion deposition printing, and direct ink writing) have been introduced to realize FGAM, there still remain prevailing issues such as stringent filler properties, narrow material choices, relatively low resolution, strict printing environment, inadequacy for the inclusion of multiple functional gradients, and its limited applicability as a 4D printing technology [37].In this sense, a different type of printing methods called Binder Jetting 3D Printing (BJ3DP) has emerged as a promising alternative with distinct advantages [38][39][40].The BJ3DP can use various materials, such as polymers [9,38], ceramics [39,40], and metals [41,42], and it is a representative technology that can quickly and elaborately create porous 3D structures [43,44].Porous structures that are created using polymeric materials have a further advantage in realizing intelligent soft robotics because they have a large surface area and can be highly sensitive to stimuli from the external environment (humidity, gas, temperature, etc) [45][46][47][48].Additionally, BJ3DP allows for the incorporation of multi-materials with functional gradients (i.e.functionally graded porous multimaterials (FGMMs)) because it can accommodate a broad spectrum of materials, making it a more accessible platform for multi-functional soft robotics.Therefore, it is rational to provide a new approach for achieving efficient 4D Printing of stable FGMs based on the advantages of the BJ3DP.
Herein, we introduce a new simple BJ4DP approach for FGMMs using rationally designed graded multiphase feeder beds.Programmable hygroscopic network structures were successfully formed within a powder comprising a uniform mixture of aqueous polymer particles and a cross-linking agent.The chemical and physical characteristics of the graded network structure were thoroughly analyzed using scanning electron microscopy (SEM), energy-dispersive x-ray spectroscopy (EDS), and attenuated total reflection infrared (ATR-IR) spectroscopy.Thereafter, bending analyses were performed on 4D-printed actuators to systematically establish the dependence of the geometrical transformations of various structures on the multiphase bed designs.Additionally, a multi-stimuliresponsive and untethered soft robot was 4D-printed using a functional agent, demonstrating that the proposed FGMM BJ4DP technique is suitable for integrating other materials into a single structure and for realizing stimulus selectivity.Finally, the environmental stability of the 4D printed object was further tested using hydrolysis degradation tests, which demonstrated that the proposed approach can inherently become a sustainable technology for zero-waste soft robotics.The simple BJ4DP approach for FGMMs presented herein is expected to provide opportunities for intelligent manufacturing suitable for soft robotics.

Materials
The polyvinyl alcohol (PVA) powder as the main material was purchased from Shandong Baovi Energy Technology Co., Ltd (17-88 for 120 mesh).The cross-linking agent powder was prepared by grinding sodium tetraborate (⩾99%, CRETEC Co.) and uniformly mixed with the PVA powder at a concentration of 20% (w/w).Carbonyl iron powder (⩾99%, Sigma-Aldrich) with a concentration of 50% (w/w) was used as a magnetic functional agent.The preparation procedure for the PVA-C mixture powder was the same as that for the PVAsodium tetraborate mixture powder.

Design and 4D printing procedure for FGAM
A desktop binder jetting 3D printer (Geeetech I3 Pro, Shenzhen Getech Co., Ltd, and Colorpod, Spitstec, Netherlands) was used to perform 4D printing for FGAM.FGAM was performed in an environment that was maintained at room temperature (∼25 • C) and 50% RH by a humidifier and a dehumidifier.An inkjet cartridge (HP45, Hewlett-Packard) was filled with 30 mL of DI water and an IPA solution.The printing speed was fixed at 2000 mm min −1 , and the inkjet nozzle was maintained at 70 • C (table S1).After the 3D printing process, the printed object was de-powdered to remove any unbound particles.

Measurement and characterization
The formation of cross-links between the PVA particles in the printed objects was confirmed using ATR-IR spectroscopy (VERTEX 70, Bruker Corporation, Germany).The functionally graded 3D-printed objects were visualized by SEM (JEOL-7001F, JEOL, Ltd, Japan), and their chemical composition was analyzed using SEM-EDS.For locomotion analysis, the photographs and videos related to the stimuli-responsive properties of the soft robots were captured using iPhone 12.The bending angle and curvature of the objects were analyzed via images using the Fiji software.Water-saturated air and dry air gas were alternately supplied during the humidity cycle experiment.The external magnetic fields are generated by a flat plate consisting of neodymium-iron-boron permanent magnets.The plate has movement below the track field using a stepper motor controller (ECOPIA, BM-111).

Swelling ratio of the 3D-printed objects
Ribbon-shaped objects measuring 35 mm in width, 5 mm in length, and 1 mm in thickness were 3D-printed for swelling tests.The objects were weighed immediately after 3D printing to determine their weight (W D ), and they were subsequently immersed in a predetermined amount of DI water/IPA (50% w/w) solution (W S -W D ) at 25 • C for 1 h.The swelling ratio of the hydrogels was calculated using equation ( 1): (1)

Biodegradation test
The fully dried actuator and soft robot were soaked in Petri dishes containing 25 ml of 0.1 M phosphate-buffered saline (PBS) (Sigma-Aldrich).Both objects were weighed (w 0 ) after 2 h to exclude the effect of swelling behavior.These objects were immersed in PBS at 37

BJ4DP of hygromorphic FGM actuators
The FGMM actuator is fabricated based on the concept of hygro-expansive deformation (figure 1(a)).It is most commonly known as the nature of pinecones, a primary organ of plants is capable of responding to changes in relative humidity (RH).The porous structures in its tissue are assisted by the capillary effect to enable moisture absorption and swelling, resulting in a significant volumetric deformation (cone opening).Inspired by such behavior, the actuator was fabricated to mimic the internal structure of a pine cone [45,47] to enable the functionally graded cross-linked polymer network of the porous structure to confer effective volumetric dynamic hygromorphic properties to the 4D-printed actuator.The fabrication of the actuator was achieved by the functionally graded BJ3DP system, as shown in figure 1(b).The powder and inkjet cartridges for the 3D printing process setup were prepared in the following manner.First, an aqueous polymer powder was mixed with each functional agent, as described in our previous study [41].Next, the feeder box and builder box were filled with the polymer powder and functional agent mixture.PVA powder, sodium tetraborate, and carbonyl iron were used for this purpose.Each powder, particularly in the builder box, was stacked in accordance with the builder bed design for the 4D FGAM of FGMMs.The feeder box supplied the powder to the builder box, where the soft robots were 3D-printed.Thereafter, the inkjet cartridge was filled with a deionized (DI) water-based solution to activate a cross-linking reaction in the powder.After completing the preparation, the printing process was initiated by depositing the first powder layer onto the builder platform.As shown in figures 1(c) and S1, the powder composition differed as the deposition of each layer progressed in the powder phase with PVA and the cross-linking agent on two beds.During the initial printing stage (P 0 ), only the polymer powder layers were deposited, and then the fraction of polymer-cross-linking agent mixture per layer increased as the process advanced (P 50 ).This cyclic process was repeated until the uppermost layer of the designed soft robot was deposited.A functionally graded phase was formed in the builder box upon completion of the printing process (P 100 ).This process was used to fabricate a soft robot on a functionally graded bed, as shown in figure 1(d).Upon completion of the printing cycle, the 4D-printed soft robot was removed from the powder pile, and the non-cross-linked powder was subsequently removed through air blowing and brushing.Sodium tetraborate was used as a functional agent to ensure the hygroscopic morphing of the 4D-printed soft robots.Sodium tetraborate is a natural mineral commonly used in industries and households.Specifically, sodium tetraborate reacts with water to produce

Structure and properties of the cross-linked porous network
Figure 2(a) shows the mechanism of the cross-linked porous network formation between the PVA particles and borax additives.In the case of only the PVA powder layer, when aqueous droplets are jetted onto the surface of the PVA layer, water permeates between the particles and gradually dissolves the particles (figure S2).Similarly, in the case of the PVA and cross-linker powder mixture, the droplets dissolve the particles while activating the cross-linker.Next, the ionized cross-linker reacts with the hydroxyl group of PVA, consequently producing cross-links and bridging the PVA chain structure.BJ3DP was performed based on this cross-linking mechanism by applying graded feeder bed powder packing.The continuous gradient within the feeder bed enabled the fabrication of functionally graded cross-linked materials (FGCMs).
The FGCM structure was formed by consecutively stacking a high-humidity-responsive layer on top of a low-humidityresponsive layer, and the layer morphology was confirmed using SEM-EDS analysis, as shown in figure 2(b).The analysis was performed by dividing the sample into three sections (A-B, B-C, and C-D).The atomic ratio of borax increased as the borax concentration on the powder gradually increased from A to D. This trend indicates that the compositional gradient in the feeder bed allows for a progressive degree of cross-linking in each printed layer.Since each layer has relative shrinkage and expansion rates, 3D-printed structures can be effectively bent based on humidity (figure S3) [49,50].
Regarding the swelling degree, the borax-cross-linked PVA (PVA-B) exhibited a threefold higher expansion rate than PVA (figure 2(c)).When the structure expanded, the layer with a high cross-linking degree expanded and bent more than the layer with a low cross-linking degree, which was confirmed to cause the bending of the entire structure.Based on these results, the optimal FGCM was designed and printed by stacking pure PVA powders and mixed PVA powders with a 20% (w/w) respectively [54].The cross-linked polymer density can be tuned based on the borax concentration, which affects the change in the hygroscopic bending curvature of FGCM objects (figure 2(e)).When the borax concentration was increased from 0% (w/w) to 20% (w/w), the change in the curvature also tended to increase.Increasing the cross-linking density enables the FGCM object to retain additional water droplet particles in the air, which can consequently expand its volume.
Conversely, when the borax concentration reached 50% (w/w), the curvature change became relatively low.The polymer chain mobility decreases when the crosslinked density reaches a certain degree, consequently increasing the elastic energy of the polymer network.This phenomenon impedes the bending actuation of FGCM structures, resulting in a low change in curvature at high concentrations.

Compositionally graded bed designs for optimal actuation
In addition to the borax concentration, the powder packing design in the feeder bed is another condition that affects the hygroscopic bending behavior of FGCMs. Figure 3(a) shows functionally graded 3D objects printed using the following proposed feeder bed packing design: θ = 0 • , 45 • , and 90 • .
Here, θ is the angle of the interface between the pure PVA powder phase and the PVA-B powder phase containing 20% (w/w) borax in the feeder bed.These three feeder bed packing designs enabled the fabrication of 3D-printed products with different material distribution phases (figure S5).The bed design of θ = 90 • enabled the three phases, namely pure PVA, PVA/PVA-B, and PVA-B, to appear in the 3D-printed object.Similarly, the bed design of θ = 0 • allowed two material phases to appear as pure PVA and PVA-B.Unlike the two designs mentioned, the bed design of θ = 45 • enabled the 3D formation of an elaborate and smooth transition region between pure PVA and PVA-B.Objects were printed with each FGCM geometry to demonstrate the structural tunability of the printed objects.As shown in figure 3(b), the bending angle of the FGCM objects was measured by exposing them to 20% and 80% RH air.Each 3D-printed object exhibited different hygroscopic actuation behaviors under a humid environment.Sample C, a 3D-printed object from the bed with a vertical phase interface angle (θ) of 0 • , had the smallest bending angle when the RH was 50%; however, its bending angle became −3.6  3(c)).Thickness is another factor that affects the actuation behavior of FGCMs because water permeation depends on it.When the object was 3D-printed with thicknesses of 500 µm, 1 mm, and 2 mm, the change in curvature was measured to be 15 m −1 , 30 m −1 , and 5 m −1 , respectively.Additionally, the highest deformation was possible when the structure had a thickness of 1 mm (figure 3(d)).Furthermore, hygromorphic soft actuators were designed and printed in various shapes, as shown in figure 3(e).When the RH reached 80%, the length of the spring structure (top panel) increased by 53.7%, demonstrating its suitability for spring-type hygrometers.Conversely, petal (daffodils) structures were also printed to demonstrate another type of actuation.As the humidity increased to 80%, the petals opened, successfully mimicking the biological motion of petals (figures 3(e) and S6).Furthermore, the directionality of the actuation was controlled and ensured by incorporating regular trench patterns on the surface of the actuators (figure 3(f) and movie S1).The FGCM structures with a diagonal pattern (figure S7) exhibited bending and twisting motions in the right and left directions at 50% RH.The structures also exhibited more vigorous morphing after being soaked in water (figure S8).After it was established that single-stimulus-responsive soft actuation can be achieved by optimizing various processing parameters and feeder packing designs, a multiphase design consisting of three areas in a feeder bed was further incorporated to provide a more complex actuation functionality to each part of an H-shaped actuator, as shown in the front view of figure 3(g).The H-shaped actuator was printed as two robot legs that comprise the PVA-B phase at both ends along with a body that comprises the PVA-only phase and connects the two legs (figure S9).The two legs bend and enable the soft robot to crawl during repeated humidification-drying cycles.

Multi-stimuli-responsive FGMM-based untethered magneto-hygrobot
To demonstrate that our developed FGM system can develop a multi-stimuli-responsive and untethered soft robot, we designed an FGMM-based soft robot by incorporating additional functional agents other than borax.First, we confirmed the feasibility of binder jetting using a magnetic-responsive functional agent and PVA powder mixture, as shown in figure 4(a).The graded feeder bed (θ = 45 • ) was filled with PVA-carbonyl iron (PVA-C) rather than PVA-B to allow the desired part of the 3D-printed object to have magnetic properties.For example, the legs of the 3D-printed octopus object were printed with the PVA-C phase.Only the legs responded when the object was placed in a silicone oil environment and a magnetic field was applied.Consequently, by adding a carbonyl iron phase to the humidity-responsive FGM system, it was confirmed that the untethered soft robot exhibited stimulus selectivity for humidity and magnetism through the FGMM system (figure S10).Thereafter, a magneto-hygrobot structure that could exhibit directional motion was further designed for locomotive applications.As schematically depicted in figure S11, a foreleg and a crawling tail with elementary geometry were attached at the head and end of the soft robot, respectively, to mimic the creeping and crawling motions of animals such as worms.The feeder bed was divided into three compartments, each consisting of pure PVA, PVA-C, and PVA-B (figure 4(b)).The foreleg of the robot was built in the PVA bed phase, while the body of the soft robot was printed in the middle layer, which was filled with only PVA-C.An untethered motion was possible because of the magnetic fields generated by the permanent magnet system.A crawling tail was created in the PVA-B bed phase, allowing the soft robot to turn left or right in response to humidity.The motion can be rectified by simply folding/unfolding the leg and body in the middle without complicating the surface patterning of the foreleg footpads, and this has the advantage of simplifying the soft robot design.Furthermore, a transverse-patterned humidityresponsive tail allowed the soft robot to change its direction while remaining untethered.Figure 4(c) describes the ratcheting motion strategy.When a magnetic field is applied, the foreleg of this object unfolds and kicks the base, causing the object to walk forward.This deformation causes the centroid of the soft robot to shift from its bend point to the front side.
When the field is removed, the object folds its foreleg and then positions its main body upward.The magneto-hygrobot was able to exhibit directional movement that resembled that of a caterpillar upon application of cyclic external magnetic fields (figure 4(d)).Autonomous locomotion in a specific direction through stimulus-selective responses enables soft robots to escape effectively even in a complex barrier environment such as track fields.An untethered diversion was achieved in the magneto-hygrobot by controlling the humidity and alternating the supply of water-saturated air and dry gas.The corresponding image is shown in figure 4(e).In section i, only unidirectional movement was performed using the magnetic field to allow the robot to enter the track while maintaining the RH at 50%.In section ii, the RH was maintained at 80% to allow the soft robot to move along the curved direction of the track.At this time, the soft robot achieved untethered diversion locomotion as the humidity-responsive crawling tail curved.Finally, in section iii, the RH was returned to 50%, and the soft robot successfully exited the track only through unidirectional movement as the tail returned to its original state.
As technology develops rapidly in the 21st century, biodegradable systems are promising ways to create new opportunities for eco-friendly systems, enabling zero-waste generation.In the sense of the systems, recent advances in both 4D printing and soft robotics have compelled the development of ecofriendly technology [23,[55][56][57][58].In this regard, a further study was conducted on the petal-shaped actuator and magnetohygrobot using hydrolysis degradation tests.Once the soft robot completes its assigned goal, its environmental-friendly disposal process can commence by completely submerging it in a PBS solution.Our developed bio-inspired soft robot can not only perform and function similarly to its natural counterparts but also have a more negligible environmental impact.During the degradation test, the hydrogen bonds between the hydroxyl groups of the PVA networks cleaved because of hydrolysis, causing the objects to lose weight noticeably.As shown in figure 4(f), immediate degradation rates of 94.5% and 96.6% occurred within 72 h.Our developed FGM printing technique, which uses fully biodegradable materials, will enable the practical achievement of zero-waste soft robotics.

Conclusion
An intelligent and facile FGMM 4D printing system is proposed, and the feasibility of the developed 4D printing system for multi-stimuli-responsive soft robots is demonstrated.The hygroscopic motion of the 4D-printed objects that resemble pinecones was achieved through the successful formation of a graded porous network structure between aqueous polymer particles.The correlation between mechanical motion and cross-linking agent density was investigated.Increased cross-linking density enables the 4D-printed object to absorb more water droplets in the air and to expand its volume, leading to its bending actuation.Based on the characterization of hygroscopic motion depending on the functional gradient, various geometrical conformation of the 4D-printed actuators was further designed and demonstrated using multiphase powder bed designs.Moreover, the multi-stimuli-responsive and untethered soft robot was developed using a magnetic functional agent was demonstrated.It shows the developed technique can achieve the multi-stimulus selectivity of soft robots.Furthermore, the biodegradability of the soft robots was demonstrated.It shows FGMM 4D printing has a significant potential to become a sustainable technology in terms of ecological footprint.The proposed facile approach of using an FGMM bed design is expected to provide new opportunities for promoting the development of intelligent and sustainable 4D printing systems for soft robotics: multi-stimuli responsive soft robots can be fabricated through a single process of 4D printing using bio-degradable polymers, expanding to a sustainable and deployable soft robotics field.

Figure 1 .
Figure 1.BJ4DP of the hygromorphic FGM actuators.(a) Photographic images (left) and SEM images (right) of the hygro-expansive pine cone and FGM actuator (scale bar: 100 µm).(b) Schematic illustration of the functionally graded BJ4DP system.(c) Powder layer deposition process for the functionally graded phase in the builder box (scale bar: 25 mm).(d) Photographic image of the 3D-printed soft robot on the functionally graded bed.(e) Chemical structure of PVA, borax, and cross-linked PVA.(f) Schematic of the absorb/desorb water molecules in the porous hygroscopic network.

Figure 2 .
Figure 2. Structure and properties of the cross-linked porous network.(a) Schematic of the mechanism underlying dissolution (top) and cross-linking (bottom) between the polymer particles.(b) SEM images (left) and EDS analysis (right) of the FGCM structure (scale bar: 100 µm).(c) Swelling ratios of PVA and PVA-B.The data are presented as mean values ± SD.(d) Photographic images (left) of the section-divided FGCM structure and ATR-IR spectra exhibiting identified vibration peaks (right).(e) Change in the hygroscopic bending curvature of the 3D-printed FGCM objects using various cross-linker concentrations.The data are presented as mean values ± SD.

Figure 3 .
Figure 3. Compositionally graded bed designs for optimal actuation of the printed object.(a) Systematic of the feeder bed designs for functionally graded 4D printing using the following proposed feeder bed packing angles (θ = 0 • , 45 • , and 90 • ).(b) Bending angles of the FGCM objects from 20% to 80% RH.The data are presented as mean values ± SD.(c) Change in the hygroscopic bending curvature of the 3D-printed FGCM objects using various packing designs (80% RH).The data are presented as mean values ± SD.(d) Change in the hygroscopic bending curvature of the 3D-printed FGCM objects using various thicknesses (80% RH).The data are presented as mean values ± SD.(e) Photographic images of the spring-type hygrometer (top) and petal structure (bottom) (scale bar: 10 mm).(f) Photographic images of the directional actuation of the 3D-printed objects with regular trench patterns (scale bar: 10 mm).(g) Schematic of the multiphase bed design for the H-shaped actuator (top) and photographic images (bottom left) of its actuation during the humidification-drying cycles at the bottom middle and bottom right (scale bar: 10 mm).

Figure 4 .
Figure 4. Multi-stimuli-responsive FGMM-based untethered magneto-hygrobot.(a) Schematic of the bed design for using the magnetic-responsive functional agent and PVA powder mixture.(b) Schematic of the multi-stimuli-responsive FGMM bed design for the untethered soft robot.(c) Ratcheting motion strategy for the soft robot (scale bar: 10 mm).(d) Untethered and directional movement of the magneto-hygrobot (scale bar: 10 mm).(e) Untethered directional movement and diversion of the magneto-hygrobot on track fields (scale bar: 20 mm).(f) Biodegradability of the FGM-printed petal structure (left) and FGMM-printed magneto-hygrobot (right).