Soft Ferrofluid Actuator Based on 3D-Printed Scaffold Removal

Abstract

Fabricating soft functional materials via additive manufacturing is an emerging field with a wide variety of applications due to their ability to respond to specifically engineered stimuli (e.g., mechanical, electrical, magnetic, chemical). This article describes an approach to engineering magnetically sensitive structures using three-dimensional printing of acrylonitrile butadiene styrene scaffolds. These scaffolds are encapsulated in polydimethylsiloxane (PDMS) and removed using organic solvents. The open channels that remain after removal are filled in with a ferrofluid to render the structure magnetically sensitive. A three-point flexural test shows that introducing a channel in this way only reduces the flexural modulus of the PDMS by a factor ∼8%. We perform magnetic deflection experiments on samples with three different channel diameters. Our results show a linear dependence between applied magnetic field strength and deflection. We also find that there is a minimum magnetic field strength that needs to be applied to achieve deflection. These results suggest that there is a minimum yield stress, beyond which deflection will occur. We perform experiments on a more complex channel geometry to find that there are multiple modes of deflection. A rational approach to channel design may enable us to tune the mechanical response and direct these actuators to undergo complex motion.

Introduction

Naturally occurring materials span a broad range of material properties (e.g., Young's modulus, fracture energy) that are dictated by the function of these materials.¹ The structural designs based on materials found in nature arise through evolutionary pressures that facilitate survival.² Animals utilize these structures to perform complex motions that are difficult for conventional robots based on metals or hard plastics to mimic.³ Advances in the development of elastomers and mechanically resilient hydrogels enable the fabrication of mechanically flexible actuators that can undergo modes of deformation that their hard counterparts cannot do. Examples of soft material-based robots include haptic robots for rehabilitation,⁴ autonomous bioinspired robots for running,⁵ robots with fingers for gripping,⁶ and underwater robots capable of aquatic locomotion.⁷ The deformability of soft elements endows these robots with a wide range of capabilities that make them ideal platforms for disaster rescue operations,^8,9 minimally invasive surgery,^10,11 and underwater exploration.^12,13

Development of soft robots relies on the material elasticity along with their proper actuation. From a fabrication standpoint, a wide variety of materials are available to drive soft robot actuation, including shape memory alloys,^14,15 electroactive polymers,^16,17 flexible fluidic actuators,¹⁸ cable-driven actuation,¹⁹ pneumatic actuation,²⁰ decomposition of a monopropellant,^21,22 magnetic-driven actuation,^23,24 hydraulically amplified self-healing electrostatic actuators,^25–27 and dielectric elastomer actuators.^28–30 The challenge in soft robot operations lies in their nonlinear mechanical behavior in the presence of a driving external force. This makes feedback control of soft robots difficult because of the absence of accurate response prediction due to infinite degrees of freedom in movement.³¹ Improvements to feedback control schemes can be achieved through a combination of model development and experimentation.³²

The choice of feedback controllers also has a direct effect on the design and fabrication of the soft robot. For example, the performance of soft magnetic actuating elements depends on actuator alignment with the driving magnetic field and the material deformation of the structure. To tune the mechanical response of magnetic actuators, ferro- or paramagnetic particles may be dispersed in a polymer medium and aligned in the presence of a magnetic field.^33–35 Magnetorheological elastomers (MREs) formed in this way are highly responsive in the direction of particle alignment.³⁶ While several soft robot concepts have been demonstrated using MREs as a base material,^37–41 there are several limitations that make it difficult to engineer anisotropic mechanical response in soft robots based on magnetic actuation. For instance, the viscosity of the polymer medium slows down the rate at which particles align, meaning that a strong magnetic field is necessary for MRE fabrication.⁴² The microstructures formed by particle alignment are primarily limited to chains, unless additional fabrication processes are implemented to create complex magnetic field patterns that drive the assembly of complex microstructures.⁴³ A particle loading of 20–30% by weight in an MRE is typically required to achieve a measurable change in mechanical response.^44,45

The limitations described above mean that engineers often resort to complex fabrication techniques to design MRE-based actuators or soft robots. Three-dimensional (3D) printing offers a pathway to simplify the fabrication of MRE-based actuators while enabling the creation of complex structures. The approach works by blending magnetic particles with a polymer base to create an ink, which is extruded and printed using fused deposition modeling to create magnetically responsive structures.^46–49 These inks can be printed in the presence of a magnetic field to modify the responsiveness and material properties of the MRE actuators.^50–52 These 3D-printed MRE structures have been used in a variety of applications, including the creation of worm-like robots,^53–55 smart grippers with individually addressable digits,⁵⁶ artificial cilium,⁵⁷ and a visual display that can change its topology on demand.⁵⁸

In this work, we introduce the 3D printing of scaffolds as a new mode of MRE actuator fabrication. Building upon prior work that utilized 3D printing for creating fluidic elements in polymers,^59–61 we use fused deposition modeling to create scaffolds that form fluid channels in polydimethylsiloxane (PDMS) after removal. The open channels are then filled with a ferrofluid to render the structure sensitive to magnetic fields, thereby creating a soft ferrofluid actuator (SFA). The process used here is advantageous in several respects. The fabrication is relatively simple and, initially, does not require a magnet or solenoid to align particles during printing. We utilize acrylonitrile butadiene styrene (ABS) as the scaffold material, which removes the need to perform extensive rheological measurements⁶² to engineer a new type of ink. And, our process uses a desktop 3D printer, which allows for the cost-effective fabrication of complex designs. The introduction of a ferrofluid to the channel created by the printed scaffold means that we can achieve magnetic actuation with an overall particle loading that is significantly less than the 20–30% often used in the conventional MRE. The actuator that results from this process is highly responsive to magnetic stimuli. Our results also show that the inclusion of a channel in the PDMS does not significantly change the bulk mechanical properties. The fabrication process described here has a number of applications beyond soft robots and actuators, including the construction of field-responsive automotive suspensions,⁶³ the enhancement of heat transfer for power electronic devices,⁶⁴ and membrane materials for the controlled release of chemicals.⁶⁵

Materials and Methods

The activity performed in this article is not research involving human subjects and 45 CFR part 46 does not apply.

Channel material

ABS with a 1.75 mm diameter filament was sourced from Argyle Materials (product number UD-B32-Bk) and serves as the scaffold material. The Sylgard 184 PDMS was purchased from Ellsworth Adhesives (product number 184 SIL ELAST KIT) and was prepared in a ratio of 20 parts by weight of polymer to 1 part cross-linking agent. Acetone sourced from Fisher Chemical (product number A18-4) was used to dissolve the ABS scaffold. The ferrofluid sourced from Lord Corporation (product number MRF-122EG) was used as the magnetic component introduced to the channels.

Channel fabrication

Figure 1 shows the fabrication process for the SFA. A standard triangle language (STL) file of the desired scaffold design was created using SolidWorks. The STL file was transferred to an open source g-code generator (Cura LulzBot version 3.6.3), which translates the design into commands that are used to print the scaffold on a LulzBot TAZ 6 desktop 3D printer. The TAZ 6 uses a modular tool head design that consists of a 0.5 mm diameter nozzle for extrusion. The nozzle temperature was set to 210°C with a print bed temperature of 110°C. We fabricated three different straight channels with fixed lengths of 36 mm and three different diameters: 0.8, 1.5, and 2 mm. The channels were designed to feature a circular cross section and were printed using multiple infill passes. After printing, the scaffolds were placed in a 60 mm diameter petri dish with 20 g of PDMS prepared using the ratios stated above. The petri dish was then placed inside a vacuum desiccator to degas the PDMS. The PDMS was placed in an oven after the degassing step to cure at a temperature of 40°C for 5 h.

FIG. 1.

The fabrication process begins with the 3D printing of an ABS scaffold (top left), followed by encapsulation in PDMS. The scaffold-PDMS construct is immersed in acetone, which dissolves the ABS and makes way for the introduction of the ferrofluid. ABS, acrylonitrile butadiene styrene; PDMS, polydimethylsiloxane.

The cured PDMS is removed from the oven and the region around the scaffold is cut out using a razor. Utilizing a process described in the literature,⁶¹ the PDMS with the embedded scaffold is immersed in acetone for 24 h to completely dissolve the ABS scaffold. The millifluidic channel that remains after the process is flushed with fresh acetone and compressed air is passed through to remove any remaining ABS. The ferrofluid (MRF-122EG; LORD Corporation) is then introduced to the channel using a syringe with an 18 gauge needle. Small pieces of PDMS are then inserted in the open ports of the channel, followed by the placement of small strips of packing tape over the two ports to complete the sealing process.

Bending stiffness measurement

Dynamic mechanical analysis was performed to measure the mechanical properties of the sample manufactured. Specifically, we aimed to quantify the relationship between a force applied to the sample and its corresponding displacement. To this end, we conducted three-point bending flexural tests (METTLER Toledo) on PDMS beams with and without a fluid channel.

Magnetic field strength and displacement

The schematic in Figure 2 shows how we experimentally quantified the deflection of the SFA in a magnetic field. The SFA was attached to a fixed sample holder. A permanent magnet was then placed next to the actuator and slowly moved toward the SFA to initiate deflection. The magnetic field strength was measured using a DSP Gaussmeter (Model 475; Lake Shore Cryotronics, Inc.) at the free end of the sample. Still pictures of the deflection were captured from above the sample and processed to identify displacement. Three soft magnetic actuator samples with channels of varying diameters (2, 1.5, and 0.8 mm, respectively) were tested.

FIG. 2.

Schematic diagram showing the deflection experiment performed on the soft ferrofluid actuator. One end of the beam is fixed, and the free end deflects under application of a concentrated magnetic field, $B^{ext}$. The schematic shows the parameters for large deflection. For small deflections, the value of ${\delta }_x$ is equal to zero.

Theory

Developing a quantitative understanding of cantilever beam deflection in the presence of an external force allows us to characterize the deflection and bending of our SFA. From Figure 2, we define a beam with length L, and uniform rectangular cross section of width w, thickness t, and φ_o as the maximum deflection angle. One end of the beam is fixed, and the action force F is applied at the free end of the beam and perpendicular to the length direction. Depending on the magnitude of the applied magnetic field, a small deflection or large deflection of the beam may result. To calculate the maximum deflection of the beam, we first evaluate the bending moment induced by the external force. The bending moment M for a linear elastic material with rectangular cross section is expressed as⁶⁶

$$M=EI\frac{d\phi }{ds},$$ (1)

where E is Young's modulus, I is the moment of inertia of the beam, and dφ/ds is the curvature at any point of the beam. By differentiating Eq. (1) with respect to s, we obtain

$$\frac{dM}{ds}=EI\frac{d^2\phi }{d{s}^2}.$$ (2)

The bending moment at any position on the beam is

$$M\left(s\right)=F\left(L-{\delta }_x-x\right),$$ (3)

where F is the force applied at a position, x, on the beam, L is the length of the beam, and δ_x is the x position of the deflection point.

In this work, the bending of the SFA is induced by magnetic torque. The applied magnetic field at the free end of the beam, $\left|B^{ext}\right|$, is set perpendicular to the SFA. The magnetically induced moment on the beam is expressed as

$$M\left(s\right)=m\left|B^{ext}\right|wt\left(L-{\delta }_x-x\right),$$ (4)

where $m$ is the magnetic moment of the beam, which is an intrinsic material property that serves as a measure of how susceptible the beam is to magnetic field alignment. Ferromagnetic materials are permanently magnetized,⁶⁷ which leaves behind a residual magnetic field of $\left|B^r\right|={\mu }_{o}m$, where μ_o is the magnetic permeability of free space.

The effective bending moment generated in a beam when a distributed force is applied is equivalent with that induced by a concentrated force at the free end. Therefore, the concentrated force applied at the free end of the beam along the direction of magnetic field can be expressed as⁶⁸

$$F\equiv \left|\frac{dM}{dx}\right|=m\left|B^{ext}\right|wt.$$ (5)

The moment of inertia of the beam I with a rectangular cross section is

$$I=\frac{1}{12}w{t}^3.$$ (6)

The bending stiffness of the beam depends on the geometry of the beam as well as the material stiffness as

$$K_b=\frac{3EI}{L^3}.$$ (7)

For a point force applied at the end of the beam perpendicular to the beam axis, the deflection can be expressed as $\delta =F∕K_b$. Combining Eqs. (5–7), the maximum deflection of the actuator under the action of vertically concentrated magnetic force at the free end of the beam can be analytically obtained as

$$\delta =\frac{4m{L}^3}{E{t}^2}\left|B^{ext}\right|.$$ (8)

Since m is an intrinsic material property that does not depend on the magnitude of the externally applied magnetic field, Eq. (8) predicts that beam deflection should scale linearly with $\left|B^{ext}\right|$.

Results

Ferrofluid migration

At the microscopic level, the iron particles that make up the ferrofluid will undergo migration in the presence of a magnetic field. This process is known as magnetophoresis,⁶⁹ and the imaging platform on our deflection experiment lacks the resolution to observe this migration. To observe the migration process, we placed a 0.8 mm diameter channel under a microscope (Olympus IX70) and imaged the channel with a CMOS camera (QImaging optiMOS). Initially, no magnetic field is applied (Fig. 3A) and the iron microparticles remain dispersed and unperturbed within the channel. A neodymium magnet (D8X0; K&J Magnetics) is moved toward the channel by hand. Figure 3B shows the iron oxide particles migrating in the direction of the neodymium magnet. This migration causes the channel wall to deform nonuniformly when the magnet is in place. The channel returns to its unperturbed state when the neodymium magnet is removed. The process is entirely reversible and is shown in Supplementary Video S1.

FIG. 3.

(A) A 3D-printed channel with a 0.8 mm diameter is filled with ferrofluid. No magnetic field is applied. (B) The walls of the channel deform when a neodymium magnet is placed nearby. Scale bar is 250 μm.

Force–displacement curve

A PDMS beam and an SFA, both with dimensions of 48 mm × 10 mm × 2.5 mm, were used to measure the material stiffness with a three-point flexural test. The PDMS beam was fabricated using the PDMS preparation process, as described in the Materials and Methods section. No channel was incorporated into the beam. The SFA consisted of a scaffold, 36 mm long and 2 mm in diameter, that was dissolved using acetone and then filled with ferrofluid. We only elected to perform flexural tests on the SFA with the largest diameter because this sample represented the removal of the largest amount of PDMS. As a result, we expect that the most significant impact on mechanical properties will occur with this channel.

Figure 4A shows the sample displacement as a function of applied force for both the beam and the actuator. At displacements below 250 μm, the profile of the two samples is indistinguishable. Above this threshold, differences in the displacement profile become apparent. To compare the relative difference between the two measurements, we fit linear curves (Fig. 4B) to estimate the slope of the displacement/load curve. This slope allows us to calculate the flexural modulus of the two samples,⁷⁰

FIG. 4.

(A) Force displacement measurements for samples with and without a channel. (B) Linear regression curve fits obtained from the data in (A) are used to determine the stiffness coefficients. (C) The maximum deflection normalized by beam length as a function of $\left|B^{ext}\right|$. Solid symbols represent data collected at different field strengths, and the dashed lines are linear regression curves fit to the data to determine the slopes for each field condition. Color images are available online.

$$E_f=\frac{k{L}^3}{4w{t}^3},$$ (9)

where k is the linear slope from Figure 4B and E_f is the flexural modulus. The values for each of these parameters are shown in Table 1. The percent difference between the two samples amounts to 8.2%, with the SFA exhibiting a slightly smaller flexural modulus. This indicates that the removal of material to form the channel and the processing in acetone do not significantly impact the bending stiffness of the two samples.

Table 1.

Slope Measured and the Flexural Modulus Associated with Each Measurement

	k (N/mm)	Ef (MPa)
PDMS beam	0.5574	98.63
Soft ferrofluid actuator	0.5136	90.88

PDMS, polydimethylsiloxane.

Magnetic bending flexibility

Figure 4C shows the maximum deflection of the SFA as a function of the externally applied magnetic field. The dimension of the actuators used in this experiment is the same as those used for the three-point flexural test (48 mm × 10 mm × 2.5 mm). Qualitatively, we observe that the beam with the largest channel diameter (2 mm) exhibits the steepest slope, indicating a higher sensitivity to the magnetic field. This actuator also exhibited the largest deflection angle (Table 2) at maximum displacement in comparison to the other actuators. The linear deflection model presented by Eq. (8) is considered valid for deflection angles under 15°, or when the beam displacement is below 18% the beam length.⁶⁶ The derivation for the maximum displacement of 18% is shown in Supplementary Data. Using this criterion, we fit a linear regression curve to all data points that fall below this limit (Fig. 4C). The slope of this regression curve is given by $4m{L}^3∕E{t}^2$.

Table 2.

The Data Used to Calculate the Residual Magnetic Field, $\left|B^r\right|$, and the Yield Stress of the Beam for Different Channel Diameters (Column 1)

Diameter (mm)	Volume fraction (%)	δmax (mm)	φo	Regression slope (mm/G)	$\left|B^r\right|$ (G)	$\left|B_{in}^{ext}\right|$ (G)	τys (Pa)
2	3.0	32.3	58.3°	1.13	2006	15.1	241
1.5	1.7	11.8	32.9°	1.00	1775	22.4	316
0.8	0.5	13.8	22.4°	0.41	728	28.6	166

Column 2 is the particle volume fraction for each channel diameter tested. Column 3 is the maximum deflection distance, δ_max, and column 4 is the maximum deflection angle, φ_o, for the experiments performed in Figure 4C. Column 5 contain the slopes found from linear regression for data below the 18% threshold (i.e., the small angle limit) in Figure 4C, which is used to calculate $\left|B^r\right|$ in Column 6. The minimum applied external field, $\left|B_{in}^{ext}\right|$, in column 7 is used to determine the beam yield stress in column 8.

The beam dimensions are known quantities, whereas the Young's modulus may be taken as 1 MPa based on literature measurements.⁷¹ The slope, dimensions, and Young's modulus may be used to calculate the magnetic moment, m, of the beam. The magnetic moment can then be used to calculate the residual magnetic field, $\left|B^r\right|={\mu }_{0}m$. The values for $\left|B^r\right|$ are found in Table 2. This parameter represents the residual magnetization of the ferrofluid in the beam that remains after the external magnetic field is removed. We find that $\left|B^r\right|$ increases with channel diameter. This is to be expected since a larger channel diameter correlates with a larger volume fraction of ferrofluid, which is listed in Table 2. A description of how we calculated ferrofluid volume fraction may be found in the Supplementary Data.

Another quality that we observe in our data is the appearance of a minimum value of $\left|B^{ext}\right|$ (Table 2) that needs to be applied to the SFA to induce deflection. This indicates that there is a minimum yield stress that needs to be applied to deflect the SFA. One limitation in our model is its inability to predict a yield stress, which is a quality that is inherent to magnetorheological systems.^72,73 This is because the expressions above are intended to describe structure elements that exhibit perfect elastic behavior. However, PDMS is a viscoelastic material that exhibits more complex mechanical properties.⁷⁴ We can modify our theory to account for this yield stress,

$$F\equiv \left|\frac{dM}{dx}\right|=wt\left(m\left|B^{ext}\right|-{\tau }_{ys}\right),$$ (10)

where τ_ys is the yield stress of the SFA. A minimum value of magnetic field strength needs to be applied in order for the SFA to deflect. Up to this point, the actuator remains in mechanical equilibrium. Therefore, we can express the yield stress as a function of experimentally measured parameters by setting Eq. (10) to zero and making use of the definition for magnetic moment, $\left|B^r\right|={\mu }_{o}m$,

$${\tau }_{ys}=\left|B_{min}^{ext}\right|\left|B^r\right|∕{\mu }_o,$$ (11)

where $\left|B_{min}^{ext}\right|$ is the minimum field strength that needs to be applied to deflect the actuator. The yield stresses are shown in Table 2. Based on our data, it appears that the 1.5 mm channel exhibits the largest yield stress, whereas the 0.8 mm exhibits the smallest yield stress. To explain this behavior, we examine how each of these parameters depends on volume fraction. The minimum field strength appears to decrease linearly with volume fraction (i.e., a stronger field is necessary to actuate at lower volume fraction). However, the magnetic moment increases as a function of volume fraction. The multiplicative effects of these parameters as a function of concentration lead to a situation where the maximum yield stress occurs at a concentration of 1.7% volume fraction. A more systematic examination of this effect will be performed in future work. Plots of $\left|B_{min}^{ext}\right|$ and $\left|B^r\right|$ as functions of concentration that illustrate this effect are shown in the Supplementary Data.

Magnetic response of a four-bar linkage

One of the key advantages of an SFA lies in its ability to undergo complex dynamical motion. To showcase this ability, we fabricated a four-bar linkage structure (Fig. 5A). The four-bar linkage was designed to be 30 mm on a side. We selected the four-bar linkage for its use in a variety of engineering applications, including prosthetics^75,76 and microrobot flight.^77,78 We explored the dynamics of a four-bar SFA by vertically pinning the structure to a ring stand clamp (Supplementary Video S2). A 0.5 in diameter neodymium (D8X0; K&J Magnetics) with a contact pull force of 73.8 N is brought close the structure (Fig. 5B) using a desktop CNC machine (Zen Toolworks). The channel closest to the magnet (marked as point 1) exhibits the largest deflection, undergoing a ∼15° rotation toward the magnet with respect to the original position of the actuator. The channel furthest from the magnet (point 2) undergoes a smaller rotation of ∼7°.

FIG. 5.

(A) An unperturbed soft ferrofluid actuator fabricated in the form of a square. (B) A neodymium magnet brought into close contact with the actuator causes a deflection in the structure. Point 1 exhibits a ∼15° rotation toward the magnet with respect to the original position of the SFA, whereas point 2 undergoes a smaller rotation of ∼7°. Dashed lines show the original unperturbed position of the actuator. (C) A side-on view of the square ferrofluid actuator. (D) The neodymium magnet comes into contact. Point 3 deflects with an angle of 61.7° with respect to the horizontal (white dashed line), whereas point 4 deflects with an angle of 56.8°. (E) Two different deflection angles at points 5 and 6 (46° and 13.8°, respectively) are observed as the magnet is retracted. SFA, soft ferrofluid actuator.

In Figure 5C, the square SFA is rotated 90° so the structure faces the neodymium magnet from the previous experiment as shown in Figure 5B. The actuator is initially at rest and hangs nearly vertical. In Figure 5D, the magnet is brought into contact with the actuator using the desktop CNC (Supplementary Video S3). The region marked as point 3 in Figure 5D deflects to the right with an angle of 61.7° with respect to the horizontal (white dashed line). Point 4 on Figure 5D deflects with an angle of 56.8°, indicating that the structure deflects differently depending where the ferrofluid channel is located in comparison to the magnet. The magnet is retracted further to the right causing the actuator to continue exhibiting two different deflection angles. Point 5 in Figure 5E exhibits a deflection angle of 46° with respect to the horizontal. At the midpoint of the structure, the deflection angle changes to a shallower angle of 13.8° (point 6) with respect to the horizontal. Conventional four-bar linkages typically transmit forces in a single plane. However, our four-bar SFA is capable of out of plane motion, which increases the dynamical complexity of this structure. Future work will focus on modeling these complex deflection modes for controlled motion.

Conclusions

This article demonstrates how 3D printing of scaffolds can be used to create an SFA. Prior work on MREs relied on blending the particles with the elastomer based, followed by a magnetic alignment step to create magnetic actuators. The process described here is comparatively simpler and does not require a magnet or solenoid for fabrication. The scaffolds created in this work are evacuated and filled with ferrofluid, allowing us to use overall particle loadings that are significantly less than would be used to fabricate a typical MRE. To quantitatively describe the deflection of our soft rheological actuators, we develop a theory based on the bending of an elastic cantilever beam. We perform three-point flexural measurements, which we used to find the flexural moduli of 98.63 and 90.88 MPa for beams without and with channel, respectively. These results indicate that our process does not significantly impact the mechanical properties of the actuator material. Our magnetic deflection results showed that the actuator with the largest channel diameter exhibited a higher sensitivity to the magnetic field in comparison to samples with smaller channel diameters. The results also indicate that there is a minimum yield stress needed to induce deflection, which is a function of particle loading. Experiments with a more complex channel geometry show that the structure can exhibit multiple deflection modes. These deflection modes can potentially be exploited using feedback control algorithms to perform complex motion. The process described may could serve as a platform for the fabrication of a variety of magnetic functional materials with anisotropic structures to tune the mechanical response of actuators for potential applications in soft robotics, heat dissipation, sensors, and controlled release of chemical and biomedical devices.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

No funding was received for this work.

Supplementary Material

Supplementary Data

Supplementary Table S1

Supplementary Video S1

Supplementary Video S2

Supplementary Video S3