Shape-Programmable Three-Dimensional Microfluidic Structures

Abstract

Microfluidic devices are gaining extensive interest due to their potential applications in wide-ranging areas, including lab-on-a-chip devices, fluid delivery, and artificial vascular networks. Most current microfluidic devices are in a planar design with fixed configurations once formed, which limits their applications such as in engineered vascular networks in biology and programmable drug delivery systems. Here, shape-programmable three-dimensional (3D) microfluidic structures, which are assembled from a bilayer of channel-embedded polydimethylsiloxane (PDMS) and shape-memory polymers (SMPs) via compressive buckling, are reported. 3D microfluidics in diverse geometries including those in open-mesh configurations are presented. In addition, they can be programmed into temporary shapes and recover their original shape under thermal stimuli due to the shape memory effect of the SMP component, with fluid flow in the microfluidic channels well maintained in both deformed and recovered shapes. Furthermore, the shape-fixing effect of SMPs enables freestanding open-mesh 3D microfluidic structures without the need for a substrate to maintain the 3D shape as used in previous studies. By adding magnetic particles into the PDMS layer, magnetically responsive 3D microfluidic structures are enabled to achieve fast, remote programming of the structures via a portable magnet. A 3D design phase diagram is constructed to show the effects of the magnetic PDMS/SMP thickness ratio and the volume fraction of magnetic particles on the shape programmability of the 3D microfluidic structures. The developed shape-programmable, open-mesh 3D microfluidic structures offer many opportunities for applications including tissue engineering, drug delivery, and many others.

Graphical Abstract

1. INTRODUCTION

Microfluidic devices are attracting increasing attention due to their potential applications in a wide range of fields, including microfluidic sensors,^1–3 microfluidic chips,^4,5 drug delivery systems,^6,7 artificial tissues,^8–11 and actuators.^12–14 Microfluidics is a technology that can deal with a small amount of fluid by using microchannels (usually tens to hundreds of microns). The flow rate and liquid volume passing through the channels can be controlled through a syringe pump connected to the inlet and outlet of the microfluidics. Current techniques for making microfluidics include soft lithography, injection molding, and laser ablation¹⁵ based on materials like plastics, hydrogels, and elastomers [such as polydimethylsiloxane (PDMS)].¹⁶ Recently, there has been an increasing interest in applying microfluidics in the biomedical field, such as the investigation of disease models, tissue development, and drug screening.^8,9,17 For these applications, to mimic the biological vascular networks in the human body, three-dimensional (3D) microfluidic structures are desired.^18,19 This is because the complexity of the blood vessels cannot be simulated well by a two-dimensional (2D) planar microfluidic structure. A number of techniques, including laminates,²⁰ molding,²¹ 3D printing,^22–24 and nanofabrication^25,26 are developed for manufacturing 3D microfluidics. For example, the laminate technique is used to fabricate 3D microfluidics by creating a stack of bonded 2D microfluidic layers.²⁰ Through injecting a shear-thinning and self-healing hydrogel “ink” into a “support” hydrogel layer with similar properties, 3D printing is utilized to fabricate complex microchannels to mimic the geometries of blood vessels.²⁷ More recently, a 3D buckling technique is employed to fabricate more complicated 3D microfluidics in open-mesh configurations, which are attached to a substrate to maintain their 3D shape.²⁸ However, due to the elastic recovery of the constituent material (PDMS), these structures tend to recover their 2D shapes after being removed from the substrate, which prevents the realization of freestanding 3D microfluidics for applications including tissue engineering, drug delivery systems, and microrobotics.

In addition, most microfluidics are made of inactive materials, which cannot be further programmed to change their shapes to enable more functionalities such as controlling the fluid flow. To address this issue, shape-memory polymers (SMPs)^29–31 are introduced into microfluidic devices to realize the shape programmability of devices. For example, by implementing SMP valves into microfluidic channels, fluid separation or flow control can be realized.³² Also, SMPs can serve as an actuator to control the opening or closing of each channel in microfluidic arrays upon exposure to thermal stimuli.³³ Despite those efforts, existing works for the integration of SMPs and microfluidics are mostly constrained to 2D designs. The overall geometry of the microfluidics is not programmable, which limits their applications in the biomedical field, such as minimally invasive devices for drug delivery by morphing between their compact configuration during injection/implantation and expanded shape inside the human body under external stimuli or upon exposure to the body environment.

Here, we report a new type of shape-programmable, open-mesh 3D microfluidic structures assembled via compressive buckling of 2D PDMS/SMP precursors. Microfluidic channels are fabricated in the PDMS layer via soft lithography and then laminated onto an SMP film to form a bilayer of PDMS/SMP, which is patterned into desired geometries and compressively buckled into 3D microfluidics by using a pre-stretched elastomer as an assembly platform. Due to the addition of SMPs, the 3D microfluidic structures can be programmed into temporary shapes and then recover their original shape under thermal stimuli and external forces. The structures can also maintain their configurations after the removal of the substrate to enable freestanding 3D microfluidics due to the shape-fixing effect of SMPs. Diverse open-mesh 3D microfluidics and their shape-programmable behavior have been demonstrated. In addition, by integrating magnetic particles into PDMS, we realize fast, remote shape programming of 3D microfluidics via a portable magnet. A constructed design phase diagram provides important guidance for the selection of the volume fraction of magnetic particles and the magnetic PDMS/SMP thickness ratio to achieve desired programmability. The developed shape-programmable 3D microfluidics have many potential applications in biomedical devices, tissue engineering, and many others.

2. RESULTS AND DISCUSSION

2.1. Design and Fabrication of Shape-Programmable 3D Microfluidics.

Figure 1A presents a schematic illustration of creating shape-programmable 3D microfluidics from a bilayer of PDMS/SMPs via the compressive buckling technique.³⁴ The fabrication of 3D microfluidics starts with the formation of 2D channel-embedded PDMS and SMP films. To fabricate the PDMS layer with microfluidic features, a lithographically patterned SU-8 mold for generating microfluidic channels (including the inlet and outlet) is designed and fabricated on a silicon wafer. Then a thin layer of PDMS, which has a thickness of 110 μm, is spin-coated onto the mold for channel fabrication. Peeling off the cured PDMS from the wafer forms a layer with embedded microfluidic channels. The PDMS layer is then laminated onto a prepared SMP film (130 μm thick), which is synthesized from styrene, butyl acrylate, poly(ethylene glycol) diacrylate (PEGDA), and dibenzoyl peroxide (BPO) (see Experimental Section for details), to form the shape-programmable microfluidics. To enhance the adhesion at the PDMS/SMP interface, a thin layer of PDMS (30 μm) is spin-coated onto the top surface of the SMP film to serve as an adhesive layer (referred to as a-PDMS throughout the rest of this paper), followed by plasma treatment for both PDMS and a-PDMS-coated SMP layers before lamination. Finally, patterning the bonded PDMS/SMP films into desired geometries with a laser (ProtoLaser U4, LPKF Laser & Electronics) creates the 2D microfluidic precursors.

Figure 1.

Shape-programmable 3D microfluidic structures formed from a bilayer of PDMS/SMPs. (A) Schematic illustration of fabricating shape-programmable 3D microfluidic structures via a compressive buckling technique. (B) Optical images of various shape-programmable 3D microfluidic structures including their magnified views. Scale bars: 3 mm.

To fabricate shape-programmable 3D microfluidics, the designed 2D precursors are laminated onto a pre-stretched elastomer substrate (Dragon Skin, Smooth-On, Easton, PA). With an ultrathin layer of super glue applied between the 2D pattern and the substrate at selective locations, defined as bonding sites, where strong adhesion is formed at these locations. Alternatively, oxygen plasma treatment of the 2D precursor and the substrate can be used to create strong adhesion at bonding sites by generating hydroxy groups due to condensation reactions, especially for small-scale structures.³⁵ Releasing the pre-strain in the substrate induces large compressive forces to trigger the buckling process, which geometrically transforms the 2D microfluidic pattern into an open-mesh 3D microfluidic structure. Figure 1B shows examples of the fabricated 3D microfluidics, where the microchannels are designed to be 100 μm wide and 50 μm high. To demonstrate the functionality of the microfluidics, diluted food dye (Nomeca Food Coloring, Amazon) is injected into the inlet through a syringe. The magnified views of structure a and b show that the diluted food dye can pass through the complex 3D microfluidic channels without any obstruction. In addition, we fabricate a complicated microfluidic structure array injected with food dye to geometrically mimic vascular networks, as shown in structure c (Figure 1B). These results show that the 3D microfluidics made from a bilayer of SMPs and PDMS can be successfully fabricated into complex geometries in open-mesh configurations. It is worth noting that with advanced soft lithography and laser patterning techniques, the dimension and feature size of the 3D microfluidics can be further reduced. However, the minimization of 3D microfluidics is not the focus of this work and will be pursued elsewhere.

2.2. Shape Programming of 3D Microfluidics.

Figure 2 shows experimental results for the shape programming of 3D microfluidics in various geometries. The thicknesses of the SMP and PDMS layers for all structures in Figure 2 are 130 and 110 μm, respectively. SMPs can be programmed from an original (permanent) shape to a deformed (temporary) shape under external forces when exposed to external stimuli, such as heat or light. In a typical shape-memory cycle for thermally-responsive SMPs, the SMP is heated above its glass transition temperature (T_trans), when the mobility and flexibility of the polymer chains are increased. Under external forces, SMPs can be deformed into a temporary shape. After it cools down, the chains are “locked” in the high-energy state, and the structure maintains its temporary shape. SMPs can recover their original shape by being reheated above their T_trans. The T_trans for the SMP used in this work is 37 °C, which is close to human body temperature and therefore promising for potential applications in implantable medical devices and sensors.

Figure 2.

Shape-memory cycle of shape-programmable 3D microfluidic structures. Diluted red food dye is injected into microfluidic channels for demonstration. (a) “Ribbon” structure. (b) “Stadium” structure. (c) “Table” structure. (d) “Umbrella” structure. (e) “Basket” structure. (f) “Box” structure, with optical and SEM images of the cross section of the SMP/PDMS interface. Scale bars for buckled structures a–f: 3 mm. Scale bars in the magnified views of structure f are 250, 100, and 250 μm from left to right.

We first study the shape-memory effect of the fabricated 3D microfluidics. Take the simple ribbon structure (structure a-1 in Figure 2) for example, diluted food dye injected from the inlet on one bonding site could flow through the channel and then to the outlet on the other bonding site. To test the shape-memory cycle of the structure, the ribbon is first heated to 37 °C using a heat gun and then deformed to a temporary shape by applying a compressive force to the arc location using a tweezer. After cooling down to room temperature, the temporary shape of the microfluidic ribbon structure is “locked” (structure a-2). In addition, the 3D microfluidic channels maintain a smooth fluid flow in the deformed state, as shown in structure a-2 demonstrated with food dye injection. Heating the deformed microfluidic structure above T_trans = 37 °C induces recovery to its original shape (structure a-3). The negligible difference between the geometry of the recovered structure (a-3) and its original shape (a-1) reveals that the shape-programmable 3D microfluidics with the SMP/PDMS bilayer design have an excellent shape recovery effect.

We further fabricate five additional 3D microfluidic structures (structure b–f in Figure 2) m)/compressive buckling, including those that resemble stadiums, tables, umbrellas, baskets, and boxes, with branched microchannels. Food dye injection is used to test the accessibility of the microchannels, demonstrating that the diluted food dye can flow through the channels of various 3D microfluidic structures without any blockage. Furthermore, each of the 3D microfluidic structures is programmed in a manner similar to that of structure a. All structures can maintain good fluid flow in their deformed configurations and can recover their originally buckled shapes within a few seconds when being reheated to T_trans = 37 °C. The results also show that the effect of PDMS as an inactive material on the shape recovery of the entire microfluidic structure is negligible due to its relatively low modulus (~1.4 MPa) under a comparable thickness as that of the SMP layer. In addition, we examine the bonding between the PDMS and SMP layers of the structure, as shown in the magnified views of the as-buckled structure f-1 and the deformed structure f-2 as well as Figure S2. The images reveal the three layers of the microfluidic structure, SMP, a-PDMS, and PDMS, with no obvious delamination among them, indicating that the SMP/a-PDMS/PDMS interface is strong even under deformation resulting from compressive buckling (structure f-1) and programming (structure f-2). Quantitative measurements of the bonding strength among those layers are not the focus of this work and will be pursued elsewhere.

Response time is an important characteristic for the application of shape-programmable microfluidics. In order to study the shape recovery time of programmed 3D microfluidic structures, a table structure made of SMP (110 μm)/a-PDMS (30 μm)/PDMS (110 μm) is used as an example. Figure 3A shows the buckled table structure, where its height (H) is determined to be the distance between the substrate and the highest point of the structure (4.66 mm for the as-fabricated structure). To characterize the response time, the structure is first deformed into a temporary shape by vertically applying a compressive force to the center of the structure under elevated temperature (37 °C). To achieve well-controlled, uniform heating for shape recovery, the deformed structure is merged into a water bath that is maintained at 37 °C, the glass transition temperature of the SMP used in this study. The recovery rate of the structure is characterized by recording the height changes of the structure during heating-induced shape recovery. As shown in Figure 3B, the height of the structure increases almost linearly with the time of being merged in 37 °C water before it reaches a plateau value of 4.66 mm (its original height) at t = 5 s, indicating the full recovery of the deformed 3D microfluidic structure.

Figure 3.

Response time and shape-fixing characteristics of shape-programmable 3D microfluidic structures. (A) Optical image of a buckled microfluidic structure, where its height (H) is determined to be the distance between the substrate and the highest point of the structure. Scale bar: 3 mm. (B) Height of the structure as a function of time during heating-induced shape recovery. Scale bars for the inset: 3 mm. (C) Comparison of structures in their freestanding state and their state attached to a substrate. Scale bars: 3 mm. (D) Experimental results for the shape–storage ratios of the two structures in (C) after removal from the substrate.

In addition to the shape programmability, another advantage of incorporating SMPs into 3D microfluidics is to enable freestanding 3D microfluidic structures due to the shape-fixing effect of SMPs. This feature can overcome the limitations of previously reported 3D microfluidics assembled from compressive buckling, which require the substrate to support their 3D configurations because of the elastic recovery of the constituent materials (PDMS) when the structure is removed from the substrate.²⁸ To fabricate freestanding 3D microfluidic structures, after compressive buckling, the structure is heated at 37 °C to fix the buckled shape. Due to the shape-fixing effect of SMPs, the 3D microfluidic structures can maintain their 3D shape after being removed from the substrate. Figure 3C presents a comparison of two 3D microfluidic structures before and after they are removed from the substrate, which shows minimal shape changes (structure i-1 vs. i-2; structure ii-1 vs. ii-2). To quantify the shape-storage effect of the freestanding 3D microfluidic structures, the distance between two bonding sites with the largest separation before and after the structure is released from the substrate are defined as L₁ and L₂, respectively, and the corresponding heights of the structure are defined as H₁ and H₂, respectively, as shown in Figure S1. The shape-storage ratios in terms of length (ε_L) and height (ε_H) are defined based on the following equations.

$${\epsilon }_L=1-\frac{|L_2-L_1|}{L_1}\times 100\%$$ (1)

$${\epsilon }_H=1-\frac{|H_2-H_1|}{H_1}\times 100\%$$ (2)

As shown in Figure 3D, ε_L and ε_H of structure i (in Figure 3C) are determined to be 99.67 and 97.19%, respectively. For structure ii, ε_L = 98.80% and ε_H = 98.76%. The results show that minimal shape changes occur after the two structures are removed from the substrate, demonstrating the reliability of achieving freestanding 3D microfluidics by utilizing the shape-fixing effect of SMPs.

2.3. Programming of 3D Microfluidic Structures Via Remote Magnetic Actuation.

Programming of SMPs usually involves an external force to deform SMPs into a temporary shape, which is typically performed through a contact force directly applied to the SMP structure. For many applications such as in biomedical devices, remote programming is desired for untethered operation. To achieve remotely-controlled deformation of shape-programmable 3D microfluidics, we add magnetic particles to the structure to enable fast, remote magnetic manipulation. More specifically, neodymium–iron–boron (NdFeB) microparticles with an average diameter of 5 μm are mixed with uncured PDMS, because the relatively viscous PDMS can be mixed more uniformly with the particles compared to the SMP solution used in this study. Following the soft lithography technique, microfluidic patterns are created on the magnetic PDMS (mPDMS) composite layer (110 μm thick). After the integration with the SMP film (110 μm thick) and compressive buckling following the procedures described in Section 2.1, magnetically responsive shape-programmable microfluidics can be obtained. Structure i-1 in Figure 4A shows a simple microfluidic ribbon structure made from mPDMS/SMP, with microfluidic channels injected with diluted white food dye for a better contrast. It is found that the food dye can flow through the channel smoothly, indicating that the magnetic 3D microfluidic structure has good fluid circulation. In addition, the magnified view in the scanning electron microscopy (SEM) image shows that magnetic particles are uniformly distributed within PDMS without large aggregation. To test the remote programmability and shape-memory effect of the 3D magnetic microfluidic structures, one end of the 2D ribbon structure is fixed on the substrate, while the other end is set free to move for more flexibility in actuation (structure i-1 in Figure 4A). When the ribbon is heated to T_trans = 37 °C, a portable magnet (D8Y0, K&J magnetics; diameter: 12.7 mm) is placed directly above the free end of the structure to pull up the structure. After cooling down to room temperature, the ribbon structure can be fixed in the deformed shape even after the magnet is removed, due to the shape-fixing effect (structure i-2 in Figure 4A). Upon reheating, the deformed ribbon quickly recovers its original shape (structure i-3 in Figure 4A). During the entire shape-memory cycle, a good fluid circulation of the channel is maintained in structures i-1, i-2, and i-3. Structure ii-1 in Figure 4A shows a magnetically shape-programmable 3D microfluidic structure in a rotated table configuration. When the entire structure is evenly heated above T_trans = 37 °C, the magnetic force generated by a portable magnet (DX08, K&J magnetics; diameter: 25.4 mm) underneath the structure attracts the circular table surface toward the substrate. After it cools down, the rotated table structure remains in its deformed state (ii-2), which subsequently recovers its original shape (ii-3) upon reheating. These results demonstrate that remote, fast magnetic actuation can be successfully applied to program 3D microfluidics made from a bilayer of SMP and mPDMS composites.

Figure 4.

Remote programming of 3D microfluidic structures via magnetic actuation. (A) Shape programming of a “ribbon” and “rotated table” structure via magnetic forces. The insets show the magnified views of the microfluidic channels and magnetic particle distribution in mPDMS. Scale bars for structures i-1 to i-3 and ii-1 to ii-3: 3 mm. Scale bars for the SEM image, 20 μm. (B) Demonstration of the SMP/mPDMS bilayer beam lattice model with experimental results for a cantilever beam with t_SMP/t_mPDMS = 0.429 and V_m = 17.5%. Scale bar: 5 mm. (C) Experimental and computational results of the normalized maximum deflection (Δ_max/L) of the cantilever beam as a function of V_m under two t_SMP/t_mPDMS values (0.429 and 0.857). (D) 3D design phase diagram showing the effect of t_SMP/t_mPDMS and V_m on the maximum deflection of the SMP/mPDMS beam structure. (E) Contour of Δ_max/L under various t_SMP/t_mPDMS and V_m values.

Previous studies show that the mechanical properties, such as Young’s modulus, of soft materials (PDMS, liquid crystal elastomers, etc.) are increased after adding relatively hard magnetic particles,^36,37 which may affect the stiffness and therefore the deformability of the whole structure. In addition, the deformability of the structure is also affected by the thickness ratio of mPDMS and SMPs. For example, when the SMP layer is relatively thick, the magnetic force may be insufficient to realize the mechanical programming of the structure. To achieve well-controlled shape-programming of 3D magnetic microfluidic structures, we study the effect of two essential parameters on the programmability of the structure: (1) the thickness ratio between the SMP layer and the mPDMS composite layer (t_SMP/t_mPDMS), and (2) the volume fraction of magnetic particles in PDMS (V_m), which is related to the magnitude of generated magnetic forces. As shown in Figure 4B, an SMP/mPDMS cantilever beam is used for the study because it can well represent the deformation of the structure programmed under magnetic forces without many constraints while serving as a building block for many complicated structures. To program the structure, the SMP/mPDMS cantilever beam is first heated above T_trans = 37 °C via a heat gun and is then mechanically deformed by applying a portable magnet (DX08, K&J magnetics; diameter: 25.4 mm), which is 31.5 mm underneath the structure (Supporting Information Movie S1). The length of the beam is fixed at L = 15.36 mm, which is significantly smaller than the diameter of the magnet to ensure that uniform external magnetic forces are applied to the beam. The deformation of the beam is characterized using the maximum beam deflection (Δ_max) and free end angle (θ). To simulate the deformation of the heated SMP/mPDMS beam under magnetic forces, we apply a 2D lattice model³⁸ (see Experimental Section for details). Figure 4B illustrates a typical simulation result (t_SMP/t_mPDMS = 0.429 and V_m = 17.5%) with the initial and the equilibrium position of the beam after the loading, along with experimental results. Figures 4C and S3 compare the normalized maximum deflection (Δ_max/L) and free end angle (θ) between the experimental and simulation results under two thickness ratios (t_SMP/t_mPDMS = 0.429 and 0.857). We can see that the model prediction matches the experimental measurement reasonably well, which validates our lattice model and the uniform magnetic force assumption.

To provide guidance for the well-controlled programmability of SMP/mPDMS microfluidic structures, we construct a 3D design phase diagram under various SMP/mPDMS thickness ratio and magnetic volume fraction conditions by using the cantilever beam as an example. Figure 4D shows the 3D phase diagram of the model-predicted normalized maximum deflection (Δ_max/L) of the beam under t_SMP/t_mPDMS = 0.28–1.57 and V_m = 0–22.5% along with denoted representative experimental results under 10 different cases of beam deflection, the optical images of which are shown in Figure S4. From the curvature of the plotted surface in Figure 4D, we find that the normalized maximum deflection Δ_max/L of the beam exhibits a linear relationship with the loading magnetic force under small deformations, but the relationship becomes nonlinear at large deformations. Figure 4E shows the contour lines of the normalized maximum deflection (Δ_max/L) under various t_SMP/t_mPDMS and V_m values. At a larger magnetic volume fraction (V_m > 20%), the cantilever beam undergoes a significant deflection of Δ_max/L > 0.6 under relatively small thickness ratios (t_SMP/t_mPDMS < 0.6) (e.g., points 1 and 2 in Figure S4). As V_m decreases (10% < V_m < 20%), the magnetic force generated under the same magnet is reduced, which becomes less sufficient to mechanically deform the structure. Further decrease of V_m below 10% causes insufficient magnetic forces to dramatically program the structure, where the shapes of the beam structure only change slightly under the actuation of a magnet (Δ_max/L < 0.2, point 9 and 10 in Figure S4), especially at a larger SMP/mPDMS of t_SMP/t_mPDMS > 1. Such a design phase diagram provides significant guidance for the design and development of programmable 3D microfluidic structures under fast, remote magnetic actuation. It should be noted that the current modeling analysis is still highly ideal and simplified, which, however, should be sufficient to provide an indicator of the deformability of the SMP/mPDMS bilayer structures under magnetic forces for controlled programming.

In addition, we perform experiments of a buckled SMP/mPDMS table structure composed of crossed beams under various t_SMP/t_mPDMS and V_m conditions, as shown in Figure S5. Due to the constraint from the substrate, the deformation of the table structure under heating and magnetic forces is more complicated but shows a similar trend to that of the cantilever beam structure, that is, a larger V_m and smaller t_SMP/t_mPDMS value enable a larger deformation of the structure, as demonstrated in the bending of the table legs in Figure S5.

3. CONCLUSIONS

To sum up, the results presented here provide a facile strategy for creating shape-programmable 3D microfluidic structures to realize thermally triggered shape morphing of complicated open-mesh microfluidics. The structures are assembled by compressive buckling of a bilayer of PDMS/SMP, where the shape can be programmed due to the shape-memory effect of the SMP layer. Fluid circulation of the channel is well maintained in both deformed and recovered shapes of the structures. In addition, the shape-fixing effect of SMPs allows previously inaccessible freestanding, open-mesh 3D microfluidic structures. Through the addition of magnetic particles, fast, remote programming of these structures is achieved. A 3D design phase diagram is constructed for controlled programming of structures by tuning the thickness ratio of the SMP/mPDMS layers and the volume fraction of magnetic particles in PDMS. The results provide significant guidance for the design and development of programmable 3D microfluidics for many applications including remotely controlled biomedical robotics, drug delivery systems, and artificial blood vessels.

4. EXPERIMENTAL SECTION

4.1. Synthesis of Shape-Memory Polymer Films.

To synthesize the SMP films used in this study, four primary materials were used as follows. Styrene (St), butyl acrylate (BA), poly(ethylene glycol) diacrylate (PEGDA, M_n = 575), and benzoyl peroxide (BPO) were purchased from Sigma-Aldrich and used as received. The synthesis started by thoroughly mixing St, BA, and PEGDA with a weight ratio of 12.1:8:1, which was followed by dissolving 0.95 wt % BPO into the mixture. The solution was then poured into a sealed glass mold and cured at 80 °C in an oven for 2 h. Demolding the fully cured polymer in water yielded SMP thin films.

4.2. Fabrication of Shape-Programmable 2D Microfluidic Patterns.

The 2D microfluidic patterns used in the shape-programmable microfluidics were fabricated with the soft lithography technique.³⁹ Polydimethylsiloxane (PDMS, SYLGARD 184) and polymethyl methacrylate (PMMA) were purchased from Sigma-Aldrich. Photoresist SU-8 2050 was purchased from Kayaku Advanced Materials, Inc., and all materials were used as received. To create the PDMS layer with microfluidic features, a lithographically patterned SU-8 mold for generating microfluidic channels (including the inlet and outlet) was designed and fabricated on a silicon wafer. The spin-coating speed and time for SU-8 2050 were 4000 rpm and 40 s, respectively, yielding channels with a thickness of 50 μm after curing. To create microfluidic channels, PDMS (mixed with a base and curing agent at a 10:1 weight ratio) was spin-coated onto the SU-8 mold, and a thin PMMA layer (1 μm thick) was spin-coated between the mold and the PDMS layer for easy release of the PDMS film. After curing at 80 °C for 1 h, the PDMS layer (110 μm thick) was peeled off from the wafer, yielding the layer with embedded microfluidic patterns. To enhance the PDMS/SMP interface, a thin layer of PDMS (~30 μm) was spin-coated onto the surface of the previously synthesized SMP layer. Oxygen plasma was used to treat both PDMS and a-PDMS-coated SMP layers, which were then laminated into a PDMS/SMP bilayer and cured in the oven at 80 °C for 1 h. The synthesized PDMS/PDMS film was patterned into desired geometries using an LPKF laser (ProtoLaser U4, LPKF Laser & Electronics). During the laser patterning process, the microfluidic channels including the inlet and outlet are aligned to ensure that they are intact after patterning.

4.3. Synthesis of Magnetic PDMS Films.

To prepare the magnetic PDMS layer, five different concentrations (2.5, 7.5, 12.5, 17.5, and 22.5 vol %) of neodymium–iron–boron (NdFeB, MQFP-B-2007609-089, Neo Magneuench) microparticles with an average diameter of 5 μm were mixed into uncured PDMS using a planetary mixer (AR-100, Thinky) and spin-coated onto the SU-8 microfluidic mold. The following steps were the same as those of fabricating 2D PDMS/SMP microfluidic patterns.

4.4. Assembly of Shape-Programmable 3D Microfluidic Structures.

2D microfluidic patterns were laminated onto a pre-stretched substrate made from Dragon Skin (Smooth-On, Easton, PA). By using an ultrathin layer of super glue between the 2D pattern and the substrate at selective locations (bonding sites), strong adhesion was formed at these sites. Releasing the pre-strain in the substrate caused compressive buckling of the 2D patterns into 3D microfluidic structures.

4.5. Computational Modeling of the Deformation of SMP/mPDMS Microfluidic Structures.

A 2D lattice model³⁸ was applied to investigate the effect of the thickness ratio (t_SMP/t_mPDMS) and volume fraction of magnetic particles embedded in the mPDMS layer (V_m) on the deformation of the bilayer cantilever beam. The beam has a fixed length of 15.36 mm and a width of 2.5 mm. The SMP/mPDMS thickness ratio was varied from 0.28 to 1.57 by fixing t_mPDMS to 140 μm while varying the thickness of the SMP layer. The bilayer beam is discretized into small rectangular lattices with 60 μm in length and 20 μm in thickness. SMP and PDMS were modeled as neo-Hookean materials, whose Young’s moduli are 10³⁴ and 1.37 MPa,⁴⁰ respectively, and the Poisson’s ratio for both materials is 0.4. The magnetic force was added to the PDMS layer as a constant downward body force, which corresponds to cases with uniformly applied and residual magnetic flux densities along the vertical direction. Under a given applied magnetic flux density, the magnitude of the magnetic force can be assumed to be linearly proportional to the volume fraction of embedded magnetic particles. We validated these assumptions by comparing the simulations with controlled experiments, with foci on the maximum beam deflection (Δ_max) and free end angle (θ), as shown in Figure 4B. To construct the 3D design phase diagram for the cantilever beam structure, a total of 40 simulations were conducted with varying SMP/mPDMS thickness ratios and force magnitudes.

Supplementary Material

1

Deformation of a SMP/mPDMS cantilever beam structure (Vm = 17.5%, tsmp/tmPDMS = 0.857) via magnetic forces when being heated above 37 °C