# Self-shrinking soft demoulding for complex high-aspect-ratio microchannels | Panda Anku

### Fabrication of soft templates

The soft demoulding technique contains two main traits: a soft template and a gentle demoulding process. The soft template can be fabricated by various methods, including 3D printing34, inkjet printing21, and injection moulding35, only if it is softer than the matrix. This work contrives the soft templates by thermal drawing36; i.e., dipping the tip of a thin rod into a polymer melt and then drawing the rod out of the melt (Fig. 2a). Attached to the rod tip, the polymer melt in the air transforms into the filament shape due to the viscosity and surface tension and solidifies quickly due to the temperature gradient. Various thermoplastic polymers are available and adaptable for this manipulation37, including low-cost, vastly applied polyethylene and polyurethane. This fabrication method is fast, simple, and productive. The filament can be produced with a circular cross section and controllable diameter in an extensive range from tens of microns to hundreds of microns. The diameter of the filament (D) is determined by36:

$$D=frac{C}{sqrt{v}}$$

(1)

where (C) is a constant, and (v) is the drawing speed (see “Methods” section ‘Fabrication of soft templates’ and Fig. 2b). The filament diameter is constant at the same drawing speed (Fig. 2c). Variable diameters, such as a tapered shape (Fig. 2d), can be generated on a single filament by simply altering the drawing speed.

In addition to the 1D template, more complex profiles can be fabricated by tuning other fabrication parameters. For example, we generated a branched structure by pulling two needle tips in two directions (see Fig. 2e). At a higher heating temperature (130 °C in this work), we created a filament with a series of spindle-knotted structures on the filament (Fig. 2f), which results from the synergistic interaction of the viscosity and surface tension38. Via postprocessing, more complex spatial shapes were produced. For instance, a helical template was fabricated by further stretching the straight filament before it was thoroughly cooled down (Fig. 2g). Moreover, we generated a plectoneme structure by twisting both ends of the filament (Fig. 2h). By template arrangement and assembly, more intricate 3D structures were created, such as a conical surface, a saddle surface, a hyperboloid surface, and a tree-like structure (Fig. 2i–m). The surface of the template fabricated by this method is smoother (e.g., ({S}_{a}) = 0.010 µm at Supplementary Fig. 2a) than those fabricated by other methods such as 3D printing (({S}_{a}) is more than 0.4 µm39) due to the fluidity of the produced material. A smooth surface can reduce the demoulding resistance force and leave a low roughness surface on the microchannels.

### Soft demoulding

Pulling out the template from the matrix is another grand challenge in forming a microchannel. With previously rigid templates7, both the shear force and the template’s fracture force determine the diameter of the channel (Fig. 3a–c and Supplementary Fig. 3). There is competition between the critical fracture force of the rigid template and the shear force during pulling. Once the shear force is larger than the critical fracture force, the template fractures and the demoulding fails. Only when the critical fracture force is larger, the template can be pulled out. Assuming the template is a simple straight wire with a round cross-section, the shear force ({F}_{{{{{{rm{shear}}}}}}}) is determined by:

$${F}_{{{{{{rm{shear}}}}}}}=tau pi {dl}$$

(2)

where (tau) is the shear stress, (d) is the filament diameter, and (l) is the embedded length. The shear force increases linearly with the diameter and the embedded length of the template, as shown in Fig. 3b. The template’s fracture force ({F}_{{{{{{rm{frac}}}}}}}) is calculated as:

$${F}_{{{{{{rm{frac}}}}}}}={sigma }_{f}A=frac{{sigma }_{f}pi {d}^{2}}{4}$$

(3)

where ({sigma }_{f}) is the fracture stress, and (A) is the cross-sectional area of the template. Hence, a longer embedded length demands a thicker diameter for successful extraction. To avoid fracture, we have ({F}_{{{{{{rm{shear}}}}}}},le, {F}_{{{{{{rm{frac}}}}}}}), and thus:

$$frac{l}{d},le, frac{sigma }{4tau }$$

(4)

which indicates that the aspect ratio of the channel is intrinsically limited by the nature of the rigid template materials, i.e., the strength and adhesive energy density. For instance, the maximum aspect ratio for the PDMS matrix and the copper template system is 258, according to Eq. (4) (σ = 6300 MPa, τ = 6.1 MPa, based on experimental results in this work). As shown in Fig. 3c and Supplementary Fig. 3b, c, when the embedded length was 30 mm, the copper (diameter: 80 µm) and nylon template (diameter: 100 µm) ruptured due to the large aspect ratios (375 and 300, respectively). Such a strong force might break a fragile matrix (e.g., agarose gels). Moreover, a rigid template inevitably causes wear on the channel surfaces due to the rigidity of the template and the large shear force.

In contrast, for the soft demoulding method, peeling instead of shearing is dominant during the extraction process due to the larger stretching ratio of the template (the ultimate strain of the thermoplastic resin (1200%) was 100 times that of the copper wire (12%), as shown in Fig. 3a). The aspect ratio of the channel doesn’t limit by the length because the large deformation of the soft template transfers the demoulding mechanism to a peeling process (see “Methods” section ‘Fabrication of the microchannels by soft demoulding’), and the peel force has no relationship with the embedded length of the soft template (Fig. 3d, f). The peel force ({F}_{{{{{{rm{peel}}}}}}}) for soft demoulding of thermoplastic resin (hot melt adhesive, 3748Q) can be expressed by ref. 40:

$${F}_{{{{{{rm{peel}}}}}}}={Delta E}_{S}frac{pi d}{left(1-{cos }theta right)}$$

(5)

where (d) is the filament diameter, (theta) is the peel angle, and ({Delta E}_{S}) is the adhesive energy. The peel force remained consistent for the samples with different embedded lengths (10, 20, 30, and 40 mm) (Fig. 3e, f), indicating that the mechanism of soft demoulding is significantly different from the rigid demoulding shown previously (see “Methods” section ‘Mechanical characterization and Demoulding tests’). As shown in Supplementary Fig. 4a, b, when subjected to a stretching force, the strain stably increases, and the peel angle expends, while the force first surges under a short strain and then remains stable over a large range for the simulation results (see “Methods” section ‘Simulation of the deformed angle’). It is observed in our soft demoulding experiments that the onset of peeling occurs when the peel force reaches a plateau (Supplementary Fig. 4c). For larger diameters, the peel force increases, and the consequent peel angles are different (Fig. 3d and Supplementary Fig. 4c). Demoulding failure always occurs in the situation where the template reaches its maximum strain before demoulding is initiated. According to the simulation, for the soft template (thermoplastic resin) in this work, demoulding fails when the diameter is less than 15.1 µm, as shown in Fig. 3d since the peel angle exceeds its largest value (30°). Moreover, according to different mechanical behaviours of soft templates, we built the demoulding model for the TPU filament (see Supplementary Note 1 and Supplementary Fig. 4d–h).

Herein, the magnitude of the pull-out force for the soft template is drastically smaller than that for the rigid template, according to peeling theory (Fig. 3f and Supplementary Fig. 4), since the direct pulling of the rigid template can be regarded as the peeling of zero angles. Hence the soft template is less susceptible to fracture and appliable for thin and high-aspect-ratio microchannels generation.

With soft demoulding, we fabricated microchannels with a diameter of as small as 10 µm (Fig. 4a). As shown in Supplementary Fig. 5a, b, a microchannel with an aspect ratio as high as 6000 (around 10 times higher than the previously available maximum value, 6299) was also generated. Moreover, the resultant microchannel inner surface is smooth (({S}_{a}) = 0.018 µm) (Supplementary Fig. 2b), which benefits soft robotics, fluidic interactions, and optical applications, such as improving the burst pressure and cycle life of soft actuators41, enhancing the switching effect of microfluidic valves42, and reducing the optical intensity loss for optical waveguides43 since the template is deformable and the radial dimensions decrease when it is extracted, which largely reduces the pull-out force. Moreover, we fabricated microchannels of various shapes from 1D to 3D patterns, including a taper, a helix, a saddle, and a tree-like structure (Fig. 4b–q and Supplementary Fig. 5). Moreover, the demoulding possibility for the spindle-shaped soft template was discussed in Supplementary Note 2. Compared to other methods, soft demoulding can generate both higher geometric flexibility and smaller feature size44 (the two primary features of microchannels) (Fig. 4r and Supplementary Table 1), comparable with human capillaries in terms of complexity and dimension.

### Applications for soft demoulding

Here, we demonstrate the extensive applications and significant impact of soft demoulding in soft robotics, wearable sensors, soft antennas, and artificial vessels (Fig. 5). Miniature soft robots have attracted increasing interest in recent decades due to their excellent compliance and adaptivity8,45 in minimally invasive surgery, inspection, and search and rescue35,46. The fabrication of micro-chambers is challenging, particularly when the characteristic dimension is small and the topology is complex. For example, directly pulling out the template from the matrix can only create a simple straight chamber. Emerging solutions, such as chemical crosslink bonding interfaces47, photo-curing 3D printing in monolithic structures48, and dip-coating methods7, suffer from rough surfaces, weaker strength, high time consumption, or limited shapes and sizes.

Herein, our soft demoulding method can create miniature soft robots with smooth, complex microchannels and monolithic structures. For example, inspired by worms that can curl up for defence, a miniature worm robot capable of bending at an angle larger than 450° was created (Fig. 5a, Supplementary Movie 2, and “Methods” section ‘Fabrication of the soft worm robot’), which is applicable to delicate manipulation and grasping during surgeries49. Its inner chamber with a plectoneme structure (diameter: 200 µm, see Supplementary Fig. 6a) fabricated by the soft demoulding method possesses a series of concaves in the elastic matrix, enabling a more effortless and quicker deformation of the actuator under inflation than a chamber with a constant cross section50. We also demonstrated a tendril-inspired ultra-long, soft robot (Fig. 5b and Supplementary Fig. 6b, and Supplementary Movie 3) integrating a helical microchannel (diameter: 150 µm) with an aspect ratio of more than 1600 (see Methods section Fabrication of the soft tendril robot). Pressured by air, the soft tendril robot winded around a rod accordingly, which can be applied for fixation and grasping, such as fixing and monitoring nerval activity51, by imitating the tendril’s survival strategy. These prototypes reveal the promising potential of creating more complex channels for more versatile miniature soft robots based on soft demoulding.

Furthermore, using the soft demoulding technique, we fabricated a stretchable sensor with smooth and round cross-sectional ultrathin channels (Supplementary Fig. 7a and “Methods” section ‘Fabrication of the soft wearable strain sensor’). The emerging stretchable elastomeric sensors, although promising for wearable devices and human-machine interfaces10,15,52, may cause uncomfortable and restricted during wearing due to the bulky structures. These problems mainly result from the limited fabrication methods. With soft demoulding, circular channels can be easily fabricated and can generate a more predictable resistive change response during extension (see Supplementary Note 3, Supplementary Fig. 7b–e, and Supplementary Movie 4) due to the isotropic cross section. We demonstrated a cotton-thread-like ultralong strain sensor fabricated by this method and seamlessly integrated it into a knitted sleeve. The soft strain sensor with the circular microchannel was manually sewn into a woven sleeve (Fig. 5c). The sensor was compatible with the sleeve and almost invisible because of its thin, long, and semitransparent characteristics, which are essential for wearable devices. This sensor accurately measured the elbow motion by the voltage signal variation (Fig. 5c and Supplementary Movie 5).

Moreover, a soft and mechanically tunable micro-antenna with a 3D helical conductive structure was fabricated by soft demoulding (see “Methods” section ‘Fabrication of the soft antenna’). Existing small antennas, although critical for wearable devices, human-machine communication systems, and implant devices53, are constricted by simple structures, such as rodlike or planar geometries54,55, or supports for the 3D structures55,56. In addition, the large size (several centimetres) and rigid frame of current antennas hinder them from more extensive applications. Here, we fabricated a soft micro-antenna (10 mm × 1.2 mm × 1.2 mm) containing a 3D helical microchannel (channel diameter: 180 µm, helical structure diameter: 450 µm at the minimum and 900 µm at the maximum) infused with the liquid metal (Fig. 5d and Supplementary Fig. 8), while most previous small antennas were in the centimetre scale53,56. The 3D conducting structure offers a more compact dimension for confined environments. Moreover, with the 3D helical structure, the antenna presents low reflection coefficients of −6.6 and −22.3 dB (lower than −10 dB is sufficient for commercial antennas57) at two resonant frequencies (6.8 and 13.1 GHz), respectively. Being bent, the micro-antenna is mechanically tunable in two broad resonant frequency ranges (from 6.8 to 7.3 GHz and 11.9 to 13.1 GHz), and the reflection coefficient becomes lower for better signal transmission, as shown in Fig. 5d (see “Methods” section ‘Reflection coefficient test for the soft antenna’). Therefore, the fabrication method of soft demoulding for micro-antenna provides a new approach toward compact soft wireless electronics.

Finally, using the soft demoulding technique, we created microchannels in the agarose gels and artificial blood vessels with straight and tapered structures. Microchannels are essential for, e.g., 3D tissue engineering development, disease analysis, and drug discovery3,4,12. Within the channels, cells can live longer and are able to develop into an organoid with a large volume, which is more suitable for customized medicine screening4. The formation of round cross sections and complex geometries, although critical for resembling the rheologic properties of blood flow58 and the vascularization of a large tissue5, is challenging. Previous rigid template demoulding is inapposite for a fragile matrix, and in the template dissolution method, the residual solvent and contaminant are cytotoxic to living cells18,23. Therefore, our solvent-free and soft demoulding process requiring gentle force is a superior approach for cell culturing in vitro. Here, we first fabricated a microchannel with a spindle-shaped structure and a microchannel with a narrow neck in agarose gels (Supplementary Fig. 9a, b, and Methods section Fabrication of biocompatible microchannel structures), which can be used for vascular disease models. Furthermore, we built a round cross-sectional artificial vessel (diameter: 150 µm) and a tapered one (the minimum diameter: 250 µm, and the maximum diameter: 500 µm) by seeding human umbilical vein endothelial cells (HUVECs) into the microchannel within the fibrin gel matrix (see Fig. 5e, Supplementary Fig. 9c–f, and “Methods” section ‘Fabrication of the artificial vascular model’). After culturing for 1–2 days, the microchannel remained circular, and cells survived around the microchannel since nutrition can penetrate the porous structure of the artificial vascular wall. The cells near the channel exhibited a high survival rate (Fig. 5e), demonstrating that the channel architectures can provide functional nutrient transport to the near cell matrix. Moreover, this vascular structure can be used for simulating vessel growth and further vascular disease prediction. To exhibit the advantages of soft demoulding, we employed two rigid templates for fabricating microchannels in fragile fibrin gels, but the large shear force caused the microchannels to rupture (see Supplementary Fig. 10a, and “Methods” section ‘Fabrication of microchannels in fibrin gels by rigid demoulding’). We also verified the negative effect of acetone, which is employed in the matrix by matrix swollen16,22 and template dissolution methods18,25, on cell growth in artificial vessels. When introducing acetone to the gels, the death rate of the 3T3 cells increased accordingly, as shown in Supplementary Fig. 10b. Therefore, with the gentle and solvent-free soft demoulding technology for 3D complex microchannel fabrication, a more complex artificial vascular system could be fabricated for prospective applications.