The widespread prevalence of commercial products made from microgels illustrates the immense practical value of harnessing the jamming transition; there are countless ways to use soft, solid materials that fluidize and become solid again with small variations in applied stress. The traditional routes of microgel synthesis produce materials that predominantly swell in aqueous solvents or, less often, in aggressive organic solvents, constraining ways that these exceptionally useful materials can be used. For example, aqueous microgels have been used as the foundation of three-dimensional (3D) bioprinting applications, yet the incompatibility of available microgels with nonpolar liquids, such as oils, limits their use in 3D printing with oil-based materials, such as silicone. We present a method to make micro-organogels swollen in mineral oil, using block copolymer self-assembly. The rheological properties of this micro-organogel material can be tuned, leveraging the jamming transition to facilitate its use in 3D printing of silicone structures. We find that the minimum printed feature size can be controlled by the yield stress of the micro-organogel medium, enabling the fabrication of numerous complex silicone structures, including branched perfusable networks and functional fluid pumps.

Keywords

Here, we develop a granular organic microgel system and demonstrate its use as an oil-based 3D printing support medium. The organogel particles are formed through the self-assembly of diblock and triblock copolymers dispersed at low concentration in mineral oil, in contrast to traditional polymerization routes to synthesizing microgels ( 1 , 2 ). Our granular organogel system has the rheological properties needed for precision 3D printing applications, including a low modulus (100 Pa), a low yield stress (3 to 4 Pa), and a short period for elastic recovery (1 s). 3D printing is performed by translating an injection needle through the organogel medium while depositing features made from numerous silicone-based materials. We investigate the interfacial instability between printed silicone features and the organogel support material, determining the limits of precision dictated by the balance of interfacial tension, yield stress, and feature size. We find that silicone features as small as 80 μm can be printed and remain indefinitely stable without cross-linking. We also find that the breakup of unstable features can be delayed markedly by increasing the viscosity of silicone inks, allowing even higher-precision (30 μm) structures to be manufactured. We demonstrate the capabilities of this method by creating 3D scaffolds, model tracheal implants, a perfusable 3D branched network, and a functional fluid pump.

Silicone elastomer can be formulated to have low elastic modulus, high extensibility and toughness, excellent thermal and oxidative stability, and chemical inertness ( 14 – 16 ). Although this combination of properties has enabled a multitude of industrial uses to be developed for solid silicone elastomer, the challenges of handling viscous liquid silicone before curing limit its use in advanced additive manufacturing ( 17 – 21 ). 3D printing with industrially relevant nonpolar inks such as silicone would be greatly enhanced if a nonpolar jammed microgel system was available; a versatile, oil-based, jammed microgel material with rheological properties that can be tuned to mimic aqueous microgels would enable the precise 3D printing of silicones and organic soft materials by eliminating deleterious interfacial instabilities between printed materials and their microgel support.

In one recently developed application area, jammed microgels are used to three-dimensionally (3D) print hydrogel and silicone structures, as well as living cell constructs ( 11 , 12 ). With this technique, printed material is physically trapped in space by packed microgels, which temporarily fluidize under the stress generated by a translating injection tip and then rapidly return to a jammed solid state ( 8 – 10 ). The jammed microgel material enables 3D printing of soft matter through its low modulus, low yield stress, localized yielding behavior, spontaneous reflow after yielding, and rapid recovery of elasticity. These properties facilitate 3D printing with a high degree of precision and control with aqueous soft materials. By contrast, demonstrations of silicone printing into microgel supports show that major challenges remain for nonaqueous soft materials. Interfacial interactions between silicone inks and aqueous support materials limit printing precision and inhibit adhesion between printed features ( 13 ); commercially available silicone-based microgels practically offer no rheological control of the support medium ( 12 ).

Swollen microscale particles made from cross-linked polymers, generally known as microgels, have extremely useful rheological properties and are produced industrially as additives in personal care products, lubricants, coatings, and oil recovery fluids ( 1 – 4 ). A distinct behavior emerges with microgels when the particles are larger than 1 μm and tightly packed together ( 5 ). In contrast to traditional shear-thinning complex fluids composed of polymers or micelles, this packed bath of granular microgels transforms from a stable solid state into a flowing fluid phase when large external forces cause the granular gel particles to rearrange, which does not happen spontaneously under thermal forces. This transition is known as unjamming and occurs when externally applied stress exceeds a threshold value called the yield stress ( 6 – 10 ). Microgels are most often synthesized, swelled, and used in aqueous solvents, limiting their breadth of potential application; traditional microgel synthesis routes in organic solvents remain challenging and mostly limited to coating technologies ( 1 , 2 ). Thus, alternative and effective methods of producing granular-scale microgels in nonpolar solvents and oils will open untapped areas of technological application.

RESULTS

Block copolymer self-assembly and rheology Block copolymer self-assembly is a well-established route for designing soft materials, offering control of nanostructure and rheological properties (22–24). To formulate an organic microgel medium, we leverage this high degree of control provided by block copolymers, using a polystyrene-block-ethylene/propylene (SEP) diblock copolymer and a polystyrene-block-ethylene/butylene-block-polystyrene (SEBS) triblock copolymer. These polymers are assembled at low concentration [4 to 5 weight % (wt %)] in light mineral oil, a solvent selective for the ethylene-containing blocks (see Materials and Methods and Fig. 1A). The SEP diblock and SEBS triblock copolymers both self-assemble into structures with 1- to 2-nm glassy polystyrene cores and with coronas containing the oil-soluble blocks (24–26). In the pure triblock system, neighboring polystyrene cores are connected by bridges of ethylene/butylene blocks, resulting in a macroscopic network (27, 28). The bridged polystyrene cores are analogous to the cross-links in more traditional formulations of aqueous microgels. The size of each polystyrene core is determined by the polystyrene length and mass density, whereas the spacing between cores is driven by the swelling of the oil-soluble block. In contrast to the pure triblock material, a suspension of discrete micelles is formed when only diblock copolymers are assembled. For both the triblock and diblock systems, the glassy polystyrene cores prevent the exchange of polymers between structures. Fig. 1 Block copolymer self-assemblies and micro-organogels. (A) Organogel support materials are formulated with light mineral oil, polystyrene-block-polyethylene/propylene diblock copolymers, and polystyrene-block-polyethylene/butylene-block-polystyrene triblock copolymers (polymers drawn are extended to illustrate their contour lengths). (B) High concentrations of diblock copolymers result in a fluid phase of packed micelles, unable to support printed structures. (C) Diblock micelles consist of polystyrene cores (red dots) surrounded by ethylene/propylene coronas. (D) At high concentrations of triblock copolymers, the support bath becomes globally cross-linked, and the printing nozzle causes permanent damage as it moves across the gel. (E) Ethylene/butylene midblocks assemble either into cross-link “bridges,” in which the polystyrene endblocks are found in different cores, or into “loops,” in which both polystyrene endblocks are located in the same core. (F and G) An equal blend of diblock and triblock copolymers results in closely packed microgels. Packed microgels provide a self-healing environment, allowing a printing nozzle to repeatedly transverse the same region while simultaneously supporting printed structures. (H) The micro-organogels form when the diblock copolymers replace the triblock copolymers, reducing the number of ethylene/butylene bridges that form until the material is no longer a continuous network. Previous work shows that fluid instabilities are overcome by 3D printing into a self-healing, jammed solid made from polymer microgels at low polymer concentration (11, 12, 29). Here, 3D printing into the diblock micelle suspension is inhibited by its fluid-dominated rheology; printed features will move under buoyancy forces or break up into droplets (Fig. 1, B and C). By contrast, 3D printing into the triblock network is inhibited by its solid properties; while the cross-linked network can support structures, the printing nozzle severs polymer bridges as it travels through the printing medium, irreversibly damaging the gel (Fig. 1, D and E). To create a solid material that can support printed structures and that is not damaged by a translating printing nozzle, we blend the diblock and triblock copolymers in search of a formulation having insufficient bridging to create a system-spanning network, but having enough bridging to create microscale organogels (Fig. 1, F to H). The addition of diblock copolymers promotes gel swelling without creating bridges. This micro-organogel system should fluidize at the location of applied stress and rapidly resolidify upon the removal of stress, much like the behavior of aqueous microgels, allowing for the precise manufacture of 3D-printed silicone structures. To identify a formulation with favorable rheological properties for silicone 3D printing, we perform several types of rheological measurement on samples with different diblock and triblock copolymer ratios and various global polymer concentrations. To classify a given formulation as solid or liquid, we conduct a frequency sweep at low strain amplitude (1%), measuring the elastic and viscous shear moduli (Fig. 2A). To identify the yield stress of the material, we measure stress under unidirectional shear at different shear rates. In these data, the yield stress corresponds to the plateau in shear stress at low shear rate. Yield stress is determined by fitting the Herschel-Bulkley model to the data, given by , where σ is the measured stress, σ y is the yield stress, and is the applied shear rate (Fig. 2B) (30, 31). Finally, we determine the rate of elastic recovery in the material after the removal of applied shear stress. This thixotropic time is the duration over which shear rate drops to 0 after a high level of applied shear stress is rapidly removed (Fig. 2C). A short thixotropic time improves 3D printing performance because it reduces the duration over which the microgel support material is fluidized and mechanically unstable. Fig. 2 Rheological characterization of block copolymer phases. The rheological properties, including frequency sweep (A) and yield stress (B) of block copolymer assemblies, are highly dependent on the ratio of diblock to triblock copolymers. At high diblock concentrations, the material demonstrates rheological properties associated with a liquid, including a crossover in the shear modulus at high frequencies and no determinable yield stress. At high triblock concentrations, the material shows rheological properties associated with an irreversibly cross-linked gel, including separated elastic and viscous shear modulus at high values and irrecoverable yielding at high stresses. Block copolymer blends show rheological properties favorable for 3D printing of soft materials, including separated elastic and viscous shear moduli with low elastic modulus, a low yield stress, and a fast recovery of elasticity after shearing. (C) Thixotropic response time of the block copolymer microgel system. (D) The samples exhibiting rheology suitable for 3D printing are found to be composed of 2- to 4-μm microgels, as seen in phase-contrast microscopy. We find that a formulation of 4.5 wt % global polymer concentration with an equal incorporation of diblock and triblock copolymers (that is, 1:1 wt %) has the rheological properties consistent with jammed microgels and needed for precise 3D printing of silicone (see the Supplementary Materials). The frequency-dependent elastic and viscous shear moduli of the 50:50 mixture are relatively flat and fully separated across a wide frequency range, exhibiting an elastic modulus of about 100 Pa. This formulation has a yield stress of 3 to 4 Pa and a thixotropic time of about 1 s (see the Supplementary Materials for further rheological characterization). This combination of rheological behaviors is the fingerprint of jammed soft granules. To test whether this formulation produces micro-organogels, we dilute the sample with mineral oil and collect optical micrographs using phase-contrast illumination. We observe 2- to 4-μm granular structures (Fig. 2D and movie S1). Using small-angle x-ray scattering (SAXS) to measure the spacing of polystyrene cores, in combination with stoichiometric calculations, we find that within the pure triblock network phase, each polystyrene core is connected to its neighbors through an average of 12 bridges. In the microgel phase, each polystyrene core only connects through an average of six bridges. It is intriguing that the organo-microgels formulated here self-assemble when the coordination number between polystyrene cores lies at the limit of the Maxwell criterion for the stability of solids (see the Supplementary Materials) (32). The rheological behavior of this copolymer system can be tuned; as the concentration of the triblock polymer is increased relative to the diblock polymer, the yield stress and modulus of the gel increase (Fig. 2A). Unrecoverable yielding of the 100% triblock material is observed in shear rate sweeps; when the applied shear stress exceeds the yield stress of the gel, SEBS triblock bridges are severed (Fig. 2B). Conversely, materials with high diblock proportions behave like non-Newtonian liquids, exhibiting a crossover of elastic and viscous shear moduli in frequency sweep measurements and having no observed yield stress in shear rate sweeps (Fig. 2, A and B). In the 50:50 formulation that forms microgels, we find that the rheological properties of the gel remain relatively unchanged up to a temperature of 50°C. At 60°C and above, the material is dominantly fluid-like (see the Supplementary Materials). The moduli and the yield stress of the different formulations can also be controlled by changing the global polymer concentration (see the Supplementary Materials).

Printing, precision, stability, and strength Printing of silicone elastomers into the organogel support medium is accomplished using a custom-made 3D printer consisting of a modified linear stage as a syringe pump attached to three linear translation stages (movie S2). The three linear translation stages follow a predetermined trajectory at a specified translation speed, whereas the syringe pump continuously deposits the silicone elastomer into the organogel medium at a set flow rate (see Materials and Methods). To test the level of control provided by the micro-organogel for silicone 3D printing, we create a series of linear features at many different combinations of nozzle translation speed (0.1 to 10 mm/s) and injection flow rate (10 to 10,000 μl/hour). A test ink is made from a vinyl-terminated polydimethylsiloxane (PDMS) polymer, mixed with a (mercaptopropyl)methylsiloxane-dimethylsiloxane copolymer cross-linking agent at a 3:1 ratio (see Materials and Methods). To enable 3D imaging with a laser scanning fluorescence confocal microscope, fluorescent beads are dispersed in the PDMS ink before printing. Side-on and end-on projections reveal very straight and smooth features that are nearly round in cross section (Fig. 3A). Quantitative analysis of the 3D stacks demonstrates that the cross-sectional areas of printed features follow a simple conservation of volume equation, A = Q/v, where A is the feature’s cross-sectional area, Q is the flow rate of the ink, and v is the translation speed of the nozzle (Fig. 3B). We also find that the features have a cross-sectional aspect ratio close to 1 across all flow rates and translation speeds. Thus, features between about 1 mm and 100 μm in diameter can be created by following this simple volume conservation law. Outside of this regime, features as small as 30 μm are generated by reducing the ink flow rate and increasing the nozzle translation speed, indicating the potential high level of precision that is possible with this 3D printing method. Fig. 3 Control of printed features. (A) The width and height of printed lines are measured using confocal microscopy at flow rates and tangential velocities of 5000 μl/hour at 2 mm/s, 5000 μl/hour at 10 mm/s, 1000 μl/hour at 3.5 mm/s, 1000 μl/hour at 10 mm/s, and 5 μl/hour at 6 mm/s. (B) Feature size of printed objects can be controlled by the tangential velocity of the nozzle (v) and the flow rate of the ink through the nozzle (Q). The printed feature size shows nearly ideal behavior across a wide range of velocities and flow rates. (C) The critical feature size in which neat silicone oil remains stable is controlled by the yield stress of the organogel; increasing the yield stress of the organogel decreases the critical feature size necessary to maintain stable features. (D) The time at which features printed below the critical feature size will begin to break up can be increased by increasing the shear viscosity of the silicone ink. We were intrigued by the accumulation of fluorescent particles at the interface between the printed PDMS structures and the supporting micro-organogel. We believe that this phenomenon is analogous to a well-known mechanism in which microphase-separated droplets are stabilized in an immiscible medium by microparticles or nanoparticles that become trapped at the fluid-fluid interface, reducing interfacial tension and preventing droplet coalescence (33, 34). This phenomenon points to challenges that may arise in 3D printing PDMS inks that are formulated with nanoparticle fillers, which may inhibit adhesion between successive layers of printed structures. These effects do not occur when printing with a miscible ink/support material pair, as the ink and support medium share a common solvent such as water. By contrast, the immiscible ink/support material pair used here creates a diffusion barrier and prevents this potential rapid molecular exchange between the ink and support material. This is a useful feature when the loss of chemical precursors from the ink into the support bath may interfere with processing steps after printing, such as photocrosslinking. To estimate the strength of interaction between the organogel support material and the PDMS ink in the absence of added particulate fillers, we perform a series of interfacial and surface tension measurements with neat mineral oil and silicone oil. We measure the surface tension of silicone oil and mineral oil against air through the pendant drop method, finding that γ s = 19.0 ± 0.9 mN/m for silicone oil and γ m = 30.4 ± 2.5 mN/m for mineral oil, comparable to those reported in the literature (35, 36). Stable hanging drops of silicone oil in a mineral oil bath were too small for reliable pendant drop measurements to be performed; increasing the size of the drop resulted in the silicone detaching from the needle before reaching an adequate size. Thus, to determine the interfacial tension between silicone oil and mineral oil, γ sm , we place a drop of neat mineral oil on the silicone oil/air interface and measure the interfacial contact angles. Using these angle measurements and the surface tension measurements from the pendant drop, we solve Young’s equation and find that γ sm = 13.1 ± 2.2 mN/m (see the Supplementary Materials). To prevent the breakup of printed structures driven by interfacial instabilities, the stresses generated by interfacial tension must be less than the yield stress of the micro-organogel material (31, 37). Thus, the minimum stable printed feature size may be controlled, in part, by the micro-organogel yield stress. We hypothesize that the minimum feature size can be predicted from a plastocapillary length, given by λ = γ ms /σ y . To test this relationship, we print features made from low-viscosity silicone oil into micro-organogels with different yield stresses and observe the feature stability over 24 hours. We find that the minimum stable feature size decreases with increasing yield stress, as predicted, although this back-of-the-envelope estimate does not quantitatively predict minimum feature size from our measurements of interfacial tension and yield stress (Fig. 3C). The block copolymer in the mineral oil phase may alter the interfacial tension with the silicone phase; thorough studies of the plastocapillary length that account for the added polymer must be performed in the future if quantitative predictions of minimum feature size are to be made (31, 38). We find that the time until unstable feature breakup depends on the viscosity of the printed material, revealing that even unstable features may be suitable for generating very fine, precise silicone structures if the curing time of the silicone is less than the time over which the interfacial instabilities dominate (Fig. 3D). The interfacial tension between PDMS ink and the surrounding organogel support material is a driving force for feature instability, yet it also assists in creating 3D-printed parts with smooth surfaces. After 3D printing linear features made from Momentive UV Electro 225 PDMS and cross-linking through ultraviolet (UV) curing, we remove the cured part from the micro-organogel support material, clean it by serially washing it with solvents and surfactant solutions (see movie S3 and Materials and Methods), and characterize the surface in multiple ways. Scanning electron microscopy images reveal a very smooth surface (Fig. 4E), and scanning white light interferometry (SWLI) measurements demonstrate that printed parts have a surface roughness of 150 nm (Fig. 4, A to C). 3D-printed “dog-bone” parts designed to test mechanical strength are printed, cured, and removed from the organic support material by using the same protocols (Fig. 4F). Extensional stress-strain tests on dog-bone samples demonstrate excellent mechanical integrity of 3D-printed silicone parts, which fail at approximately 700% strain (see Fig. 4, D and G, and the Supplementary Materials). This physical robustness of the 3D-printed parts reveals that strong adhesion occurs between neighboring features during fabrication. To test whether layer-to-layer and lateral feature adhesion is achieved, we printed silicone sheets out of Momentive UV Electro 225 silicone in both the vertical and horizontal orientations. Both types of structures were found to be very robust, indicating good feature adhesion along both directions and enabling us to wash the structures and perform SWLI scans of their surfaces (see the Supplementary Materials). Fig. 4 Surfaces and mechanical properties of printed structures. (A to C) SWLI of a printed silicone surface shows a surface roughness of 150 nm [2D scan (A), slice along the x axis (B), and slice along the y axis (C)]. (D) Stress-strain curve of printed silicone dog-bone specimens; printed silicone structures are capable of enduring more than 700% strain before mechanical failure. Tensile tests maintain a linear stress-strain relationship at low strains (inset). (E) Scanning electron microscopy of the cross section of a printed silicone structure demonstrates the uniformity of printed structures. (F) Macrophotographic image of a dog-bone specimen printed from silicone elastomer for tensile testing. (G) Macrophotographic images of printed dog-bone structures in the relaxed and highly strained states.