Differential diffusion driven far-from-equilibrium shape-shifting of hydrogels

Active, externally triggered shape-shifting materials are important for technologies such as bioelectronics, sensors, medical devices, and soft robotics. Designing unconventional morphing pathways can expand functionality. Stimuli-responsive hydrogels are attractive due to their water-swollen networks and rich responsiveness, but typically morph monotonically between equilibrium shapes. Prior strategies, such as mechanically induced buckling in gel assemblies, convert continuous evolution into abrupt actions but still follow a monotonic direction and require time to build energy. Self-oscillating hydrogels driven by chemical fuels can cycle autonomously but still transition monotonically between equilibria within each cycle. In contrast, this work introduces a far-from-equilibrium (FFE) shape-shifting behavior in hydrogels. Under mild temperature changes, a single stimulus triggers two opposite, non-monotonic shape-shifting events, occurring much faster than in comparable hydrogels lacking this mechanism. The hydrogel network is designed so its pathway can be programmed post-synthesis via inducing anisotropy by freeze–thaw crystallization of PVA within a PNIPAM network; unexpectedly, this programming gives rise to an FFE-like morphing pathway.

The authors survey prior work on advanced shape-shifting materials: buckling-enabled hydrogel assemblies can provide abrupt actions and amplified outputs but maintain monotonic morphing direction and require energy accumulation. Self-oscillating gels, driven by oscillatory chemical reactions or chemo-mechanical feedback loops, exhibit unique autonomous cycles yet still transition monotonically between equilibrium shapes during each actuation. Other advances include multi-shape memory polymers and responsive gel lithography enabling sophisticated morphing. However, these approaches do not provide non-monotonic dual actions under a single stimulus, motivating exploration of FFE-inspired mechanisms to broaden accessible shape-shifting behaviors.

Materials and synthesis: Hydrogels were formed as semi-interpenetrating networks by free-radical copolymerization of N-isopropylacrylamide (NIPAM) with N,N'-methylenebisacrylamide (MBA) in aqueous poly(vinyl alcohol) (PVA). Typical formulation: 1.0 g NIPAM with 0.25 wt% MBA in 5 mL of 10 wt% PVA solution, initiated by 200 µL APS (4 wt%) and 40 µL TEMED, cast between glass slides with PDMS spacers, polymerized at 4 °C for 24 h. Photothermal variant: add 0.1 wt% graphene oxide (GO). pH-responsive variant: poly(acrylic acid) (AA) with 0.25 wt% MBA in 10 wt% PVA; initiated with 100 µL APS (4 wt%), polymerized at 70 °C for 12 h. All gels were soaked in deionized water 1 day to remove unreacted monomers. Programming (inducing anisotropy): Samples were mechanically deformed (bending, stretching, twisting) and subjected to repeated freeze–thaw (FT) cycles while maintaining the deformation to crystallize PVA and fix partial strain. Typical protocol: seven FT cycles; freezing time 6 h and melting time 30 min; reported freezing and melting temperatures 20 °C and 15 °C, respectively. After FT, samples equilibrated in 15 °C water for 1 day. Strain fixation ratio was evaluated after 100% stretch and FT; anisometry was measured from square films after equilibration at 50 °C. Characterization: Mechanical properties and swelling ratios were assessed for varying MBA and PVA contents. Equilibrium swelling behavior was measured across temperatures; swelling ratio Ws/Wd, with Wd obtained after drying at 70 °C for 1 day. 2D SAXS (Nano-inXider, Pilatus 200K) confirmed network anisotropy; q-range 0.09–4.49 nm^-1; samples mounted in a rotatable stage; data merged and background corrected. Finite element analysis (FEA): ABAQUS thermal diffusion/expansion analogy was used to simulate water diffusion-induced swelling and shape change, employing a neo-Hookean hyperelastic model with modulus decreasing upon swelling. Linear swelling strain modeled as αT ΔT(X), with swelling ratio βs = exp(3αT ΔT). Experimental βs = 8.26 for stress-free gel yielded αT = ln(βs)/3 = 0.70. Young’s modulus E decreased with swelling: E = E0 exp(-αT ΔT), with E0 = 129 kPa. Boundary conditions: for stress-free samples, ΔT = 1 on outer surfaces; for prestressed bent samples, ΔT = 1.6 (outer side) and 0.8 (inner side) at the bend, ΔT = 1 elsewhere. Although ΔT denotes temperature in the solver, it represents local water concentration for the hydrogel. Modeling reproduced diffusion-driven transient closing and reopening and stress-enhanced differential diffusion. Experimental protocols for FFE demonstrations: Programmed geometries (zig-zag, four-arm gripper, bent strips, twisted strips) were actuated by temperature changes (e.g., 50 °C to 15 °C for cooling; 15 °C to 50 °C for heating). Some control experiments used silicone oil baths during cooling to test for internal water redistribution effects. Kinetics were recorded via folding angle or pitch counting over time. Device demonstrations included an eight-arm construct shrinking then expanding to pass through a hole; photothermal actuation with near-IR (808 nm) localized exposure for 20 s to trigger spatially resolved FFE behavior. pH-responsive PAA-PVA hydrogels were similarly programmed and actuated by pH changes.

- Discovery of a non-monotonic, far-from-equilibrium (FFE) shape-shifting in PNIPAM-PVA hydrogels programmed by freeze–thaw-induced PVA crystallization. A single stimulus (temperature change) elicits two opposite actions (e.g., close-then-open or twist-then-untwist) along the morphing pathway between two equilibrium shapes. - Mechanism: Programmed stress anisotropy induces uneven water diffusion. Diffusivity depends on hydrostatic stress via D = D0 exp(σh Ω / kBT). Tensile regions swell faster (higher D), compressive regions slower (lower D), creating and amplifying differential swelling that transiently drives shapes off the natural monotonic pathway. Geometry alone yields minor transient effects; stress is the dominant contributor. Control in silicone oil (no external water exchange) shows no appreciable FFE, supporting the diffusion mechanism. - Kinetics: For a programmed bent sample cooled to 15 °C, the folding angle drops from 90° to 0° in ≈2.9 min (fully closed), remains for ≈0.8 min, then reopens to an equilibrium ≈55° by ≈12.5 min. Compared to a conventional bilayer hydrogel, the initial FFE stage is more than one order of magnitude faster than the bilayer’s characteristic turning point. - Reversibility and bidirectionality: FFE shape-shifting is highly reproducible over cycles. Upon heating from 15 °C to 50 °C, a non-monotonic open–close dual action occurs rapidly (within 10 s). FFE shapes revert to the initial equilibrium shape within 10 s when returned to 50 °C water. - Twisted geometry: Upon cooling, number of twists (pitches) increases sharply (e.g., from 3 to 7 in 5.0 min) then decreases more slowly (to ~4 by 50 min), evidencing twist–untwist dual action. Thickness strongly affects FFE: 0.50 mm samples show pronounced behavior; 1.50 mm diminished; 2.00 mm behavior vanishes. Width also modulates effect via stress distribution. - Composition dependence: Higher PVA content increases physical crosslinking upon FT, strengthening FFE expression. At 10 wt% PVA with 0.25 wt% MBA, FFE is remarkable; at 1 wt% PVA, FFE is not visible. FT reduces equilibrium swelling below the PNIPAM VPT (~32 °C) and programming strain slightly reduces swelling (≈15% effect), while swelling above VPT is unaffected by FT/strain. - Modeling: FEA based on diffusion-driven swelling with stress-enhanced differential diffusivity reproduces transient closing and reopening in stress-free and prestressed samples; predicts deviation of final equilibrium angle (≈55° vs initial 90°), consistent with stress effects on equilibrium water uptake. - Devices and generality: An eight-arm device exhibits cooling-triggered shrink-then-expand, enabling passage through a hole smaller than both equilibrium diameters. Incorporation of GO enables near-IR light-triggered spatial actuation and subsequent FFE transformation. A PAA-PVA pH-responsive hydrogel shows similar non-monotonic FFE shape-shifting upon pH change, demonstrating generality beyond thermo-responsiveness.

The study addresses the limitation of conventional hydrogels that morph monotonically between equilibrium shapes by introducing a programmed, diffusion–stress coupled mechanism that drives the system along a non-monotonic, far-from-equilibrium pathway. The differential diffusion, amplified by stress-induced changes in water diffusivity, transiently propels the material into shapes inaccessible via the natural, monotonic trajectory. This results in dual opposite actions under a single stimulus and markedly accelerated actuation kinetics. The approach leverages mild stimuli (temperature, pH, light via photothermal fillers) and simple mechanical programming (freeze–thaw-induced anisotropy), making it attractive for engineering. The observations align with broader FFE paradigms where systems traverse unstable, high-energy intermediate states that enable unusual macroscopic phenomena, but here achieved without extreme conditions. The results suggest new functionalities, such as single-stimulus bidirectional operations and large, rapid transformations, relevant to soft robotics, minimally invasive devices, and sensors.

This work demonstrates that mechanically programmed PNIPAM-PVA hydrogels can undergo far-from-equilibrium, non-monotonic shape transformations driven by differential diffusion under stress, enabling dual opposite actions from a single stimulus and significantly faster actuation. The mechanism is validated experimentally and by FEA, shows strong dependence on geometry, stress state, thickness, and PVA content, and is generalizable to other stimuli (near-IR photothermal, pH-responsive PAA-PVA). The concept expands the design space of shape-shifting materials and devices, enabling functions (e.g., pass-through-and-expand operations) inaccessible to conventional hydrogels. Future research could explore quantitative control of stress distributions and diffusion pathways, broaden material systems and stimuli, integrate sensing/feedback for closed-loop control, optimize scalability and durability, and develop application-specific devices in soft robotics, biomedical deployment, and high-sensitivity actuation.

- The FFE effect depends strongly on material composition and structure: high PVA content (e.g., 10 wt%) and sufficient freeze–thaw-induced crystallization are needed; low PVA content (1 wt%) shows no visible FFE transformation. - Thickness and geometry constraints: pronounced in thin samples (≈0.5 mm), diminishes at 1.5 mm, and vanishes at 2.0 mm; geometry and width influence stress distribution and thus the effect. - Requires solvent exchange and water diffusion; no appreciable FFE was observed when cooling in silicone oil, indicating dependence on external water uptake. - The final equilibrium shapes can deviate from initial programmed geometries due to stress effects on equilibrium swelling (e.g., bent angle settling at ~55° vs initial 90°). - Programming relies on repeated freeze–thaw under mechanical load; process parameters (cycle number, times, temperatures) and stability of PVA crystals constrain reproducibility and may limit processing speed. - Modeling employs a thermal-diffusion analogy with simplified parameters (e.g., constant αT, prescribed ΔT distributions), which, while capturing trends, may not encompass all coupled chemo-mechanical complexities.