A 3D-printed molecular ferroelectric metamaterial

Three-dimensional SLA printing enables the creation of volumetric architectures consisting of nanoscale feature size using programmed automation processes (28–30). By analogy, we inferred that this SLA strategy could be incorporated for the volumetric design of ferroelectric metamaterials if the following fundamental prerequisites are met: transparent ferroelectric precursor for the curing light and sufficient curing depth, light-sensitive polymers, and sufficient density to trigger electromechanical coupling and ferroelectricity. If these challenges can be addressed by molecular ferroelectrics, a rapid 3D fabrication strategy would allow control over the geometry, feature size, and polarization direction of molecular ferroelectric metamaterials. Fig. 1A illustrates the schematic diagram of SLA printing for molecular ImClO₄ ferroelectrics with high dimensional accuracy, structural complexity, and high throughput. The molecular ferroelectric ImClO₄ crystal is water-soluble and can mix with photopolymerizable material to achieve transparent printable precursor ink solution with a viscosity of 1.70 cSt (SI Appendix, Table S1 and Fig. S3) (31). The transparent and highly concentrated ferroelectric precursor solution plays a key role in the SLA printing as its low diffraction index can facilitate light penetration and prevent light scattering. This ultimately allows for a reliable, accurate, and efficient 3D printing process.

In the bottom-up SLA process (Fig. 1A), a smaller traction force between the structure being printed and the material container is the vital factor in printing speed and reliability (32), and such force is linearly proportional to viscosity (33). Therefore, the low viscosity of the precursor material enables continuous rapid printing, which reduces the manufacturing time from hours to minutes for the same structure (Movie S1). This represents a game-changing molecular ferroelectric manufacturing technique and offers the unique advantages of the prevention of hydrogel dehydration and printing failure, as well as process efficiency and structural accuracy. During printing (Fig. 1C), the precursor solution is exposed to ultraviolet (UV) light, and poly(ethylene glycol) diacrylate (PEGDA) is then cross-linked to form the scaffold network with the encapsulated ions of the ImClO₄ precursor. As shown in Movie S1, a complex geometric structure (Schwarz primitive structure, 25 × 25 × 25 mm³) can be printed in 8 min as opposed to 3 h by conventional methods. The large pore size of the scaffold (about a few micrometers, SI Appendix, Fig. S5) provides higher controllability and flexibility. Additionally, the electrical resistance measurement (SI Appendix, Fig. S6) shows that the as-printed sample is electrically conductive due to the abundance of ions. Dehydration then crystallizes molecular ferroelectric ImClO₄, while the polymer skeleton holds the as-printed structure after water evaporation due to the elasticity of the PEGDA polymer network (34). It has to be mentioned that a high loading of molecular ferroelectric component is required to maintain the high polarization in printed structures. The volume ratio of ferroelectric phase can be easily tuned to serve for the desired ferroelectric performance by changing the concentration of ImClO₄ or the ratio of PEGDA. Thus, we prepare the precursor with saturated ImClO₄ solution and low volume ratio of PEGDA (5 vol %). Finally, dried printed samples with around 50 vol% ratio of ImClO₄ are obtained.

In general, the crystal growth in a liquid environment is controlled by two processes: the diffusion of ions through the liquid phase to the growth front and the reorganization of crystal grains into the polycrystal. In our experiments, the diffusion of ions should not be the limiting factor because of the highly concentrated ImClO₄ precursor solution and large pore size of the hydrogel scaffold. Thus, the crystal grain reorganization is the limiting step during the growth. By applying a biased electric field, we can organize the orientation of small grains formed right after the nucleation. As shown in Fig. 1C, the dehydration process was conducted under an electric field, which was applied to obtain a high-quality polycrystal with a preferred polarization orientation of ImClO₄. The small single-crystal ImClO₄ grains can merge into a large polycrystalline structure with preferred crystal orientation as water continuously and slowly evaporates under the biased electric field. Printed ImClO₄ with and without the biased electric field are denoted as the printed and control sample, respectively, in the following discussion.

As shown in Fig. 2A, the printed sample maintains its geometry with uniform shrinkage after it is fully dried. Fig. 2B shows its in situ resistance measurement during the drying, while the resistance escalates continuously until the formation of the ImClO₄ crystal. As shown in Fig. 2C, if the biased electric field is applied together with drying, the obtained sample shows the preferred orientations with the diffraction peaks at 22.36° and 24.62° representing the ($2\overline{1}0$) and ($10\overline{2}$) planes, respectively. A high diffraction intensity for the ($10\overline{2}$) planes suggests that its preferred growth orientation matches with its polarization axis for the pronounced ferroelectric properties (22), confirmed by our theoretical modeling (SI Appendix, Figs. S7–S9). Since the ferroelectric ordering temperature of ImClO₄ is far above its crystallization temperature, the anisotropic energy associated with this ferroelectric state is large enough to align the grains under the electric field (SI Appendix, Supporting Text 5). The anisotropic energy leads to the rotation of the crystal nucleus parallel to the external electric field. Moreover, the scaffolds not only have superlative intrinsic properties, such as optical transparency and light weight, but they are also geometrically compatible with the ImClO₄ crystal. A cubic ImClO₄ sample (SI Appendix, Fig. S4) is printed for optical measurement. Similar to the single crystal (2, 23), the printed ImClO₄ is transparent in the visible range (Fig. 2D) with a large energy band gap of 4.1 eV (SI Appendix, Fig. S8). The transparency of the printed sample renders it a promising candidate for electrooptic devices (2).

Fig. 3A shows the temperature dependence of dielectric permittivity of the ImClO₄ single crystal, the printed sample, and the control sample, which all show the characteristic sharp dielectric anomalies around the phase transition temperature. The second-order phase transition occurs at 375 K from the paraelectric to the ferroelectric phase, suggesting that the transition is not influenced by the crystallization process. However, these samples show distinct dielectric behavior around the first-order phase transition (around 210 K with large hysteresis as shown in SI Appendix, Fig. S10). The peaks of dielectric permittivity for the first-order transition in the printed sample indicate that the applied electric field improves its crystal order with the dielectric anomaly appearing at 237 and 222 K, respectively. More importantly, its dielectric permittivity shows an abrupt jump at 222 K, suggesting the single-crystal–like ferroelectric properties.

The ferroelectricity can be attributed to the small permanent dipole moment of the slightly distorted ClO₄⁻ anion together with the contribution from the off-center displacement of the imidazolium cations (SI Appendix, Fig. S9). We further carried out the polarization vs. electric-field hysteresis loops (P-E loops) at room temperature. As shown in Fig. 3B, the polarization of the ImClO₄ single crystal, the printed sample, and the control sample are 1.49, 0.22, and 0.08 μC/cm² at 3-kV/cm poling electric field, respectively. As shown in SI Appendix, Fig. S11, the Raman spectrum for printed ImClO₄ suggests that the chemical bonding is not influenced by the scaffold when compared with the ImClO₄ single crystal. The thermogravimetric analysis (TGA) measurement shows one broad decomposition temperature range from 500 to 700 K; such broad decomposition can be considered as a combination of the decomposition temperature for ImClO₄ and PEGDA. The 50% volume ratio for printed ImClO₄ is projected to decrease its polarization. In comparison, the 3D-printed PEGDA does not show any P-E loop behavior (SI Appendix, Fig. S12), suggesting that the measured polarization originated from the ImClO₄ phase. Often, ferroelectric property degradation could appear in ferroelectrics due to electrical conduction under repetitive cycling or high, local electric field. As shown in Fig. 3C, the degraded sample shows lower polarization when compared with printed ImClO₄. But here, the water-based printable ferroelectrics provide an effective way toward self-healing: the printed sample with degraded ferroelectric property could be healed by dissolving into the ImClO₄ solution followed by recrystallization. As shown in Fig. 3E and Movie S2, the degraded ImClO₄ can be dissolved into ImClO₄ solution and lead to the formation of the hydrogel state containing Im⁺ and ClO₄⁻ ions. Additional electrical-field assistant drying process could help to recover its ferroelectric property.

The printed ferroelectric ImClO₄ is expected to show response to an external electric field, particularly a change in material stiffness due to the ferroelectric alignment in the direction of the external field. To investigate this property, the stress–strain curves of the printed sample are recorded under varying electric-field strength and its Young’s modulus is measured, as presented in Fig. 3D and SI Appendix, Table S2. These experiments demonstrate an initial Young’s modulus of 12.0 MPa in the absence of electric field and variation in elastic modulus up to 25% as the field strength increases from 0 to 2,000 V/cm (Fig. 3D and SI Appendix, Table S2), demonstrating significant programmable tunability in the ferroelectric material stiffness. This successful design of a printed molecular ferroelectric material opens up new avenues in the increasingly popular domain of active electroacoustic metamaterials with highly responsive and tunable mechanical properties. To illustrate an application of this tunable material, a “hard–soft–hard” locally resonant metamaterial (LRM) is architected with the printed molecular ferroelectric material as the filler component, in which the soft printed ferroelectric is attached to stiffer matrix and resonator elements to form each unit cell of the periodic structure. This LRM comprises multiple such unit cells in a two-dimensional (2D) array and is schematically depicted in Fig. 4A.

An illustration of the behavior of this ferroelectric metamaterial is presented in SI Appendix, Fig. S16, showing the frequency response from 500 to 2,000 Hz at three distinct measurement locations (SI Appendix, Fig. S16A) and illustrating the array’s vibration profile both outside (M1, 630 Hz) and inside (M2, 845 Hz) the emergent frequency band gap (SI Appendix, Fig. S16B) using aluminum and brass as the matrix and resonator materials, respectively (material properties are provided in SI Appendix, Table S3). The metamaterial is excited via transverse z-directional flexural waves at the bottom corner of the array which propagate in the xy plane of the structure, permitted to propagate through the metamaterial at pass-band frequencies but forbidden in the frequency band gap indicated by the shaded region of SI Appendix, Fig. S16A. SI Appendix, Fig. S16A pits the displacement response of the finite metamaterial (top portion; generated from a finite-element model) against the wave dispersion behavior of an infinite array of the constitutive unit cell (bottom portion; predicted via a Bloch-wave band structure). The band gap calculated from the dispersion analysis spans the 759–1,266-Hz range (SI Appendix, Table S2) and provides excellent agreement with the displacement transfer function captured in the frequency response.

Using this passive configuration as a benchmark, the metamaterial’s versatility is then expanded by exploiting the sensitivity of the printed ferroelectric material’s elastic modulus to an externally applied electric field. Different simulated scenarios for electric field strengths of 0, 300, 700, and 2,000 V/cm are depicted in Fig. 4, showing the response and band gap shift at the same measurement locations used in SI Appendix, Fig. S16 (Fig. 4B) and demonstrating the change in the metamaterial’s displacement field at a single fixed frequency of 810 Hz (Fig. 4C). Fig. 4D presents a direct quantitative comparison between the displacement transfer function and the electric-field strength at the three measurement locations, demonstrating an ability to fully control the elastic deformation level in prescribed regions by selectively tuning the external stimulation. Due to the increased stiffness of the soft ferroelectric filler, large electric-field strengths of 700 and 2,000 V/cm drive the band gap to higher frequencies, while little to no electric field strengths of 0 and 300 V/cm yield a lower-frequency band gap for the same geometry and configuration, thus causing an incident excitation of the same frequency to lie both inside and outside the forbidden regime depending on electric-field strength (Fig. 4 C and D and Movie S3). Furthermore, a change in field strength from 0 to 2,000 V/cm instigates a band gap shift from 759–1,266 Hz to 847–1,411 Hz (SI Appendix, Table S2), culminating in an 11.6% increase in center band gap frequency corresponding to the maximum change in electric-field strength.