Large polarization and record-high performance of energy storage induced by a phase change in organic molecular crystals

Dielectrics that undergo electric-field-induced phase changes are promising for use as high-power electrical energy storage materials and transducers. We demonstrate the stepwise on/off switching of large polarization in a series of dielectrics by flipping their antipolar or canted electric dipoles via proton transfer and inducing simultaneous geometric changes in their π-conjugation system. Among antiferroelectric organic molecular crystals, the largest-magnitude polarization jump was obtained as 18 μC cm−2 through revisited measurements of squaric acid (SQA) crystals with improved dielectric strength. The second-best polarization jump of 15.1 μC cm−2 was achieved with a newly discovered antiferroelectric, furan-3,4-dicarboxylic acid. The field-induced dielectric phase changes show rich variations in their mechanisms. The quadruple polarization hysteresis loop observed for a 3-(4-chlorophenyl)propiolic acid crystal was caused by a two-step phase transition with moderate polarization jumps. The ferroelectric 2-phenylmalondialdehyde single crystal having canted dipoles behaved as an amphoteric dielectric, exhibiting a single or double polarization hysteresis loop depending on the direction of the external field. The magnitude of a series of observed polarizations was consistently reproduced within the simplest sublattice model by the density functional theory calculations of dipole moments flipping over a hydrogen-bonded chain or sheet (sublattice) irrespective of compounds. This finding guarantees a tool that will deepen our understanding of the microscopic phase-change mechanisms and accelerate the materials design and exploration for improving energy-storage performance. The excellent energy-storage performance of SQA was demonstrated by both a high recoverable energy-storage density Wr of 3.3 J cm−3 and a nearly ideal efficiency (90%). Because of the low crystal density, the corresponding energy density per mass (1.75 J g−1) exceeded those derived from the highest Wr values (∼8–11 J cm−3) reported for several bulk antiferroelectric ceramics , without modification to relaxor forms.


Introduction
Highly polarizable dielectrics have been used in diverse electronic, mechatronic, and optoelectronic applications. 1,2 In particular, phase-change dielectrics accompanied by a large polarization jump are desired for high-power electrical energy storage, which is increasingly demanded with the expansion of modern commercialization. 3, 4 One of the most suitable dielectrics is the antiferroelectric, 5,6 in which permanent dipoles can be reversibly switched between antiparallel and parallel arrangements by changing the amplitude of an externally applied electric eld. [7][8][9][10][11] The reversibility between the antiferroelectric (AFE) and ferroelectric (FE) phases yields electric polarization (P) vs. electric eld (E) hysteresis, where the P-E curves exhibit double loops instead of the single loop exhibited by ferroelectrics. The stored energy density W s during the forward (antiferroelectric-to-ferroelectric phase) switching, the recoverable energy density W r during the backward (ferroelectric-to-antiferroelectric AFE phase) switching, and the efficiency h can be evaluated through numerical integration of the P-E curves according to the following equations:

EdP
(1) where P m and P r are maximum and remanent polarizations, respectively. While the voltage across conventional capacitors decreases linearly as they are discharged, the strongly nonlinear-type capacitors that exhibit the polarization jump can retain their voltage. This characteristic can simplify the electronics required to deliver a constant voltage from a capacitor. In addition, antiferroelectrics can store energy at a high density more effectively than linear dielectrics and ferroelectrics. Especially high performance has been achieved with leadcontaining antiferroelectrics, [12][13][14] as exemplied by (Pb,La)(Zr,Ti)O 3 (PLZT) compounds, which have been commercially used in dc link condensers. Also, extensive research has led to remarkable improvements in the electric storage performance of lead-free alternatives. [15][16][17][18] Ultrahigh energy storage has also been achieved by modifying these antiferroelectrics into relaxors. [19][20][21][22] Organic molecular compounds have additional advantages when used in energy storage devices, such as mechanical exibility, low density, and environmental benignity, as well as good dielectric strength. For instance, free-standing polycrystalline ferroelectric lms have been prepared from small organic molecules. 23 Over the past decade, we have discovered antiferroelectric switching or analogous metaelectric transitions in several hydrogen-bonded compounds. [24][25][26][27] Highly efficient energy storage in a squaric acid (SQA) crystal, which comprises an antiparallel array of polar sheets, has been highlighted. The molecular dipole moments are reoriented through proton tautomerism (also known as prototropy), which simultaneously relocates the double bonds of a p-conjugated system and a proton of the adjacent hydrogen bond. 26 The next challenge is to increase the stored energy density, which requires increasing the polarization jump DP and the switching eld E sw .
Here, we develop a series of prototropic organic dielectrics having antipolar or canted electric dipoles. Excellent polarization performance, with a DP exceeding 15 mC cm À2 , is achieved by improving the dielectric strength of SQA and by preparing new antiferroelectrics: deuterated SQA-d 2 and furan-3,4dicarboxylic acid (FDC). The materials development is accompanied by the discovery of multiple phase changes in another new antiferroelectric: 3-(4-chlorophenyl)propiolic acid (CPPLA). The alternative approach to antiferroelectric phase switching is to exploit the crystal anisotropy of a ferroelectric having canted dipoles. For each prototropic antiferroelectric investigated, the polarization of the polar subunit (i.e., a hydrogen-bonded sheet or chain) is theoretically simulated and its simple ipping model is examined to explain the polarization jump. Record high energy-storage performances are also claried in comparison with the corresponding performances of inorganic antiferroelectrics.

Results and discussion
SQA and deuterated SQA-d 2 The SQA crystal 28-30 is a layered antiferroelectric at temperatures less than 373 K. Its structure belongs to the monoclinic P2 1 /m space group with pseudotetragonal symmetry. The twodimensional hydrogen-bonding network constructs dipolar molecular sheets, the polarities of which alternate along the c tetra -direction. Although previous polarization hysteresis experiments 26 showed that the best eld-induced polarization was achieved at that time, their maximum eld amplitude was set at $150 kV cm À1 to avoid electric breakdown of the test single crystal. Higher-quality single crystals enabled us to increase the maximum eld strength (to 220-230 kV cm À1 ) in this re-examination of the SQA and to conduct new tests on the deuterated SQA-d 2 . In Fig. 1b and c, the entire switching process is shown together with a steep polarization jump in the corresponding P-E curve and a sharp peak in the corresponding current density (J)-E curve. With an Ek[100] tetra conguration at room temperature, the polarization jump DP was optimized to 17.2 and 18.4 mC cm À2 for the SQA and SQA-d 2 crystals, respectively. These polarizations are greatly improved Orange and blue areas correspond to the recoverable energy density W r (orange) and the unrecoverable energy density W loss (blue area). (c) P-E hysteresis loops and corresponding J-E curves with Ekh100 i tetra and Ekh110i tetra configurations for an SQA crystal at room temperature and at f ¼ 50 Hz. compared with that previously reported for SQA (10.5 mC cm À2 ) 26 and are the largest polarizations reported for organic molecular antiferroelectric compounds.
Immediately aer the discovery of antiferroelectricity, Kittel introduced the Landau-type macroscopic model comprising two interpenetrating sublattices with opposite polarizations. 7 For the antiferroelectrics and a dipole-canted ferroelectric examined herein, the sublattices can also be dened by the periodic array of the polar subunits (chains or sheets) of identical polarities. The SQA crystal contains two sublattices with polarizations P 1 and P 2 (¼ ÀP 1 ) being parallel to the h110i tetra direction. As theoretically simulated elsewhere, 31 the external eld induces a 90 rotation of P 1 or P 2 , causing the polarization jump DP ¼ ffiffiffi 2 p jP 1 j (16.4 mC cm À2 ) along the h100i tetra direction, rather than a 180 ip of P 1 or P 2 , which would give DP ¼ 2jP 1 j (23.2 mC cm À2 ) along the h110i tetra direction. Notably, this interpretation does not change under this revision because the easy switching axes are h100i tetra and the observed polarization jump DP is very similar to ffiffiffi 2 p jP 1 j, as clearly shown in Fig. 1c.

Furan-3,4-dicarboxylic acid (FDC) with large polarization
While the polar crystal structures of ferroelectrics usually reveal some additional hidden crystal symmetries (pseudosymmetries), similar key signatures are available for researchers searching for new antiferroelectric candidates. Here, we have discovered the new antiferroelectric furan-3,4-dicarboxylic acid (FDC) crystals, which exhibit the second-best polarization jump among organic antiferroelectrics. In the Cambridge Structure Database, all three available datasets concern the identical monoclinic polymorph (denoted as the a-form hereaer) grown from aqueous solution. In the rst structural analysis (ref code: FURDCB), Williams et al. found that both acidic protons were disordered by crystal symmetry (space group P2 1 /m). 32 Later, Semmingsen et al. redetermined the crystal structure at T ¼ 125 K and found that the appearance of weak Bragg spots was caused by the antipolar arrangement of protons with twofold periodicity along the c-axis (ref code: FURDCB01). 33 Our careful reassessment conrmed the validity of the latter structure even at room temperature. The c/2-translation symmetry is hidden in this antipolar structure. In the presence of pseudosymmetry, the antipolar and polar structures can be interconverted by rearranging the protons with minimalized modulation of the host lattice. The actual crystal structure belongs to the P2 1 /c space group (#14). The global crystal symmetry except the two protons has a mirror plane normal to the molecular plane, in addition to the aforementioned c/2-translation. The hydrogenbonded molecular chains parallel to the b-direction have longitudinal dipoles whose polarities alternate along the cdirection. Two additional polymorphs were newly generated by sublimation under reduced pressure: rhombus plates of b-FDC (major form; see ESI Fig. S1 † for detailed molecular packing with orthorhombic Pbcm symmetry) and rectangular plates of g-FDC (minor form; triclinic). Although both crystal forms are similar to a-FDC with respect to their hydrogen-bonded molecular sequence (Fig. S2 †), polarization switching is hardly expected in the b-FDC crystal, which lacks the corresponding pseudosymmetry.
The crystal structure of g-FDC exhibits a C-centered monoclinic lattice but exhibits only inversion symmetry. Instead of the unconventional space group C 1, we used the equivalent triclinic space group P 1 for the structural determination. The a/ 2-translation symmetry is hidden in this antipolar structure. The large unit cell of the g-FDC crystal accommodates four sublattices P 1 , P 2 (¼ ÀP 1 ), P 3 , and P 4 (¼ ÀP 3 ). Therefore, ipping P 1 and P 3 (or P 2 and P 4 ) gives rise to DP ¼ j2P 1 + 2P 3 j.
We demonstrated the expected phase-change phenomena described in the preceding paragraph for the g-FDC crystal (Fig. 2d). The results of P-E hysteresis measurements with the applied ac electric eld conguration Ek [ 102] show the double loop characteristic of the antiferroelectric-ferroelectric transition. The observed polarization jump DP, which was as large as 15.1 mC cm À2 , is slightly smaller than those of SQA but the second-highest among those of organic antiferroelectric crystals. The switching at $70 kV cm À1 is accompanied by a large hysteresis width of $50 kV cm À1 .
Although the a-form crystal is predicted to show a similarly large DP, its small size precluded satisfactory measurements. For the b-FDC crystal, no signatures of phase-change phenomena were detected at least up to 180 kV cm À1 in the measurements at room temperature and at 80 C, as suggested by the aforementioned structural assessments.

Antiferroelectric with multiple switching processes
We discovered the new antiferroelectric CPPLA crystal while seeking for additional hidden crystal symmetries (pseudosymmetries) in the reported crystal structures. Das et al. reported a polar monoclinic crystal structure for the iodinesubstituted derivative 3-(4-iodophenyl)propiolic acid (ref code: BEFSUB), 34 in which we noticed pseudo-inversion symmetry, suggesting a possible ferroelectric. They also reported paraelectric-like crystal structures of CPPLA, in which the hydrogen-bonded molecular sequence pinpoints the disordered (or centered) hydrogen atom on each hydrogen bond because of inversion symmetry (ref code: SUHSET). 34,35 In contrast, our reexamination of the single-crystal structure by X-ray diffraction revealed additional weak Bragg spots indicative of the doubled periodicity as (a, b, c) ¼ (Àa p À c p , Àa p + c p , b p ). The unit-cell doubling is caused by the antipolar ordering of asymmetrically located hydrogen atoms in the revised crystal structure, which contains two sublattices with polarizations P 1 and P 2 (¼ ÀP 1 ) and thus suggests possible antiferroelectricity along the bdirection.
Consistent with this expectation, the P-E curve (top panel of Fig. 3b) shows a double hysteresis loop when the maximum eld amplitude of 70 kV cm À1 is applied in the Ek[110] conguration (instead of the ideal Ekb conguration because of the crystal shape). However, the application of a higher eld amplitude induced an additional polarization jump, causing a quadruple polarization hysteresis loop. This behavior is the manifestation of eld-induced successive phase transitions with the antiparallel dipoles ipped half-by-half. Therefore, the intermediate phase is regarded as the ferrielectric state.

Amphoteric behavior of a dipole-canted ferroelectric
While most ferroelectric crystals have fully aligned dipoles, the ferroelectric 2-phenylmalondialdehyde (PhMDA) single crystal exhibits a canted arrangement of dipolar chains. 36 Here, we report amphoteric behavior, where a single or double polarization hysteresis loop is obtained depending on the direction of the external eld (Fig. 4a). In the orthorhombic crystal with space group Pna2 1 , the PhMDA molecules form polar hydrogenbonded chains (Fig. 4b). As indicated by small open arrows in Fig. 4c, each chain has a sublattice polarization P 1 along the [102] direction or P 2 along the [ 102] direction. Here, the crystal symmetry demands P 1x ¼ -P 2x , P 1y ¼ P 2y ¼ 0, P 1z ¼ P 2z ; the net polarization 2jP 1z j then emerges in the c-direction. Specically, the conguration of chain dipoles is antiparallel in the adirection components and parallel in the c-direction components. The ferroelectricity observed with the Ekc conguration corresponds to the polarization reversal induced by ipping both P 1 and P 2 according to process (i) in Fig. 4c.
In the Eka conguration, the antiferroelectric-like switching with a DP of 5.8 mC cm À2 appears at $110 kV cm À1 , which is substantially greater than the magnitude of the coercive eld along the c-direction ($20 kV cm À1 ). The most plausible mechanism is process (ii) in Fig. 4c. The increasing/decreasing electric eld ips either P 1 or P 2 , which causes the observation of DP x ¼ 2jP 1x j through a 90 rotation of the spontaneous polarization from the the c-to the a-direction and vice versa. In this example, the antiferroelectric-like functionalities can be achieved even by rotating polarizations through the eldinduced transition between two different ferroelectric phases.

Theoretical evaluation of polarization
The experimentally optimized spontaneous polarizations of organic ferroelectrics have recently been reproduced with excellent accuracy using density functional theory (DFT) calculations and the Berry phase formalism of electric polarization. 37 Although the corresponding theoretical evaluations are rare for organic antiferroelectrics, SQA represents an example in which the microscopic switching process has been successfully iden-tied in terms of a sublattice polarization model through comparisons with experimental data. 31 In the present work, the sublattice polarizations are simulated for other prototropic antiferroelectrics (FDC, CPPLA, and benzimidazoles). Except for the g-FDC crystal, the two sublattices, which interpenetrate each other, construct the antipolar or dipole-canted structure. First, one of them is extracted as a periodic polar crystal lattice and its sublattice polarization P 1 is computed. Together with its symmetry-related sublattice polarization P 2 , the theoretical polarization DP cal is calculated by ipping either P 1 or P 2 . For the g-FDC crystal, two of four sublattices were extracted for calculating the crystallographically independent P 1 and P 4 . The sublattice polarizations were calculated for different degrees of polar distortion l between the reference symmetrized (hypothetical paraelectric, l ¼ 0) and fully polar (ferroelectric, l ¼ 1) congurations. As shown in Fig. S3, † the smooth ldependence conrms the validity of each simulation.
In the g-FDC crystal, each hydrogen-bonded chain is highly polarized and the resultant large jDP cal j of 13.2 mC cm À2 directed along the [ 102] is similar to the experimentally observed polarization jump jDP exp j (15.1 mC cm À2 ). Note that nearly the same jDP cal j values were computed for both the aand b-forms, which have similar hydrogen-bonded molecular sequences (Fig. S2 †). Likewise, excellent agreement between jDP cal j and jDP exp j is conrmed for a series of prototropic antiferroelectrics, as demonstrated in Fig. 5. Regarding the CPPLA crystal, the entire polarization jump of the quadruple hysteresis loops (4.3 mC cm À2 ) is explained well by the full alignment of chain polarizations (the Ek[110]-direction component of DP cal is 4.8 mC cm À2 ).

Energy-storage performance
The P-E curves of FDC, CPPLA, and PhMDA crystals were also measured at higher temperatures (Fig. S4 †). The FDC crystal revealed very weak temperature dependence up to 420 K. For CPPLA and PhMDA as well as for SQA, 26 both the DP and switching eld decrease with heating, and thus the stored energy densities are diminished from the room-temperature performance. Regarding the energy-storage performance of all of the prototropic antiferroelectrics, Table 1 summarizes the room-temperature performance obtained according to eqn (1)-(3). Fig. 6 shows a plot of these data in comparison with those of  bulk antiferroelectric ceramics and their relaxor modications, which exhibit high or ultrahigh energy-storage densities. Among the prototropic antiferroelectrics, SQA (and SQA-d 2 ) crystals exhibit both the highest recoverable energy-storage density (W r ¼ 3.3 J cm À3 ) and nearly ideal efficiency (h ¼ 0.90). As shown in Fig. 6a, the excellent W r of SQA is justied by its best performance with respect to both the maximum polarization P m and the switching eld E sw (the average of forward and backward phase switching elds). However, the W r , P m , and E sw values are smaller than those of the bulk antiferroelectric ceramics and their relaxor modications, [12][13][14][15][16][17][18][19][20][21][22][38][39][40][41][42][43][44] as evident in Fig. 6a and b. The magnitude relation of the performance is drastically different in Fig. 6c, which is a replot of the data against the stored energy density per weight ðW 0 r Þ instead of that per unit volume (W r ). This difference is attributed to the crystal density r of the organic antiferroelectrics (1.3-1.9 g cm À3 ) being substantially lower than those 45 of leadcontaining (8.5-10.3 g cm À3 ) and lead-free antiferroelectrics (4.6-8.1 g cm À3 ). The W 0 r (1.75 J g À1 ) of SQA (r ¼ 1.88 g cm À3 ) exceeds those derived from the highest W r values (approximately 8-11 J cm À3 ) reported for several bulk antiferroelectric ceramics ðW 0 r \1:3 J g À1 Þ. Notably, the SQA crystal retains the highest h without resorting to its modication to relaxor forms. These ndings are encouraging for the future applications of these materials in portable and/or mobile devices.

Conclusions
Various dielectric phase-change phenomena have been demonstrated via studies on revisited SQA, newly developed antiferroelectrics, and the "amphoteric dielectric" PhMDA. In terms of the magnitude of the eld-induced polarization jump, the best ($18 mC cm À2 ) and second-best performances ($15 mC cm À2 ) among organic antiferroelectrics were achieved. In particular, the improvement of the dielectric strength of SQA resulted in excellent energy-storage performance, including a high recoverable energy-storage density (W r ¼ 3.3 J cm À3 ), while maintaining nearly ideal efficiency (h ¼ 90%). The advantage of organic molecular systems is their low crystal density, which resulted in corresponding energy densities per mass as high as W 0 r ¼ 1:75 J g À1 , which exceeds those derived from the highest W r values ($8-11 J cm À3 ) reported for several bulk antiferroelectric ceramics ðW 0 r \1:3 J g À1 Þ. Notably, the present SQA crystal has not yet been modied into relaxor forms.
In addition to the antiferroelectrics exhibiting conventional double hysteresis loops, the CPPLA crystal was found to exhibit quadruple polarization hysteresis loops caused by the two-step phase transition with moderate polarization jumps. The ferroelectric PhMDA single crystal represents a novel "amphoteric dielectric" that can exhibit a single or double polarization hysteresis loop depending on the direction of the applied external eld relative to the directions of its canted dipole moments. Irrespective of the details of their variation, all of the observed polarizations are consistently explained by the DFT calculations combined with the simplest sublattice model. Such a theoretically precise prediction ability provides a powerful tool for improving the energy-storage performance; it will accelerate the materials design and exploration as well as deepening our understanding of the microscopic phase-change mechanisms.

Preparation and electric measurements
Commercially available SQA, FDC, PhMDA, and CPPLA were puried by repeated recrystallizations and/or temperaturegradient vacuum sublimation. The temperature-gradient sublimation under reduced pressure gave single crystals with shapes of elongated rectangular plates in the case of FDC, parallelogram-shaped plates in the case of CPPLA, and thick plates in the case of PhMDA. The bipyramidal crystals of SQA and SQA-d 2 , which were grown by recrystallization from hot deionized water and 99.5% D 2 O, respectively, were cut with a blade for electric measurements according to previously reported procedures. 26 All of the electric measurements were conducted using single crystals with painted silver electrodes. The P-E hysteresis measurements were performed by applying a high-voltage triangular wave eld and various alternating frequencies to single crystals, which were immersed in silicone oil to prevent atmospheric discharge. The system used to evaluate ferroelectrics (Toyo Corporation, FCE-1) comprised a current/charge-voltage converter (model 6252), an arbitrary waveform generator (Biomation 2414B), an analog-to-digital converter (WaveBook 516), and a voltage amplier (NF Corporation, HVA4321).

Crystallographic studies
The crystallographic data and experimental details are summarized in Table S1. † X-ray diffraction data were collected from single crystals at room temperature using graphitemonochromated Mo Ka radiation (l ¼ 0.7107Å) and a fourcircle diffractometer equipped with a two-dimensional detector [hybrid pixel detector (Rigaku AFC10 with PILA-TUS200K)]. CrystalStructure crystallographic soware packages [Molecular Structure Corp. (MSC; Woodlands, TX) and Rigaku Corp. (Tokyo)] were used for the direct method and for the renement of the structures. Final renements of the nonhydrogen atoms were performed with anisotropic thermal factors. The hydrogen-bonded hydrogen atoms were found by differential Fourier synthesis and were rened isotropically; the remaining hydrogen atoms were calculated in their ideal geometrical positions.

Theoretical calculations
First, for the experimentally obtained AFE structures, hydrogen positions were computationally optimized to minimize the total energy. Next, for each system, all of the atoms except for one polar subunit were removed from the unit cell (l ¼ 1). Reference nonpolar structures (l ¼ 0) were constructed by symmetrization. The polarization as a function of l was calculated using the Berry phase approach. 46,47 All the calculations were performed using the QMAS code 48 based on the projector augmented-wave method 49 and the plane-wave basis set. To describe the electronic exchange-correlation energy, the Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) 50 was used.

Author contributions
S. H. prepared the puried single crystals, performed the dielectric measurements, conceived the study design, and wrote most of the paper. S. I performed the theoretical calculations.

Conflicts of interest
There are no conicts to declare.