Facet-modulated ferroelectric polymers

Domain: neuroscience
Published: 2026-01-27
Editorial outcome: major_revision

Abstract
Ferroelectrics holds significant promise for a wide range of applications owing to their spontaneous polarization characteristics. Despite exhibiting multiple polarization mechanisms that demonstrate significant potential for electromagnetic functional materials, the practical deployment of ferroelectric polymers has been inhibited by the lack of precise control over polymer chains at the atomic scale and the relatively low stability of the polar phase. Here, a procedure of fortifying the ferroelectric polyvinylidene fluoride phase is proposed by the facet modulation, achieving stable ferroelectric polymer through engineering the interaction between the inorganic rigid crystal facets and organic flexible molecular chains at the atomic scale. The constructed polar ferroelectric polymers composite systems exhibit a broad distribution of relaxation times along with multi-polarization characteristics from megahertz to terahertz frequencies. The composite system mitigates the apparent loss-bandwidth trade-off, thereby achieving broadband polarization properties across multiple frequency bands while maintaining a dissipation efficiency above 99.9%. The demonstrated approach presents a breakthrough in achieving the stable ferroelectric polymers through facet-induced stabilization, providing deep insights for the development of high-performance electromagnetic functional materials.

Introduction
Organic ferroelectric polymers demonstrate considerable promise for versatile material systems due to their distinctive crystalline polymorphism, tunable spontaneous polarization, and diverse molecular relaxation mechanisms1. For ferroelectric polymers, their molecular chains possess abundant internal rotational degrees of freedom. This enables chain segments to undergo various types of internal motions akin to Brownian motion, where each specific internal rotation mode corresponds to a characteristic relaxation time and dipole moment2. In contrast to inorganic materials, whose rigid crystalline lattices inherently constrain the diversity and quantity of intrinsic polarization mechanisms3–5, ferroelectric polymers possess inherently dynamic polarization and relaxation characteristics, making them promising candidates for achieving highly efficient electromagnetic (EM) responses.

Poly(vinylidene fluoride) (PVDF) is a representative ferroelectric polymer that has been extensively investigated due to its remarkable polarization properties6–8. The most common α-phase is thermodynamically stable but non-polar, whereas the ferroelectric β-phase, obtained through phase-transition induction strategies, significantly enhances the intrinsic polarization strength and introduces notable dielectric loss behavior. This provides an effective pathway for developing advanced functional materials with multi-band compatibility and efficient electromagnetic energy dissipation. Nevertheless, the practical application of β-phase PVDF still faces several challenges, including low content, poor phase uniformity, and insufficient structural stability9. Owing to the difficulty in precisely controlling polymer chain conformations at the atomic scale, conventional thermal or electrical poling methods tend to cause macroscopic deformation and heterogeneous domain structures in β-PVDF10. This results in reduced ferroelectric phase content, non-uniform distribution, and a consequent significant decline in polarization performance and stability, ultimately impairing device reliability.

In the frontier of scientific fields such as electromagnetics, next-generation communications, and electromagnetic protection, overcoming the technical bottleneck of multi-band efficient EM loss represents a core requirement for addressing complex EM environments11–13. This imposes stricter requirements on the operational stability of ferroelectric PVDF. Effective regulation of PVDF molecular chain conformations at the atomic scale to reduce the system energy of the β-phase below that of the α-phase represents a crucial strategy for enhancing its thermodynamic stability and application potential. Furthermore, the narrow energy difference between the α- and β-phases makes the ferroelectric β-phase susceptible to irreversible transition to the non-ferroelectric α-phase under external disturbances14. This inherent instability significantly limits its applicability under electromagnetic fields. Thus, maintaining a sufficiently large energy difference between the two phases is essential for ensuring structural stability and functional reliability under service conditions.

To fully exploit the effect of PVDF ferroelectric phase on EM wave loss, this study introduces a crystal facet engineering strategy to induce ferroelectric phase transformation within the polymer. Through precisely controlled synthesis to selectively expose the {100} and {111} crystal facets of NiS2, stable and precise control of ferroelectric polymer molecular chains has been achieved at the atomic scale. The mediation of polymer interfaces by specific plane orientations was systematically investigated, elucidating the key microscopic factors through which inorganic fillers influence the stability of the ferroelectric phase of PVDF. This work establishes the crystal facet control of inorganic fillers as a variable for manipulating the ferroelectric phase and molecular dipole distribution in PVDF. Furthermore, the crystal facet-stabilized PVDF matrix significantly enhances the operational stability and reliability of the composite. This study elucidates that ferroelectric polymers exhibit enhanced cross-frequency polarization loss and tunable electromagnetic attenuation, operating from the MHz to GHz range and extending into the THz band. These properties originate from their enhanced polarization intensity along with multiple polarization mechanisms accompanied by a broad distribution of relaxation times. Concurrently, we propose an electromagnetic modulation mechanism based on polarons in highly ferroelectric polymers, enabling multi-band operation, which breaks the trade-off between high loss and wide bandwidth.

Results
PVDF is one of the most researched ferroelectric polymers due to its electroactive properties and ability to form complex structures15,16. Figure S1 shows the most studied and used TGTḠ conformation (T: trans; G: gauche, non-polar α-phase), and the all-trans TTTT conformation (ferroelectric polar β-phase) of PVDF. The presence of an electric dipole moment in the PVDF monomer unit is caused by the larger electronegativity of the fluorine atom, when compared to the neighboring carbon and hydrogen atoms. Therefore, each chain possesses a dipole moment perpendicular to the polymer chain.

Density functional theory (DFT) calculations yielded the crystal structures of the different phases of PVDF with their charge density distributions along the (001) plane. The monomers in the α-phase show a non-polar crystal structure due to the centrosymmetric stacking of their charge density distributions (Fig. S2). The monomers in the β-phase are stacked in a parallel fashion within the unit cell, determining the modulation of the charge density, and resulting in a larger dipole moment (Figs. S3, S4).

Figure 1A demonstrates the polar phase transition mechanism of PVDF on the {100} and {111} crystal facets of NiS2 17. Figure S5 shows the adsorption energies per unit (CH2-CF2) (Ē ads) of α-phase PVDF and β-phase PVDF on the {100} and {111} crystal facets of NiS2. By comparing the interactions of different crystal facets with different phases of PVDF (Fig. S6), it can be observed that the adsorption energies of different PVDFs relative to NiS2 under the same facets ({100} or {111}) differ significantly, which leads to the determination of the dominant conformation of PVDFs on different facets. This provides a theoretical basis for the effect of crystal facet engineering on the phase transition of PVDF.

In Fig. S5A, using DFT calculations, the Ē ads of NiS2 {100} facet with α-phase PVDF is −0.054 eV, while the Ē ads with β-phase PVDF is significantly reduced to −0.186 eV. As seen in Fig. S5B, the Ē ads of NiS2 {111} facet with α-phase PVDF is −0.069 eV, while the Ē ads is slightly reduced to −0.097 eV for β-phase PVDF. This shows that the β-phase of PVDF has a stronger adsorption capacity than the α-phase on the {100} facet, and that the {100} facet is more susceptible to inducing a ferroelectric phase transition in PVDF. This phenomenon can be attributed to the fact that the all-trans conformation of the β-phase allows for greater polarity and a good complementary contact interface with the NiS2 surface. In this case, the average distance between the S atoms and H atoms in the β-phase is significantly shorter for the {100} facet (2.758 nm) than for the {111} one (2.938 nm). The closer proximity, combined with the coplanar arrangement of S atoms in the {100} facet, results in stronger S-H interactions. Consequently, the β-phase of PVDF demonstrates enhanced adsorption stability when interacting with the NiS2 {100} facet. Compared with the {100} facets, the {111} ones show a relatively small energy difference in the interaction with PVDF (Fig. S6). This result suggests that the variation in energy under different combinations of crystal facets and phases reflects the complexity of material interactions under different environments. The differences in adsorption energies reflect the orientation of the PVDF molecular chains, the distribution of polar centers and their effectiveness in surface interactions.

On the {111} facet, the coordination environment of surface S atoms is near complete saturation, whereas on the {100} facet, both surface Ni and S atoms possess a high density of unsaturated coordination sites, resulting in a higher surface energy (Fig. S7). These unsaturated sites form high-density local polarization centers, making the {100} facet more polar and significantly enhancing interfacial electron coupling and charge transfer capabilities (Figs. S8–S10, Supplementary Tables S1, S2). The higher polarity implies that the {100} facet readily undergoes strong dipole-dipole interactions with β-PVDF molecular chains, which themselves exhibit relatively high surface energy and polarity. This, in turn, makes the {100} facet key to inducing and stabilizing the strongly polar β-phase of PVDF.

Scanning electron microscopy (SEM) observations reveal distinct morphological differences in NiS2 particles on different facets. Figure 1B demonstrates that NiS2 particles on the {100} facet exhibit a uniform nanocube (NCs) structure, while Fig. 1D shows that those on the {111} facet adopt an octahedra (OC) morphology. These morphological variations further highlight the differences in crystal structure between the two planes. Additionally, spherical aberration-corrected High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) in Fig. 1C, E reveals differences in the atomic arrangement on both crystal facets. Energy dispersive X-ray spectroscopy (EDS) was employed to characterize the composition and spatial distribution of the elements Ni and S (Fig. S11).

A systematic investigation was performed on the crystal structure and electronic states of NiS2 with distinct crystal facets, as well as PVDF/NiS2 (P/N) samples. Figure S12 presents the detailed results of the X-ray powder diffraction (XRD) analysis of NiS2 samples with two main crystal facets, {100} and {111}. The XRD spectra show that the {111} facet exhibits a higher diffraction intensity ratio of the (111) to (200) facets compared to the {100} facet of NiS2. The X-ray Photoelectron Spectroscopy (XPS) spectra of elemental Ni and S for the two crystal facets are illustrated in Fig. S13, which show similar features in the high-resolution XPS spectra of Ni and S. The peaks of Ni 2p3/2 and Ni 2p1/2 in the Ni 2p spectra indicate that Nickel is primarily present in the oxidation state (Ⅱ). At 855.8 eV, the secondary spectral peak intensity of the {100} facet of NiS2 exceeds that of the {111} facet, which is attributed to the higher density of undercoordinated Ni sites on the {100} facet18,19. These sites exhibit enhanced susceptibility to oxidation, thus forming higher oxidation states. In addition, the characteristic peaks of the S 2p spectrum reveal that different valence states of sulfur exist on these two crystal facets, suggesting that there is a significant difference in the electronic states of Ni and S on different crystal facets, which originates from the varying surface structure and atomic arrangement20.

The crystal structure of pure PVDF and the P/N samples were analyzed using XRD (Figs. S14, S15) and Fourier transform infrared spectroscopy (FTIR) characterizations (Fig. S16) to investigate their optical properties. The XRD spectra of P/N samples containing 15 wt.% and 25 wt.% different crystal facets of NiS2 are presented in Fig. 2A, B, respectively. In both compositions, the presence of α and β phases is significant, and the intensity and sharpness of the diffraction peaks vary with increasing NiS2 content. Specifically, the (020) and (110) α-phase diffraction peaks at 18.30° and 19.90° weaken with increasing NiS2 content, while the β-phase (110)/(200) peak at 20.26° intensifies21,22. Moreover, compared to the P/N{111}, the P/N{100} sample exhibits stronger β-phase PVDF diffraction peaks, demonstrating that the {100} facet of NiS2 promotes a higher proportion of ferroelectric β-phase PVDF. The changes in the IR absorption features suggest a shift in the internal molecular structure of the material, which arises from the varying degrees of phase transformation in PVDF. As illustrated in Figs. 2C, D, S17, S18, and Table S3, NiS2 with different crystal facets induces differing ratios of β-phase PVDF, where P/N{100} exhibits a higher β-phase PVDF content. The observed pattern aligns with the conclusions derived from analysis of XRD results. The filler loading (Figs. S19, S20, Supplementary Table S4), shape distributions (Figs. S21–S23, Supplementary Table S5) and filler size (Figs. S24, S25, Supplementary Table S6) were systematically varied. Through comparative analysis, the effects of these macroscopic geometric variables were isolated, thus establishing the specific crystal facet as a core variable in influencing performance.

HRTEM characterizations (Fig. 2E, F) were performed on the P/N samples. PVDF at the nanoparticle/polymer interface exhibits a mixture of TGTḠ and all-trans conformations, which clearly indicates the boundaries of the NiS2 crystal facets and the interactions with the PVDF23. In order to provide direct evidence of the polar phase network induced in the PVDF at different crystal facets, we performed spatial chemical analyses using atomistic-microscopy-based infrared spectroscopy (AFM-IR) with a laser irradiated at 1280 cm−1 (Fig. 2G–I). Localized IR spectroscopy demonstrates that the addition of NiS2 to PVDF induces the growth of an all-trans conformation (Fig. 2J–L), while no ferroelectric phase is evident in the PVDF spectrum.

In the ferroelectric polymer PVDF, molecular chains with an all-trans conformation stack to form a hexagonal crystal structure (Fig. 3A)17,24. Analysis of the system energy and polarization degree of the PVDF ferroelectric phase during the ferroelectric reversal process was performed using DFT calculations. The results indicate that its polarization response mainly stems from the reorientation of dipoles under the action of an external electric field (Fig. 3B, C). Further analysis of the system energy during the reversal process reveals that the electric field-induced polarization change is achieved through the continuous 60° rotation of dipoles (Fig. S26). It is noteworthy that when the dipoles rotate from 0° to 180°, a significant polarization change occurs, and the lattice strain remains zero during this process2.

To explore the differential induction effect of different crystal facets of NiS2 on the ferroelectric phase of PVDF, piezoelectric force microscopy (PFM) was used to detect the local electrical activity on the surface of P/N samples. In PFM measurements, a conductive probe with higher stiffness (k=20 N/m) was used to suppress long-range electrostatic forces. To eliminate the influence of electrostatic fields on the piezoelectric response, the surface potential was measured via Kelvin probe force microscopy (KPFM) (Fig. S27)25. Subsequently, during PFM testing, a direct-current bias of equal magnitude but of opposite polarity to the measured surface potential was used over the same region to compensate for the surface potential. Figure 3D–G shows the phase (Fig. 3D, F) and amplitude (Fig. 3E, G) hysteresis loops of the PVDF composites induced by different crystal facets. The piezoelectric signal is related to the local polarization switching and ferroelectric properties of P/N samples26. With the increase of voltage, a 180° phase change is observed, and a hysteresis loop is observed during voltage sweep back, which indicates the presence of ferroelectric polarization characteristics in P/N samples. This is direct evidence for the existence of polar polymer crystals and the induction of ferroelectric phase transition in PVDF by crystal facets. In comparison, the coercive voltage of the P/N{100} is 0.68 V, which is lower than that of the P/N{111} (2.85 V). Moreover, the P/N{100} exhibits a larger piezoelectric coefficient with d33=215.31 pm·V−1, indicating that the {100} crystal facet can induce the ferroelectric phase transition of PVDF at a higher efficiency (Figs. S28–S31, Table S7)27. Macroscopic ferroelectric performance tests at room temperature were conducted on pure PVDF, P/N{111}, and P/N{100} samples. The measurement results (as shown in Fig. S32) clearly demonstrate that the P/N{100} exhibits a typical ferroelectric P–E hysteresis loop with well-defined remnant polarization (Pr) and coercive field (Ec). Compared to pure PVDF and P/N{111}, P/N{100} shows significantly higher remnant polarization and saturation polarization (Ps)28. This result directly confirms that the {100} facet not only induces the formation of a local ferroelectric phase in PVDF (as revealed by PFM phase hysteresis) but also enables the composite to exhibit enhanced and switchable ferroelectric polarization at the macroscopic level. Meanwhile, temperature-dependent dielectric measurements demonstrate pronounced relaxor ferroelectric behavior in the P/N{100} (Fig. S33)1,28.

However, despite advances in promoting formation of the β-phase through inorganic doping29–31, existing methodologies struggle to precisely elucidate the regulatory relationship between PVDF phase structure and EM polarization loss performance. The impact of crystal facet engineering on the ferroelectric phase transition of PVDF is evaluated through EM response, where an increase in the β-phase of PVDF content significantly enhances the EM loss capability across various frequency bands. Figure 4A illustrates the complex permittivity (ε‘ and ε“) of PVDF composites with different crystal facets (NiS2 filler loading of 30 wt.%, 40 wt.%, and 50 wt.%) compared to pure PVDF within the frequency range of 0.05 MHz to 100 MHz. Experimental results reveal that the permittivity of pure PVDF is consistently lower than that of P/N samples under the same conditions, consistent with characterization data indicating that hot-pressed PVDF primarily consists of the non-polar α-phase. Further analysis of the frequency-dependent behavior of the imaginary permittivity (ε“) reveals that the ε“ peak for the P/N samples occurs at frequencies below 0.05 MHz. This peak corresponds to a characteristic relaxation process within the P/N samples. According to Debye theory, the relationship between polarization loss and frequency is governed by the relaxation time (τ)32, the observation of this peak below 0.05 MHz directly implies that the corresponding τ exceeds a value of 3.18 μs (Fig. S34). The EM loss capability of the materials can be assessed by the dissipation factor within the 0.05 MHz-100 MHz range31. Figures 4B, S35 and 4C demonstrate that the dissipation factors of both P/N{111} and P/N{100} surpass those of pure PVDF. Due to the varying degrees of interaction between different crystal facets and β-phase PVDF, the dissipation factors of P/N{100} are generally higher than those of P/N{111}. Notably, the maximum dissipation factor of P/N{100}-50% reaches 448.46, significantly higher than that of P/N{111}-50% (322.49). Both sample values, however, are substantially greater than the maximum dissipation factor observed for pure PVDF (0.28). Moreover, the dissipation factors for both samples increase with higher filler loading, a phenomenon attributed to the rise in ferroelectric β-phase PVDF content driven by crystal facet engineering.

The microwave frequency band of 2–18 GHz is widely applicable in various scenarios, particularly in communication, radar, and electronic warfare. To validate the EM loss capabilities resulting from polarization enhancement induced by the PVDF ferroelectric phase transition through crystal facet engineering, microwave absorption performance was selected as a key criterion33. In consideration of impedance matching (MZ), a lower filler loading was chosen for sample testing. Figure 4D illustrates that P/N{100} exhibits higher permittivity compared to P/N{111} at the same filler loading. Within the 2–18 GHz frequency band, the dielectric loss peak of the P/N sample occurs at 6.95 GHz, corresponding to a polarization relaxation process with a relaxation time of 22.91 ps (Fig. S36). To further investigate the root cause of dielectric loss in P/N samples, conduction loss and polarization loss were evaluated separately (Fig. 4E)34. The results indicate that, due to the low conductivity of P/N samples (Figs. S37–S39, Table S8), the dominant loss mechanism in the 2–18 GHz range is polarization loss, which aligns with the trend observed in the imaginary part of the dielectric constant. Additionally, NiS2 with different crystal facets mixed with paraffin exhibits lower and nearly identical dielectric constants, indirectly confirming that the enhancement in dielectric constant originates from the presence of β-phase PVDF (Fig. S40). Based on these findings, it can be concluded that the varying degrees of PVDF phase transition induced by NiS2 with different crystal facets are the primary factor influencing polarization loss in the 2–18 GHz range. The dielectric loss tangent exhibits the same trend. (Figs. 4F, S41). The comparative analysis of the electromagnetic parameters of NiS2 with varying size and shape distributions further underscore the critical role of specific crystal facets in regulating β-PVDF content (Figs. S42, S43).

By evaluating the EM wave absorption performance calculated from the EM parameters of the P/N{100} and P/N{111} with varying filler loadings (Figs. 4G, S44–S46), P/N{100}-20% sample demonstrates optimal performance, achieving a minimum reflection loss (RLmin) value of -62.08 dB and a maximum effective absorption bandwidth (EAB) of 4.35 GHz (Fig. S47). Two key factors influencing EM wave absorption capacity analyzed include: impedance matching (MZ) and attenuation constant (α)35. For impedance matching characteristics, the MZ contour plots reveal that the P/N{100}-20% sample exhibits a larger contour in the region where MZ exceeds 0.8 (Fig. 4H), indicating superior impedance matching. Meanwhile, among samples with different crystal facets, the attenuation constants of the P/N{100} are consistently higher than those of the P/N{111} at the same filler loading. Additionally, the attenuation constants of all samples increase with higher filler loading (Figs. 4I, S48), which can be attributed to the increased β-phase PVDF content as the NiS2 filler loading rises, leading to enhanced polarization loss. The attenuation performance of the P/N{100} was systematically compared with state-of-the-art polymer composites reported in recent literature within the 2–18 GHz frequency band. The results demonstrate that the P/N{100} exhibits superior attenuation characteristics across the entire frequency band, outperforming the aforementioned reference systems (Fig. S49)36–41. To further elucidate the unique contribution of the PVDF ferroelectric phase, the attenuation performance of NiS2 composites was also compared with other polymer matrices, as shown in Figs. S50, S51. These results confirm that the formation of the ferroelectric β-phase in PVDF plays a critical role in enhancing electromagnetic wave absorption. The Cole-Cole curve for P/N samples exhibits more pronounced semicircles, indicating the presence of stronger polarization relaxation processes (Fig. S52)41,42. These findings underscore the critical role of crystal facet engineering in optimizing the polar structure of ferroelectric PMs and thereby enhancing microwave absorption properties.

To further evaluate the electromagnetic compatibility (EMC) stealth capability of the P/N samples, radar cross-section (RCS) simulations of perfect electrical conductor (PEC) substrates coated with P/N{100}-20% sample were performed43. The results are presented in the form of three-dimensional RCS intensity images. The major flap reflection signal of the P/N{100}-20% coated PEC substrate is 34.83 dBm2 lower than that of the uncoated PEC substrate, indicating its enhanced EM wave absorption capability (Fig. S53). Figure S53B also shows the simulated RCS values in polar coordinates over the −90 to 90 detection range, highlighting its potential for wide-angle stealth applications. These results indicate that a higher content of PVDF in the β-phase is favorable for enhancing microwave absorption, while different degrees of the ferroelectric phase transition in PVDF can be induced by different crystal facets.

The terahertz band, as a key frequency range for the sixth generation of mobile communication, operates at higher frequencies and energies, making the study of EM wave loss in this band particularly important44. Terahertz time-domain spectroscopy (THz-TDS) was conducted in transmission mode to evaluate the properties of P/N sample films (Fig. 5A)45. Compared to the air reference, the terahertz signal experiences significant attenuation when passing through the P/N sample films (Fig. 5B–D). Shielding performance and transmittance were used to assess the EM properties of these films in the 0.2–2.0 THz range46. The results show that the terahertz shielding performance of P/N{111} films is lower than that of P/N{100} at the same filler loading, further confirming that the presence of PVDF in the β-phase enhances the terahertz shielding performance (Figs. S54, S55). For the total terahertz shielding effectiveness (SET) at a low thickness of 0.25 mm, P/N{100}-50% sample demonstrates the best performance with a maximum value of 29.91 dB (shielding efficiency (α SE) of 99.90%), an average value of 21.91 dB, and a minimum value higher than 10 dB (Figs. 5E, F, S56). Through the measurement and calculation of the reflection and multiple reflection components within regions of effective shielding, it is determined that the shielding performance of P/N{100}-50% is primarily attributed to absorption loss, while the contributions from multiple reflections and scattering are negligible (Figs. S57–S59)47–49.

Further analysis indicates a statistically significant linear positive correlation between β-phase content and terahertz shielding effectiveness (Figs. S60, S61). The established regression model (Table S9, Fig. S62) exhibits excellent goodness-of-fit (R2=0.94442) and high statistical significance (p=0.00738), providing robust quantitative evidence that β-phase content is a key determinant of terahertz attenuation performance. This statistically confirms that as the β-phase content in the sample increases systematically, its terahertz shielding effectiveness demonstrates a linear growth trend. This outcome is entirely consistent with our proposed theoretical mechanism: a higher proportion of β-phase PVDF results in stronger dipole and interfacial polarization, which are primary factors of terahertz wave energy dissipation. The transmittance of the two materials aligns with their shielding performance trends (Figs. 5G, H, S63). The minimum transmittance of the P/N{100}-50% sample is 0.032, with an average of 0.090; both values are higher than those of the other P/N samples.

The extinction coefficients of P/N-50% samples were calculated from the frequency domain spectra (Fig. S64). This enables the derivation of ε“ (Fig. 5I) and the absorption coefficients (αT) (Fig. 5J). Here, ε“ elucidates THz-band relaxation dynamics, whereas αT serves as a metric for terahertz EM wave attenuation50. The ε“ of the P/N samples exhibits a distinct peak at 0.3 THz, corresponding to a relaxation process in the THz band with a relaxation time of 0.53 ps. This process coexists with multiple secondary relaxation modes across the terahertz spectrum. The P/N samples show higher absorption coefficients compared to pure PVDF, and the αT of the P/N{111} is lower than that of the P/N{100}. This suggests that the presence of the β-phase in PVDF increases EM loss in the THz band. This confirms that the crystal facet-mediated ferroelectric polarity in PVDF drives polarization response mechanisms in the THz spectrum.

Polarization mechanisms are the core for regulating the EM response of P/N ferroelectric samples. Benefiting from their abundant molecular chain rotational freedom and spontaneous polarization characteristics, organic ferroelectric polymers can leverage intrinsic multi-relaxation mechanisms to reconfigure the distribution of extreme values in electromagnetic parameters. This broadens the relaxation time, thus facilitating highly efficient broadband electromagnetic energy response51. In multi-band EM loss, it plays a crucial role through the synergistic effects of interfacial, spatial, and orientational dipole polarizations. The functions of each polarization mechanism in different frequency bands are as follows: As shown in Fig. S65, in the MHz frequency band, the loss mode of P/N ferroelectric samples is dominated by interfacial dipole polarization loss. The difference in permittivity between the ferroelectric phase PVDF and the inorganic filler induces interfacial dipoles. Under the action of an external EM field, these interfacial dipoles undergo rotational polarization. Through the dipole relaxation process, the EM energy in the MHz frequency band is converted into heat energy and dissipated, achieving EM loss in this frequency band52. When entering the GHz frequency band, the polar groups of the ferroelectric phase PVDF are affected by EM fluctuations, resulting in changes in dipole moment in the spatial dimension. The spatial distribution state of molecular chains directly affects the polarization efficiency, enabling targeted dissipation capability for EM waves in the GHz frequency band. At this time, the dipoles dissipate the EM waves in the GHz frequency band through vibration and rotation53.

As the frequency increases, the orientational rotation of dipoles in the alternating EM field becomes increasingly intense. In the THz frequency band, since the ferroelectric phase PVDF is a semi-crystalline polymer, the synergistic effect of the crystalline and amorphous phase structures in the sample promotes the orientational adjustment of dipole molecules under the THz high-frequency EM field (Fig. S66). Factors such as the characteristics of the crystal-amorphous interface and the degree of molecular chain orientation determine the polarization relaxation characteristics, which can precisely match the EM loss requirements in the THz frequency band, and realize energy dissipation through the orientational adjustment process of dipoles54. In summary, P/N ferroelectric samples utilize the synergy of interfacial, spatial, and orientational dipole polarizations. Different polarization mechanisms jointly regulate the EM response of the material across multiple frequency bands to achieve multi-band EM loss (Fig. S67).

Compared to ferroelectric EM loss materials reported in recent studies, the P/N samples proposed in this work maintain superior loss capability across various frequency bands. The evaluation metrics for material performance vary with electromagnetic frequency bands: in the MHz band, it is determined by the dissipation factor; in the GHz band, it is based on effective bandwidth and reflection loss; and in the THz band, the shielding effectiveness per unit thickness is employed (Fig. S68, Table S10)50,55–68. This performance stems from the diverse polarization types generated by the ferroelectric phase transition of PVDF and the broad distribution of relaxation times in PM samples. These provide valuable insights for developing advanced broadband EM compatibility materials.

In summary, this study demonstrates a facet-induced strategy for modulation of stable and uniform polymer ferroelectric phase, revealing the pivotal regulatory role of intrinsic polarization properties in the ferroelectric polymer matrix for governing multi-band efficient electromagnetic responses. By the combination of first-principle calculations and AFM experimental procedures, it is demonstrated that the {100} crystal facet of NiS2 stabilizes the ferroelectric β-phase PVDF by reducing its energy below that of the non-ferroelectric phase and increasing its energy difference, thereby achieving a stabilized ferroelectric PVDF system and multi-band EM dissipation performance. This effect arises from the spontaneous polarization induced by the ferroelectric phase β-PVDF, leading to a broad distribution of relaxation times and enhancing multiple types of polarization mechanisms, with relaxation frequencies across megahertz, gigahertz, and terahertz frequency ranges. As a direct manifestation of these phenomena, enhanced polarization loss and a systematic increase in absorption coefficient are observed. These findings not only elucidate the mechanism of crystal facet engineering-driven PVDF ferroelectric phase transition evolution but also establish a synergistic principle linking the ferroelectric polarization of organic PM, multi-band frequency response expansion, and enhanced EM wave loss.

Methods
Preparation of NiS2 nanocrystals with {111}-exposed surfaces: 0.20 mmol NiCl2·6H2O, 0.50 mmol Na2S2O3·5H2O, and 0.165 g of PVP with MW∼58,000 were dissolved in 76 ml deionized water, and then stirred for 30 min at room temperature and normal pressure to make the solution well mixed and homogeneous, and then placed in a 100 ml hydrothermal reactor. The reaction was carried out in a 100 ml hydrothermal reactor at 150 °C for 12 h, and then naturally cooled to room temperature. The obtained product was centrifuged several times with deionized water and anhydrous ethanol, and the black precipitate was taken and dried in an oven to obtain NiS2 nanocrystals with {111} exposed surfaces, which were named as NiS2{111}.

Preparation of NiS2 nanocrystals with {100} exposed faces: 2.40 mmol of Ni(NO3)2·6H2O, 10.00 mmol of C2H4N2S, 0.65 g of Mw~58000 PVP and 0.05 mmol of NaOH were dissolved in 40 ml of deionized water, and then stirred for 30 min at room temperature and pressure to make the solution fully mixed and homogeneous, and then placed in a 100 ml hydrothermal reactor. The reaction was carried out in a 100 ml hydrothermal reactor at 150 °C for 12 h, and then naturally cooled to room temperature. The obtained product was centrifuged several times repeatedly with deionized water and anhydrous ethanol, and the black precipitate was taken and dried in an oven to obtain NiS2 nanocrystals with {100} exposed surfaces, which were named as NiS2{100}.

Preparation of NiS2/PVDF samples: NiS2 nanocrystals with {100} and {111} exposed surfaces were mixed with pure PVDF at different mass fillings, dissolved and dispersed in DMF, and dried at 80 °C to form a thin film. The films were hot-pressed at 220 °C and 5 MPa for 20 min and then cooled naturally to form NiS2/PVDF cylindrical-shaped samples (Φ out=7.00 mm and Φ in=3.04 mm). NiS2/PVDF sample films were pressed to a thickness of 0.25 mm using the same temperature and pressure. NiS2/PVDF samples are named P/N{hkl}-X, where {hkl} is the crystal facet of NiS2 and X is the filler loading of NiS2.

Material characterizations: The morphology of the resulting nanoparticles was studied by scanning electron microscopy (SEM, Quanta 250 FEG) and scanning transmission electron microscopy (STEM, Thermofisher Spectra 300). The elemental composition and spatial distribution were characterized via energy dispersive X-ray spectrometry (EDS, Super X EDS detector). The crystal structure of the nanostructures was analyzed by X-ray diffraction (XRD) on a Bruker D8 Advance X-ray diffractometer equipped with a copper target at a wavelength of 1.5418 Å. The elemental composition was characterized by X-ray photoelectron spectroscopy (Thermo Scientific K-Alpha). The U-I curves of the samples were measured by a semiconductor analyzer (Keithley 2400). AFM-IR measurements were carried out on a Bruker Anasys nanoIR3 system. Both topography and chemical images were simultaneously collected in the tapping mode. The local IR spectra were obtained by placing the atomic force microscope tip on top of the sample. The HRTEM images were captured on FEI Talos F200X transmission electron microscope at an accelerating voltage of 200 kV. The film was precisely sectioned using a Leica EM UC7 ultramicrotome. After that, the sectioned samples were placed on the copper carrier network support carbon film for transmission electron microscopy imaging. Kelvin probe force microscopy (KPFM) and Piezoelectric reaction force microscopy (PFM) were performed on a commercial atomic force microscope (OXFORD-MFP-3D Origin+). High-stiffness conductive probes (k≈20 N/m) were used in the experiments. To obtain a local piezoelectric response loop, the DC switch is switched from −30 V to 30 V. The ferroelectric P-E hysteresis loops were measured using a Radiant Precision LC II tester (USA). The temperature-dependent dielectric constant was measured using an Agilent 4294A impedance analyzer (USA) over a temperature range of 20 °C to 150 °C at frequencies of 10 kHz, 100 kHz, 1 MHz, and 2 MHz.

DFT calculations: The DFT calculations were performed using the Vienna ab initio simulation package (VASP) in the projected augmented wave framework. The generalized gradient approximation proposed by Perdew, Burke and Ernzerhof (PBE) was chosen for the exchange-correlation potential. The energy cutoff of the plane wave was set to 550 eV. We used k-point grids of 10×6×3 for PVDF, 2×2×1 for NiS2, and 1×1×1 for NiS2/PVDF. The convergence criteria for geometry optimizations were a maximum residual force of less than 0.05 V·Å−1 and an energy change of less than 10−5 eV.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript reports a facet-engineering approach using NiS₂ crystal planes ({100} and {111}) to stabilize the β-phase of PVDF, achieving broadband electromagnetic (EM) loss from MHz to THz. The authors combine DFT calculations, structural characterizations (SEM, TEM, XRD, FTIR, AFM-IR, PFM), and EM response analysis to demonstrate that facet modulation enables enhanced polarization and relaxation dynamics, breaking the Kramers–Kronig trade-off. The topic is original, the data are extensive, and the idea of facet-modulated ferroelectricity in polymers is both novel and technologically relevant. However, several methodological, mechanistic, and presentation aspects require significant improvement before acceptance.\n1. The manuscript claims that {100} facets of NiS₂ stabilize β-PVDF by lowering its energy below α-PVDF. However, the underlying electronic or interfacial mechanism is insufficiently elaborated.\n2. How does charge transfer or dipole alignment differ quantitatively between facets?\n3. Can authors provide charge density difference maps or Bader charge analysis to support the interfacial polarization claims?\n4. The statement that this mechanism “breaks the Kramers–Kronig constraint” seems physically overstated, since these relations are fundamental. The authors should instead clarify that multi-relaxation mechanisms mitigate the apparent loss–bandwidth trade-off.\n5. Is there any specific cause of choosing NiS2 as the filler material?\n6. Provide the investigation of a control composite with randomly oriented NiS₂ or another inert filler to confirm that the observed effects are truly facet-specific.\n7. The role of NiS₂ conductivity in EM attenuation must be disentangled from ferroelectric polarization effects (conductivity data in Table S1 suggest notable variation).\n8. The PFM data (Fig. 3D–G) show phase hysteresis, but there is no macroscopic polarization–electric field (P–E) loop. A P–E measurement or Sawyer–Tower loop is essential to confirm bulk ferroelectricity.\n9. The reported coercive voltages (0.41 V and 0.62 V) are relatively low. Clarify whether these values refer to local switching or macroscopic measurement.\n10. Table S2 shows strong EM loss compared to other materials, but normalization (per thickness, per filler loading, etc.) is inconsistent.\n11. Please include a clear benchmark plot (e.g., attenuation constant vs. frequency) comparing state-of-the-art polymer composites.\n12. The claim that the system “overcomes the limitation imposed by Kramers–Kronig relations” is conceptually problematic. These relations are not breakable for causal, linear systems. The authors could instead argue that nonlinear ferroelectric polarization and multi-relaxation processes expand the effective response bandwidth.\n13. The reported THz shielding effectiveness (≈30 dB for 0.25 mm) is impressive but could also arise from multiple reflection and scattering effects. Consider adding complex refractive index or impedance spectra to clarify this.\n14. The correlation between β-phase fraction and THz attenuation should be statistically supported (e.g., regression of β-phase ratio vs. SET).\n15. The SEM/TEM images (Fig. 1B–E) show morphological differences, but facet indexing and atomic models should be more explicitly correlated.\n16. A surface energy or coordination number comparison would reinforce the claim that {100} facets are more polarizing.\n17. The Introduction could better emphasize how this work differs from previous PVDF–inorganic interface engineering (e.g., doped or hybridized PVDF systems).", "reviewer_2": "Facet-Modulated Ferroelectric Polymers-Major comments to the authors:\nThe present work tried to correlate the effect of facets of the crystal on the PVDF structure and its properties is a novel idea for research, however, the approach the authors followed requires further improvements with following suggestions/modifications/required new experiments.\n1. The individual crystal facet implication on the β-phase of PVDF has been elaborated, however, the quantitative analysis of increase in β-phase as a function of particle size distribution and shape distribution is required as the physical properties measured are average properties of over the area of the samples. Hence it is desired to understand the shape and size distributions and their effect on β-phase is required.\n2. A clear comparison between the PFM results for pure PVDF and composite is required. The effect of enhancement of β-phase on the PFM related physical quantities must be emphasized. The piezoelectric tensor matrix analysis for the pure and composites has to be incorporated with respect to observed PFM results.\n3. However, the butterfly loop is not fully saturated, the reason and a comparison with earlier literature need to be incorporated.\n4. The title “Facet-Modulated Ferroelectric Polymers” showcases the ferroelectric nature of the composite, however the ferroelectric properties such as Polarization versus Electric field and Analysis of Curie’s Temperature from temperature dependent dielectric properties has not been incorporated. The authors are strongly suggested to incorporate the same for further consideration.\nWith the above suggestions, the manuscript is not suggested for publication in nature communications in the present form, however if the authors would like to add the above measurements/provide the appropriate data, the manuscript may be reconsidered after thorough revision.", "reviewer_3": "The manuscript by B. Cai et al. reports a method for preferential crystallization of the ferroelectric β-phase of PVDF on specific facets of NiS2 nanocrystals. The authors attribute this effect to enhanced S-H interactions at the {100} surface. However, the experimental data do not convincingly support this conclusion, and several key interpretations are either incomplete or unsupported.\n1. The XRD diffractograms (Figs. 2A,B and S11) show a dominant β-phase peak in all sample, while the differences in FTIR spectra are minimal and even disappears at 25% NiS2 loading (Figs. 2C,D and S12). These variations fall within the usual batch-to-batch variability of PVDF and cannot be taken as solid evidence of facet-induced β-phase enhancement.\n2. A more fundamental issue is that the influence of processing conditions is barely addressed. It is well known that mechanical stretching and elevated temperatures promote α- to β-phase transition in PVDF [https://doi.org/10.1039/C3RA45134H]. The hot-pressing method used by the authors can itself induce β-phase formation, with nanoparticles acting as stress concentrators. A similar effect has already been reported for PVDF-BaTiO3 system [https://doi.org/10.1016/j.polymertesting.2024.108516]. The authors fail to decouple the contribution of thermal–mechanical processing from any alleged facet-specific effects.\n3. The characterization of the PVDF/NiS2 composites physical properties also raises concerns. The PFM data are not convincing. V-shape amplitude loops such of those in Figs. 3E,G are typical of electrostatic artefacts caused by tip-sample interaction, not of genuine piezoresponse [https://doi.org/10.1016/j.ultramic.2019.112839]. For samples dominated by non-polar α-phase, the authors should have used stiffer AFM probes, controlled surface potential via KPFM, and performed PFM in both contact and non-contact modes to verify that the response is truly piezoelectric rather than electrostatic.\n4. The dielectric measurements are also problematic. The authors conclude (lines 253-254) that “…due to the low conductivity of P/N composites (Figure S17, Table S1), the dominant loss mechanism in the 2-18 GHz range is polarization loss…”. This is contradicted by their own data. Table S1 shows a 4-orders-of-magnitude (!) conductivity increase in P/N{100}, when NiS2 loading increases from 15% to 25%. Such a dramatic change should strongly influence conductive losses, yet Fig. 4E shows no effect at all. This discrepancy is ignored, making further discussion of the electromagnetic properties unreliable.\n5. The novelty of the “facet engineering” approach proposed by the authors is overstated. Surface-induced polymorphism in both organic and inorganic systems is well established in literature [https://doi.org/10.1002/adfm.201503169; https://doi.org/10.1039/C8CS00283E]. β-phase enhancement in PVDF composites with inorganic nanoparticles has already been demonstrated [https://doi.org/10.1016/j.polymertesting.2024.108516]. The work does not introduce a sufficiently new concept or mechanism.\nIn summary, the “facet engineering” concept presented here is not novel, and β-phase enhancement in PVDF-nanoparticle composites has already been demonstrated. The experimental evidence is weak, key controls are missing, and several interpretations are questionable or unsupported. Overall, the originality and scientific rigor of the work do not meet the standards of Nature Communications, and the manuscript should not be accepted for publication."}, "author_response": "Response to Reviewers’ Comments\nReviewer 1 (P1-P38), Reviewer 2 (P39-P52), Reviewer 3(P53-P77)\nReviewer 1：\nComments: The manuscript reports a facet-engineering approach using NiS crystal\n2\nplanes ({100} and {111}) to stabilize the β-phase of PVDF, achieving broadband\nelectromagnetic (EM) loss from MHz to THz. The authors combine DFT calculations,\nstructural characterizations (SEM, TEM, XRD, FTIR, AFM-IR, PFM), and EM\nresponse analysis to demonstrate that facet modulation enables enhanced polarization\nand relaxation dynamics, breaking the Kramers-Kronig trade-off. The topic is original,\nthe data are extensive, and the idea of facet-modulated ferroelectricity in polymers is\nboth novel and technologically relevant. However, several methodological, mechanistic,\nand presentation aspects require significant improvement before acceptance.\nReply: We are very grateful for the insightful review and constructive comments, and\nwelcome the opportunity to address these comments and describe our revisions below.\nSpecific comments are listed as follows:\nQ1: The manuscript claims that {100} facets of NiS stabilize β-PVDF by lowering its\n2\nenergy below α-PVDF. However, the underlying electronic or interfacial mechanism is\ninsufficiently elaborated.\nReply: Thank you for your careful review and valuable comments on our manuscript.\nTo address this valuable feedback, we have performed additional calculations,\nincluding charge density differential analysis, to further reveal the underlying electronic\nand interfacial mechanisms. Below is our detailed response:\nWe systematically calculated the charge density difference at the interfaces\nbetween the {100} and {111} facets of NiS and α-PVDF/β-PVDF, respectively, to\n2\nevaluate the charge transfer and electronic interactions at the interface. The results\nindicate that compared to the {111} facet, significant charge redistribution at the\ninterface between the {100} facet of NiS and β-PVDF is observed, where electrons are\n2\ntransferred from the PVDF molecules to NiS . This phenomenon is particularly\n2\n1\npronounced between the polar groups of β-PVDF and the exposed {100} facet of NiS ,\n2\nleading to the formation of strong interfacial dipole interactions. (Figure R1).\nFigure R1. The Z-direction average of the electron density difference of A,\nNiS {100}/α-PVDF, B, NiS {100}/β-PVDF, C, NiS {111}/α-PVDF and D,\n2 2 2\nNiS {111}/β-PVDF. The cyan spheres represent Ni atoms; orange spheres denote S\n2\natoms. At the interface, regions shaded in cyan indicate a reduction in charge density,\nwhereas yellow regions signify an enhancement in charge density. The dashed line\nmarks the position where the differential charge density across the interface equals to\n0 e/Å. The value range for the difference charge density isosurface is: A, -\n0.0031~0.0036 e/Bohr3, B, -0.0102~0.0167 e/Bohr3, C, -0.0026~0.0040 e/Bohr3 and\nD, -0.0031~0.0045 e/Bohr3.\nBy averaging the planar differential charge density along the Z-direction across\nthe interface region, we obtained the following quantitative results: Analysis of the\nplanar-averaged charge density difference along the Z-direction across different\ninterfaces reveals that the NiS {100}/β-PVDF interface exhibits the most pronounced\n2\ncharge transfer, with a peak density of 0.491 e/Å. In contrast, the peak density at the\nNiS {111}/β-PVDF interface is only 0.071 e/Å. Meanwhile, the charge response at both\n2\n2\nthe NiS {100}/α-PVDF (0.019 e/Å) and NiS {111}/α-PVDF (0.047 e/Å) interfaces\n2 2\nremains relatively weak.\nAnalysis of the spatial extent of charge redistribution reveals that the interaction\nregion at the NiS {100}/β-PVDF interface (1.62 Å) is narrower than that at its interface\n2\nwith α-PVDF (2.12 Å). This indicates that the charge transfer is more concentrated and\nlocalized at the {100}/β interface, revealing stronger interfacial electronic coupling.\nOur calculations demonstrate that the NiS {100}/β-PVDF interface exhibits\n2\ngreater charge transfer and a more localized interaction range, thereby generating a\nstronger interfacial dipole. This quantitative difference, revealed at the electronic\nstructure level, precisely constitutes the physical origin of its ability to specifically\nstabilize β-PVDF.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 5, Paragraph 2, Line 1-6 and Page 6, Paragraph 1, Line 1-3 in the revised\nmanuscript:\n“On the {111} facet, the coordination environment of surface S atoms is near\ncomplete saturation, whereas on the {100} facet, both surface Ni and S atoms possess\na high density of unsaturated coordination sites, resulting in a higher surface energy\n(Figure S7). These unsaturated sites form high-density local polarization centers,\nmaking the {100} facet more polar and significantly enhancing interfacial electron\ncoupling and charge transfer capabilities (Figure S8-S10, Supplementary Table S1 and\nS2). The higher polarity implies that the highly polar {100} facet readily undergoes\nstrong dipole-dipole interactions with β-PVDF molecular chains, which themselves\nexhibit relatively high surface energy and polarity. This, in turn, makes the {100} facet\nkey to inducing and stabilizing the strongly polar β-phase of PVDF.”\nTo address this comment, we have supplemented the calculation results in Figure\nS7, S8, S9 and S10, Supplementary Table S1, Supplementary Table S2 and revised the\nrelevant statements in the revised supporting information accordingly.\nReply: Thank you for this insightful question. We have quantified the differences by\ncalculating the Z-direction average of the electron density difference. The results\nclearly reveal distinct charge redistribution patterns and dipole strengths at the different\ninterfaces.\nBy averaging the planar differential charge density along the Z-direction across\nthe interface region, we obtained the following quantitative results:\nAnalysis of the planar-averaged charge density difference along the Z-direction\nacross different interfaces reveals that the NiS {100}/β-PVDF interface exhibits the\n2\nmost pronounced charge transfer, with a peak density of 0.491 e/Å. In contrast, the peak\ndensity at the NiS {111}/β-PVDF interface is only 0.071 e/Å. Meanwhile, the charge\n2\nresponse at both the NiS {100}/α-PVDF (0.019 e/Å) and NiS {111}/α-PVDF (0.047\n2 2\ne/Å) interfaces remains relatively weak (Figure R1).\nAnalysis of the spatial extent of charge redistribution reveals that the interaction\nregion at the NiS {100}/β-PVDF interface (1.62 Å) is narrower than that at its interface\n2\nwith α-PVDF (2.12 Å). This indicates that the charge transfer is more concentrated and\nlocalized at the {100}/β interface, revealing stronger interfacial electronic coupling.\nOur calculations demonstrate that the NiS {100}/β-PVDF interface exhibits\n2\ngreater charge transfer and a more localized interaction range, thereby generating a\nstronger interfacial dipole. This quantitative difference, revealed at the electronic\nstructure level, precisely constitutes the physical origin of its ability to specifically\nstabilize β-PVDF.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 5, Paragraph 2, Line 1-6 and Page 6, Paragraph 1, Line 1-3 in the revised\nmanuscript.\nS8, S9 and S10, Supplementary Table S1, Supplementary Table S2 and revised the\nrelevant statements in the revised supporting information accordingly.\nQ3: Can authors provide charge density difference maps or Bader charge analysis to\nsupport the interfacial polarization claims?\nReply: We systematically calculated the charge density difference at the interfaces\nbetween the {100} and {111} facets of NiS and α-PVDF/β-PVDF, respectively, to\n2\nevaluate the charge transfer and electronic interactions at the interface. The results\nindicate significant charge redistribution at the interface between the {100} facet of\nNiS and β-PVDF, where electrons are transferred from the PVDF molecules to NiS .\n2 2\nThis phenomenon is particularly pronounced between the polar groups of β-PVDF and\nthe exposed {100} facet of NiS , leading to the formation of strong interfacial dipole\n2\ninteractions. Such directional charge transfer not only enhances the interfacial\nadsorption energy but also effectively reduces the total system energy, thereby\npromoting the preferential stabilization of β-PVDF at the electronic level (Figure R2).\nFigure R2. The charge density difference of A, NiS {100}/α-PVDF, B, NiS {100}/β-\n2 2\nPVDF, C, NiS {111}/α-PVDF and D, NiS {111}/β-PVDF. The cyan spheres\n2 2\n5\nrepresent Ni atoms; orange spheres denote S atoms. At the interface, regions shaded\nin cyan indicate a reduction in charge density, whereas yellow regions signify an\nenhancement in charge density. The value range for the difference charge density\nisosurface is: A, -0.0031~0.0036 e/Bohr3, B, -0.0102~0.0167 e/Bohr3, C, -\n0.0026~0.0040 e/Bohr3 and D, -0.0031~0.0045 e/Bohr3.\nBy averaging the planar differential charge density along the Z-direction across\nthe interface region, we obtained the following quantitative results:\nAnalysis of the planar-averaged charge density difference along the Z-direction\nacross different interfaces reveals that the NiS {100}/β-PVDF interface exhibits the\n2\nmost pronounced charge transfer, with a peak density of 0.491 e/Å. In contrast, the peak\ndensity at the NiS {111}/β-PVDF interface is only 0.071 e/Å. Meanwhile, the charge\n2\nresponse at both the NiS {100}/α-PVDF (0.019 e/Å) and NiS {111}/α-PVDF (0.047\n2 2\ne/Å) interfaces remains relatively weak (Figure R1).\nAnalysis of the spatial extent of charge redistribution reveals that the interaction\nregion at the NiS {100}/β-PVDF interface (1.62 Å) is narrower than that at its interface\n2\nwith α-PVDF (2.12 Å). This indicates that the charge transfer is more concentrated and\nlocalized at the {100}/β interface, revealing stronger interfacial electronic coupling.\nFigure R3. The Bader charge of NiS {100}/β-PVDF. A, Ni atoms of NiS {100}, B, S\n2 2\n6\natoms of NiS {100}, C, F atoms of β-PVDF and D, H atoms of β-PVDF. The cyan\n2\nspheres represent Ni atoms; orange spheres denote S atoms; light green spheres\nrepresent F atoms; white spheres represent H atoms.\nTo clarify the charge distribution and transfer behavior at the NiS {100}/β-PVDF\n2\ninterface, we conducted Bader charge analysis (Figure R3). The results reveal a\nsignificant asymmetric charge redistribution at the interface. Specifically, on the\nNiS {100} side near the interface, the Ni atoms exhibit an average Bader charge of\n2\napproximately -0.54 e, while the S atoms show an average charge of about +0.27 e. On\nthe β-PVDF side, the interfacial F atoms carry an average charge of around +0.64 e,\nand an average -0.09 e for H atoms. These results quantitatively demonstrate a net\nelectron transfer from the β-PVDF side to the NiS {100} side. This quantitative\n2\nconclusion is consistent with the differential charge density map, which shows electron\nloss in the β-PVDF region (indicated by cyan areas) and electron gain in the NiS {100}\n2\nregion (indicated by yellow areas). The Bader analysis thus provides explicit charge\nvalues that further confirm the directional charge migration across the interface. Such\ndirectional charge transfer establishes a localized built-in electric field between the two\nsides of the interface, offering an explanation for the origin of interfacial polarization.\nOur calculations demonstrate that the NiS {100}/β-PVDF interface exhibits\n2\ngreater charge transfer and a more localized interaction range, thereby generating a\nstronger interfacial dipole. This quantitative difference, revealed at the electronic\nstructure level, precisely constitutes the physical origin of its ability to specifically\nstabilize β-PVDF.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 5, Paragraph 2, Line 1-6 and Page 6, Paragraph 1, Line 1-3 in the revised\nmanuscript.\nTo address this comment, we have supplemented the calculation results in Figure\nS8, S9 and S10, Supplementary Table S1, Supplementary Table S2 and revised the\nrelevant statements in the revised supporting information accordingly.\nphysically overstated, since these relations are fundamental. The authors should instead\nclarify that multi-relaxation mechanisms mitigate the apparent loss-bandwidth trade-\noff.\nReply: We thank the reviewers for your suggestions and have amended our wording in\naccordance with your requirements.\nTo address this comment, we have supplemented the revised manuscript\naccordingly.\nPage 1, Paragraph 1, Line 13-15 in the revised manuscript:\n“The composite system mitigates the apparent loss-bandwidth trade-off, thereby\nachieving broadband polarization properties across multiple frequency bands while\nmaintaining a dissipation efficiency above 99.9%.”\nPage 3, Paragraph 2, Line 5-10 in the revised manuscript:\n“The mediation of polymer interfaces by specific plane orientations was\nsystematically investigated, elucidating the key microscopic factors through which\ninorganic fillers influence the stability of the ferroelectric phase of PVDF. This work\nestablishes the crystal facet control of inorganic fillers as a new variable for\nmanipulating the ferroelectric phase and molecular dipole distribution in PVDF.\nFurthermore, the crystal facet-stabilized PVDF matrix significantly enhances the\noperational stability and reliability of the composite.”\nPage 15, Paragraph 3, Line 4-6 in the revised manuscript:\n“This broadens the relaxation time, thus facilitating highly efficient broadband\nelectromagnetic energy response50.”\nPage 16, Paragraph 2, Line 10-11 in the revised manuscript:\n“Different polarization mechanisms jointly regulate the EM response of the\nmaterial across multiple frequency bands to achieve multi-band EM loss (Figure S67).”\nPage 17, Paragraph 2, Line 8-11 in the revised manuscript:\n8\n“This effect arises from the spontaneous polarization induced by the ferroelectric\nphase β-PVDF, leading to a broad distribution of relaxation times and enhances\nmultiple types of polarization mechanisms, with relaxation frequencies across\nmegahertz, gigahertz, and terahertz frequency ranges.”\nPage 84, Paragraph 3, Line 10-11 and Page 85, Paragraph 1, Line 1-2 in the revised\nsupporting information:\n“This multi-relaxation behavior results in pronounced nonlinear dielectric\ncharacteristics, thereby mitigating the apparent loss-bandwidth trade-off, and ultimately\nenables highly efficient electromagnetic energy dissipation simultaneously across\nmultiple frequency bands.”\nQ5: Is there any specific cause of choosing NiS as the filler material?\n2\nmaterial is based on a comprehensive evaluation of crystal plane control, material\nstability, electromagnetic properties, and economic and environmental sustainability.\nThe specific reasons are as follows:\n1. Feasibility of Crystal Plane Control: Our research focuses on optimizing the\nferroelectric phase transition of materials by controlling the exposed crystal planes.\nNiS can be synthesized via facile methods such as hydrothermal synthesis to\n2\neffectively control its macroscopic morphology. This enables selective exposure of\nspecific crystal planes featuring highly ordered and stable atomic arrangements,\nproviding an ideal model for investigating the interaction mechanisms between crystal\nplanes and ferroelectric polymers (Angew. Chem. Int. Ed., 2019, 131, 18849-18855).\n2. The Comprehensive Advantages of Nickel-Based Materials: We prioritize\nnickel-based materials for the following reasons: High Stability: Compared to iron-\nbased and cobalt-based materials, nickel sulfides exhibit superior stability in air and are\nless prone to oxidation. This ensures long-term effectiveness during material\npreparation and application. Simultaneously, NiS eliminates magnetic interference: As\n2\ndemonstrated by our electromagnetic parameter testing (Figure S44), NiS exhibits a\n2\n9\nreal magnetic permeability (μ') close to 1 and an imaginary permeability (μ'') near 0,\nindicating negligible magnetic properties. This eliminates magnetic losses from\ncontributing to absorptive performance, enabling a purer investigation of dielectric\npolarization (including crystal-plane-induced interfacial polarization and dipole\npolarization) in electromagnetic wave attenuation.\n3. Economic and Environmental Considerations: Nickel is abundant in the\nEarth's crust, relatively inexpensive, and its compounds exhibit low environmental\ntoxicity, aligning with the requirements for sustainable material development.\nIn summary, NiS combines stable, tunable crystal planes, excellent chemical\n2\nstability, distinct nonmagnetic properties, economic and environmental advantages,\naligning perfectly with the design objectives of our study. Consequently, it was selected\nas the ideal filler material.\nQ6: Provide the investigation of a control composite with randomly oriented NiS or\n2\nanother inert filler to confirm that the observed effects are truly facet-specific.\nReply: We thank the reviewer for this important suggestion. To address this, we\nprepared and systematically characterized a control P/N composite (denoted as P/N)\ncontaining randomly oriented NiS nanoparticles for comparison with the facet-specific\n1. Preparation and Characterization of Control Samples:\nThe P/N composite was synthesized by randomly oriented NiS nanoparticles\n2\nwithout specific facet control into the PVDF matrix. SEM analysis confirmed its\nrandom morphology. All other preparation conditions and filler loadings were\nmaintained identical to those of the facet-controlled samples to ensure the validity of\nthe comparison (Figure R4).\n2 2\nμm (B), 500 nm (C).\n2. Comparative Analysis of Key Performance Parameters:\nWe systematically compared the P/N sample with the facet-specific P/N{100} and\nP/N{111} samples in terms of critical performance metrics, the β-phase fraction\ninduced by the P/N-random sample was notably lower than that achieved by the\nP/N{100} sample (Figure R5, R6, Table R1).\nFigure R5. XRD profiles of P/N, P/N{111} and P/N{100}. A, 15 wt.%, B, 25\nwt.%.\nB, 25 wt.%.\nTable R1. The β phase ratio of P/N, P/N{111} and P/N{100}\nSample β phase ratio\nP/N-15% 0.477\nP/N{111}-15% 0.472\nP/N{100}-15% 0.496\nP/N-25% 0.587\nP/N{111}-25% 0.603\nP/N{100}-25% 0.637\nAttenuation Performance: The dielectric constant of the P/N-random sample in\nthe 2-18 GHz frequency range was substantially lower than that of the P/N{100}\nsample. Furthermore, with increasing filler loading, its dielectric constant also\nremained inferior to that of the P/N{100} and P/N{111} sample (Figure R7).\npermittivity of P/N, P/N{111} and P/N{100} samples at EMWs from 2 GHz to 18\nGHz.\nThese comparative results strongly indicate that NiS itself can moderately\n2\npromote β-phase formation, while full exposure of its {100} facet enables a more\neffective enhancement of β-phase content, thereby yielding optimal electromagnetic\nattenuation performance. This facet-dependent behavior strongly supports our proposed\nmechanism of crystal-facet-induced ferroelectric phase transition, highlighting the\ncrucial importance of facet-specific engineering in designing high-performance\nelectromagnetic functional samples.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 7, Paragraph 1, Line 14-18 in the revised manuscript:\n“The filler loading (Figure S19, S20 and Supplementary Table S4), shape\ndistributions (Figure S21-S23 and Supplementary Table S5) and filler size (Figure S24,\nanalysis, the effects of these macroscopic geometric variables were isolated, thus\nestablishing the specific crystal facet as a core variable in influencing performance.”\nPage 12, Paragraph 1, Line 1-4 in the revised manuscript:\n“The comparative analysis of the electromagnetic parameters of NiS with varying\n2\nsize and shape distributions further underscores the critical role of specific crystal facets\nin regulating β-PVDF content (Figure S42, S43).”\nTo address this comment, we have supplemented the results in Figure S21, S22\nand S23, Supplementary Table S5 and revised the relevant statements in the revised\nsupporting information accordingly.\nQ7: The role of NiS conductivity in EM attenuation must be disentangled from\n2\nferroelectric polarization effects (conductivity data in Table S1 suggest notable\nvariation).\nReply: Thank you for the questions raised by the reviewers. Dielectric materials\nattenuate electromagnetic energy and convert it into thermal energy, primarily relying\non two microscopic mechanisms: conductive loss ( ) and polarization loss ( ).\n″ ″\nThe polarization loss and conduction loss value𝜀 𝑐can be calculated by the f𝜀o𝑝llowing\nformula (Nat. Commun.,2024, 15, 9077):\n- (R1)\n″ 2𝜋𝑓𝜏\n𝜀𝑝 = (𝜀𝑠 𝜀∞)1+(2𝜋𝑓) 2 𝜏 2\n(R2)\n″ 𝜎\n𝜀𝑐 = 2𝜋𝑓𝜀0\n(R3)\n″ ″ ″\n𝜀 = 𝜀𝑐 +𝜀𝑝\nWhere the , , , are the static permittivity, the relative permittivity at\nhigh frequency li\n𝜀\nm𝑠it,\n𝜀\nt∞he e\n𝜎\nlect\n𝜏\nric conductivity, the relaxation time, respectively.\nAmong them, conductive loss can be directly calculated from the material's\nintrinsic conductivity; whereas polarization loss, particularly the contribution from\n14\nferroelectric polarization as focused on in this study, can be estimated by subtracting\nthe conductive loss from the total loss.\nIn the original figure, for clearer representation and emphasis of polarization loss\ndominance in the PVDF material system, we adjusted the vertical scale of the\nconductive loss to enhance visual comparison. As shown in Figure R7 and R8, the\nratio in the P/N sample system is less than 0.15%. This value clearly indicates\n″ ″\n𝜀th𝑐a/t𝜀 t𝑝he contribution of conductive loss to the total dielectric loss is negligible, thereby\nconfirming that the electromagnetic attenuation in the material primarily follows a\npolarization-dominated mechanism. The polarization loss originating from ferroelectric\npolarization is the core loss mechanism (Figure R8, R9).\nFigure R8. The polarization loss of A, P/N{111} and B, P/N{100} samples and the\nconductive loss of C, P/N{111} and D, P/N{100} samples at EMWs from 2 GHz to\n″ ″\n𝜀𝑐/𝜀𝑝 to 18 GHz.\nTo address this comment, we have supplemented the results in Figure S37, S38 and\nrevised the relevant statements in the revised supporting information accordingly.\nQ8: The PFM data (Fig. 3D-G) show phase hysteresis, but there is no macroscopic\npolarization–electric field (P-E) loop. A P-E measurement or Sawyer-Tower loop is\nessential to confirm bulk ferroelectricity.\nReply: Thank you for this important comment. We fully agree with your perspective\nand, following your suggestion, have systematically supplemented the macroscopic P-\nE hysteresis loop measurements for key samples. We conducted macroscopic\nferroelectric performance tests at room temperature on pure PVDF, P/N{111}, and\nP/N{100} samples. The measurement results (as shown in Figure R10) clearly\ndemonstrate that the P/N{100} exhibits a typical ferroelectric P-E hysteresis loop with\nwell-defined remnant polarization (P) and coercive field (E ). Compared to pure PVDF\nr c\nand P/N{111}, P/N{100} shows significantly higher remnant polarization (P) and\nr\nsaturation polarization (P ). This result directly confirms that the {100} facet not only\ns\ninduces the formation of a local ferroelectric phase in PVDF (as revealed by PFM phase\nhysteresis) but also enables the composite to exhibit enhanced and switchable\nferroelectric polarization at the macroscopic level.\nThe supplemented macroscopic P-E measurements confirm the overall\nferroelectricity of the P/N{100} and extend the performance enhancement achieved\nthrough facet engineering from micro-local effects to macroscopic bulk material\nproperties. This significantly strengthens and supports our core conclusion regarding\n“facet-modulated ferroelectric polymers.”\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 9, Paragraph 2, Line 18-27 in the revised manuscript:\n“Macroscopic ferroelectric performance tests at room temperature were conducted\non pure PVDF, P/N{111}, and P/N{100} samples. The measurement results (as shown\nin Figure S32) clearly demonstrate that the P/N{100} exhibits a typical ferroelectric P-\nE hysteresis loop with well-defined remnant polarization (P) and coercive field (E ).\nr c\nCompared to pure PVDF and P/N{111}, P/N{100} shows significantly higher remnant\npolarization (P) and saturation polarization (P )27. This result directly confirms that the\nr s\n{100} facet not only induces the formation of a local ferroelectric phase in PVDF (as\nrevealed by PFM phase hysteresis) but also enables the composite to exhibit enhanced\nand switchable ferroelectric polarization at the macroscopic level.”\nTo address this comment, we have supplemented the results in Figure S32 and\nrevised the relevant statements in the revised supporting information accordingly.\nQ9: The reported coercive voltages (0.41 V and 0.62 V) are relatively low. Clarify\nwhether these values refer to local switching or macroscopic measurement.\nclarify that the coercive voltage values reported indeed refer to local switching\nmeasurements.\nThese data were obtained through piezoresponse force microscopy. This technique\napplies a DC bias through the probe tip and detects the local piezoresponse to measure\nferroelectric switching behavior at the nanoscale. Therefore, the reported voltage values\nreflect the local switching characteristics at the nanoscale, rather than the overall\nperformance of macroscopic devices (Adv. Funct. Mater., 2025, 35, 2413130).\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 18, Paragraph 2, Line 17-18 in the revised manuscript:\n“To obtain a local piezoelectric response loop, the DC switch is switched from -\nQ10: Table S2 shows strong EM loss compared to other materials, but normalization\n(per thickness, per filler loading, etc.) is inconsistent.\nReply: Thank you very much for your keen insight and valuable comments. Due to\ndifferences in testing methods, evaluating the loss characteristics of materials across\ndifferent frequency bands requires the application of corresponding standards suited to\nthe specific characteristics of each band.\nIn the megahertz (MHz) band, the loss factor is directly derived from its intrinsic\nelectromagnetic parameters. This metric is independent of macroscopic thickness and\neffectively reflects the intrinsic loss mechanisms of the material. In the terahertz (THz)\nband, shielding effectiveness per unit thickness is typically adopted for comparative\nanalysis (Appl. Phys. A-Mater., 2021, 127, 382, Polymer, 2014, 55, 226-234, Nature,\n2025, 647, 80-85).\nIn the gigahertz (GHz) frequency band, the core of material performance\nevaluation lies in assessing its “ultimate loss potential”—specifically, the strongest\nreflection loss and the broadest absorption bandwidth achievable at a given thickness.\ndependent on sample thickness and frequency (J. Mater. Chem. A, 2021, 9, 24571-\n24581), it is challenging to fully characterize them using a single intrinsic parameter.\nTherefore, the existing literature commonly employs multidimensional comparisons of\nloss performance to demonstrate the comprehensive advantages of a material. (Nat.\nCommun., 2025, 16, 3163, Nat. Commun., 2024, 15, 10337, Nat. Commun., 2024, 15,\n3299, Adv. Mater., 2022, 34, 2106195). We evaluate our material system based on two\nkey metrics—effective bandwidth and reflection loss—to highlight its advanced\nperformance characteristics (Table R2).\nTable R2. Testing and Data characteristics of electromagnetic waves in different\nfrequency bands\nElectro-\nEvaluation of\nmagnetic\nTesting methods Raw data loss Ref.\nwave\ncharacteristics\nbands\nContact electrode The capacitance Dissipation factor Appl. Phys. A-\nmethod by Impedance (C ) and loss ( ) Mater., 2021, 127,\np\nAnalyzer angle tangent\n(N𝐷𝑡\not dependent on 382, Polymer, 2014,\nMHz\n(Agilent 4294A, (D) values sample thickness) 55, 226-234, Ceram.\nAmerica) int., 2021, 47, 34278-\n34288.\nCoaxial wire method The complex Multidimensional Nat. Commun., 2025,\nby Vector Network permittivity and comparisons of 16, 3163, Nat.\nAnalyzer permeability loss performance: Commun., 2024, 15,\nGHz (VNA, ZNA43, values Reflection Loss 10337, Nat.\nROHDE&SCHWAR (RL), bandwidth, Commun., 2024, 15,\nZ, Germany) etc. (dependent on 3299, Adv. Mater.,\nsample thickness) 2022, 34, 2106195.\ndomain spectrometer time-domain effectiveness per 80-85, ACS Appl.\nsystem spectroscopy unit thickness. Mater. Interfaces,\n(TPF 15K, Terahertz (Not dependent on 2024, 16, 54731-\nPhotonics, China) sample thickness) 54741.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 16, Paragraph 3, Line 1-6, in the revised manuscript:\n“Compared to ferroelectric EM loss materials reported in recent studies, the P/N\nsamples proposed in this work maintains superior loss capability across various\nfrequency bands. The evaluation metrics for material performance vary with\nelectromagnetic frequency bands: in the MHz band, it is determined by the dissipation\nfactor; in the GHz band, it is based on effective bandwidth and reflection loss; and in\nthe THz band, the shielding effectiveness per unit thickness is employed (Figure S68,\nTable S10)49, 54-67.”\nQ11: Please include a clear benchmark plot (e.g., attenuation constant vs. frequency)\ncomparing state-of-the-art polymer composites.\nReply: We thank the reviewer for this important constructive comment. We have\nsystematically compared the results of our study with state-of-the-art polymer\ncomposites to objectively evaluate the performance ranking of our developed material.\nFollowing your suggestion, we have systematically compared the attenuation\nperformance of our developed P/N{100} with state-of-the-art polymer composites\nreported in recent literature within the 2-18 GHz frequency range in the revised\nmanuscript. The benchmark materials include representative high-performance\nconductive polymer composites such as NFO@BFO@PPy (Nat. Commun., 2024, 15,\n3299), PAN/CNT/Fe O (Adv. Funct. Mater., 2019, 29, 1807624), HPPy-1500 rpm\n3 4\n(Chem. Eng. J., 2022, 427, 131582), S-NiSe/HG (ACS Nano, 2024, 18, 8411-8422),\n2 3 4\n18, 2204303) (Figure R11).\n[Figure Redacted]\nFigure R11. The attenuation constants of state-of-the-art polymer and P/N{100}\ncomposites.\nThe performance comparison reveals that our P/N{100} exhibits superior\nattenuation characteristics across the entire 2-18 GHz band, with a peak attenuation\nconstant of 344.40 m-1, surpassing the aforementioned reference systems.\nTo further investigate the contribution of the PVDF ferroelectric phase, we also\ncompared the attenuation performance of NiS composites with other polymer matrices\n2\n(Poly(methyl methacrylate) (PMMA) and Polystyrene (PS)), as shown in Figure R12,\nR13. The results confirm that the formation of the ferroelectric β-phase in PVDF\nplays a critical role in enhancing electromagnetic wave attenuation.\nFigure R12. A, Real part of permittivity, B, Imaginary part of permittivity, C,\nReal part of permeability and D, Imaginary part of permeability of NiS -PVDF, NiS -PS\n2 2\nand NiS -PMMA composites (The NiS loading is 25 wt.%).\n2 2\n2 2 2\ncomposites.\nWe attribute this outstanding performance to the unique facet-induced ferroelectric\nphase transition between the {100} facet of NiS and PVDF molecular chains. This\n2\ninteraction effectively promotes the formation of a high proportion of β-phase PVDF,\nsignificantly enhancing the dipole polarization strength of the material, thereby\noptimizing the polarization loss mechanism and ultimately leading to a substantial\nimprovement in the attenuation constant.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 12, Paragraph 2, Line 13-20, in the revised manuscript:\n“The attenuation performance of the P/N{100} were systematically compared\nwith state-of-the-art polymer composites reported in recent literature within the 2-18\nGHz frequency band. The results demonstrate that the P/N{100} exhibits superior\nattenuation characteristics across the entire frequency band, outperforming the\naforementioned reference systems (Figure S49)35-40. To further elucidate the unique\ncontribution of the PVDF ferroelectric phase, the attenuation performance of NiS\n2\ncomposites were also compared with other polymer matrices, as shown in Figure S50\nand S51. These results confirm that the formation of the ferroelectric β-phase in PVDF\nplays a critical role in enhancing electromagnetic wave attenuation.”\nS51 and revised the relevant statements in the revised manuscript accordingly.\nQ12: The claim that the system “overcomes the limitation imposed by Kramers–Kronig\nrelations” is conceptually problematic. These relations are not breakable for causal,\nlinear systems. The authors could instead argue that nonlinear ferroelectric polarization\nand multi-relaxation processes expand the effective response bandwidth.\nReply: We thank the reviewers for your suggestions and have amended our wording in\naccordance with your requirements.\nTo address this comment, we have supplemented the revised manuscript\naccordingly.\nPage 1, Paragraph 1, Line 13-15 in the revised manuscript:\n“The composite system mitigates the apparent loss-bandwidth trade-off, thereby\nachieving broadband polarization properties across multiple frequency bands while\nmaintaining a dissipation efficiency above 99.9%.”\nPage 3, Paragraph 2, Line 5-10 in the revised manuscript:\n“The mediation of polymer interfaces by specific plane orientations was\nsystematically investigated, elucidating the key microscopic factors through which\ninorganic fillers influence the stability of the ferroelectric phase of PVDF. This work\nestablishes the crystal facet control of inorganic fillers as a new variable for\nmanipulating the ferroelectric phase and molecular dipole distribution in PVDF.\nFurthermore, the crystal facet-stabilized PVDF matrix significantly enhances the\noperational stability and reliability of the composite.”\nPage 15, Paragraph 3, Line 4-6 in the revised manuscript:\n“This broadens the relaxation time, thus facilitating highly efficient broadband\nelectromagnetic energy response50.”\nPage 16, Paragraph 2, Line 10-11 in the revised manuscript:\n“Different polarization mechanisms jointly regulate the EM response of the\nmaterial across multiple frequency bands to achieve multi-band EM loss (Figure S67).”\n“This effect arises from the spontaneous polarization induced by the ferroelectric\nphase β-PVDF, leading to a broad distribution of relaxation times and enhances\nmultiple types of polarization mechanisms, with relaxation frequencies across\nmegahertz, gigahertz, and terahertz frequency ranges.”\nPage 84, Paragraph 3, Line 10-11 and Page 85, Paragraph 1, Line 1-2 in the revised\nsupporting information:\n“This multi-relaxation behavior results in pronounced nonlinear dielectric\ncharacteristics, thereby mitigating the apparent loss-bandwidth trade-off, and ultimately\nenables highly efficient electromagnetic energy dissipation simultaneously across\nmultiple frequency bands.”\nQ13: The reported THz shielding effectiveness (≈30 dB for 0.25 mm) is impressive but\ncould also arise from multiple reflection and scattering effects. Consider adding\ncomplex refractive index or impedance spectra to clarify this.\nReply: We thank the reviewer for their positive feedback on our work. Indeed, multiple\nreflection and scattering effects have been identified among the key mechanisms that\nsignificantly influence the electromagnetic wave shielding performance of the material.\nAccording to Schelkunoff’s theory, EMI shielding effectiveness is defined as the\ncombined contribution of three mechanisms for electromagnetic wave attenuation,\nnamely reflection namely reflection (SE ), absorption (SE ) and multiple reflections\nR A\n(SE ). (Nano-Micro Lett., 2021, 13, 181, J. Appl. Phys., 2021, 130, 225108, Nature,\nM\n2025, 647, 356-363, Nature, 2025, 647, 80-85.)\n(R4)\n2\n2\n(𝐸𝑠𝑎𝑚−𝑇)\n𝑇 = |S21| = (𝐸𝑟𝑒𝑓−𝑇) 2\n(R5)\n𝑆𝐸𝑇 = −10log10𝑇\n(R6)\n2\n2\n(𝐸𝑠𝑎𝑚−𝑅)\n𝑅 = |S11| = (𝐸𝑟𝑒𝑓−𝑅) 2\n(R7)\n𝑆𝐸𝑅 = −20log10(1− 𝑅) (R8)\n24\n𝑆𝐸𝐴 = 𝑆𝐸𝑇 −𝑆𝐸𝑅\n(R9)\n−𝑆𝐸𝐴/10\nWhere the , 𝑆𝐸𝑀 = −a2re0 tlhoeg 1 s 0 ig(1na−l e1l0ectric int)ensity of transmission and\ncorresponding re 𝐸 f𝑠e𝑎r𝑚en−c𝑇e, 𝐸 th𝑟𝑒e𝑓 −𝑇 , are the signal electric intensity of\nreflection and corresponding ref𝐸e𝑠r𝑎e𝑚n−ce𝑅 res𝐸p𝑟e𝑒c𝑓t−iv𝑅ely.\nWe conducted terahertz reflection mode testing on the samples, obtaining their\nreflection time-domain spectra. Through these spectra, we determined the samples’ SE\nR\nand SE , subsequently calculating their SE . The figure indicates that multiple\nA M\nreflections constitute a negligible proportion within the PVDF material system (Figure\nR14, R15).\nFigure R14. The THz time-domain spectroscopy of A, P/N{111}-30%, B, P/N{111}-\n40%, C, P/N{111}-50%, D, P/N{100}-30%, E, P/N{100}-40%, F, P/N{100}-50%\nfor reflection mode at 0.2-2.0 THz.\nR A M R A\nSE of P/N{100} at 0.2-2.0 THz.\nM\nWe further calculated the refractive index of the P/N-50% samples, finding that\nP/N{111}-50% exhibits refractive indices similar to P/N{100}-50% and its intensity\nreflectance is calculated to be low using the Fresnel equation (Figure R16) (Nat.\nPhotonics, 2007, 1(3), 176-179.). Concurrently, considering that the wavelength of\nterahertz waves is significantly longer than that of visible light, their scattering effects\nwithin the nanocomposite material are consequently diminished. Given these findings\nand combined with the negligible multiple reflection loss (SE ) calculation results, we\nM\nconclude that the shielding performance of P/N{100}-50% primarily stems from\nabsorption, with limited contributions from multiple reflection and scattering.\n(R10)\n2\n𝑛𝑠𝑎𝑚−𝑛𝑟𝑒𝑓\n𝑅𝑠𝑎𝑚 = |𝑛𝑠𝑎𝑚+𝑛𝑟𝑒𝑓|\nWhere the is the intensity reflectance of the sample and the ,\nare the refractive𝑅 in𝑠𝑎d𝑚ex of the sample and corresponding reference respectiv𝑛e𝑠l𝑎y𝑚. 𝑛𝑟𝑒𝑓\n[Figure Redacted]\nFigure R16. The A, refractive index and B, reflected intensity of P/N-50% at 0.2-2.0\nTHz.\naccordingly.\nPage 14, Paragraph 1, Line 8-12 in the revised manuscript:\n“Through the measurement and calculation of the reflection and multiple\nreflection components within regions of effective shielding, it is determined that the\nshielding performance of P/N{100}-50% is primarily attributed to absorption loss,\nwhile the contributions from multiple reflections and scattering are negligible (Figure\nS57-S59)46-48.”\nTo address this comment, we have supplemented the calculation results in Figure\nS57, S58 and S59 and revised the relevant statements in the revised supporting\ninformation accordingly.\nQ14: The correlation between β-phase fraction and THz attenuation should be\nstatistically supported (e.g., regression of β-phase ratio vs. SE ).\nT\nReply: Following the reviewer’s suggestion, we have performed systematic regression\nanalyses, the results of which strongly validate the proposed mechanism.\nWe compiled the β-phase fraction (calculated via FTIR) and average shielding\neffectiveness in the terahertz band for pure PVDF, P/N{100}, and P/N{111} samples,\nwith specific data presented in Figure R17-R21 and Table R3.\nFigure R17. A, The correlation between β-phase ratio and NiS {100} loading. B, The\nFigure R19. The THz time-domain spectroscopy of A, P/N{100}-20%, B, P/N{100}-\n30%, C, P/N{100}-40%, D, P/N{100}-50% for transmission mode at 0.2-2.0 THz.\n30%, C, P/N{111}-40%, D, P/N{111}-50% for transmission mode at 0.2-2.0 THz.\nFigure R21. A, The total THz shielding effectiveness of P/N-20% and B,\nTransmission of P/N-20% samples at 0.2-2.0 THz.\nTable R3. The β phase ratio and its corresponding average shielding effectiveness\nSample β phase ratio average SE\nT\nPVDF 0.406 3.076\nP/N{100}-20% 0.607 12.007\nP/N{100}-40% 0.813 20.829\nP/N{100}-50% 0.898 21.907\nP/N{111}-20% 0.541 9.965\nP/N{111}-30% 0.660 11.270\nP/N{111}-40% 0.678 12.966\nP/N{111}-50% 0.693 12.803\nUsing the β-phase fraction as the independent variable (X) and average shielding\neffectiveness as the dependent variable (Y), we performed regression analysis on the\nsample data.\nFigure R22. A, The correlation between β-phase fraction and THz attenuation. B, The\nregression of β-phase ratio vs. SE .\nT\nThe analysis reveals a statistically significant linear positive correlation between\nthe two variables. The established regression model (Figure R22) exhibits a high\ngoodness-of-fit (R2 = 0.94442) and significant statistical validity (p = 0.00738),\nproviding solid quantitative evidence that the β-phase ratio is a key factor determining\nthe terahertz attenuation performance.\nThese regression results statistically confirm that as the β-phase content in the\ncomposite material increases, the terahertz shielding performance shows a systematic\nenhancement, further supporting the proposed mechanism in the manuscript that\nenhanced polarization capability of the β-phase contributes to increased terahertz wave\n30\nenergy loss.\nThis outcome is fully consistent with our theoretical mechanism: a higher\nproportion of β-phase PVDF leads to stronger dipole polarization which is the core\nmechanisms responsible for the dissipation of terahertz wave energy.\nTo address this comment, we have supplemented the revised manuscript\naccordingly.\nPage 15, Paragraph 1, Line 1-9 in the revised manuscript:\n“Further analysis indicates a statistically significant linear positive correlation\nbetween β-phase content and terahertz shielding effectiveness (Figure S60-S61). The\nestablished regression model (Table S9, Figure S62) exhibits excellent goodness-of-fit\n(R2=0.94442) and high statistical significance (p=0.00738), providing robust\nquantitative evidence that β-phase content is a key determinant of terahertz attenuation\nperformance. This statistically confirms that as the β-phase content in the sample\nincreases systematically, its terahertz shielding effectiveness demonstrates a linear\ngrowth trend. This outcome is entirely consistent with our proposed theoretical\nmechanism: a higher proportion of β-phase PVDF results in stronger dipole and\ninterfacial polarization, which are primary factors of terahertz wave energy dissipation.”\nTo address this comment, we have supplemented the calculation results in Figure\nS60, S61 and S62, Supporting Table S9 and revised the relevant statements in the\nrevised supporting information accordingly.\nQ15: The SEM/TEM images (Fig. 1B-E) show morphological differences, but facet\nindexing and atomic models should be more explicitly correlated.\nReply: Thank you for your constructive comments. We have revised the schematic\nrepresentations of the structural characterization in Figure 1 accordingly, as detailed\nbelow:\nIn the SEM images shown in Figures 1B and 1D, to clearly reflect the macroscopic\nstructural differences caused by variations in the exposed facets, we have explicitly\n31\nlabeled the corresponding exposed facets in the schematic diagrams of the cube\nstructure (corresponding to the {100} facets) and the octahedral structure\n(corresponding to the {111} facets).\nFurthermore, in the TEM images presented in Figures 1C and 1E, we have\noptimized the original atomic arrangement illustrations by incorporating the unit cell\nstructure model. The circular schematic representations in the actual atomic images\nhave been modified to more accurately reflect the actual crystal structure, thereby\nestablishing a clearer correlation between the microscopic morphology and the atomic\nmodel.\nTo address this comment, we have supplemented the Figure 1 in the revised\nmanuscript accordingly.\nQ16: A surface energy or coordination number comparison would reinforce the claim\nthat {100} facets are more polarizing.\nReply: We thank the reviewer for this important suggestion. Using first-principles\ncalculations, we quantitatively compared the surface energies of different NiS₂ facets.\nThe results show that the surface energy of the {100} facet (0.1460 eV/Å2) is higher\nthan that of the {111} facet (0.1219 eV/Å2). This difference stems directly from their\natomic structures: on the {111} facet, the coordination environment of surface S atoms\nis nearly saturated, whereas on the {100} facet, both surface Ni and S atoms possess a\nhigh density of unsaturated coordination sites (e.g., vacant orbitals on Ni2+ and lone-\npair electron sites on S 2-), leading to higher surface energy. These unsaturated sites\n2\ncreate a high density of local polarization centers, endowing the {100} facet with\n32\nstronger polarity, which significantly enhances interfacial electron coupling and charge\ntransfer capability (as confirmed by charge density difference analysis) (Figure R2).\nThe higher polarity implies that the highly polar {100} facet more readily engages\nin strong dipole-dipole interactions with β-PVDF molecular chains, which also exhibit\nrelatively high surface energy and polarity, thereby serving as the key to inducing and\nstabilizing the strongly polar β-phase of PVDF. Therefore, the higher surface energy\nand more unsaturated coordination environment together constitute the fundamental\nphysicochemical reason why the {100} facet possesses stronger polarizing capability\ncompared to the {111} facet.\nFigure R2. Schematic structure of A, NiS {100} and B, NiS {111}.\n2 2\nWe have included a brief description of the surface energy calculation results in\nthe corresponding section of the manuscript and strengthened the discussion linking\ncoordination environment to polarizing ability in the revised discussion section. We\nbelieve this further supports our core argument with a cohesive chain of evidence. We\nthank the reviewer again for helping us enhance the depth and rigor of this work.\nTo address this comment, we have supplemented the calculation results in Figure\nS7, Table S1, Table S2 and revised the relevant statements in the supporting\ninformation accordingly.\nQ17: The Introduction could better emphasize how this work differs from previous\nPVDF–inorganic interface engineering (e.g., doped or hybridized PVDF systems).\na comparison between this work and previous studies on PVDF-inorganic interface\nengineering to highlight the novelty of our research. Following your suggestion, we\nhave supplemented and strengthened this aspect in the Introduction section of the\nrevised manuscript (Table R4).\nTable R4. Preparation, Formation Mechanism, and Content of the β-phase in PVDF\nsamples\nβ-phase\nMechanism for the\nSample Processing techniques content Ref.\nformation of β-phase\n(F(β) (%))\nThe electrostatic\ninteractions between\nPVDF/Gold Polymers,\nSolution casting from DMF surface charge Au\nnanoparticle 66.0 2020, 12,\nsolution. nanoparticles and CF\ns (Au) 2630\ndipoles in the PVDF\nchain.\nThe surface charge\nPVDF/Zinc interaction between ZnO Polym. Adv.\noxide Solution casting from DMF nanoparticles and PVDF Technol.\n76.1\nnanorods solution. dipoles responsible for 2018, 29,\n(ZnO) the enhancement of β 143-150.\nphase.\nDue to nucleating effect Macromol.\nPVDF/bariu\n3D printing and in situ of BaTiO . Mater. Eng.\n3\nm titanate 55.9\npoling. 2017, 302,\n(BaTiO )\n3\n1700229\nstretching, and\nACS Appl.\nsimultaneous local poling\nMater.\nElectrospinning at applied during the\nPVDF/BaTi Interfaces\nvoltage of 10 kV and flow electrospinning processes 91.0\nO 2020, 12,\n3\nrate of 2 mL h-1. are responsible for the\n33989-\ntransformation of the α-\n33998\nphase into the polar β-\nphase.\nPVDF/GO The interface bonding Mater. Des.\ncomposite Selective laser sintering between GO and PVDF 49.1 2020, 190,\nscaffolds 108564\nDue to the fluorine group\nPVDF/fluori in GOF, which can trap ACS Omega\nnated GO Electrospinning electrons and lead to large 89.0 2018, 3,\n(GOF) charge accumulation at 5317-5326\nthe interface.\nThe specific interactions\nPVDF/Bi Al between the Bi3+/Al3+\nO /rGO- nanorods with CF\n4 9 2\nCompd.\nbased Solution casting dipoles of PVDF and the 76.0\n2020, 843,\nnanocompos O2– nanorods of Bi Al O\n2 4 9\n156019\nite with CH dipoles of\nThe electrostatic ACS\nNiO@SiO 2 / interaction between the Sustainable\nSolution casting 80.0\nPVDF positive CH group of Chem. Eng.\n35\ncharged surface of the 10505-\nNiO@SiO nanoparticles 10516\nPVDF/ZnO attraction between CH in J. 2021,\n@C the PVDF segment and 426,\nthe carbon surface 130345\nHeating to the temperature The modified dipole\nPVDF/BaTi at the set value at a rate of interaction between\nPolym. Test.\nO 40 °C/min respectively and oxygenic groups attached\n3\n79.0 2024, 138,\nnanocompos stretching at a constant to the BaTiO and\n3\n108516\nites strain rate of 50 μm s−1 until CH /CF in PVDF.\n2 2\nbreak.\nAtomic-scale interface\nNiS {100}/P\n2\ninteractions between\nVDF\nHot press PVDF chains and NiS 89.8 This work\n2\nwith different crystal\nVDF\nfacets\nThis study breaks through the conventional paradigm of regulating PVDF\nperformance by altering filler “type”, and pioneers the introduction of “crystal facet\nengineering” into this system. Instead of merely selecting different inorganic fillers, we\nachieve precise and controllable modulation at the atomic scale by accurately\ncontrolling the exposure of specific crystal facets ({100} vs. {111}). We systematically\ninvestigate how specific plane orientations mediate differential interactions of polymer\nchains at the interface, elucidating the key microscopic factors through which inorganic\nfillers influence the stability of the ferroelectric phase in PVDF. This work establishes\ncrystal facet control of inorganic fillers as a new variable for manipulating the\nferroelectric phase and molecular dipole distribution in PVDF. It reveals that, due to\ndifferences in atomic arrangement and electronic structure, different crystal facets\n36\nexhibit fundamentally distinct interfacial interactions with PVDF molecular chains.\nThis deepens the understanding from a generalized “surface effect” to a microscopic\nmechanism based on adsorption energy, surface energy, and charge transfer. Ultimately,\nthis strategy not only effectively enhances the β-phase content but also synergistically\noptimizes its thermodynamic stability and dielectric/ferroelectric activity. It represents\nan advancement in the structure-property relationship from merely pursuing content to\nthe co-design of quality and function, providing a rational and controllable new\nparadigm for developing high-performance ferroelectric polymer-based\nelectromagnetic functional materials.\nWe have incorporated the comparative analysis and discussion above into the\nIntroduction and Discussion sections of the revised manuscript. We believe this will\nallow the unique contributions and innovative value of this work relative to existing\nresearch to be presented more accurately and convincingly.\nTo address this comment, we have supplemented the presentation of the\nintroduction in the revised manuscript accordingly.\nPage 3, Paragraph 2, Line 5-10 in the revised manuscript:\n“The mediation of polymer interfaces by specific plane orientations was\nsystematically investigated, elucidating the key microscopic factors through which\ninorganic fillers influence the stability of the ferroelectric phase of PVDF. This work\nestablishes the crystal facet control of inorganic fillers as a new variable for\nmanipulating the ferroelectric phase and molecular dipole distribution in PVDF.\nFurthermore, the crystal facet-stabilized PVDF matrix significantly enhances the\noperational stability and reliability of the composite.”\nComments: Facet-Modulated Ferroelectric Polymers-Major comments to the authors:\nThe present work tried to correlate the effect of facets of the crystal on the PVDF\nstructure and its properties is a novel idea for research, however, the approach the\nauthors followed requires further improvements with following\nsuggestions/modifications/required new experiments.\nReply: We are very grateful for the recommendations and positive comments made by\nthe reviewer. The concerns of the reviewer are thoroughly addressed in a point-by-point\nmanner as follows, upon which the manuscript is revised accordingly.\nHere are my comments:\nQ1: The individual crystal facet implication on the β-phase of PVDF has been\nelaborated, however, the quantitative analysis of increase in β-phase as a function of\nparticle size distribution and shape distribution is required as the physical properties\nmeasured are average properties of over the area of the samples. Hence it is desired to\nunderstand the shape and size distributions and their effect on β-phase is required.\nReply: We thank the reviewer for this important and constructive suggestion. In\naccordance with your suggestion, we have conducted supplemental experiments\ninvolving NiS nanoparticles with different size and shape distributions, and have\n2\nquantitatively analyzed the increase of β-phase content with respect to these two\nparameters. The detailed supplementary experiments and analyses are provided below.\n1. Effect of Nanoparticle Size on β-phase Content\nThrough systematic analysis of SEM images of three different-sized NiS\n2\nnanoparticles with {100} facets, we quantified their size distribution (132±6 nm,\n272±14 nm, 320±10 nm) (Figure R23). Under fixed filler loading conditions (20 wt.%),\nwe compounded these three distinct-sized {100}-facet NiS nanoparticles with PVDF,\n2\nrespectively, establishing three sample systems: P/N{100}-132, P/N{100}-272,\nand\nP/N{100}-320.\nAccording to the XRD and FTIR results (Figure R24 and Table R5), the β-phase\ncontent of the samples shows an increasing trend with decreasing particle size. This can\nbe primarily attributed to the significant increase in the specific surface area of the\nparticles as their size decreases, which leads to a greater total exposed area of the\nspecific, active crystal facets (such as the {100} facet). Consequently, this promotes the\nenhancement of the β-phase content.\nP/N{100}-272 and P/N{100}-320 samples.\nTable R5. The β phase ratio in sample with nanoparticles of different sizes\nSample β phase ratio\nP/N{100}-132 0.622\nP/N{100}-272 0.615\nP/N{100}-320 0.607\nTo further validate this conclusion, we tested the electromagnetic parameters of\nthe different-sized samples in the GHz frequency range. The results show that as\nparticle size decreased, the real part of the complex permittivity (ε′) exhibited a slight\nincrease, while the imaginary part (ε″) remained relatively stable. This trend aligns with\nthe FTIR analysis observations regarding β-phase content variation with size (Figure\nR25).\nReal part of permeability and D, Imaginary part of permeability of P/N{100}-132,\nP/N{100}-272 and P/N{100}-320 samples.\n2. Effect of Nanoparticle Shape on β-phase Content\nWe systematically compared samples with cubic morphology (corresponding to\nthe {100} facet), octahedral morphology (corresponding to the {111} facet), and\nirregular morphology. The irregular morphology NiS /PVDF (denoted as P/N) was\n2\nsynthesized by randomly oriented NiS nanoparticles without specific facet control into\n2\nthe PVDF matrix. SEM analysis confirmed its random morphology. Meanwhile, all\npreparation conditions and filler loadings were maintained identical for both the cubic\nand octahedral samples to ensure the validity of the comparison (Figure R26).\n2 2\nμm (B), 500 nm (C).\nWe systematically compared the P/N sample with the facet-specific P/N{100} and\nP/N{111} in terms of critical performance metrics, the β-phase fraction induced by the\nP/N-random sample was notably lower than that achieved by the P/N{100} sample\n(Figure R27, R28, Table R6).\nFigure R27. XRD profiles of P/N, P/N{111} and P/N{100}. A, 15 wt.%, B, 25\nwt.%.\nwt.%, B, 25 wt.%.\nTable R6. The β phase ratio of P/N, P/N{111} and P/N{100}\nSample β phase ratio\nP/N-15% 0.477\nP/N{111}-15% 0.472\nP/N{100}-15% 0.496\nP/N-25% 0.587\nP/N{111}-25% 0.603\nP/N{100}-25% 0.637\nThe dielectric constant of the P/N-random sample in the 2-18 GHz frequency range\nwas substantially lower than that of the P/N{100} sample. Furthermore, with increasing\nfiller loading, its dielectric constant also remained inferior to that of the P/N{100} and\nP/N{111} (Figure R29).\npermittivity of P/N, P/N{111} and P/N{100} samples at EMWs from 2 GHz to 18\nGHz.\nThese comparative results strongly indicate that NiS itself can moderately\n2\npromote β-phase formation, while full exposure of its {100} facet enables a more\neffective enhancement of β-phase content. Furthermore, the induced β-phase content\nexhibits a positive correlation with the exposed area of the {100} facet. This facet-\ndependent behavior robustly supports our proposed mechanism of crystal facet-induced\nferroelectric phase transition and highlights the critical role of facet engineering in\nregulating and enhancing β-phase content.\nWe believe this additional work significantly enhances the rigor and\npersuasiveness of the manuscript. We once again thank the reviewer for their invaluable\ninput, which has helped us improve the quality of this study.\nmanuscript accordingly.\nPage 7, Paragraph 1, Line 14-18 in the revised manuscript:\n“The filler loading (Figure S19, S20 and Supplementary Table S4), shape\ndistributions (Figure S21-S23 and Supplementary Table S5) and filler size (Figure S24,\nS25 and Supplementary Table S6) was systematically varied. Through comparative\nanalysis, the effects of these macroscopic geometric variables were isolated, thus\nestablishing the specific crystal facet as a core variable in influencing performance.”\nPage 12, Paragraph 1, Line 1-4 in the revised manuscript:\n“The comparative analysis of the electromagnetic parameters of NiS with varying\n2\nsize and shape distributions further underscores the critical role of specific crystal facets\nin regulating β-PVDF content (Figure S42, S43).”\nTo address this comment, we have supplemented the results in Figure S21, S22\nS23, S24, S25, S42 and S43, Supplementary Table S5 and Supplementary Table S6 and\nrevised the relevant statements in the revised supporting information accordingly.\nQ2: A clear comparison between the PFM results for pure PVDF and composite is\nrequired. The effect of enhancement of β-phase on the PFM related physical quantities\nmust be emphasized. The piezoelectric tensor matrix analysis for the pure and\ncomposites has to be incorporated with respect to observed PFM results.\nReply: We thank the reviewer for this important comment. Following your suggestions,\nwe have systematically compared the PFM results between pure PVDF and the\ncomposite (Figure R30), emphasized the effect of β-phase enhancement on PFM\nphysical quantities, and supplemented the analysis based on the piezoelectric tensor\nmatrix. Our detailed responses are provided below:\n1. Clear comparison of PFM results between pure PVDF and composites\nWe have supplemented quantitative comparative data (Table R7), with the key\nPFM parameters as follows:\nTable R7. the key PFM parameters between pure PVDF and composites\nParameter Piezoelectric Amplitude Phase Contrast (°)\n(pm∙V-1)\nPure PVDF - -\nP/N{111} 105.18 ± 0.46 179.79 ± 0.11\nP/N{100} 215.31 ± 1.59 177.75 ± 1.05\nPure PVDF did not exhibit significant piezoelectric response, indicating its\ninherent lack of prominent piezoelectric properties (Figure R30). In contrast, both\nP/N{111} and P/N{100} demonstrated strong PFM amplitude signals, with P/N{100}\nshowing notably larger amplitude, suggesting higher local piezoelectric coefficients\nand stronger electromechanical coupling efficiency. Furthermore, the phase curves of\nboth samples were similar with a phase difference approaching 180°, further confirming\ntheir consistent out-of-plane polarization orientation.\n2. Effect of β-phase enhancement on PFM physical quantities\nWe have placed particular emphasis on the structure-property relationship\nbetween β-phase content and the enhancement of PFM signals. The all-trans\nconformation of β-phase PVDF gives it the highest spontaneous polarization strength\nand piezoelectric coefficients among all crystalline phases. The enhancement in both\nPFM amplitude and phase serves as direct evidence at the nanoscale of the increased β-\nphase proportion. A higher β-phase content implies a greater net dipole moment that\n46\ncan be mechanically detected (amplitude) and an electrically switchable polarization\ndirection (phase). We have strengthened the explanation of this mechanism in the\nmanuscript.\n3. Analysis Integrating Piezoelectric Tensor Matrix with PFM Results\nBuilding upon the PFM findings, we have incorporated an analysis based on the\npiezoelectric tensor matrix:\nPure PVDF (predominantly α-phase): Its piezoelectric tensor contains limited non-\nzero elements, and the intrinsic value of the out-of-plane response component d₃₃ is\nvery small, which aligns with the weak PFM signals observed in pure PVDF.\nP/N{111} and P/N{100} (predominantly β-phase): The β-phase belongs to a polar\nphase, and its piezoelectric tensor takes the form (Adv. Mater. 2016, 28, 7633-7639,\nAdv. Mater., 2019, 31, 1901378):\n(R11)\nd11 d12 d13 d14 d15 d16\nd =\n[d21 d22 d23 d24 d25 d26\n]\nThe significantly enhancde3d1 oudt-3o2f-pdla3n3e pdie3z4oeldec35tric dre3s6ponse in both P/N{111}\nand P/N{100} samples primarily originates from the non-zero d piezoelectric\n33\ncoefficient characteristic of the β-phase. The notable increase in PFM amplitude\ndirectly reflects the activation and dominant role of the β-phase d component.\nThe\n33\ntransition from pure PVDF (α-phase dominant) to the composite (β-phase dominant)\nfundamentally represents an evolution of the material’s piezoelectric tensor from a low-\nactivity to a high-activity form. This transformation process aligns perfectly with the\ncrystal physics mechanism governed by the dominant role of the β-phase d component.\nthe {100} facet of NiS in inducing β-phase formation, thereby yielding a more\n2\npronounced out-of-plane piezoelectric enhancement effect. Based on the\n47\naforementioned analysis, the PFM results conclusively demonstrate the differential\ninduction of the ferroelectric β-phase in PVDF.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 9, Paragraph 2, Line 16-18 in the revised manuscript:\n“Moreover, the P/N{100} exhibits a larger piezoelectric coefficient with\nd =215.31 pm∙V-1, indicating that the {100} crystal facet can induce the ferroelectric\n33\nphase transition of PVDF at a higher efficiency (Figure S28-S31, Table S7)26.”\nTo address this comment, we have supplemented the results in Figure S28, S29 and\nS30, Supplementary Table S7 and revised the relevant statements in the revised\nsupporting information accordingly.\nQ3: However, the butterfly loop is not fully saturated, the reason and a comparison\nwith earlier literature need to be incorporated.\nReply: Thank you to the reviewer for their keen observation. This phenomenon is\nrelatively common in conductive filler/ferroelectric polymer sample systems. The main\nreason for the unsaturated loops lies in the leakage current generated by the sample\nunder high-voltage testing due to the introduction of conductive NiS fillers. This\n2\nleakage current superimposes on the intrinsic polarization signal from ferroelectric\ndomain switching, preventing the loops from achieving full saturation and resulting in\nthe observed slender shape (Ceram. Int., 2021, 47, 23659-23664). This phenomenon\nhas also been reported in similar conductive filler/ferroelectric polymer systems (such\nas graphene/PVDF composites (J. Mater. Chem. A, 2023, 11, 4280-4291)) and\nrepresents a common challenge in the study of such materials.\nWe note that similar non-saturated P-E loops have been repeatedly reported in\nrelated studies on ferroelectric composites (Adv. Mater., 2021, 33, 2106308, J. Mater.\nChem. A, 2023, 11, 4280-4291, Nat. Commun., 2024, 15, 4702, Nat. Commun., 2025,\n16, 3071). The phenomenon of filler-induced leakage currents leading to loop non-\n48\nsaturation is observed in such material systems. Therefore, the behavior observed in our\nstudy aligns with the general physical mechanism common to this class of materials.\nAlthough the incomplete saturation of the loops may affect the absolute accuracy\nof the ferroelectric parameters, all samples were prepared and measured under identical\ntesting conditions. Therefore, these data remain effective for comparing the relative\ndifferences in ferroelectric performance among different samples (e.g., P/N{100} vs.\nP/N{111}).\nTo address this comment, we have supplemented the results in Supplementary\nTable S7 and revised the relevant statements in the revised supporting information\naccordingly.\nQ4: The title “Facet-Modulated Ferroelectric Polymers” showcases the ferroelectric\nnature of the composite, however the ferroelectric properties such as Polarization versus\nElectric field and Analysis of Curie’s Temperature from temperature dependent\ndielectric properties has not been incorporated. The authors are strongly suggested to\nincorporate the same for further consideration.\nReply: Thank you for this important comment. Following your suggestion, we have\nsupplemented key ferroelectric characterizations and analyses, as detailed below:\n1. Supplementary Ferroelectric P-E Hysteresis Loop Data\nWe have supplemented the measurements of macroscopic ferroelectric P-E\nhysteresis loops (Polarization vs. Electric field) for pure PVDF and composites with\ndifferent crystal facets (20 wt.%). The relevant data are shown in Figure R31.\nCompared to pure PVDF and the P/N{111}, the P/N{100} demonstrates a significantly\nenhanced remnant polarization (P) and higher saturation polarization (P ). This directly\nr s\nconfirms the superior role of the {100} facet in improving the macroscopic ferroelectric\npolarization of the sample. This enhancement in macroscopic ferroelectric performance\nis fully consistent with our PFM observations—namely, the stronger local piezoelectric\nresponse (higher d ) and higher β-phase content. Together, these results form a\n33\ncomplete chain of evidence from microstructure to macroscopic performance.\n2. Clarification Regarding Curie Temperature Analysis\nWe performed temperature-dependent dielectric measurements on pure PVDF and\ntwo composites, P/N{111}-20% and P/N{100}-20%, over a temperature range of 20°C\nto 150°C at multiple frequencies: 10 kHz, 100 kHz, 1 MHz, and 2 MHz (Figure R32).\nThe results show that pure PVDF exhibits no distinct dielectric peak across the entire\ntemperature-frequency range, and its dielectric constant shows little variation with\nfrequency, indicating typical non-ferroelectric characteristics. In contrast, P/N{100}-\n20% exhibits more pronounced relaxor ferroelectric behavior than P/N{111}-20%,\nwith its dielectric peak observed around 40-42°C. This can be explained as a\nferroelectric-to-paraelectric phase transition near the Curie temperature (Nat. Mater.,\n2023, 22, 873-879). Moreover, the more distinct dielectric peak of P/N{100}-20%\nshifts slightly toward higher temperatures with increasing frequency, accompanied by\na gradual decrease in peak intensity, demonstrating clear characteristics of a diffuse\nphase transition (Science, 2022, 375, 1418-1422). Further comparison reveals that the\nP/N{100}-20% not only exhibits a higher dielectric constant but also a more\npronounced dielectric peak, indicating more definite ferroelectric properties in this\ncomposite.\nP/N{111}-20%, C, P/N{100}-20%.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 9, Paragraph 2, Line 18-27 in the revised manuscript:\n“Macroscopic ferroelectric performance tests at room temperature were conducted\non pure PVDF, P/N{111}, and P/N{100} samples. The measurement results (as shown\nin Figure S32) clearly demonstrate that the P/N{100} exhibits a typical ferroelectric P-\nE hysteresis loop with well-defined remnant polarization (P) and coercive field (E ).\nr c\nCompared to pure PVDF and P/N{111}, P/N{100} shows significantly higher remnant\npolarization (P) and saturation polarization (P )27. This result directly confirms that the\nr s\n{100} facet not only induces the formation of a local ferroelectric phase in PVDF (as\nrevealed by PFM phase hysteresis) but also enables the composite to exhibit enhanced\nand switchable ferroelectric polarization at the macroscopic level. Meanwhile,\ntemperature-dependent dielectric measurements demonstrate pronounced relaxor\nferroelectric behavior in P/N{100} (Figure S33)1, 27”\nTo address this comment, we have supplemented the results in Figure S32, S33 and\nrevised the relevant statements in the revised supporting information accordingly.\nComments: The manuscript by B. Cai et al. reports a method for preferential\ncrystallization of the ferroelectric β-phase of PVDF on specific facets of NiS\n2\nnanocrystals. The authors attribute this effect to enhanced S-H interactions at the {100}\nsurface. However, the experimental data do not convincingly support this conclusion,\nand several key interpretations are either incomplete or unsupported.\nReply: We sincerely appreciate the time you have taken to review our manuscript, and\nfor the highly constructive and insightful comments you have provided. In response to\nthe reviewer’s critiques, we have supplemented the study with necessary experimental\ndata, essential characterizations, and calculation work, thereby enhancing the depth of\nthe mechanistic investigation. Below, we present a summary of our additional efforts\nand responses.\nHere are my comments:\nQ1: The XRD diffractograms (Figs. 2A, B and S11) show a dominant β-phase peak in\nall sample, while the differences in FTIR spectra are minimal and even disappears at\n25% NiS loading (Figs. 2C, D and S12). These variations fall within the usual batch-\n2\nto-batch variability of PVDF and cannot be taken as solid evidence of facet-induced β-\nphase enhancement.\nReply: To rigorously address your concern regarding the batch-to-batch variability of\nPVDF, we conducted supplementary experiments and analyses using PVDF from\nindependent batches. We also incorporated new critical experimental evidence to\nenhance the reliability of our conclusions. The details are outlined below:\nFirst, we clarify that all original data in this study were based on PVDF raw\nmaterial from a single batch. To directly respond to your concern about batch variability,\nwe performed a systematic verification experiment: we selected two additional,\nindependent batches of PVDF raw material and, under conditions identical to the\noriginal experiment, resynthesized the core P/N{100} and P/N{111} (labeled P/N-2\nand P/N-3, respectively, with the original system labeled P/N-1). These samples were\n52\ncharacterized by XRD and FTIR under the same testing conditions, followed by\nquantitative analysis.\nThe results show that within the PVDF systems from both independent batches,\nthe β-phase content of P/N{100} remains systematically higher than that of P/N{111},\nfully reproducing the core finding of the original study (Figure R33, R34, Table R8).\nThis conclusively demonstrates that the observed difference in β-phase content between\nthe crystal facets is a reproducible, robust, and systematic trend independent of the\nPVDF raw material batch, further supporting the reliability of the facet effect in\nenhancing β-phase PVDF content.\nFigure R33. XRD profiles of A, P/N{100}-15%-1, 2, 3, B, P/N{100}-20%-1, 2,\n3, C, P/N{100}-25%-1, 2, 3 samples and FTIR transmission of D, P/N{100}-15%-1,\n2, 3, E, P/N{100}-20%-1, 2, 3, F, P/N{100}-25%-1, 2, 3 samples.\n3, C, P/N{111}-25%-1, 2, 3 samples and FTIR transmission of D, P/N{111}-15%-1,\n2, 3, E, P/N{111}-20%-1, 2, 3, F, P/N{111}-25%-1, 2, 3 samples.\nTable R8. The β phase ratio in sample with nanoparticles of different batches\nSample β phase ratio Batch\nP/N{100}-15%-1 0.4962\nP/N{100}-15%-2 0.5050 {100}-15%\nP/N{100}-15%-3 0.5072\nP/N{100}-20%-1 0.6067\nP/N{100}-20%-2 0.5809 {100}-20%\nP/N{100}-20%-3 0.5948\nP/N{100}-25%-1 0.6366\nP/N{100}-25%-2 0.6268 {100}-25%\nP/N{100}-25%-3 0.6469\nP/N{111}-15%-1 0.4716\nP/N{111}-15%-2 0.4706 {111}-15%\nP/N{111}-15%-3 0.4513\nP/N{111}-20%-1 0.5406 {111}-20%\n0.5658\nP/N{111}-20%-3\nP/N{111}-25%-1 0.6028\nP/N{111}-25%-2 0.6039 {111}-25%\nP/N{111}-25%-3 0.5963\nWe have further supplemented the systematic characterization data of materials\nfabricated using the same batch of PVDF but compounded with NiS nanoparticles of\n2\ndifferent morphologies and sizes. This provides additional supporting evidence for the\nconclusion that the enhancement of the β-phase is induced by specific crystal facets.\nWe systematically compared samples with cubic morphology (corresponding to\nthe {100} facet), octahedral morphology (corresponding to the {111} facet), and\nirregular morphology. The irregular morphology NiS /PVDF (denoted as P/N) was\n2\nsynthesized by randomly oriented NiS nanoparticles without specific facet control into\n2\nthe PVDF matrix. SEM analysis confirmed its random morphology. Meanwhile, all\npreparation conditions and filler loadings were maintained identical for both the cubic\nand octahedral samples to ensure the validity of the comparison (Figure R35).\nFigure R35. Scanning electron microscopy (SEM) image of A, NiS {100}, B,\n2 2\nμm (B), 500 nm (C).\nWe systematically compared the P/N sample with the facet-specific P/N{100} and\nP/N{111} in terms of critical performance metrics, the β-phase fraction induced by the\nP/N-random composite was notably lower than that achieved by the P/N{100} sample\n(Figure R36, R37, Table R9).\nwt.%.\nFigure R37. The FTIR transmission of P/N, P/N{111} and P/N{100}, A, 15\nwt.%, B, 25 wt.%.\nTable R9. The β phase ratio of P/N, P/N{111} and P/N{100}\nSample β phase ratio\nP/N-15% 0.477\nP/N{111}-15% 0.472\nP/N{100}-15% 0.496\nP/N-25% 0.587\nP/N{111}-25% 0.603\nP/N{100}-25% 0.637\nrange was substantially lower than that of the P/N{100} sample. Furthermore, with\nincreasing filler loading, its dielectric constant also remained inferior to that of the\nP/N{100} and P/N{111} (Figure R38).\nFigure R38. A, B, Real part of permittivity and C, D, Imaginary part of\npermittivity of P/N, P/N{111} and P/N{100} at EMWs from 2 GHz to 18 GHz.\nUsing the same batch of PVDF, we separately compounded it with three different-\nsized NiS {100} nanoparticles to fabricate a series of composites (denoted as\nthese three NiS nanoparticles with {100} facets, we quantitatively characterized their\n2\nsize distribution. The results are 132±6 nm, 272±14 nm, and 320±10 nm, respectively\n(Figure R39).\nAccording to the XRD and FTIR results (Figure R40 and Table R10), the β-phase\ncontent of the samples shows an increasing trend with decreasing particle size. This can\nbe primarily attributed to the significant increase in the specific surface area of the\nparticles as their size decreases, which leads to a greater total exposed area of the\nspecific, active crystal facets (such as the {100} facet). Consequently, this promotes the\nenhancement of β-phase content.\nP/N{100}-272 and P/N{100}-320 samples.\nTable R10. The β phase ratio in sample with nanoparticles of different sizes\nSample β phase ratio\nP/N{100}-132 0.622\nP/N{100}-272 0.615\nP/N{100}-320 0.607\nTo further validate this conclusion, we tested the electromagnetic parameters of\nthe different-sized samples in the GHz frequency range. The results show that as\nparticle size decreased, the real part of the complex permittivity (ε′) exhibited a slight\nincrease, while the imaginary part (ε″) remained relatively stable. This trend aligns with\nthe FTIR analysis observations regarding β-phase content variation with size (Figure\nR41).\nReal part of permeability and D, Imaginary part of permeability of P/N{100}-132,\nP/N{100}-272 and P/N{100}-320 samples.\nIn summary, through a series of experiments and analyses—including the use of\nPVDF raw material from the same batch, conducting reproducibility syntheses, and\nsystematically controlling filler size and morphology—we confirm that the observed\ndifferences in β-phase content are not due to random material fluctuations but represent\na systematic trend. The fundamental cause of this trend lies in the differentiated\ninterfacial interactions between the distinct crystallographic facets of NiS and the\n2\nmolecular chains of PVDF. We believe that these supplementary efforts and in-depth\nanalyses have significantly enhanced the reliability of the data and the rigor of the\nconclusions in this study. Once again, we sincerely thank you for your profound and\nprofessional review.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 7, Paragraph 1, Line 11-18 in the revised manuscript:\n60\n“As illustrated in Figure 2C, 2D, S17, S18 and Table S3, NiS with different\n2\ncrystal facets induces differing ratios of β-phase PVDF, where P/N{100} exhibits a\nhigher β-phase PVDF content. The observed pattern aligns with the conclusions derived\nfrom analysis of XRD results. The filler loading (Figure S19, S20 and Supplementary\nTable S4), shape distributions (Figure S21-S23 and Supplementary Table S5) and filler\nsize (Figure S24, S25 and Supplementary Table S6) was systematically varied. Through\ncomparative analysis, the effects of these macroscopic geometric variables were\nisolated, thus establishing the specific crystal facet as a core variable in influencing\nperformance.”\nPage 12, Paragraph 1, Line 1-4 in the revised manuscript:\n“The comparative analysis of the electromagnetic parameters of NiS with varying\n2\nsize and shape distributions further underscores the critical role of specific crystal facets\nin regulating β-PVDF content (Figure S42, S43).”\nTo address this comment, we have supplemented the results in Figure S17-S25,\nS42 and S43, Supplementary Table S3-S6 and revised the relevant statements in the\nrevised supporting information accordingly.\nQ2: A more fundamental issue is that the influence of processing conditions is barely\naddressed. It is well known that mechanical stretching and elevated temperatures\npromote α- to β-phase transition in PVDF [https://doi.org/10.1039/C3RA45134H]. The\nhot-pressing method used by the authors can itself induce β-phase formation, with\nnanoparticles acting as stress concentrators. A similar effect has already been reported\nfor PVDF-BaTiO system [https://doi.org/10.1016/j.polymertesting.2024.108516]. The\n3\nauthors fail to decouple the contribution of thermal–mechanical processing from any\nalleged facet-specific effects.\nReply: We have explicitly included pure PVDF samples subjected to identical hot-\npressing conditions as a key control in the revised manuscript. As shown in Figure R42-\nR44, despite undergoing the same hot-pressing process, the β-phase content of pure\nPVDF (0.406) is significantly lower than that of all P/N samples. This result\n61\ndemonstrates that hot-pressing treatment alone is insufficient to account for the\nmarkedly high β-phase content observed in the samples.\nFigure R42. A, XRD profiles and B, FTIR transmission of PVDF.\nFigure R43. A, The correlation between β-phase ratio and NiS {100} loading. B, The\nFigure R44. A, The correlation between β-phase ratio and NiS {111} loading. B, The\nThe reviewer notes that nanoparticles can act as stress concentrators. To\ninvestigate whether β-phase formation primarily stems from hot-pressing-induced\nmechanical stress, we added new experimental evidence.\n2\na control nanoparticle system. With particle sizes comparable to NiS , SiO should\n2 2\ngenerate similar stress concentration effects during hot-pressing (Figure R45). We\nprepared SiO /PVDF composites with the same filler loading as NiS and characterized\n2 2\ntheir electromagnetic parameters. As shown in Figure R46, the variation in properties\nwith changing SiO content was negligible. This suggests that the stress concentration\n2\neffect of nanoparticles during hot-pressing contributes only minimally to PVDF phase\ntransition, likely due to the relatively low stress levels involved.\nFigure R45. A, SEM images and B, the particle size distribution of SiO .\nReal part of permeability and D, Imaginary part of permeability of SiO /PVDF-15%,\n2 2\n3\npromoting β-phase formation through stretching. However, the superior induction\ncapability of the {100} facet of NiS in this work likely stems from a mechanism that\n2\nextends beyond physical stress. Our DFT calculations reveal stronger interfacial\nelectronic coupling between the {100} facet and PVDF molecules, manifested as more\nsignificant charge transfer. This provides a more favorable thermodynamic driving\nforce for the nucleation and stabilization of the β-phase.\nThus, the role of facet engineering is to provide a more efficient nucleation\ninterface, while the hot-pressing process primarily supplies the kinetic environment that\nfacilitates molecular chain motion and rearrangement. The two factors act\nsynergistically, but the specificity of the crystal facet ultimately determines the\neffectiveness of the final outcome.\nTo address this comment, we have supplemented the results in Figure S14, S19,\nS20, Supplementary Table S4 and revised the relevant statements in the revised\nsupporting information accordingly.\nQ3: The characterization of the PVDF/NiS composites physical properties also raises\n2\nconcerns. The PFM data are not convincing. V-shape amplitude loops such of those in\nFigs. 3E, G are typical of electrostatic artefacts caused by tip-sample interaction, not of\ngenuine piezoresponse [https://doi.org/10.1016/j.ultramic.2019.112839]. For samples\ndominated by non-polar α-phase, the authors should have used stiffer AFM probes,\ncontrolled surface potential via KPFM, and performed PFM in both contact and non-\ncontact modes to verify that the response is truly piezoelectric rather than electrostatic.\nReply: We thank the reviewer for this important comment. To directly address your\nconcerns regarding potential electrostatic artifacts, we have systematically optimized\nour experimental approach and supplemented key verifications. Specifically, in the\nadditional PFM measurements, a conductive probe with higher stiffness (k = 20 N/m)\nwas used to suppress long-range electrostatic forces. To eliminate the influence of\nelectrostatic fields on the piezoelectric response, we first performed surface charge\nremoval on the sample using an ion beam and measured its surface potential via Kelvin\n64\nprobe force microscopy (KPFM) (Figure R47). Subsequently, during PFM testing, we\napplied a direct-current bias of equal magnitude but opposite polarity to the measured\nsurface potential over the same region to compensate for the surface potential. A\ncomparison of the PFM signals before and after compensation revealed no significant\nchange in the piezoelectric response of the sample. This result indicates that the\nobserved signal originates from the intrinsic piezoelectric properties of the material\nrather than from electrostatic artifacts. Furthermore, newly acquired local switching\nspectroscopy piezoresponse force microscopy (SS-PFM) imaging provides direct\nevidence of ferroelectric polarization switching behavior. Together, this new\nexperimental evidence indicates that the signals we observed originate from genuine\npiezoelectric/ferroelectric responses, rather than electrostatic artifacts.\nFigure R47. The KPFM surface potential for A, pure PVDF, B, P/N{111} and C\nP/N{100}.\nBy comparing the test results before and after compensation on the sample surface\nand contrasting them with the PFM results of non-polar α-phase PVDF, we confirmed\nthat the P-E loops obtained from polar β-phase PVDF samples exhibit definitive and\nreproducible characteristics. These loops are accompanied by an approximately 180°\nphase reversal, and the reversal points correlate with the extreme points of the\namplitude loops. Thus, we conclude that the piezoelectric response arises from\nferroelectric polarization switching behavior in the β-phase PVDF samples, rather than\nfrom electrostatic artifacts (Figure R48-R50).\nPVDF before compensation and C, D, pure PVDF after compensation.\nFigure R49. The PFM phase and amplitude hysteresis loops measured for A, B,\nP/N{111} before compensation and C, D, P/N{111} after compensation.\nP/N{100} before compensation and C, D, P/N{100} after compensation.\nIn parallel, to investigate direct evidence of domain switching, we performed local\nswitching spectroscopy piezoresponse force microscopy (SS-PFM) imaging on regions\nwith the same domain size within the samples. The intrinsic coercive voltage ( ) and\nthe intrinsic internal bias voltage ( ) are the relevant parameters that determ\n𝑉\nin𝑐e the\ndomain switching behavior. Their e\n𝑉\nx𝑖pressions are:\n(R12)\n|𝑉𝑝|+|𝑉𝑛|\n𝑉𝑐 = 2\n(R13)\n|𝑉𝑝|−|𝑉𝑛|\n𝑉𝑖 = 2\nwhere represents the switching voltage when the DC voltage changes from\nnegative to p𝑉𝑝ositive, while indicates the switching voltage when the DC voltage\nchanges from positive to neg\n𝑉\na𝑛tive (Adv. Funct. Mater., 2025, 35, 2413130).\nThe experimental results demonstrate that the P/N{100} sample exhibit\nsignificantly lower and values compared to those in the P/N{111} sample.\nThis\nindicates that ferroel\n𝑉\ne𝑐ctric do\n𝑉\nm𝑖 ains in P/N{100} can undergo switching at substantially\nlower voltages, providing direct evidence of the enhanced polarization arising from the\nincreased β-PVDF content (Figure R51).\nA, B, PVDF, C, D, P/N{111} and E, F, P/N{100}.\nTo address this comment, we have revised the relevant statements in the revised\nmanuscript accordingly.\nPage 9, Paragraph 2, Line 3-8 in the revised manuscript:\n“In PFM measurements, a conductive probe with higher stiffness (k = 20 N/m)\nwas used to suppress long-range electrostatic forces. To eliminate the influence of\nelectrostatic fields on the piezoelectric response, the surface potential was measured via\nKelvin probe force microscopy (KPFM) (Figure S27)28. Subsequently, during PFM\ntesting, a direct-current bias of equal magnitude but of opposite polarity to the measured\nsurface potential was used over the same region to compensate for surface potential.”\nTo address this comment, we have supplemented the results in Figure S27-S31,\nSupplementary Table S7 and revised the relevant statements in the revised supporting\ninformation accordingly.\n253-254) that “…due to the low conductivity of P/N composites (Figure S17, Table S1),\nthe dominant loss mechanism in the 2-18 GHz range is polarization loss…”. This is\ncontradicted by their own data. Table S1 shows a 4-orders-of-magnitude (!) conductivity\nincrease in P/N{100}, when NiS loading increases from 15% to 25%.\nno effect at all. This discrepancy is ignored, making further discussion of the\nelectromagnetic properties unreliable.\nReply: Thank you for the questions raised by the reviewers. We would like to clarify\nthat there is no contradiction between the experimental data and the conclusions.\nAlthough changes in electrical conductivity do contribute to conductive loss, such loss\nconstitutes only a minor portion of the overall dielectric loss within the 2-18 GHz\nfrequency range. Therefore, we maintain that polarization loss remains the dominant\nloss mechanism in this frequency band.\nDifference in electrical conductivity primarily stems from the distinct geometric\npacking characteristics of cubic and octahedral particles. Cubic particles can achieve\ndense packing more easily through face-to-face or face-edge contacts, resulting in a\nlarger effective contact area between particles, which facilitates the formation of\nconductive pathways. In contrast, octahedral particles, with their numerous vertices and\nedges, tend to form point-to-point or line-to-point contacts during packing. This often\nleads to the creation of arch-like structures and voids between particles, thereby\nreducing the efficiency of constructing conductive pathways. Consequently, as the filler\ncontent increases, the cubic particle system more readily forms an efficient percolation\nnetwork through dense packing, leading to a more pronounced rise in electrical\nconductivity (Nature, 2009, 460, 876–879).\nDielectric materials attenuate electromagnetic energy and convert it into thermal\nenergy, primarily relying on two microscopic mechanisms: conductive loss ( ) and\n″\npolarization loss ( ). 𝜀𝑐\n″\n𝜀𝑝\nformula (Nat. Commun.,2024, 15, 9077):\n- (R14)\n″ 2𝜋𝑓𝜏\n𝜀𝑝 = (𝜀𝑠 𝜀∞)1+(2𝜋𝑓) 2 𝜏 2\n(R15)\n″ 𝜎\n𝜀𝑐 = 2𝜋𝑓𝜀0\n(R16)\n″ ″ ″\n𝜀 = 𝜀𝑐 +𝜀𝑝\nWhere the , , , are the static permittivity, the relative permittivity at\nhigh frequency li\n𝜀\nm𝑠it,\n𝜀\nt∞he e\n𝜎\nlect\n𝜏\nric conductivity, the relaxation time, respectively.\nAmong them, conductive loss can be directly calculated from the material's\nintrinsic conductivity; whereas polarization loss, particularly the contribution from\nferroelectric polarization as focused on in this study, can be estimated by subtracting\nthe conductive loss from the total loss.\nIn the original figure, to present the data more clearly and emphasize the\ndominance of polarization loss in the PVDF material system, we adjusted the vertical\nscale of the conductive loss to enhance visual comparison. As shown in Figure R52 and\nR53, the ratio in the P/N composite system is less than 0.15%. This value\n″ ″\nclearly ind𝜀i𝑐ca/t𝜀e𝑝s that the contribution of conductive loss to the total dielectric loss is\nnegligible, thereby confirming that the electromagnetic attenuation in the material\nprimarily follows a polarization-dominated mechanism. The polarization loss\noriginating from ferroelectric polarization is the core operating mechanism.\nconductive loss of C, P/N{111} and D, P/N{100} at EMWs from 2 GHz to 18 GHz.\nFigure R53. of A, P/N{111} and B, P/N{100} at EMWs from 2 GHz to 18\n″ ″\n𝜀𝑐/𝜀𝑝 to 18 GHz.\nTo address this comment, we have supplemented the results in Figure S37, S38 and\nrevised the relevant statements in the revised supporting information accordingly.\nQ5: The novelty of the “facet engineering” approach proposed by the authors is\noverstated. Surface-induced polymorphism in both organic and inorganic systems is\nwell established in literature\n[https://doi.org/10.1002/adfm.201503169; https://doi.org/10.1039/C8CS00283E]. β-\nphase enhancement in PVDF composites with inorganic nanoparticles has already been\ndemonstrated [https://doi.org/10.1016/j.polymertesting.2024.108516]. The work does\nnot introduce a sufficiently new concept or mechanism.\nReply: We thank the reviewer for this comment. We have carefully studied the\nreferenced literature cited and would like to provide a clearer elaboration on the novelty\nof our work based on this foundation.\nSurface/interface effects have been widely demonstrated to regulate the crystalline\nmorphology of polymers. We note that strategies such as inorganic/organic composites\nor nanoparticle composites can effectively influence the phase transitions of polymers\nlike PVDF. Building upon this foundation, our study further proposes that\nsystematically designing specific crystal facets can significantly enhance and maximize\nsuch interfacial interactions. Our work represents the first systematic application of\ncrystallographic facet engineering to ferroelectric polymer systems, establishing an\neffective link from atomic-scale interface modulation to macroscopic multi-frequency\nelectromagnetic responses. This approach not only deepens the understanding of the\nregulatory mechanisms behind polymer polymorphism but also provides a transferable\npathway for optimizing interfacial effects in other material systems through facet\nengineering.\nThis study breaks through the conventional paradigm of regulating PVDF\nperformance by altering filler “type”, and pioneers the introduction of “crystal facet\nengineering” into this system. Instead of merely selecting different inorganic fillers, we\nachieve precise and controllable modulation at the atomic scale by accurately\ncontrolling the exposure of specific crystal facets ({100} vs. {111}). We systematically\ninvestigate how specific plane orientations mediate differential interactions of polymer\nchains at the interface, elucidating the key microscopic factors through which inorganic\nfillers influence the stability of the ferroelectric phase in PVDF. This work establishes\ncrystal facet control of inorganic fillers as a new variable for manipulating the\nferroelectric phase and molecular dipole distribution in PVDF. It reveals that, due to\ndifferences in atomic arrangement and electronic structure, different crystal facets\n72\nexhibit fundamentally distinct interfacial interactions with PVDF molecular chains.\nThis deepens the understanding from a generalized “surface effect” to a microscopic\nmechanism based on adsorption energy, surface energy, and charge transfer. Ultimately,\nthis strategy not only effectively enhances the β-phase content but also synergistically\noptimizes its thermodynamic stability and dielectric/ferroelectric activity. It represents\nan advancement in the structure-property relationship from merely pursuing content to\nthe co-design of quality and function, providing a rational and controllable new\nparadigm for developing high-performance ferroelectric polymer-based\nelectromagnetic functional materials (Table R11).\nTable R11. Preparation, Formation Mechanism, and Content of the β-phase in PVDF\ncomposites\nβ-phase\nMechanism for the\nSample Processing techniques content Ref.\nformation of β-phase\n(F(β) (%))\nThe electrostatic\ninteractions between\nPVDF/Gold Polymers,\nSolution casting from DMF surface charge Au\nnanoparticle 66.0 2020, 12,\nsolution. nanoparticles and CF\ns (Au) 2630\ndipoles in the PVDF\nchain.\nThe surface charge\nPVDF/Zinc interaction between ZnO Polym. Adv.\noxide Solution casting from DMF nanoparticles and PVDF Technol.\n76.1\nnanorods solution. dipoles responsible for 2018, 29,\n(ZnO) the enhancement of β 143-150.\nphase.\nPVDF/bariu\n3D printing and in situ of BaTiO . Mater. Eng.\n3\nm titanate 55.9\npoling. 2017, 302,\n(BaTiO )\n3\n1700229\nThe elongation forces,\nstretching, and\nACS Appl.\nsimultaneous local poling\nMater.\nElectrospinning at applied during the\nPVDF/BaTi Interfaces\nvoltage of 10 kV and flow electrospinning processes 91.0\nO 2020, 12,\n3\nrate of 2 mL h-1. are responsible for the\n33989-\ntransformation of the α-\n33998\nphase into the polar β-\nphase.\nPVDF/GO The interface bonding Mater. Des.\ncomposite Selective laser sintering between GO and PVDF 49.1 2020, 190,\nscaffolds 108564\nDue to the fluorine group\nPVDF/fluori in GOF, which can trap ACS Omega\nnated GO Electrospinning electrons and lead to large 89.0 2018, 3,\n(GOF) charge accumulation at 5317-5326\nthe interface.\nThe specific interactions\nPVDF/Bi Al between the Bi3+/Al3+\nO /rGO- nanorods with CF\n4 9 2\nCompd.\nbased Solution casting dipoles of PVDF and the 76.0\n2020, 843,\nnanocompos O2– nanorods of Bi Al O\n2 4 9\n156019\nite with CH dipoles of\ninteraction between the Sustainable\nNiO@SiO / positive CH group of Chem. Eng.\n2 2\nSolution casting 80.0\nPVDF PVDF and the negatively 2018, 6,\ncharged surface of the 10505-\nNiO@SiO nanoparticles 10516\nPVDF/ZnO attraction between CH in J. 2021,\n@C the PVDF segment and 426,\nthe carbon surface 130345\nHeating to the temperature The modified dipole\nPVDF/BaTi at the set value at a rate of interaction between\nPolym. Test.\nO 40 °C/min respectively and oxygenic groups attached\n3\n79.0 2024, 138,\nnanocompos stretching at a constant to the BaTiO and\n3\n108516\nites strain rate of 50 μm s−1 until CH /CF in PVDF.\n2 2\nbreak.\nAtomic-scale interface\nNiS {100}/P\n2\ninteractions between\nVDF\nHot press PVDF chains and NiS 89.8 This work\n2\nwith different crystal\nVDF\nfacets\nTo address this comment, we have supplemented the presentation of the\nintroduction in the revised manuscript accordingly.\nPage 3, Paragraph 2, Line 5-10 in the revised manuscript:\n“The mediation of polymer interfaces by specific plane orientations was\nsystematically investigated, elucidating the key microscopic factors through which\ninorganic fillers influence the stability of the ferroelectric phase of PVDF. This work\n75\nestablishes the crystal facet control of inorganic fillers as a new variable for\nmanipulating the ferroelectric phase and molecular dipole distribution in PVDF.\nFurthermore, the crystal facet-stabilized PVDF matrix significantly enhances the\noperational stability and reliability of the composite.”\nWe have revised the paper with a focus on strengthening the contextual positioning\nof the work, clarifying its distinctions from prior research, and elaborating on the\nspecific new mechanisms and performance advantages we propose. We believe the\nrevised manuscript presents the scientific value of this work more accurately and\nrobustly.\n76"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The manuscript has been rigorously revised to address my concerns. I am satisfied with the provided responses. Therefore, I suggest its acceptance in current form.", "reviewer_2": "The authors responded and completed the suggetsed analysis with suitable experiments. Now, i feel the manuscript can be accepted for publication in nature communications.", "reviewer_3": "B. Cai and colleagues have made a big piece of work providing exhaustive explanations and additional data verifying and validating their conclusions. New XRD, FTIR, and PFM experiments successfully support previous data. Although the suggested dominant loss mechanism is still debatable and requires additional studies, the experimental methods and analyses are correct and do not raise doubts anymore. All this makes the work by B. Cai et al. of great interest to a broad community. Therefore, the revised version of the paper should be published in Nature Communications in its current form."}, "author_response": ""}]

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