Thermal-stress enhanced pyroelectricity in piezoelectric bimorphs

Domain: chemistry
Published: 2026-04-13
Editorial outcome: major_revision

Abstract
Enhancing pyroelectric performance is essential for advancing thermal sensing and energy-harvesting applications. This study presents an effective strategy to achieve highly enhanced pyroelectricity in a flexible polyvinylidene fluoride/muscovite bimorph. Unlike conventional approaches that focus on domain-phase engineering to enhance intrinsic pyroelectric contribution, we engineer a more dominant role for the secondary pyroelectric contribution by a stress-induced shape change that couples to a change in the polarization via the piezoelectric effect. This mechanism is enabled by the favorable combination of a large thermal-expansion mismatch between the polymer (polyvinylidene fluoride) and the ceramic (muscovite), together with the inherent mechanical compliance of mica’s flexibility, which allows interfacial thermal stresses to efficiently generate piezoelectricity. By combining experimental characterization with finite element modeling of the heterostructure’s temperature-dependent curvature, interfacial thermal stress is identified as the dominant contributor to the large effects. Direct pyroelectric measurements reveal a highly enhanced pyroelectric coefficient  -359 µC/m2K, more than an order of magnitude greater than that of single-layer polyvinylidene fluoride, highlighting its potential for applications in flexible electronics, thermal sensors, and energy harvesting systems.

Introduction
Pyroelectric materials, which generate current through temperature-driven polarization changes, are essential for applications such as waste-heat harvesting 1, and thermal sensing 2, 3. Research on pyroelectric materials has focused on strategies to increase the pyroelectric coefficient (π), necessitating a comprehensive understanding of each contributing factor to design materials. The π typically comprises four components4, 5:

total
𝜋 =[𝜙( ∂𝑃s) +𝑃 ( ∂𝜙 ) ] + [( ∂𝑃s) ( ∂𝜎 ) ( ∂ɛ ) ] + [𝜀 𝐸( ∂𝜀r(𝐸) )] + [𝜋] (1)
𝑡𝑜𝑡𝑎𝑙 ∂𝑇 𝜎 s ∂𝑇 𝜎 primary ∂𝜎 𝑇 ∂𝜀 𝑇 ∂𝑇 𝜎 secondary 0 ∂𝑇 dielectric tertiary

where P is the spontaneous polarization, T is temperature, ϕ is the fraction of ferroelectric domains contributing to the pyroelectric response, 𝜎 is the stress, ɛ is the strain, ɛ is the permittivity of free space, ɛ is the relative permittivity, and E is the electric field. Each term in the equation corresponds to a distinct mechanism contributing to the total pyroelectric response.

Among these components, most prior efforts have focused on enhancing the primary pyroelectric contribution (π primary ), which includes the intrinsic (π intrinsic = 𝜙( ∂𝑃s) , arising from polarization changes within the bulk) and extrinsic (π extrinsic = 𝑃 s ( ∂ ∂ 𝜙 𝑇 ) 𝜎 , arising from thermally induced domain-wall motion) contributions. However, additional contributions exist, such as the secondary contribution (π , arising from a cross-coupled effect wherein thermally induced secondary shape changes induce changes in polarization via the piezoelectric effect), the dielectric contribution (associated with temperature-dependent permittivity changes, ɛ), and tertiary contributions (arising from non-uniform stresses caused by inhomogeneous heating). For example, in the polymer ferroelectric polyvinylidene fluoride (PVDF), most efforts have focused on enhancing the π alone. Phase engineering approaches, such as mechanical stretching6, nanoparticle inclusion7, and electrical poling and annealing process8, have been employed to maximize the β-phase fraction and enhance the spontaneous polarization (P ). These modifications, however, typically yield only a small improvement in π total (increasing values by, at most, 25%), highlighting the fundamental challenge of solely relying on π for significant primary enhancement.

In contrast, π presents a promising alternative to manipulate to increase overall secondary response. In the electroceramics and precision thermal sensing literature, this stress-induced contribution is generally regarded as a "parasitic" effect or a source of noise that must be minimized to ensure measurement accuracy9. However, our work represents a conceptual departure from the conventional paradigm: instead of suppressing thermal expansion mismatch, we intentionally engineer the device structure to maximize it, transforming this "parasitic" effect into the dominant mechanism for energy harvesting. The π is governed by three key factors: secondary the piezoelectric coefficient ( ∂𝑃s) , the elastic stiffness ( ∂𝜎 ) , and the thermal-expansion ∂𝜎 𝑇 ∂𝜀 𝑇 coefficient (CTE) , expressed as ( ) . Together, these factors enable the π secondary to effectively ∂𝑇 𝜎 leverage thermally induced mechanical stress to generate additional polarization changes and thereby amplify the overall pyroelectric response. While the dielectric and tertiary components may also contribute under certain conditions, they are considered negligible in this study as compared to the dominant primary and secondary effects. Given that pyroelectric materials inherently exhibit piezoelectric properties, harnessing thermal energy to simultaneously activate both π and π can significantly amplify pyroelectric performance by inducing a larger primary secondary polarization change under thermal stimuli (Fig. 1A). One of the well-established methods to generate thermally induced mechanical deformation is the bimorph geometry10, a structure composed of two materials with different CTEs. When heated or cooled, these materials expand or contract at unequal rates, generating mechanical stress at their interface that drives thermal actuation (strain or bending). Therefore, by incorporating a polar material into the bimorph, thermal energy not only triggers the π but also induces the π through thermally induced primary secondary stress, potentially amplifying the material’s ability to convert thermal energy of temperature oscillations into electrical energy. The flexible polar system used in this study is PVDF, a flexible polymer known for its ferroelectric, piezoelectric, and pyroelectric properties. Its mechanical flexibility, relatively low dielectric constant11, and stability under ambient conditions make it an ideal candidate for this application.

In previous studies on flexible nanogenerators based on PVDF-based heterostructures, researchers have extensively investigated their piezoelectric and pyroelectric effects10, 12, 13. For example, the piezoelectric and pyroelectric properties of a PVDF/thermoplastic polyurethane (TPU) heterostructure were investigated for wearable electronics10. However, since TPU has a CTE similar to that of PVDF, π was negligible due to the lack of significant thermal- secondary expansion mismatch (Δα). While extensive efforts have been made to enhance piezoelectric and pyroelectric response of PVDF-based heterostructures, there is considerably less understanding of how large thermal-interfacial stresses can be leveraged to control and enhance the π . secondary Therefore, to achieve a larger Δα between PVDF and the substrate, in this case mica, a two-dimensional layered ceramic was selected as an optimal candidate. It offers exceptional mechanical flexibility and thermal stability, making it well-suited for forming thermal bimorphs and efficiently accommodating thermally induced stresses14, 15. Here, we developed a PVDF/mica bimorph structure, where the combination of polymer (PVDF) and ceramic (mica) maximizes the Δα, inducing significant interfacial stress that enhances the π via the piezoelectric response. secondary Through a combination of structural optimization, theoretical modeling, and experimental validation, π  -359 µC/m2K was achieved in the PVDF/mica system, exceeding that of a single-layer PVDF (-29 µC/m2K) by over an order of magnitude. This study paves the way for using an interface-coupling mechanism to address the current bottleneck in optimizing the π and expanding potential applications in thermal-energy harvesting and temperature sensing.

Results
To investigate the structural, piezoelectric, and optical properties of PVDF, mica, and their heterostructures (fabrication details in the Methods; Supplementary Fig. S1A), a combination of analytical techniques was employed (Methods). The crystalline phases of PVDF were analyzed using Fourier-transform infrared spectroscopy (FTIR) and Raman spectroscopy. PVDF can exist in different crystalline forms (α, β, γ, and δ), determined by variations in molecular-chain arrangement16. Among these, the α (non-polar) and β (polar) phases dominate at room temperature. The β-phase is particularly desirable for pyroelectric and piezoelectric applications due to its aligned dipole structure, leading to enhanced spontaneous polarization and results in a higher pyroelectric response. In contrast, the non-polar α phase has randomly oriented dipoles, resulting in a much weaker π. To synthesize PVDF with a higher β-phase proportion, the fabrication process and parameters can be optimized and refined based on the FTIR and Raman spectroscopy results, which reveal the relative fractions of the α and β phases in the fabricated PVDF.

First, the FTIR spectrum (Fig. 1B, Method) exhibits various absorption valleys attributed to its crystalline phases. Since different PVDF phases exhibit distinct infrared absorption features, both α and β phases were identified16. Furthermore, the Raman spectroscopy was further employed as a more precise method for quantifying the β-phase fraction17. The number of Raman-active modes is determined by the vibrations of linear (-CH -CF -) PVDF molecular chains (Fig. 1C, 2 2 n inset) crystallized in either the α phase with a trans–gauche (TGTG′) conformation or the β phase with an all-trans (TTTT) conformation. Consistent with the FTIR results, the Raman spectrum lacks the signature γ-phase peak typically observed around 811-814 cm-1. Consequently, the material was modeled as a binary system of α and β phases , which were identified by the CH 2 group rocking vibrations characteristic of the α phase and the β phase, respectively (Fig. 1C). By analyzing these peaks, the β-phase portion was quantified, enabling ready process optimization. Therefore, the fabrication process was refined by adjusting key parameters, including processing temperature and PVDF concentration in solution (details of the optimization process are provided, Supplementary Fig. S1). Following optimization, the maximum β-phase proportion achieved was approximately 61% (supplementary Fig. S1B and S1C).

The remaining ≈39% corresponds to the α phase, which is nonpolar and does not contribute to the piezoelectric or pyroelectric response. The functional dominance of the β phase was further experimentally verified by piezoresponse force microscopy (PFM). PFM was further utilized to probe the piezoelectric response and investigate the domain structure of the fabricated heterostructure. In the PFM measurements (Methods, and Supplementary Fig. S2.), a thin indium-tin oxide (In O :SnO =90:10, ITO) layer was placed between the PVDF and mica, serving as a 2 3 2 conductive-bottom electrode that accommodates thermal mismatch while remaining inherently non-pyroelectric due to its centrosymmetric crystal structure, ensuring no additional signal generation. PFM amplitude measurements were conducted under sweeping AC voltages from 1 V to 5 V (Fig. 1D). The amplitude exhibited a linear dependence on the applied voltage, confirming the intrinsic piezoelectric nature of the heterostructure. By comparing the slope of this amplitude-voltage curve with that of a standard BiFeO (BFO) reference (d ≈ 70 pm/V), we determined the 3 33 effective piezoelectric coefficient (d ) of the PVDF/mica heterostructure to be approximately 29 33 pm/V. This value is consistent with reported literature values for high-quality PVDF 11. To investigate the polar domain structure, PFM amplitude and phase images (Supplementary Note. S2) were acquired in both out-of-plane and in-plane directions. As the β phase of PVDF is polar, it contributes to the detectable out-of-plane piezoresponse, while the non-polar α phase yields no signal. Furthermore, the macroscopic piezoelectric response was characterized using a single-electrode-based transparent flexible nanogenerator technique (Methods)18.

The measured average open-circuit voltages for the bending process (Fig. 1E) were +2.1 V (convex, tensile) and -1.8 V (flat, release), indicating that tensile stress induces a positive output, while the returning-to-flat process (which involves compressive stress) yields a negative output. The polarity reversal and asymmetric signal output confirm that interfacial stress induced by bending leads to opposite charge generation, confirming the piezoelectric behavior of the heterostructure. Moreover, the device maintained a highly stable output voltage over 1,000 mechanical bending cycles without observable degradation, indicating a good interfacial adhesion of the bilayer. The optical transmittance was obtained by using the UV-Vis spectroscopy (Methods) , the wide band gaps of mica (5.0 eV), ITO (4.0 eV), and PVDF ( 6.0 eV) ensure high optical transparency (> 75%) in the visible range (400-700 nm), minimizing parasitic optical absorption and enhancing signal stability. This feature is beneficial for thermal-sensing applications, as it reduces interference from ambient visible light (Fig. 1F).

The thermal properties of the PVDF/muscovite heterostructures, including the CTE of PVDF and mica, and the bending curvature induced by thermal stress, were studied as schematically illustrated in Fig. 2A. Temperature-dependent X-ray diffraction and Raman spectroscopy were utilized to evaluate the CTE (Methods and Supplementary Fig. S3). Reciprocal space mapping of mica (Fig. 2B and Supplementary Fig. S3) using the 048 diffraction condition revealed an increase in lattice parameter from 6.86 Å at 30 °C to 6.88 Å at 230 °C, corresponding to calculated in-plane and out-of-plane CTEs of ≈ 7.9 ppm/K and ≈ 15.7 ppm/K, respectively. The in-plane thermal expansion is identified as the governing factor in the bimorph bending mechanism. For PVDF (Fig. 2C), which is considered to exhibit isotropic thermal expansion, the CTE was determined to be  120 ppm/K by analyzing the temperature-dependent Raman shift of the CH 2 wagging vibration mode at 840 cm-1. With increasing temperature, the Raman peak shifted toward lower wavenumbers from 841.7 cm-1 at 25 °C to 841.1 cm-1 at 74 °C. These experimental results confirm a significant difference in CTEs between PVDF and mica. As PVDF tends to expand more significantly than mica, this mismatch effectively produces in-plane compressive stresses within the PVDF and tensile stresses in the mica.

We further analyzed the deformation behavior induced by thermal stress, using the PVDF/mica heterostructure as a thermally actuated device for heating tests. The sample was heated from room temperature to 100°C in a preheated oven, and its deformation was recorded using camera-based imaging (Methods and Supplementary Fig. S4A). The evolution of bending curvature over time was analyzed (Fig. 2D). Initially flat, the heterostructure exhibited a rapid increase in curvature with a rise time < 1 s, followed by a slower recovery to its original state > 5 s. A positive correlation between curvature and temperature was observed, indicating that differential thermal expansion between the layers drives the bending deformation. To optimize the thermal-actuation performance, the mica thickness was systematically varied while maintaining the optimized β-phase-rich PVDF at a fixed thickness of 20 µm. The goal was to identify the mica thickness that yields the largest bending curvature in response to temperature variations. Thinner mica layers resulted in greater bending curvature (Fig. 2E). The optimal configuration was identified as 20 µm PVDF paired with 20 µm mica. A thinner mica layer positions the neutral axis of the heterostructures closer to the PVDF/mica interface, which is more effective for inducing interfacial thermal stress. Notably, reducing the mica thickness below 20 µm presents significant challenges for practical applications. Thinner layers are difficult to reliably exfoliate using mechanical methods, often resulting in damage or non-uniform thickness. Furthermore, while reducing thickness theoretically enhances the bending curvature, it significantly lowers the critical load that the substrate can sustain. This renders the samples mechanically fragile and challenging to handle, making them highly susceptible to fracture under bending-induced stress.

To quantitatively estimate the thermally induced deformation, we applied the classical Timoshenko bilayer bending curvature model 19, which describes the curvature (𝜅) of a bimorph under differential thermal expansion:

6(𝛼 −𝛼 )⋅Δ𝑇 1 2
𝜅 = ⋅ (2)
ℎ(1+𝑚)2 4𝑚 𝑛
1+ ⋅
(1+𝑚)2 1+𝑛

where α and α are the coefficients of thermal expansion for the top and bottom layers, 1 2 corresponding to PVDF and mica, respectively. The total bilayer thickness is given by h = h 1 (PVDF) + h (mica). The thickness ratio is defined as m = h / h , and the Young’s modulus ratio 2 1 2 is n = E (PVDF) / E (mica). This model captures the competing effects of thickness and stiffness 1 2 on thermal bending. Using the experimentally extracted CTEs (α = 120 ppm/K for PVDF, α = 1 2 7.9 ppm/K for mica) and mechanical properties (E = 3.9 GPa, E = 110 GPa), the calculated 1 2 curvature of the 20 µm PVDF / 20 µm mica heterostructures increased linearly with ΔT (Fig. 2F dotted line), yielding κ ≈ 40.6, 121.9, 203.2 m-1 at ΔT =10 °C, 30 °C, and 50 °C, respectively.

While the Timoshenko bilayer model provides a useful baseline to estimate the thermal bending curvature and strain (Supplementary Fig. S4C), the calculation assumes uniform strain distribution and temperature-independent, isotropic material properties. Specifically, it neglects the anisotropy inherent in mica (e.g., E ≠ E , α ≠ α ) and the temperature-dependent elastic x z x z stiffness tensors of both PVDF and mica (Tables S1-S2). To more accurately simulate the deformation behavior under realistic thermal environments, we performed finite element method (FEM) simulations (Supplementary Fig. S4D, Fig. S5) incorporating temperature-dependent and anisotropic material properties (Table S2). The FEM model also accounts for thermal conductivity, specific-heat capacity, and convective heat transfer at the exposed surfaces, enabling a more comprehensive treatment of coupled thermomechanical behavior. The curvature values predicted by FEM simulations (Fig. 2F, dashed line) agree well with experimental trends, confirming the reliability of the model across the operational temperature range.

For benchmarking (Fig. 2F), the thermal-actuation performance of the PVDF/mica heterostructures was compared with those using silver (Ag), copper (Cu), and amorphous copper metal layers in place of PVDF. Among all configurations, PVDF/mica demonstrates the largest bending curvature. This enhancement is attributed to the pronounced Δα: PVDF possesses a high coefficient of thermal expansion (120 ppm/K), while metals typically range from 6-35 ppm/K and mica remains much lower at 7.9 ppm/K. This resulting large mismatch drives strong interfacial thermal stress, enabling enhanced thermal-actuation performance.

To investigate the role of Δα and substrate mechanical effects on the pyroelectric properties, we conducted pyroelectric measurements using the PVDF/mica system. In addition, two reference systems, including PVDF on sapphire and a single-layer PVDF film, were prepared to serve as comparisons, revealing how differences in substrate stiffness and thermal-expansion behavior impact the pyroelectric performance (Fig. 3A). Devices were fabricated with a layered structure of 200 nm ITO / 20 µm PVDF / 200 nm ITO on mica, on commercial sapphire substrates, and as a single-layer film, where ITO serves as both the top and bottom electrodes.

Pyroelectric measurements were conducted using the Garn-Sharp method21, 22, in which sinusoidal temperature oscillations (ΔT(t) = T sin (ωt)) were induced to heat up the devices and 0 the resulting pyrocurrent can be expressed as:

d𝑇
𝐼 = 𝜋 𝐴 = 𝜋 𝐴 ωT cos(ωt) (3)
pyro 0
d𝑡

Where A is the electrode area and ω the angular heating frequency. This expression shows that the pyrocurrent is phase-shifted by approximately 90° relative to the temperature profile, serving as a signature to distinguish the genuine pyroelectric response from in-phase thermal or leakage artifacts. The measured temperature profile (red curves, right axis) and corresponding pyroelectric currents for PVDF/mica, PVDF/sapphire, and single-layer PVDF (blue, green and purple curves, left axis) were recorded (Fig. 3B). Given the thermal mass of Peltier-based measurement setup, we evaluated the frequency dependence (Supplementary Note 6) and selected a low heating frequency of 0.05 Hz to ensure sufficient thermal equilibration. At higher frequencies, thermal damping occurs as the heat transfer rate limits the effective temperature oscillation amplitude inside the sample. The PVDF/mica device exhibits the largest pyrocurrent amplitude and a clean sinusoidal waveform with the expected 90° phase shift relative to temperature, while the PVDF/sapphire and single-layer PVDF samples show much smaller amplitudes.

Further, to quantitatively determine the π, the amplitude of the temperature oscillations (T ) o was varied, the peak of pyrocurrent amplitude was extracted, and the slope of the linear fit (πAω) was used to calculate the π. A higher slope indicates a higher π for devices with the same electrode area (A) and heating frequency (ω). The π determined from such measurements (Fig. 3C) were as follows: PVDF on mica (-359 µC/m2K), PVDF on sapphire (-32 µC/m2K), and a single-layer PVDF film (-29 µC/m2K). Among these samples, the PVDF/mica heterostructure exhibits the highest π, achieving an enhancement of more than one order of magnitude, attributed to the favorable combination of a large Δα and the mechanical compliance of mica. This strain, acting through the film’s piezoelectric coefficient, contributes to a considerable π . It should be secondary noted that the sign of the π is the same as the π , with both being negative since the d secondary primary 31 coefficient of PVDF is positive, and the PVDF/mica interface experiences compressive stress under thermal stimuli, thus the resulting piezoelectric polarization change is negative.

In contrast, the PVDF/sapphire heterostructures, despite also exhibiting a large Δα, show no significant π enhancement. We attribute this behavior to interfacial mechanical coupling. secondary Sapphire possesses a rigid 3D covalently/ionically bonded surface with a high Young’s modulus( 360 GPa)23, which is expected to strongly constrain interfacial deformation and limit effective thermal stress transfer into the PVDF layer. Under such conditions, the stress-mediated piezoelectric contribution to the total pyroelectric response is suppressed. This accounts for the low pyroelectric response ( -32 µC/m2K) observed in our PVDF/sapphire control samples. Conversely, while mica is also a ceramic material, its unique 2D-layered structure governed by weak van der Waals forces; thus, we propose that this van der Waals surface acts as a mechanically compliant interface. The mica interface facilitates the thermal stress required for the secondary pyroelectric effect. This behavior is consistent with an enhanced dipolar response to the induced stress, yielding the large pyroelectric coefficient (-359 µC/m2K). Therefore, the role of mica extends beyond providing macroscopic flexibility for actuator-related applications. The specific interfacial compliance is a factor for amplifying the stress-induced response, a feature that intrinsically rigid 3D crystals like sapphire lack.

In the case of the single-layer PVDF film, free thermal expansion is isotropic and does not generate in-plane anisotropic strain, resulting in no π . Collectively, these results highlight secondary that only substrates which have both a large thermal-expansion-coefficient difference with the pyroelectric layer and sufficient mechanical flexibility, such as mica, can be used to effectively induce sufficient Δα to dramatically enhance the π in PVDF-based heterostructures. secondary Furthermore, the PVDF/mica heterostructures demonstrate robust thermal stability and durability (Supplementary Note 7). The pyroelectric coefficient remained constant with the initial temperature increased from 24°C to 65°C. Supporting this macroscopic stability, temperature-dependent P-E loop analysis (Supplementary Fig. S7B) confirmed that the ferroelectric polarization is fully reversible even after heating. This ensures that the intrinsic piezoelectric coefficient remains robust without permanent degradation within the operating range. In addition to thermal stability, the device exhibits good durability as described in Supplementary Note 8. The device maintained stable output performance during repeated thermal cycling, although the output voltage varied with different pre-bending states (Supplementary Fig. S8A and S8B). Moreover, extended fatigue tests demonstrated good durability, where the device showed minimal degradation (< 4% variation) during the first 5,000 thermal cycles (Supplementary Fig. S8C), suggesting its potential suitability for long-term practical applications.

Finally, we compared our approach with representative CTE-driven secondary (stress-mediated) pyroelectric mechanisms (Fig. 3D). To effectively enhance the π through the π , total secondary it is essential to understand the underlying mechanism and ensure that both the π and π primary secondary are aligned in sign. These mechanisms can be broadly divided into two categories: inorganic ferroelectric systems (bulk single crystals, epitaxial thin films) and polymer-based systems (PVDF composites, liquid-crystalline elastomer (LCE) nanocomposites, macro-fiber composites (MFCs) and PVDF/mica heterostructures).

Inorganic ferroelectrics provide the first basis for comparison. In bulk single crystals, such as LiNbO 24, π dominates (negative sign, from reduced spontaneous polarization with 3 primary temperature), while π , arising from positive thermal expansion along the polar axis, secondary typically has the opposite sign, reducing π . In epitaxial polydomain ferroelectric thin-films on total rigid oxide substrates, the film is clamped in-plane, and in-plane Δα is converted into biaxial stress. The sign of the resulting π depends on both the polarization orientation and the relative secondary coefficients of thermal expansion of the film and substrate25 . For example, PbZr Ti O ( α= 0.2 0.8 3 5.4 ×10-6 /K) thin film on GdScO (110) substrate (α= 12.1 ×10-6 /K), the tensile stress leads to the 3 change of volume fraction of c-domain and decreases the out-of-plane polarization, which c-axis contraction and a negative π that adds constructively to the π , enhancing the π by secondary primary total 25%-50%.

In the case of polymer-based systems, the effectiveness of the π depends on how secondary the Δα is engineered, and the structural connectivity and mechanical boundary conditions that determine whether the resulting thermally generated stress can be efficiently accommodated. Unlike rigid epitaxial films where stress is intrinsically imposed through biaxial clamping, polymers are mechanically compliant and therefore require specific structural designs to ensure effective stress transfer. A common approach is embedding ferroelectric particles in a polymer matrix (0-3 connectivity), where local Δα around discrete particles generates stress; however, π is modest because stress is generated locally and remains spatially fragmented. Chew et secondary al.26 showed experimentally and via effective-medium modeling that increasing the PZT volume fraction in PVDF from 0.2 to 0.6 raises the π (-18 to -42 µC/m2K), mostly through the primary total term, with only a modest rise in the π (-6 to -11 µC/m2K). To further improve, secondary nanocomposites with liquid-crystalline elastomers have been reported27 , where the nematic-isotropic transition of the LCE provides a much larger thermomechanical drive and amplifies π , increasing the π from -27 to -40.1 µC/m2K (≈ 49%). Likewise, in MFC architectures, secondary total the π is highly tunable in both magnitude and sign, depending on fiber orientation and matrix secondary properties. Acosta et al. 28 demonstrated that controlling the poling direction of PbZr Ti O fiber 1–x x 3 relative to thermal expansion anisotropy can switch π from opposing (Δα ∥ poling axis, secondary max +178 µC/m2K) to aligning constructively (Δα ⊥ poling axis, -221 µC/m2K) with π . These max primary examples highlight the importance of structural design in controlling the interplay between π primary and π for practical device optimization. Complementary approaches have also shown that secondary morphology-driven enhancement of the piezoelectric coefficient (d ), for example through 33 electrospun nanofiber architectures, can indirectly amplify π , enabling absolute pyroelectric secondary coefficients of approximately 63 µC/m2K in PVDF-based systems29. In contrast, the PVDF/mica bilayer (2-2 connectivity) exploits a large Δα between film and substrate together with its unique van der Waals interactions to provide a compliant boundary condition.

Beyond comparisons of secondary-contribution mechanisms, we also evaluated the performance of the PVDF/mica heterostructures using the voltage figure of merit (FoM = π/ε) 30, r which is defined as the change in output voltage per unit temperature change. For the PVDF/mica heterostructures, the FoM was  32.6 µC/m2K, a substantial improvement of FoM attributed to the combined effects of a significantly enhanced π and the intrinsically low ε r of PVDF ( 11; Supplementary Note S9). A detailed comparison with other pyroelectric materials is provided in the Supporting Information 10.

Methods
Sample Fabrication of PVDF/mica heterostructures. The integration of PVDF and mica was achieved using the tape-casting method, a scalable technique well-suited for fabricating large-area and uniform films. In this process, the PVDF solution was prepared by dissolving PVDF powder in Dimethylacetamide (DMAC) under continuous stirring at 70 °C for 4 hours to ensure complete molecular dispersion before casting. DMAC was selected as the solvent to facilitate uniform coating. Subsequently, the solution was coated onto the substrate using a doctor blade, followed by controlled solvent evaporation in an oven at 80 °C for  1 h. The overall fabrication process is illustrated in Supplementary note Fig. S1A.

Phase Composition Characterization. Fourier transform infrared (FTIR) spectroscopy was conducted using a Spectrum 100 FTIR spectrometer (PerkinElmer) in transmission mode. Spectra (Fig.1B) were collected in the wavenumber range of 600-1500 cm-1 at room temperature to evaluate the phase composition of the PVDF films.

Raman Spectroscopy Measurement. Raman spectroscopy (Fig. 1C) was performed using a spectrometer (Horiba Jobin Yvon iHR550) coupled with a backscattering confocal microscope. A 532 nm laser was used as the excitation source. Temperature-dependent Raman spectra were collected from 25 °C to 80 °C at 7 °C intervals using a long working distance 50× objective lens (numerical aperture, NA = 0.5).

UV-Vis Spectroscopy. Optical spectra (Fig. 1D) were collected using a PerkinElmer Lambda 900 UV-visible spectrophotometer in transmission mode in the wavelength of 300–900 nm at room temperature.

Scanning Probe Microscopy (SPM). The piezoelectric coefficient (d ) (Fig. 1D) was measured 33 using a Cypher S atomic force microscope (AFM) equipped with conductive AC160 probes. To ensure accurate quantification and account for tip-sample contact resonance, we employed a comparative calibration method using a standard BiFeO thin film with a known piezoelectric 3 coefficient as a reference. A thin ITO layer (200 nm) was used as the bottom electrode to facilitate the measurement. Instead of relying solely on phase contrast, we performed local piezoelectric spectroscopy by sweeping the AC bias voltage from 1 V to 5 V. We observed a linear increase in PFM amplitude with increasing bias, confirming the film's intrinsic piezoelectric nature. By comparing the slope of the amplitude-voltage curve of our PVDF/mica heterostructure with that of the BFO reference sample, the effective d value was determined. 33

Macroscopic Piezoelectricity Measurement. The macroscopic piezoelectric response (Fig. 1F) was characterized using a single-electrode-based transparent flexible nanogenerator configuration. Wires were connected to the top and bottom electrodes of the sample, which were then linked to a low-noise current preamplifier and a low-noise voltage preamplifier to measure the output voltage. A custom-built mechanical setup was employed to repeatedly bend the samples at a frequency of 0.5 Hz, enabling evaluation of their piezoelectric performance under cyclic mechanical deformation.

Temperature-dependent XRD Measurement. Reciprocal space mapping (RSM) measurements (Fig. S3) were conducted using a Bruker D8 ADVANCE diffractometer equipped with a heater stage. A Cu Kα radiation source (λ = 0.15418 nm) and a LYNXEYE XE-T detector were employed. Compared to standard symmetric scans, asymmetric scans targeting off-axis reflections were performed to decouple the lattice expansion vectors, allowing for the independent extraction of both in-plane and out-of-plane lattice parameters. The CTEs were derived from the linear fit of the calculated lattice strain (ΔL/L ) versus temperature. The measurements were performed over a 0 temperature range from 30 °C to 230 °C, with data collected at 50 °C intervals. Prior to each measurement, the sample was equilibrated at the target temperature to ensure thermal stability.

Bending Curvature Measurement. The PVDF/mica heterostructures were mounted onto a custom-built stainless-steel stage, with one end clamped and the other end left free (Fig. S4A). To maintain thermal stability, the oven was preheated to the target temperature, monitored by a thermocouple to ensure the reliability of the thermal gradient. Once the set temperature was reached, the sample stage was placed in the oven, and the bending behavior of the sample was recorded. The curvature of the samples was subsequently quantified using ImageJ software by analyzing the recorded images.

Dynamic Mechanical Analysis (DMA). The elastic coefficients of PVDF and mica (Fig. S4B) were characterized using a DMA 850 system (TA Instruments) operated in a standard three-point bending configuration. Rectangular specimens with dimensions of 5 mm × 30 mm were prepared and mounted on the fixture. To ensure accurate mechanical characterization, measurements were conducted under a fixed frequency with the dynamic strain amplitude maintained strictly within the linear viscoelastic region. The temperature was ramped from -75 °C to +75 °C using a gas cooling accessory, where low-temperature nitrogen gas generated from the evaporation of liquid nitrogen was utilized to precisely control the thermal environment. The storage modulus (E') was continuously recorded as a function of temperature to quantify the mechanical stiffness evolution across the operating range.

Capacitance Measurements. Capacitance-voltage (C-V) characteristics (Fig. S5) were measured using a TF Analyzer 3000 system (AIXACCT Systems GmbH). Measurements were carried out under an applied voltage range of ±4 V DC bias with a 100 mV AC signal, sweeping across a frequency range from 1 kHz to 100 kHz.

Quantification of Pyroelectric Coefficient. The PVDF/mica, PVDF/sapphire, and pristine PVDF samples were individually mounted onto a Peltier chip (Fig. S6), which functioned as a controllable thermal source. The thickness of the sapphire is 500 μm. There is no macroscopic bending occurred during the temperature oscillation. To distinguish and accurately quantify the effective pyroelectric current, measurements were conducted using the Garn-Sharp method. A low-frequency sinusoidal thermal stimulus (0.05 Hz) was applied using a function generator (TFG-3605E, Twintex), and the resulting current was measured with a low-noise current preamplifier (SR570, Stanford Research Systems), starting from an initial temperature of approximately 25 °C.

Finite Element Modeling. A finite element (FE) model of the PVDF/mica bilayer was constructed using ANSYS with SOLID226 elements to simulate coupled mechanical, electrical, and thermal behaviors. Material properties were sourced from experimental measurements and tabulated data (Tables S1 and S2), considering temperature-dependent effects. Boundary conditions were applied to replicate the experimental fixation setup, with voltage-coupled nodes assigned to the PVDF surfaces. The top surface was grounded, and a 3 MΩ external resistance (CIRCU94 element) was incorporated to simulate the measurement circuit. Grounding primarily serves to establish a fixed reference potential (V = 0), which is essential for unambiguously determining the polarity of the pyroelectric response and the sign of the pyroelectric coefficient (π = dP/dT). Convective heat transfer (100 W/m2K) was applied to all outer surfaces. Simulations were performed at ambient temperatures ranging from 25 °C to 119 °C to extract curvature.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "- What are the noteworthy results?\nThe results offer limited novelty. The use of thermal expansion mismatch to create a pseudo-pyroelectric response has been\nrecognised for a long time. It is a well known issue with pyroelectric sensors and great care is taken to minimise the effect in\nthis instance - e.g. as stated in Electroceramics my Moulson & Herbert in 2003.\n- Will the work be of significance to the field and related fields? How does it compare to the established literature? If the work\nis not original, please provide relevant references.\nThere is extensive prior art in this area.for example:\nGustarov et al. Thermal energy harvesting by piezoelectric PVDF polymer coupled with shape memory alloy, Sensors and\nActuators A: Physical\nVolume 243, 1 June 2016, Pages 175-181 - https://doi.org/10.1016/j.sna.2016.03.026\nKyoung-Bum Kim et al 2013 Jpn. J. Appl. Phys. 52, Energy Harvesting Characteristics from Water Flow by Piezoelectric\nEnergy Harvester Device Using Cr/Nb Doped Pb(Zr,Ti)O3 Bimorph Cantilever http://dx.doi.org/10.7567/JJAP.52.10MB01\nSeung-Bum Kim et al. A synergetic effect of piezoelectric energy harvester to enhance thermoelectric Power: An effective\nhybrid energy harvesting method, Energy Conversion and Management,\nVolume 298, 15 December 2023, 117774, https://doi.org/10.1016/j.enconman.2023.117774\nNaser S. Al-Hunit, A Novel Piezoelectric System for Thermal Energy Harvesting from Temperature Fluctuations International\nJournal of Applied MechanicsVol. 12, No. 10, 2050112 (2020)https://doi.org/10.1142/S1758825120501124\n- Does the work support the conclusions and claims, or is additional evidence needed?\nyes.\n- Are there any flaws in the data analysis, interpretation and conclusions? - Do these prohibit publication or require revision?\nyes\n1. use of Xray differaction to measure CTE for mica is flawed as mica is anisotropic. XRD will provide information on CTE in\nthrough-thickness direction.The relevant CTE for bending and charge generation is the CTE in the in-plane direction.\n2. ultrathin mica is not less brittle. It simply has smaller dimensions and so can sustain a lower load.\n3. authors state that even if the alumina were thinned to 20um that it would still behave rigidly. While it would be more rigid, it\nwould only be 2x as rigid. they ascribe this to it's crystal bonding and lack of slip planes. Mica to has these limits.\n4. discussion of polymer based systems requiring alternative stress-transfer pathways is very ambiguous. Stress in any\nlayered system is transferred in the same way - across interfaces where bonding exists.\n- Is the methodology sound? Does the work meet the expected standards in your field?\nyeas\n- Is there enough detail provided in the methods for the work to be reproduced?\nyes", "reviewer_2": "This article presents an interesting approach to improving the pyroelectric response in flexible PVDF/mica heterostructures.\nThe authors highlight the dominant role of interfacial thermomechanical stresses, exploiting the thermal expansion mismatch\nbetween PVDF and mica, rather than relying solely on conventional phase engineering. The results are remarkable, with a\npyroelectric coefficient of –359 µC/m²K, more than an order of magnitude higher than that of a single PVDF film. The study\ncombines experimental analyses with modeling (Timoshenko and FEM) in a coherent way, which strengthens the scientific\nvalidity of the conclusions. The work is well structured and opens promising perspectives for applications in flexible thermal\nsensors, energy harvesting devices, and wearable electronics.\nHowever, some points deserve clarification:\n1. How does the pyroelectric performance evolve at higher operating frequencies, closer to real application conditions?\n2. Is the β-phase proportion of PVDF (≈61%) sufficient to ensure reproducibility and stability at large scale?\n3. Could the intermediate ITO electrode introduce capacitive or thermal effects that influence the measured response?\n4. Does the device maintain its high pyroelectric coefficient under extended cycling and across a wider temperature range?\nI thank the authors for the quality of this work, which makes a significant contribution to the field of flexible pyroelectric\nmaterials and their applications.", "reviewer_3": "The manuscript presents an engaging and well-structured study on piezoelectric biomorph heterostructures based on\nPVDF/mica, where the authors effectively demonstrate the secondary contributions of the pyroelectric response and\nhighlight the dominant role of thermally induced interfacial stress as a governing mechanism. The concept of utilizing\nsignificant coefficients of thermal expansion (CTE) mismatch between distinct material layers to amplify the overall\npyroelectric response represents a novel and promising direction in multifunctional energy conversion research.\nThe study is scientifically sound and methodologically consistent, yielding results that provide valuable insights into the\ncoupling mechanisms between pyroelectricity and thermomechanical stress. However, a few points raised during the review\nrequire minor clarification and elaboration for completeness. Once these clarifications are incorporated, the manuscript will\nmeet the journal’s standards and can be recommended for acceptance after minor revision.\n1. How do the thermal expansion coefficients of the individual components in the PVDF/mica bilayer affect the overall strain\nresponse during temperature changes?\n2. Could the authors elaborate on the selection criteria for the thermal and mechanical properties used in the finite element\nmodel for the PVDF/mica bilayer?\n3. What specific methodologies were used to analyze the thermal expansion coefficient of mica, and are they clearly\nexplained?\n4. Are the results of the PFM analysis of the PVDF/mica heterostructure adequately detailed in terms of both processes and\noutcomes?\n5. What specific techniques were utilized to ensure the optimal crystalline phase distribution within the synthesized PVDF\nmaterial?\n6. How does the piezoelectric coefficient of the PVDF/mica system change with varying temperature conditions, and what\nexperimental data support this?\n7. How do the structural properties of the PVDF/mica heterostructure affect its performance in thermal-energy harvesting\napplications?\n8. It would be helpful if the authors included a comparison of their findings with existing literature on similar composite\nmaterials to highlight the novelty and significance of their work.\n9. How does the inclusion of mica substrates impact the thermomechanical properties compared to traditional substrates,\nand what experimental evidence supports this assertion?\n10. The study mentions the grounding of the top surface; could the authors justify this choice and discuss how it might impact\nthe electrostatic properties of the system?\n11. A more thorough discussion on the interfacial adhesion between PVDF and mica would be beneficial; what methods\nwere used to evaluate this, and how do the results impact the mechanical robustness of the bilayer?\n12. What specific parameters were used in the finite element simulations to account for the anisotropic properties of mica,\nand how do these compare to isotropic assumptions in similar studies?\n13. Can the authors discuss the reliability of their thermal gradient measurements and how these may impact the accuracy of\nthe curvature predictions in practical applications?\n14. What were the criteria used for selecting the specific thicknesses of the layers in the heterostructure, and how do these\nchoices influence the mechanical and electrical performance?\n15. On page 10, line 264, the term “purocurrent amplitude” appears to be a typographical error. It should be corrected to\n“pyrocurrent amplitude” (or “pyroelectric current amplitude”) to align with standard terminology used in pyroelectric current\nanalysis.\n16. Were any external factors, such as humidity or environmental conditions, considered in the experiments, and how might\nthey influence the bending curvature?\n17. What are the implications of the obtained results for practical applications, and how do they compare to existing\ntechnologies in terms of efficiency and performance?\n18. Can you elaborate on the protocol used to measure the temperature-dependent elastic moduli of PVDF and mica? Were\nany specific standards or methods followed during the dynamic mechanical analysis (DMA)?\n19. How were the compressive stresses applied to the PVDF film, and what methods were used to quantify the effects of these\nstresses on thermal strain development?\n20. Were there specific control experiments conducted using only PVDF or mica to isolate the effects of each material on the\nobserved thermal actuation?", "reviewer_4": "The manuscript by Ying-Hao Chu and co-workers demonstrates the use of mica, a two-dimensional layered ceramic, in\ncombination with the polymer ferroelectric polyvinylidene fluoride (PVDF) to enhance the pyroelectric performance,\nparticularly the pyroelectric coefficient. The technical quality of the work is inadequate, and the manuscript presents some\nexperimental supporting the fabrication process and related measurements. Further, numerous articles in the literature have\nalready reported the fabrication of PVDF with a high β-polar phase (e.g., https://doi.org/10.3390/polym17040481;\nhttps://doi.org/10.3390/polym15224344; https://doi.org/10.1021/acsomega.4c01221 , among others). In the present work, the\nauthors report only 61% β-phase content, which raises reasonable questions about the accuracy and exclusivity of the β-\nphase quantification in the presence of other dominant PVDF phases. In addition, while the reported enhancement in the\npyroelectric coefficient is notable, it does not significantly exceed values demonstrated in previous studies such as,\nhttps://doi.org/10.1016/j.matlet.2020.127514. Therefore, despite the rigorous experimental approach and detailed materials\ncharacterization, the manuscript lacks sufficient novelty and impact to justify publication in a high-impact journal such as\nNature Communications."}, "author_response": "Comment: What are the noteworthy results? The results offer limited novelty. The use of\nthermal expansion mismatch to create a pseudo-pyroelectric response has been recognised for\na long time. It is a well known issue with pyroelectric sensors and great care is taken to\nminimise the effect in this instance - e.g. as stated in Electroceramics my Moulson & Herbert\nin 2003.\nResponse: We thank the reviewer for this critical comment and for citing the classic text\nElectroceramics by Moulson & Herbert. We completely agree with the reviewer’s observation\nthat the secondary (stress-induced) pyroelectric effect is well known and has historically been\nregarded as a parasitic issue in precise thermal sensing applications.\nHowever, the novelty of our work lies precisely in reversing this conventional paradigm.\nInstead of treating the thermal expansion mismatch as a noise source to be minimized, we have\nintentionally engineered the device structure to maximize it, transforming a \"parasitic\" effect\ninto the dominant energy-harvesting mechanism.\nWe highlight three key aspects of novelty that distinguish our PVDF/Mica heterostructure from\nthe conventional understanding described in standard texts:\n1. Magnitude of Contribution: Moulson & Herbert (2003) explicitly state that while polar\nmaterials exhibit secondary pyroelectricity due to thermal expansion, \"this is a small effect that\nseldom exceeds 10 % of the primary pyroelectric effect\". In contrast, our work demonstrates\nthat by coupling PVDF with Mica, the secondary contribution is not merely 10 %, but enhances\nthe total pyroelectric coefficient by more than an order of magnitude. This massive\nenhancement challenges the conventional view that secondary effects are negligible or merely\nartifacts.\n2. Structural Engineering of CTE Mismatch: Standard ferroelectric ceramics are often rigid,\nwhich suppresses the secondary effect. Our novelty lies in using a flexible bimorph structure\nthat exploits a significant difference in the coefficients of thermal expansion (CTE) between\nthe polymer (PVDF, ≈ 120 ppm/K) and the substrate (Mica, ≈ 7.9 ppm/K). As detailed in our\nmanuscript, this specific pairing, combined with the mechanical compliance of the 2D mica\nsubstrate, allows the device to undergo macroscopic bending. This converts thermal\nfluctuations into large in-plane strains, which are efficiently transferred to the PVDF layer,\nthereby activating a giant piezoelectric response that far exceeds that observed in traditional\nrigid-sensor designs.\n3. Constructive Alignment of Primary and Secondary Effects: In many inorganic ferroelectric\nsystems (e.g., LiNbO ), the secondary pyroelectric effect often opposes the primary impact,\n3\nreducing the total response. In our PVDF/Mica system, we demonstrate that the stress-induced\npolarization is engineered to align constructively with the intrinsic polarization.\nTherefore, while the physical principle is indeed known, our work is noteworthy because it\nshifts the design strategy from \"intrinsic phase engineering\" (which typically yields only 25%\nimprovement) to \"extrinsic structural engineering,\" yielding a 1100 % improvement. This\nestablishes a new design route for high-performance thermal energy harvesters, prioritizing\ntotal output over the noise suppression required for precision radiometry.\nComment: Will the work be of significance to the field and related fields? How does it\ncompare to the established literature? If the work is not original, please provide relevant\nreferences. There is extensive prior art in this area. for example:\nGustarov et al. Thermal energy harvesting by piezoelectric PVDF polymer coupled with shape\nmemory alloy, Sensors and Actuators A: Physical Volume 243, 1 June 2016, Pages 175-181-\nhttps://doi.org/10.1016/j.sna.2016.03.026 Kyoung-Bum Kim et al 2013 Jpn. J. Appl. Phys. 52,\nEnergy Harvesting Characteristics from Water Flow by Piezoelectric Energy Harvester Device\nUsing Cr/Nb Doped Pb(Zr,Ti)O Bimorph Cantilever\n3\nhttp://dx.doi.org/10.7567/JJAP.52.10MB01 Seung-Bum Kim et al. A synergetic effect of\npiezoelectric energy harvester to enhance thermoelectric Power: An effective hybrid energy\nharvesting method, Energy Conversion and Management, Volume 298, 15 December 2023,\n117774, https://doi.org/10.1016/j.enconman.2023.117774, Naser S. Al-Hunit, A Novel\nPiezoelectric System for Thermal Energy Harvesting from Temperature Fluctuations\nInternational Journal of Applied MechanicsVol. 12, No. 10, 2050112 (2020)\nhttps://doi.org/10.1142/S1758825120501124\nResponse: Our work introduces a distinct paradigm in thermal energy harvesting by\nengineering the secondary pyroelectric effect via a flexible PVDF/Mica bimorph structure.\nUnlike conventional approaches that rely on intrinsic material optimization or complex hybrid\nsystems, our device exploits the giant thermal expansion coefficient (CTE) mismatch between\nthe polymer and the layered ceramic substrate.\nBelow is a detailed comparison with the specific references raised:\n1. Comparison with Shape Memory Alloy (SMA) Hybrids, TiNiCu SMA/PVDF composite,\nGusarov et al., Sensors and Actuators A, 2016.\nMechanism Difference: Gusarov et al. rely on the shape memory effect driven by a martensitic\nphase transformation in TiNiCu alloys. This mechanism generates strain only when the\ntemperature crosses specific transformation thresholds (Austenite starts ≈ 35 °C) and exhibits\nsignificant thermal hysteresis (≈ 5 °C).\nOur Novelty: In contrast, our PVDF/M ica system operates via a linear thermal-expansion-\nmismatch mechanism. It does not require a specific phase-transition temperature trigger,\nallowing for continuous energy harvesting over a broader temperature range without the non-\nlinear hysteresis losses associated with SMAs. Furthermore, our fabrication is a direct, scalable\ntape-casting process that avoids the complexity of gluing aligned metal ribbons to polymer\nfilms, as required for the SMA composite.\n2. Comparison with Hybrid Thermoelectric/Piezoelectric (TEG-PEG) Systems, Kim et al.,\nEnergy Conv. Manag., 2023.\nMechanism Difference: This work describes a hybrid system where the primary power source\nis a Thermoelectric Generator (TEG). The piezoelectric cantilever serves primarily as an active\ncooling fin; it requires external vibration (0.5 g) to oscillate and dissipate heat, thereby\nmaintaining the temperature gradient across the TEG.\nOur Novelty: Our device is a standalone thermal harvester that converts temperature\nfluctuations (dT/dt) directly into electricity via the secondary pyroelectric effect. It does not\nrequire an auxiliary vibration source to function, nor does it rely on a steady-state temperature\ngradient like a TEG. This makes our system uniquely suited to low-frequency thermal\nfluctuations (e.g., respiration), where mechanical vibration may be absent.\n3. Comparison with Fluid Kinetic Energy Harvesters, Kim et al., Jpn. J. Appl. Phys., 2013.\nMechanism Difference: This study utilizes a PZT bimorph cantilever to harvest kinetic energy\nfrom water flow (2 m/s). The piezoelectric effect is activated by mechanical bending forces\nexerted by the fluid stream, not by thermal energy.\nOur Novelty: Our work is strictly a thermal energy harvester. We demonstrate that macroscopic\nbending and electrical output can be induced solely by thermal stress arising from the CTE\nmismatch between PVDF and Mica. This proves that waste heat can be harvested via structural\nengineering without requiring kinetic fluid flow or mechanical impact.\n4. Comparison with Theoretical Thermal Stress Models, Al-Huniti & Al-Nimr, Int. J. Appl.\nMech., 2020.\nMechanism Difference: This paper presents a theoretical analysis of a piezoelectric layer\nbounded by a solid elastic material or pressurized gas. It focuses on the mathematical modeling\nof stress generation in a constrained volume.\nOur Novelty: Our work provides an experimental realization of a stress-induced thermal\nharvester. Moreover, we use a flexural (bending) mode in a bimorph configuration, which\namplifies the effective strain relative to bulk expansion/compression models often treated in\ntheoretical studies. We experimentally validate this using the \"Neutral Axis\" concept,\noptimizing the substrate thickness (20 μm Mica) to maximize stress-transfer efficiency.\nIn summary, the PVDF/Mica heterostructure offers a distinct approach compared to the cited\nliterature in the following aspects:\n1. Mechanism: It exploits extrinsic secondary pyroelectricity driven by CTE mismatch,\nproviding an alternative to avoid the hysteresis of SMAs and the vibration requirements of\nhybrid TEGs.\n2. Performance: It achieves a pyroelectric coefficient that is significantly higher than that of\nintrinsic PVDF by an order of magnitude, validating the structural engineering approach.\n3. Process: It utilizes a facile, scalable tape-casting method on a flexible 2D mica substrate,\noffering significant processing advantages over complex composite assembly or rigid ceramic\nsintering.\nComment 1: use of Xray differaction to measure CTE for mica is flawed as mica is anisotropic. The relevant CTE for bending and charge generation is the CTE in the in-plane direction.\nResponse: We appreciate the reviewer's comment regarding mica's anisotropy. We fully agree\nthat standard symmetric XRD scans are limited to detecting out-of-plane variations; however,\nin-plane thermal expansion is indeed the governing factor in bimorph bending and charge\ngeneration. Owing to this, we employed asymmetric Reciprocal Space Mapping (RSM) to\nexplicitly decouple and measure lattice variations in both directions. As shown in Figure S3\nand Table S1, our RSM analysis yielded a CTE of 15.7 ppm/K in the through-thickness\ndirection (z-axis) and 7.9 ppm/K in the in-plane direction (x-axis). These results are physically\nconsistent with the crystal structure of muscovite mica: the lower in-plane CTE arises from the\nrigid confinement of strong Si-O and Al-O covalent bond networks, whereas the higher out-of-\nplane CTE results from the weak van der Waals forces and potassium ion (K+) bonds between\nthe layers. We have enhanced the structural explanation in the revised manuscript to address\nthis concern and to improve clarity.\nComment 2: ultrathin mica is not less brittle. It simply has smaller dimensions and so can\nsustain a lower load.\nResponse: We appreciate the reviewer for pointing out the imprecise usage of the term 'brittle.'\nWe agree that the increased susceptibility to fracture in ultrathin mica is primarily due to its\nreduced dimensions, which lowers the critical load it can sustain, rather than a change in\nintrinsic material brittleness. We have revised the manuscript to clarify that while reducing\nthickness below 20 µm theoretically enhances bending curvature, it renders the samples\nmechanically fragile and challenging to handle. The text has been corrected to reflect this\ngeometric limitation.\nComment 3: authors state that even if the alumina were thinned to 20um that it would still\nbehave rigidly. While it would be more rigid, it would only be 2x as rigid. they ascribe this to\nit's crystal bonding and lack of slip planes. Mica to has these limits.\nResponse: We thank the reviewer for this insightful comment regarding the mechanical\ncomparison between alumina (sapphire) and muscovite mica. We appreciate the opportunity to\nclarify our quantitative analysis and, more importantly, to refine the physical interpretation of\n\"rigidity\" in our system.\nFirst, regarding the mechanical stiffness, our experimental data indicates a larger difference\nthan the 2x factor suggested. As detailed in Supplementary Note 4 and Fig. S4B, we measured\nthe Young's modulus of our muscovite mica to be ≈110 GPa via Dynamic Mechanical Analysis,\nwhereas the standard modulus for single-crystal sapphire is approximately 360 GPa (Ref. 22).\nThus, sapphire is approximately 3.3 times stiffer than mica.\nHowever, we sincerely apologize if our original discussion on \"macroscopic bending\" caused\nconfusion. We fully agree with the reviewer that attributing the enhancement solely to\nmacroscopic flexural rigidity or neutral axis shifting was physically imprecise, especially given\nthat the heterostructures remain macroscopically flat during measurement. Prompted by this\ncomment, we have re-evaluated the micromechanical boundary conditions and revised our\ntheoretical framework to focus on the substrate clamping effect. This provides a more accurate\nphysical explanation for why sapphire, even if thinned to 20 µm, may not replicate the\nperformance of mica.\nThe critical factor is the nature of the interface coupling. Sapphire possesses a rigid 3D\ncovalently/ionically bonded surface with a high modulus. This creates a \"hard clamping\"\nboundary condition that mechanically locks the PVDF lattice. Even if the sapphire substrate\nwere thinned to reduce its bulk stiffness, its intrinsic surface rigidity would still severely restrict\nthe in-plane Poisson deformation of the PVDF film, effectively suppressing the piezoelectric\ncontribution to the total pyroelectric response. This explains the low signal (≈ 32 µC/m2K)\nobserved in our PVDF/Sapphire control samples.\nIn contrast, while mica is indeed a ceramic, its unique 2D-layered structure held by weak van\nder Waals forces (\"slip planes\") fundamentally alters the boundary condition. We propose that\nthis van der Waals surface acts as a mechanically compliant interface. Unlike the rigid anchor\nof sapphire, the mica interface effectively transmits the thermal stress required for the\nsecondary pyroelectric effect but minimizes the rigid clamping on the PVDF lattice. This\nallows the PVDF dipoles to respond freely to the induced stress, unlocking the giant\npyroelectric coefficient (-359 µC/m2K). Therefore, the choice of mica is essential not merely\nfor bulk flexibility, but for providing the specific interfacial compliance necessary to amplify\nthe stress-induced response, a feature that intrinsically rigid 3D crystals like sapphire lack\nregardless of their thickness.\nWe have revised the description in the manuscript to this potential mechanism and to modified\nthe previous discussion.\nComment 4: discussion of polymer based systems requiring alternative stress-transfer\npathways is very ambiguous. Stress in any layered system is transferred in the same way -\nacross interfaces where bonding exists.\nResponse: We agree with the reviewer that the fundamental mechanism of stress transfer—via\ninterfacial bonding—remains the same across layered systems. The phrase \"alternative stress-\ntransfer pathways\" in our original manuscript was indeed ambiguous and has been corrected.\nWe intended to highlight the distinct structural accommodation mechanism that preserves the\ninterface in our device.\nWe have revised the text to clarify that while the stress transfer mechanism is universal, the\nefficiency of converting this stress into usable strain is dictated by structural connectivity and\nmechanical boundary conditions.\nSpecifically, rigid substrates dominated by strong 3D covalent bonding (such as sapphire) lack\nthe compliance to accommodate the massive shear stress generated by the coefficient of\nthermal expansion (CTE) mismatch. This \"hard clamping\" leads to stress concentrations that\nfrequently exceed the bonding strength, resulting in interfacial delamination or structural\nfailure and terminating effective stress transfer.\nIn contrast, the muscovite mica substrate features unique van der Waals interactions that enable\npartial interlayer slipping and low flexural rigidity. This capability allows the substrate to\nrelieve excessive destructive shear stress through macroscopic bending (bimorph actuation)\nwhile maintaining interfacial integrity. Therefore, the \"alternative\" mechanism refers to mica's\nself-accommodation, which prevents mechanical failure and ensures that thermal strain is\ncontinuously and effectively coupled to the PVDF layer, thereby driving the secondary\npyroelectric effect.\nReviewer #2\nThis article presents an interesting approach to improving the pyroelectric response in flexible\nPVDF/mica heterostructures. The authors highlight the dominant role of interfacial\nthermomechanical stresses, exploiting the thermal expansion mismatch between PVDF and\nmica, rather than relying solely on conventional phase engineering. The results are remarkable,\nwith a pyroelectric coefficient of –359 µC/m²K, more than an order of magnitude higher than\nthat of a single PVDF film. The study combines experimental analyses with modeling\n(Timoshenko and FEM) in a coherent way, which strengthens the scientific validity of the\nconclusions. The work is well structured and opens promising perspectives for applications in\nflexible thermal sensors, energy harvesting devices, and wearable electronics.\nResponse: We sincerely thank the reviewer for their support and constructive suggestions. We\nwill provide thorough, complete responses to any points that need further clarification.\nComment 1: How does the pyroelectric performance evolve at higher operating frequencies,\ncloser to real application conditions?\nResponse: We appreciate the reviewer’s insightful question regarding the frequency\ndependence of the pyroelectric performance. We have evaluated the device at temperature-\ntuning frequencies ranging from 0.01 to 0.05 Hz. As shown in Fig. R1, the pyroelectric\ncoefficient remains highly stable within this range, indicating reliable performance. Regarding\nthe limitation at higher frequencies, we would like to clarify that it is governed by the\nmeasurement system's thermal time constant rather than the material's intrinsic response. As\nnoted in our experimental methods (referencing the Garn-Sharp method), the sample possesses\na finite thermal mass. When the driving frequency exceeds 0.05 Hz, the heat transfer rate from\nthe Peltier module cannot keep pace with the modulation signal. This leads to thermal damping,\nin which the amplitude of the actual temperature oscillation inside the sample decreases\nsignificantly. Consequently, the sample temperature stabilizes near the average value rather\nthan following the sinusoidal modulation, preventing the accurate extraction of the pyroelectric\ncoefficient. Despite this testing limit, the operating range (0.01-0.05 Hz) is highly\nrepresentative of our target applications. Our PVDF/Mica bimorph is designed for low-grade\nthermal energy harvesting, utilizing environmental temperature fluctuations which naturally\noccur at very low frequencies. For instance, human respiration, a significant source of\nbiomechanical and thermal energy, typically operates at ≈ 0.2-0.3 Hz (ACS Appl. Electron.\nMater. 2021, 3, 1, 248–259), and ambient waste heat fluctuations are often even slower.\nTherefore, the stable performance demonstrated in the low-frequency regime confirms the\ndevice's suitability for these real-world scenarios. We have included these results and\ndiscussion in the supporting materials.\nFig. R1. Frequency dependence of the pyroelectric coefficient.\nComment 2: Is the β-phase proportion of PVDF (≈ 61%) sufficient to ensure reproducibility\nand stability at a large scale?\nResponse: We appreciate the reviewer's concern about the phase content and the\nmanufacturing stability. While the β-phase fraction is approximately 61%, our results indicate\nthat this proportion is highly consistent and sufficient to ensure device stability, primarily due\nto the uniformity of our fabrication process. We utilized tape casting (doctor-blade coating),\nan industrially established technique designed explicitly for large-area, scalable film fabrication.\nTo rigorously assess the reproducibility and spatial homogeneity, we performed Raman\nspectroscopy characterization at five randomly selected locations across a 1 cm × 3 cm\nspecimen. As presented in Figure S1C, the β-phase fraction exhibits minimal fluctuation across\nthe sample surface, showing negligible standard deviation. Furthermore, we distributed six\ndistinct samples across a 10 cm × 8 cm coating area for simultaneous fabrication and\nmeasurement. The results revealed that the compositional difference between these widely\nspaced positions was similar. These results confirm that our method yields excellent spatial\nhomogeneity, ensuring consistent material properties throughout the device area. Therefore,\ndespite the presence of mixed phases, the fabrication process is robust and reproducible,\nsupporting its feasibility for large-scale production.\nComment 3: Could the intermediate ITO electrode introduce capacitive or thermal effects that\ninfluence the measured response?\nResponse: We appreciate the reviewer for raising this point. We selected ITO primarily for its\nmechanical compatibility with muscovite mica, as its coefficient of thermal expansion is\ncomparable to that of muscovite mica, ensuring structural stability. Regarding the measured\nresponse, we conclude that the ITO electrode does not introduce significant artifacts for three\nreasons: First, the ITO layer functions solely as a conductive electrode rather than a dielectric;\ntherefore, it does not contribute to capacitive storage within the functional stack. Second, since\nITO possesses a centrosymmetric crystal structure, it is inherently non-pyroelectric and does\nnot generate any additional signal. Finally, the ITO film (≈ 200 nm) is approximately 100 times\nthinner than the PVDF layer (≈ 20 µm) and the mica substrate. Due to the negligible thermal\nmass of the intermediate electrode relative to the active layers, it does not significantly\ninfluence the measured pyroelectric response.\nComment 4: Does the device maintain its high pyroelectric coefficient under extended cycling\nand across a wider temperature range?\nResponse: : In the main manuscript, we investigated the pyroelectric response primarily at\nroom temperature (24 °C). To address the reviewer’s comment on device stability, we extended\nour characterization to a broader temperature range and long-term cycling. Temperature\nStability: As shown in Fig. R2, the pyroelectric coefficient remains highly stable (≈ −350 µC\nm-2 K-1) as the base temperature is elevated from 24 °C to 65 °C. This indicates that the device\noperates well within the ferroelectric phase of PVDF, without thermal depolarization, making\nit suitable for wearable and waste-heat harvesting applications. To rigorously evaluate fatigue\nresistance, the device was subjected to an extended test of 10,000 thermal cycles (total duration\n≈ 2.3 days). Fig. R3 presents the peak output current retention across the testing period. The\nresults demonstrate exceptional stability during the first 5,000 cycles, with the output current\nvariation remaining within ≈ 4 %. While a larger fluctuation (≈ 20 %) was observed as the\ncycling approached 9,000 cycles, we attribute this variation to thermal heat accumulation\nwithin the testing setup during the prolonged continuous operation (> 200,000 seconds), rather\nthan intrinsic material degradation. The highly consistent performance over the initial 5,000\ncycles demonstrate the potential of the heterostructure for long-term practical applications. We\nhave included these results in the supporting materials.\nFig. R2. Pyroelectric coefficient measured across various initial base temperatures.\nFig. R3 Normalized pyroelectric current retention (I/I ) measured over continuous thermal\n0\ncycles.\nReviewer #3\nThe manuscript presents an engaging and well-structured study on piezoelectric biomorph\nheterostructures based on PVDF/mica, where the authors effectively demonstrate the secondary\ncontributions of the pyroelectric response and highlight the dominant role of thermally induced\ninterfacial stress as a governing mechanism. The concept of utilizing significant coefficients of\nthermal expansion (CTE) mismatch between distinct material layers to amplify the overall\npyroelectric response represents a novel and promising direction in multifunctional energy\nconversion research.\nThe study is scientifically sound and methodologically consistent, yielding results that provide\nvaluable insights into the coupling mechanisms between pyroelectricity and thermomechanical\nstress. However, a few points raised during the review require minor clarification and\nelaboration for completeness. Once these clarifications are incorporated, the manuscript will\nmeet the journal’s standards and can be recommended for acceptance after minor revision.\nResponse: We sincerely thank the reviewer for their positive assessment and valuable guidance.\nWe appreciate the recognition of the scientific soundness and novelty of our study. In this\nrevised submission, we have provided a complete point-by-point response to all the comments\nand have incorporated the requested clarifications into the main text to further improve the\nquality and completeness of the manuscript.\nComment 1: How do the thermal expansion coefficients of the individual components in the\nPVDF/mica bilayer affect the overall strain response during temperature changes?\nResponse: In our bimorph structure, the in-plane coefficient of thermal expansion (CTE) of\nPVDF is approximately 120 ppm/K, whereas that of mica is only 7.9 ppm/K. Upon heating, a\nfree-standing PVDF layer would naturally expand significantly more than the mica; however,\nin the bonded bilayer (assuming intact interfacial adhesion without macroscopic delamination),\nthe PVDF is constrained by the lower-CTE mica substrate. Consequently, the PVDF layer\ndevelops in-plane compressive stress, while the mica substrate experiences in-plane tensile\nstress. This stress asymmetry across the thickness produces a bending moment, resulting in\ncurvature and a finite strain field in the PVDF layer. (Conversely, upon cooling, the stress signs\nreverse, and the curvature direction changes accordingly.) To quantify the strain induced by\nthis CTE mismatch, we employed the Euler-Bernoulli beam theory (σ ≈ E · κ · y) to calculate\nthe strain magnitude, incorporating the experimentally measured curvature values (κ). The\nresulting calculated strain as a function of temperature change is presented in Fig. R4. This\nthermally generated strain is crucial for activating the piezoelectric contribution to the overall\nresponse (i.e., the secondary pyroelectric effect).\nIn addition, Finite element (FEM) simulations show that the overall strain response agrees well\nwith Timoshenko's analytical model, and the resulting curvatures match with those measured\nin the experiment. It is worth to mention that FEM can further provide detailed local stress\ndistributions. An example (∆T = 94 K) is shown in Fig.R5, and addressed as follows.1. Along\nthe PVDF thickness, the top surface (at the PVDF/mica interface) exhibits higher compressive\nstress than the bottom surface due to its proximity to the constrained mica layer, as shown in\nFig. R5A and B. 2. The clamped edge of the mica substrate restricts deformation of all\ndirections, leading to high in-plane (X and Y directions) compressive stress and complicated\nstress distribution in PVDF near the clamped region, as shown in Fig. R5A and C. 3. The out-\nof-plane (Z-direction) stress in PVDF is much smaller (about three orders of magnitude) than\nthe in-plane components, since it is unrestrained in that direction, as shown in Fig. R5D. 4.\nOverall stress magnitudes increase with temperature and, however, the overall stress\ndistribution remains unaltered.\nWe have revised the manuscript description and added the corresponding analyses and figures\nto the Supporting Information to clarify the relationship among temperature change, stress\ngeneration, and the resulting strain response.\nFig. R4. Calculated strain magnitude within the PVDF layer as a function of temperature\nvariation (∆T)\nFig. R5. Stress distribution of PVDF in the FEM model under a temperature increase of ΔT =\nPVDF surface; (C) Y-direction stress at the top surface; and (D) Z-direction stress at the top\nsurface. The results indicate dominant in-plane compressive stresses in PVDF and negligible\nout-of-plane stress.\nComment 2: Could the authors elaborate on the selection criteria for the thermal and\nmechanical properties used in the finite element model for the PVDF/mica bilayer?\nResponse: The finite element (FEM) model involves multiple coupled physical phenomena,\nincluding thermal conduction, convection, thermo-mechanical interaction, and piezoelectric\ncoupling. Because of the large number of parameters, it is impractical to measure all material\nproperties experimentally; therefore, only key parameters were measured.\nSpecifically, the in-plane Young’s moduli and thermal expansion coefficients of mica were\nmeasured, as the mica substrate critically defines the boundary constraints of the PVDF layer.\nFor PVDF, the piezoelectric coefficient 33, the elastic constant 33, and the thermal\nexpansion coefficient were measured because the out-of-plane (3-direction) properties\nd 𝐶\ndominate the measured electrode voltage 3. The temperature dependence of mica’s in-plane\nmodulus and PVDF’s 33 was also characterized experimentally to incorporate accurate\n𝑉\ntemperature-dependent material behavior in the FEM model. Since the piezoelectric\n𝐶\nconstitutive matrices contain multiple coupling terms (e.g., 31, 32), the anisotropy of the\nmaterial system must be fully considered. To reduce experimental cost and time, the remaining\nd 𝑑\nparameters were obtained from the literature. Furthermore, to simulate the temperature-\nramping process in the experimental chamber, the FEM model incorporated thermal properties\nincluding specific heat, convection heat transfer coefficient, and thermal conductivity, enabling\nrealistic heat transfer and temperature-gradient behavior within the bilayer structure.\nAs for the properties obtained from the literature, priority was given to sources that employed\nsimilar modeling frameworks, such as Mishra and Das, Mechanics of Composite Materials,\n58(5), 657–672 (2022); Chakhchaoui et al., Polymer Advanced Technologies, 28(9), 1170–\n1178 (2017). If similar modeling data were unavailable, experimentally derived literature\nvalues were adopted in the current work.\nComment 3: What specific methodologies were used to analyze the thermal expansion\ncoefficient of mica, and are they clearly explained?\nResponse: To ensure a precise and rigorous determination of the thermal expansion coefficient\n(CTE), specifically the critical in-plane component, we employed temperature-dependent\nAsymmetric Reciprocal Space Mapping (RSM). Standard symmetric θ-2θ scans are\ninsufficient, as they probe only the out-of-plane (z-axis) expansion. Therefore, our\nmethodology involved specific asymmetric scans (tracking off-axis reflections) across a\ncontrolled temperature range. By mapping the reciprocal lattice points at each temperature step,\nwe decoupled the lattice expansion vectors, allowing us to independently extract the lattice\nparameters for both the a-axis (in-plane) and c-axis (out-of-plane). The CTE values were then\nderived from the linear fit of the lattice strain (ΔL/L ) versus temperature. This approach\n0\nyielded quantitative in-plane and out-of-plane CTEs of 7.9 ppm/K and 15.7 ppm/K,\nrespectively. To ensure clarity, we have expanded the Experimental Section in the revised\nmanuscript.\nComment 4: Are the results of the PFM analysis of the PVDF/mica heterostructure adequately\ndetailed in terms of both processes and outcomes?\nResponse: We thank the reviewer for this constructive comment. We have expanded the\nmanuscript to provide a comprehensive description of the PFM methodology and quantification\nprocess. PFM measurements were conducted using a Cypher atomic force microscope\nequipped with conductive probes. To ensure accurate quantification and account for tip-sample\ncontact resonance, we employed a comparative calibration method using a standard BiFeO\n3\nthin film with a known piezoelectric coefficient as a reference. A thin ITO layer (200 nm) was\nused as the bottom electrode to facilitate the measurement. Instead of relying solely on phase\ncontrast, we performed local piezoelectric spectroscopy by sweeping the AC bias voltage from\nthe film's intrinsic piezoelectric nature. By comparing the slope of the amplitude-voltage curve\nof our PVDF/mica heterostructure with that of the BFO reference, we determined the effective\npiezoelectric coefficient to be ~29 pm/V, which is consistent with literature values for high-\nquality PVDF.\nFurthermore, our analysis defined the \"effective polarized region\" as areas exhibiting a uniform\nphase response within ± 5°. This statistical analysis confirmed that approximately 61 % of the\nsurface area exhibits vigorous piezoelectric activity. Crucially, we observed a strong contrast\nin the OP-PFM amplitude images (bright regions) compared to a relatively weak IP-PFM signal.\nThis confirms that the dominant polarization vector of the PVDF β-phase on the mica substrate\nis oriented in the out-of-plane direction. This spatial distribution is in excellent agreement with\nour Raman spectroscopy results, which independently quantified the β-phase content at 61 %,\nconfirming the effectiveness of our tape-casting and thermal processing optimization.\nComment 5: What specific techniques were utilized to ensure the optimal crystalline phase\ndistribution within the synthesized PVDF material?\nResponse: To ensure optimal crystalline phase distribution and homogeneity, we integrated\nthe tape-casting (doctor-blade) technique with strict control over crystallization kinetics.\nSpecifically, we utilized DMAC as a high-polarity solvent to promote molecular chain\nextension. Furthermore, we systematically optimized the processing parameters, identifying\n80°C as the critical evaporation temperature and 15 wt% as the optimal concentration. This\ncombination enables uniform solvent evaporation and internal stress development, both of\nwhich are essential for maximizing the polar β-phase content while minimizing local phase\nsegregation. The resulting homogeneity was subsequently confirmed via Raman spectroscopy\nmapping and FTIR analysis.\nComment 6. How does the piezoelectric coefficient of the PVDF/mica system change with\nvarying temperature conditions, and what experimental data support this?\nResponse: We evaluated the temperature dependence of the piezoelectric coefficient by\ncorrelating the macroscopic pyroelectric response with microscopic ferroelectric phase stability.\nAs established in our manuscript, the secondary pyroelectric effect, which is piezoelectric in\norigin, is the dominant contributor to our device's output. Our temperature-dependent\nmeasurements within the device's operating range show a stable total pyroelectric coefficient.\nSince the total signal is primarily driven by the piezoelectric conversion of thermal strain, this\nstability confirms that the piezoelectric coefficient (d ) remains robust and does not degrade\n33\nsignificantly under standard operating thermal conditions. To further investigate the intrinsic\ndipole behavior and thermal limits, we conducted in-situ temperature-dependent P-E loop\nmeasurements, as shown in Figure R6. The results reveal that at the initial state (25 °C), the\ndevice exhibits a well-defined ferroelectric hysteresis loop with distinct remnant polarization\n(red curve), confirming the strong dipole alignment essential for piezoelectricity. As the\ntemperature is elevated to 145 °C, the hysteresis loop transitions into a linear, slim shape with\nnegligible remnant polarization (black curve). Crucially, upon cooling back to room\ntemperature, the ferroelectric hysteresis is fully recovered and overlaps well with the initial\nstate (blue curve). This analysis demonstrates that while the piezoelectric effect undergoes a\nreversible phase transition at extreme temperatures (> 140 °C), the structural integrity and\ndipole alignment capability are fully preserved. Consequently, within the targeted energy-\nharvesting temperature range, the piezoelectric coefficient remains stable, ensuring reliable\ndevice operation without permanent degradation. We have included this discussion in the\nmanuscript.\nFig. R6. (A) pyroelectric coefficient measured across various initial base temperatures. (B) P-\nE hysteresis loops under a heating-cooling thermal cycle.\nComment 7: How do the structural properties of the PVDF/mica heterostructure affect its\nperformance in thermal-energy harvesting applications?\nResponse: The structural properties, particularly the thickness of the mica substrate, are critical\nto determining the device's performance and suitability for different energy-harvesting\nscenarios. Since pyroelectric generation fundamentally relies on temporal temperature changes\n(dT/dt), practical applications generally fall into two categories: static devices exposed to time-\nvarying environmental temperatures, and mobile devices moving across fixed spatial\ntemperature gradients to induce cyclic variations. Our results demonstrate that the mica\nthickness is the key factor governing the mechanical reversibility required for these\napplications. For spatial gradient harvesting via mechanical actuation, an optimal, thinner mica\nsubstrate is essential to reduce flexural rigidity, enabling the device to trigger reversible\nbending and effectively harvest energy from the temperature gradient; excessive stiffness from\na thicker substrate would hinder this mechanical response. Conversely, in static mode, for\nenvironments where temperature varies with time, the heterostructure can still generate stable\npyroelectric output driven by the internal thermal stress (bimorph effect) and the intrinsic\npyroelectric response, without the need for macroscopic bending. However, it is crucial to note\nthat increasing mica thickness increases the thermal mass. This inherently increases the device's\nthermal time constant, directly affecting the operating frequency. Therefore, tuning the mica\nthickness allows us to tailor the heterostructure's structural properties to meet the specific\nrequirements of the target energy-harvesting mechanism.\nComment 8: It would be helpful if the authors included a comparison of their findings with\nexisting literature on similar composite materials to highlight the novelty and significance of\ntheir work.\nResponse: We appreciate the reviewer’s suggestion to benchmark our results against existing\nliterature. To better contextualize the significance of our findings, we have incorporated a\ndetailed comparison with relevant existing literature into the Figure of Merit (FOM) plot in the\nrevised manuscript. This updated figure explicitly demonstrates the competitive performance\nof our device relative to other reported composite materials, thereby underscoring the novelty\nof our stress-engineering strategy.\nComment 9: How does the inclusion of mica substrates impact the thermomechanical\nproperties compared to traditional substrates, and what experimental evidence supports this\nassertion?\nResponse: The inclusion of mica substrates fundamentally alters the thermomechanical\ncoupling mechanism compared to traditional rigid substrates. Our experimental evidence and\ntheoretical modeling support this assertion through specific mechanical and interfacial\ndistinctions. Traditional substrates such as sapphire exhibit a high Young’s modulus (≈ 360\nGPa). As detailed in our analysis, these high-stiffness pins the neutral axis of the heterostructure\ndeep within the substrate, mechanically clamping the PVDF film and preventing the\nmacroscopic bending required to generate significant in-plane strain. In contrast, mica (≈ 110\nGPa) serves as a mechanically compliant substrate. The critical factor is the nature of the\ninterface coupling. Furthermore, sapphire possesses a rigid 3D covalently/ionically bonded\nsurface with a high modulus. This creates a \"hard clamping\" boundary condition that\nmechanically locks the PVDF lattice. Even if the sapphire substrate were thinned to reduce its\nbulk stiffness, its intrinsic surface rigidity would still severely restrict the in-plane Poisson\ndeformation of the PVDF film, effectively suppressing the piezoelectric contribution to the\ntotal pyroelectric response. This explains the low signal (≈ -32 µC/m2K) observed in our\nPVDF/Sapphire control samples.\nIn contrast, while mica is indeed a ceramic, its unique 2D-layered structure held by weak van\nder Waals forces (\"slip planes\") fundamentally alters the boundary condition. We propose that\nthis van der Waals surface acts as a mechanically compliant interface. Unlike the rigid anchor\nof sapphire, the mica interface effectively transmits the thermal stress required for the\nsecondary pyroelectric effect but minimizes the rigid clamping on the PVDF lattice. This\nallows the PVDF dipoles to respond freely to the induced stress, unlocking the giant\npyroelectric coefficient (-359 µC/m2K). This order-of-magnitude enhancement confirms that\nthe \"compliant\" nature of the mica substrate is the decisive factor in enabling the giant\nsecondary pyroelectric response.\nComment 10: The study mentions the grounding of the top surface; could the authors justify\nthis choice and discuss how it might impact the electrostatic properties of the system?\nResponse:\nWe grounded the top surface for two critical reasons: to eliminate surface electrostatic charge\naccumulation and, more importantly, to strictly define the direction of current flow.\nEstablishing a fixed reference potential (V = 0) is essential for determining the sign of the\npyroelectric coefficient (π = dP/dT).\nFor ferroelectric polymers like PVDF, the coefficient is typically negative. This means that as\ntemperature increases, thermal agitation reduces the net dipole alignment (spontaneous\npolarization). Without a fixed grounding configuration, the polarity of the measured current\ncould be ambiguous, leading to a misinterpretation of the coefficient’s sign.\nHeating causes a release of compensating charges due to the reduction of polarization (T ↑, P\n↓). By grounding the top electrode, we allow these excess positive charges to flow out,\ngenerating a defined current direction. Our comparative data (Figure R7) shows that both the\npristine PVDF and the PVDF/Mica heterostructure exhibit current flow in the same direction\nupon heating. Therefore, the grounding choice ensures that we accurately capture the physical\nresponse and rule out artifacts caused by polarity reversal or floating potentials.\nFig. R7. Schematic of electron flow (A) pure PVDF, (B) PVDF/mica heterostructure.\nComment 11: A more thorough discussion on the interfacial adhesion between PVDF and\nmica would be beneficial; what methods were used to evaluate this, and how do the results\nimpact the mechanical robustness of the bilayer?\nResponse:\nIn this work, the interfacial integrity was evaluated through cyclic mechanical bending tests,\nas shown in Fig. 1E. The bimorph structure exhibits a stable output voltage without any\nobservable degradation after 1,000 continuous mechanical bending cycles. If delamination or\nweak bonding between the PVDF and mica layers would have resulted in mechanical\ndecoupling and a drop in the electrical signal. The results indicate a good interfacial adhesion\nand mechanical robustness of the bilayer. Therefore, the consistent performance confirms that\nthe tape-casting process ensures good interfacial adhesion, demonstrating the bilayer system is\nmechanically robust and suitable for repeated operation. We have emphasized this result in the\nrevised manuscript to address the interfacial adhesion between PVDF and mica.\nComment 12: What specific parameters were used in the finite element simulations to account\nfor the anisotropic properties of mica, and how do these compare to isotropic assumptions in\nsimilar studies?\nResponse: As shown in Table S2, the in-plane Young’s moduli of mica (along the x and y\ndirections) exhibit nearly a 10 % variation around 50 °C. Because the mica substrate’s in-plane\nstiffness critically defines the boundary constraints of the PVDF layer, anisotropy must be\nconsidered in the FEM simulations. If mica were treated as an isotropic material with a single\nYoung’s modulus (≈ 60.9 GPa) and a uniform CTE of 15.4 ppm/K, as often assumed in\nliterature, the thermal constraint on the PVDF layer would be smaller, resulting in reduced\ncurvature and consequently a lower output voltage after heating.\nFurthermore, the PVDF layer in this study was modeled with full anisotropy, with the elastic\nconstants set to C11 = 3.8 GPa and C = 3.2 GPa. This leads to simulated in-plane compressive\n22\nstress in x-direction being slightly higher than that along the y-direction. In contrast, isotropic\nassumptions with C = C would fail to capture this stress asymmetry, and both the curvature\n11 22\nand the piezoelectrically induced voltage would deviate significantly from experimental\nobservations.\nComment 13: Can the authors discuss the reliability of their thermal gradient measurements\nand how these may impact the accuracy of the curvature predictions in practical applications?\nResponse: We appreciate the reviewer’s query regarding the reliability of the thermal\nmeasurements and the predictive accuracy of our models. We ensured the reliability of the\nthermal gradient by conducting experiments in a preheated oven, where the environment was\ncontinuously monitored with thermocouples to maintain thermal stability. Regarding the\ncurvature predictions, we assert that our Finite Element Method (FEM) model provides a\nhighly reliable basis for practical applications for the following reasons: 1. Unlike the\nsimplified Timoshenko bilayer model, which assumes isotropic material properties and\ntemperature-independent stiffness, our FEM model explicitly incorporates the temperature-\ndependent Young’s moduli of both PVDF and mica (experimentally determined via Dynamic\nMechanical Analysis,) and accounts for the inherent anisotropy of the mica substrate. 2. The\nmodel goes beyond simple thermal loading by accounting for thermal conductivity, specific\nheat capacity, and convective heat transfer at the surfaces (h = 100 W/m2K). This ensures that\nthe coupled thermomechanical behavior is accurately simulated. As shown in Fig. 2F, the FEM\npredictions agree well with the experimental trends, with the curvature discrepancy remaining\nwithin a narrow range (< 23 m-1) across the operational window. We attribute this minor\nvariation to non-ideal interfacial bonding or microscopic structural imperfections rather than\nerrors in the applied thermal gradient. Therefore, the FEM model provides a reliable and robust\ntool for predicting device curvature in real-world energy-harvesting scenarios.\nComment 14: What were the criteria used for selecting the specific thicknesses of the layers in\nresponse: the heterostructure, and how do these choices influence the mechanical and\nelectrical performance?\nResponse: We apologize for not clarifying this point more clearly in the original manuscript.\nThe layer thicknesses were selected to optimize the coupling between thermal deformation and\nelectrical output while maintaining mechanical robustness. We fixed the PVDF thickness at 20\nµm based on our fabrication optimization and varied the mica substrate thickness. Our results\n(Fig. 2E, as shown in Fig. R8) demonstrate that the bending curvature increases as the mica\nthickness decreases. The choice of 20 µm for the mica substrate was critical for two reasons.\nFirst, experimentally and theoretically, a thinner mica layer positions the neutral axis closer to\nthe PVDF/mica interface. This maximizes the interfacial thermal stress transfer required to\nactivate the secondary pyroelectric effect. Second, we observed a practical lower limit: mica\nlayers thinner than 20 µm became too fragile to handle without fracturing during tape casting.\nThus, the 20 µm thickness was chosen as the optimal balance between maximizing the stress-\ninduced electrical output and ensuring device yield.\nFig. R8. Bending curvature as a function of temperature variation for PVDF/mica bilayers with\nvarying mica thicknesses.\nComment 15: On page 10, line 264, the term “purocurrent amplitude” appears to be a\ntypographical error. It should be corrected to “pyrocurrent amplitude” (or “pyroelectric current\namplitude”) to align with standard terminology used in pyroelectric current analysis.\nResponse: We thank the reviewer for pointing out this typographical error. It has been\ncorrected to “pyrocurrent amplitude” in the revised manuscript.\nComment 16: Were any external factors, such as humidity or environmental conditions,\nconsidered in the experiments, and how might they influence the bending curvature?\nResponse: We appreciate the reviewer’s query regarding environmental factors. We carefully\nconsidered the influence of humidity and ruled it out based on our experimental protocols and\nthe materials' intrinsic stability. During the pyroelectric current measurements, we used a\nPeltier chip to modulate the temperature starting from different initial temperatures. The\nobtained pyroelectric coefficients at various starting temperatures were nearly identical,\nindicating that device performance is stable across different thermal conditions (Fig. R9). Our\nbending curvature measurements were conducted in a temperature-controlled oven setup (Fig.\nS4). The elevated temperatures during these tests naturally mitigate moisture adsorption.\nFurthermore, the elastic moduli of PVDF and mica, which determine the theoretical bending\ncurvature, were experimentally determined via Dynamic Mechanical Analysis (DMA) using a\nnitrogen gas-cooling accessory. This ensures that the mechanical parameters driving the\nbending response were characterized in a dry, inert atmosphere, free from humidity artifacts.\nPVDF is well-documented for its high thermal and hydrolytic stability (ACS Appl. Mater.\nInterfaces 2021, 13, 23, 27245–27254). Consequently, the polymer matrix is resistant to\nmoisture uptake that might otherwise induce swelling or alter the mechanical strain. In addition,\nas shown in Fig. S6B, the device exhibited excellent durability over 5,000 thermal cycles. If\nenvironmental factors such as humidity were influencing the response, we would expect\nsignificant performance degradation or hysteresis over prolonged cycling, which was not\nobserved. Therefore, we conclude that the measured bending and pyroelectric outputs are\ndriven by the designed thermal stresses rather than environmental artifacts.\nFig. R9. Pyroelectric coefficients measured at different initial temperatures.\nComment 17: What are the implications of the obtained results for practical applications,\nand how do they compare to existing technologies in terms of efficiency and performance?\nResponse: The implications of our results are best understood by evaluating both efficiency,\nas measured by the Figure of Merit (FoM), and the technology's scalability. 1. Efficiency and\nPerformance: While inorganic ferroelectrics (e.g., PMN-PT single crystals) exhibit ultrahigh\npyroelectric coefficients, their performance in voltage-mode applications is often compromised\nby their high dielectric permittivity (> 1000). In contrast, our PVDF/mica heterostructure\ncouples a highly enhanced pyroelectric coefficient with PVDF's intrinsically low permittivity\n(≈ 11). This results in a superior FoM that outperforms many standard materials, such as PZT\nfilms and PVDF, as detailed in Table S3. This high voltage sensitivity is critical for efficient\nthermal sensing without complex amplification circuits. 2. Practical Application & Scalability:\nUnlike complex nanomembranes or epitaxial thin films that require expensive synthesis or\ntransfer processes, our solution-processed tape-casting method offers a scalable, low-cost route\nfor large-area fabrication. Furthermore, the device is optimized for low-grade thermal energy\nharvesting at low frequencies (e.05 Hz). This frequency response aligns perfectly with\nenvironmental thermal fluctuations, such as human respiration (≈ 0.2-0.3 Hz) and industrial\nwaste heat cycles, making it practically viable for wearable electronics and self-powered\nsystems (ACS Appl. Electron. Mater. 2021, 3, 1, 248–259). We have included this discussion\nin the revised manuscript and supporting information.\nComment 18: Can you elaborate on the protocol used to measure the temperature-dependent\nelastic moduli of PVDF and mica? Were any specific standards or methods followed during\nthe dynamic mechanical analysis (DMA)?\nResponse: The temperature-dependent elastic moduli were characterized using Dynamic\nMechanical Analysis (DMA) following standard experimental protocols. We employed the\nthree-point bending mode for the bilayer structure. The measurements were conducted on\nrectangular specimens measuring 5 mm × 30 mm, mounted on a standard three-point bending\nfixture. During the analysis, a fixed frequency and a dynamic strain amplitude within the linear\nviscoelastic region were applied, while the temperature was ramped at a constant rate. This\nallowed us to continuously record the storage modulus (E') as a function of temperature (T),\nensuring accurate mechanical characterization across the operating range. We have added\nrelevant descriptions to the main text to enhance clarity.\nComment 19: How were the compressive stresses applied to the PVDF film, and what\nmethods were used to quantify the effects of these stresses on thermal strain development?\nResponse: The compressive stresses in the PVDF layer arise naturally from the thermal\nexpansion mismatch between PVDF and mica during heating. PVDF has a coefficient of\nthermal expansion (CTE) of approximately 120 ppm/K, whereas mica’s in-plane CTE is only\nabout 7.9 ppm/K. Since PVDF tends to expand more than mica, the adhesion between the two\nlayers constrains PVDF, producing in-plane compressive stresses in PVDF and tensile stresses\nin mica.\nThese stresses were not externally applied but were generated intrinsically through the thermo-\nmechanical coupling. In the FEM model, the stress and strain fields were calculated directly\nfrom the constitutive material matrices, allowing quantitative correlation between temperature\nrise, mechanical strain, and the resulting piezoelectric output voltage. The FEM results show\nthat both the compressive stress and the corresponding strain in PVDF increase with\ntemperature, consistent with experimental trends.\nComment 20: Were there specific control experiments conducted using only PVDF or mica\nto isolate the effects of each material on the observed thermal actuation?\nResponse: To isolate the effect of each material, as shown in Figure R10, we placed a PVDF\nfilm and an ITO/mica substrate under the same thermal cycling conditions (heating to 70 °C).\nThis confirms that when isolated, neither component exhibits noticeable macroscopic\ndeformation or bending. Theoretically, based on their respective coefficients of thermal\nexpansion (CTE), a 45 K temperature rise induces a linear strain of approximately 0.54 % for\nPVDF (120 ppm/K) and 0.036 % for mica (7.9 ppm/K). While these materials undergo slight\nisotropic thermal expansion, they do not possess the internal stress gradient required for\nactuation in an unconstrained state. These results demonstrate that the observed thermal\nactuation originates from the interfacial CTE mismatch rather than the intrinsic behavior of the\nindividual components.\nFurthermore, to assess the practical robustness of this mechanism, we evaluated the device\nperformance across a broad range of initial operating temperatures (20-70 °C), as illustrated in\nFigure R10. The results indicate that the pyroelectric coefficient exhibits minimal variation\nthroughout this range. This stability confirms that the device maintains consistent energy-\nharvesting performance regardless of the ambient thermal baseline, ensuring reliability in\npractical applications under varying environmental conditions.\nFig. R10. Thermal stability test of isolated components.\nReviewer #4\nComment 1: The manuscript by Ying-Hao Chu and co-workers demonstrates the use of mica,\na two-dimensional layered ceramic, in combination with the polymer ferroelectric\npolyvinylidene fluoride (PVDF) to enhance the pyroelectric performance, particularly the\npyroelectric coefficient. The technical quality of the work is inadequate, and the manuscript\npresents some experimental supporting the fabrication process and related measurements.\nFurther, numerous articles in the literature have already reported the fabrication of PVDF with\na high β-polar phase (e.g., https://doi.org/10.3390/polym17040481;\nhttps://doi.org/10.3390/polym15224344; https://doi.org/10.1021/acsomega.4c01221 , among\nothers).\nResponse: We thank the reviewer for directing us to these relevant studies, which demonstrate\nadvanced strategies to achieve high β-phase content in PVDF. We fully acknowledge that\noptimizing intrinsic β-phase crystallinity is a vital route to enhancing pyroelectric performance.\nTo explore the feasibility of achieving higher β-phase fractions, we further investigated\na sol-gel spin-coating approach. This method effectively suppresses the non-polar α-phase and\npromotes the formation of β and γ phases, as evidenced by the Raman spectra (Figure R11).\nHowever, achieving uniform film coverage on mica substrates while preserving the bottom-\nelectrode contact regions proved technically challenging using spin-coating. Although spin-\ncoating improves phase purity, the associated thickness limitations and integration challenges\ncurrently restrict its applicability in our bimorph architecture.\nUpon carefully re-evaluating the cited literature, we found that while these methods\nachieve high β-phase contents exceeding 70-90 %, they often rely on multi-step or\nmechanically intensive processes. For instance, Yasar et al. (ACS Omega, 2024) achieved high\nperformance through solvent casting followed by hot pressing, mechanical rolling, stretching,\nand corresponding thermal treatment. While effective for free-standing films, these methods\nare physically incompatible with our rigid, two-dimensional Mica substrates. While Tariq et al.\n(Polymers, 2023) employed high-voltage electrospinning, and Roni et al. (Polymers, 2025)\nutilized Nonsolvent-Induced Phase Separation (NIPS) with specific additives (Citric Acid and\nTiO ), introducing additional compositional complexity compared to our facile tape-casting\n2\napproach.\nWhile an increased β-phase fraction is generally associated with enhanced intrinsic\npyroelectric properties, the primary aim of our study is to demonstrate that interfacial strain\ncoupling can effectively enhance the secondary pyroelectric response. Within this framework,\nwe focus on secondary enhancement rather than pursuing the highest possible intrinsic\ncoefficients. Further, to demonstrate that our material quality was not compromised by the\nmoderate β-phase, we compared our PVDF with commercial standards. Our measured\npiezoelectric coefficient (d ) is approximately 29 pC/N, which falls within the range of\n33\nstandard commercial PVDF films (e.g., PolyK Technologies, typically 20-30 pC/N). This\nconfirms that our tape-casting method yields a piezoelectric performance comparable to\ncommercial standards. This value is comparable to, and in some cases exceeds, values reported\nin the suggested literature (e.g., ≈ 9.2 pC/N in Yasar et al., ACS Omega 2024). Therefore, the\norder-of-magnitude enhancement in the pyroelectric coefficient demonstrates our mechanism\nthat the interfacial strain induced by the mica substrate, known as the secondary pyroelectric\neffect, is the dominant enhancement mechanism. We conclude that the tape-casting method\nremains the optimal trade-off between phase crystallinity, film thickness, and bimorph structure\nperformance. Strategies for further increasing the β-phase have been included in the revised\nmanuscript as a future direction for performance enhancement.\nFig. R11. Raman spectrum of the PVDF film fabricated via sol-gel spin coating.\nComment 2: In the present work, the authors report only 61 % β-phase content, which raises\nreasonable questions about the accuracy and exclusivity of the β-phase quantification in the\npresence of other dominant PVDF phases.\nResponse: We appreciate the reviewer’s insightful question regarding phase exclusivity and\nthe accuracy of phase quantification in PVDF. Given the complexity of PVDF polymorphism\n(α, β, and γ phases), we adopted a multi-technique approach to ensure rigorous phase\nidentification and reliable quantification.\n1. Exclusion of γ-phase: the FTIR spectrum exhibits absorption features characteristic of PVDF\ncrystalline phases. To further and more determine the phase composition, Raman spectroscopy\nwas employed. The Raman spectrum lacks the γ-phase signature peak typically observed in the\n811-814 cm-1 range. Based on these complementary analyses, the material can be reliably\ntreated as a binary system consisting of α and β phases.\n2. Precise Quantification via Raman: To accurately quantify the β-phase within this binary\nsystem, we used Raman spectroscopy, which offers high precision in distinguishing the\nvibrational modes of the polymer chains. We calculated the phase fraction based on the\nintegrated areas of the distinct peaks at 795 cm−1 (α-phase) and 840 cm−1 (β-phase) (Fig. 1C).\nThis method specifically separates the TGTG' conformation of the α-phase from the all-trans\nTTTT conformation of the β-phase.\n3. Confirmation of Exclusivity via Piezoresponse Force Microscopy (PFM): We acknowledge\nthat the remaining ≈ 39 % content corresponds to the α-phase. However, the α-phase is non-\npolar and does not contribute to the piezoelectric or pyroelectric response. This was\nexperimentally verified using PFM (Fig. 1D and Fig. S2), where only the β-phase domains\nexhibited piezo-activity, while the α-phase regions yielded no signal. Thus, the reported\nfunctional performance is exclusively driven by the 61 % β-phase content. We have revised the\nmanuscript to mention the FTIR exclusion of the γ-phase explicitly and to clarify that the\nremaining phase fraction is the non-polar, inactive α-phase.\nComment 3: In addition, while the reported enhancement in the pyroelectric coefficient is\nnotable, it does not significantly exceed values demonstrated in previous studies such as,\nhttps://doi.org/10.1016/j.matlet.2020.127514. Therefore, despite the rigorous experimental\napproach and detailed materials characterization, the manuscript lacks sufficient novelty and\nimpact to justify publication in a high-impact journal such as Nature Communications.\nResponse: We thank the reviewer for bringing this reference (Mater. Lett., 2020) to our\nattention. Upon careful re-examination of this work, we identified a critical discrepancy in their\nreported values. While the abstract mentions a value of 87,000 µC/m2K, this number appears\nto result from a unit-conversion error. This interpretation is supported by the authors' own\nstatement in the same paper, which claims a \"roughly 3-fold enhancement\" over pristine PVDF.\nGiven that the intrinsic pyroelectric coefficient value of PVDF is approximately 27–30 µC/m2K,\na 3-fold enhancement corresponds to 87 µC/m2K, rather than 87,000 µC/m2K.\nCompared to the corrected reference value of 87 µC/m2K, our device exhibits a pyroelectric\ncoefficient of -359 µC/m2K. This corresponds to an approximately 13-fold enhancement\nrelative to pristine PVDF and a nearly fourfold increase over values reported in the literature.\nAdditionally, we achieve this superior performance using only pure PVDF, driven by our\nunique structural mechanics, without the need for complex dopants such as diamond particles\nused in the cited study. Thus, our work demonstrates a significant performance improvement\nover existing research."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I thank the reviewers for making the changes to the manuscript. based on the changes I have the below points of\nclarification.\nplease make it clear how thick the Sapphire substrate is (it is not mentioned in the main text) -\nthe statement one lines 306-308 \"Even if the sapphire substrate were thinned to reduce its bulk stiffness, its intrinsic surface\nrigidity would still severely restrict the in-plane Poisson deformation of the PVDF film, effectively suppressing the\npiezoelectric contribution to the total pyroelectric response.\" implies that it is a) not 20 microns thick and b) that the authors\nhave not experimentally verified behaviour. A more correct statement would refer to Sapphire's and mica 's flexural modulus\ndifferences (mica is about 5-10x lower, depending on orientation of crystals\nT - if it is substantially different to that of the 20 micron mica the bending will be different.\nThe revised text mentioning slippage due to the VdW bonding may explain the better bending on the mica, but it is not clear\nhow bonding with a material can affect the bonding at its surface with another material. When two materials bond together\nthe interface is often complex, especially when you are dealing with such different materials as polymers and ceramic. In all\nlikelihood there will be quite sparse atom-atom bonding across this interface (when compared to ceramic-ceramic lattice-\nmatched bonding). The PVDF dipoles are able to better respond simply because the mica sheets are better able to bend\nand allow the PVDF structure to adapt. The 'hard clamping' of the sapphire is simply due to the fact that it's not moving.", "reviewer_2": "The authors have satisfactorily addressed all comments raised during the previous minor revision, and the revised\nmanuscript is clear, scientifically sound, and significantly improved.\nThe work presents a robust and original strategy to enhance pyroelectric performance in flexible PVDF/mica bimorphs\nthrough thermally induced interfacial stress, leading to a giant pyroelectric coefficient (~ −359 µC/m²·K) driven by a dominant\nsecondary pyroelectric contribution.\nThe results represent a clear advance beyond existing PVDF-based systems and are highly relevant to the fields of\npyroelectric materials, flexible electronics, and thermal energy harvesting. The experimental data, control comparisons, and\nfinite element modeling consistently support the authors’ conclusions, and the methodology and data analysis meet the\nexpected standards of the field.\nThe methods are described with sufficient detail to ensure reproducibility, and no remaining scientific or technical concerns\nare identified.\nI therefore recommend acceptance of the manuscript in its present form.", "reviewer_3": "The authors have satisfactorily addressed all the comments and concerns raised in the previous review. The revised\nmanuscript has significantly improved in clarity and technical quality. I therefore recommend the manuscript for acceptance\nin its present form.", "reviewer_4": "After reviewing the revised manuscript, I find that the authors have successfully resolved the primary technical, novelty and\nconceptual issues identified. The additional data and clarifications provided fully satisfy my earlier concerns, and I am happy\nto support the acceptance of this work."}, "author_response": "Reviewer #1 (Remarks to the Author)\nI have the below points of clarification. please make it clear how thick the Sapphire\nsubstrate is (it is not mentioned in the main text) - the statement one lines 306-308\n\"Even if the sapphire substrate were thinned to reduce its bulk stiffness, its intrinsic\nsurface rigidity would still severely restrict the in-plane Poisson deformation of the\nPVDF film, effectively suppressing the piezoelectric contribution to the total\npyroelectric response.\" implies that it is a) not 20 microns thick and b) that the authors\nhave not experimentally verified behaviour. A more correct statement would refer to\nSapphire's and mica 's flexural modulus differences (mica is about 5-10x lower,\ndepending on orientation of crystals\nT - if it is substantially different to that of the 20 micron mica the bending will be\ndifferent. The revised text mentioning slippage due to the VdW bonding may explain\nthe better bending on the mica, but it is not clear how bonding with a material can affect\nthe bonding at its surface with another material. When two materials bond together\nthe interface is often complex, especially when you are dealing with such different\nmaterials as polymers and ceramic. In all likelihood there will be quite sparse atom-\natom bonding across this interface (when compared to ceramic-ceramic lattice-matched\nbonding). The PVDF dipoles are able to better respond simply because the mica sheets\nare better able to bend and allow the PVDF structure to adapt. The 'hard clamping' of\nthe sapphire is simply due to the fact that it's not moving.\nResponse: We apologize for the lack of clarity regarding the substrate details in our\nprevious revision and appreciate the reviewer’s comment, which has helped us refine\nthe interpretation of the mechanical boundary conditions. The reviewer correctly\npointed out the critical role of flexural rigidity, D = Eh3 / 12(1-ν2), which implies that\nD is proportional to Eh3.\nFor substrates of identical thickness, sapphire exhibits a flexural rigidity approximately\n3-4 x. When considering the actual dimensions used in our experiments, the 500-μm-\nthick sapphire wafer possesses a flexural rigidity that is roughly four orders of\nmagnitude (≈ 40,000-50,000 x) larger than that of the 20-μm-thick mica substrate. As\nnoted by the reviewer, such a massive disparity in rigidity means that the thermal\nexpansion mismatch alone is insufficient to drive appreciable macroscopic bending in\nthe sapphire substrate; similar behavior is observed in thicker mica (Fig. R1A/Fig. 2E).\nFrom an experimental standpoint, thinning sapphire to a thickness comparable to mica\n(20 μm) while maintaining mechanical integrity is technically infeasible; thus, a direct\nexperimental comparison at identical thicknesses could not be performed. Furthermore,\nregarding our measurement setup, the samples were fixed flat on the Peltier chip. Under\nthis configuration, there is no macroscopic bending. Consistently, our additional\nexperiments on pre-bent samples (Fig. R1B-C/Fig. S8) demonstrated that externally\nimposed curvature leads to a change in the pyroelectric output compared to the flat state.\nTaken together, these results indicate that the observed pyroelectric enhancement is not\ncaused by the macroscopic bending or CTE-induced actuation. Owing to this, we\nattribute the effect to interfacial mechanical coupling. In this context, our use of the\nterm \"hard clamping\" for sapphire refers to resistance to accommodating strain. As the\nreviewer noted, both polymer/sapphire and polymer/mica interfaces likely involve\nsparse atom-to-atom bonding. However, the van der Waals nature of the mica surface\nprovides a \"mechanically compliant\" interface. This compliance allows the PVDF\nstructure to effectively adapt to thermally induced stress, whereas the thick sapphire\nimposes a rigid constraint.\nTo avoid potential ambiguity, we have revised the manuscript to replace the term\n\"clamping\" with \"mechanical compliance,\" removed the hypothetical discussion\nregarding sapphire thinning, and expanded the description of the experimental\nconfiguration and mechanical boundary conditions. We hope these revisions clarify our\nphysical interpretation and more accurately reflect the underlying mechanism.\nFig R1 (A) Bending curvature as a function of temperature variation for PVDF/mica\nbilayers with varying mica thicknesses. (B) Dependence of output voltage on initial\nbending curvature. (C) Thermal cycling stability under repeated heating–cooling cycles\nwith different bending curvatures."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The manuscript has been modified sufficiently to be published"}, "author_response": ""}]

Decision letter