Measurement of the d₃₁ piezoelectric coefficient of compliant materials by non-contact polarization and resonant signal enhancement

Abstract

An apparatus for the measurement of converse piezoelectric coefficient in transversal direction (d₃₁) is developed for testing of compliant materials in form of stripes, wires, or thin films. The measurement is not invasive, since it does not require to metallize or contact the sample with conductive electrodes, therefore it can be conveniently applied to nanostructured polymeric devices, like for instance electrospun nanofiber meshes. Low values of piezoelectric coefficients can be detected by exploiting an amplification method based on a mechanical resonance. Piezoelectric coefficients can be determined quantitatively thanks to a suitable calibration method, not depending on the spring constant of the sample.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-29842-1.

Introduction

Piezoelectric materials, thanks to their ability to convert mechanical energy into electrical energy and vice versa, are essential for sensors^1,2 and actuators³, with critical applications including medical imaging, non-destructive testing (NDT), and infrastructure monitoring^4–6.

The piezoelectric coefficient d₃₁ represents one of the most exploited properties of piezoelectric materials, characterizing their ability to produce electrical charge perpendicularly to the direction of an applied mechanical stress. This parameter is predominantly determined by both intrinsic material characteristics and experimental conditions, including temperature, frequency, and the magnitude of applied mechanical or electrical excitation⁷.

Fabrication methods used to synthesize piezoelectric materials, and the eventual doping characteristics, have been demonstrated to influence the resulting atomic structure of the piezoelectric material, causing drastic changes in the d₃₁ coefficient⁸. Consequently, developing new and more accurate measurement techniques to determine the true d₃₁ value is essential for tailoring and optimizing material performance for specific applications^1–6.

Conventional piezoelectric ceramics, including lead zirconate titanate (PZT), lead magnesium niobate-lead titanate (PMN-PT), and barium titanate (BaTiO₃), are widely employed in these applications thanks to their superior piezoelectric performance. For instance, PZT exhibits d₃₃ values ranging from 100 to 500 pC/N⁹. However, the significant lead content in these materials raises substantial environmental and toxicity concerns^10,11. This has driven urgent research efforts to develop lead-free piezoelectric alternatives that can meet both performance requirements and environmental sustainability goals¹².

Polymer-based piezoelectric ultrafine fibers and nanofibers, typically produced via electrospinning, represent a flexible and biocompatible alternative to conventional brittle ceramics^13,14. Their compliant mechanical properties and compatibility with biological systems make them particularly suited for applications in which rigid piezoelectric materials face limitations.

The relatively high d₃₁ coefficients reported for flexible piezoelectric materials have created new demands for accurate characterization methods. Several experimental approaches have emerged to address this need, including laser interferometry for strain measurement, piezoelectric force microscopy (PFM) for localized response analysis⁸, and direct charge collection techniques such as the Berlincourt method, also known as quasi-static method⁹. These complementary techniques enable comprehensive evaluation of both direct and converse piezoelectric effects in compliant material systems.

Accurate piezoelectric characterization in flexible materials must overcome inherent methodological challenges across different measurement scales. Conventional laser vibrometry and related stroboscopic techniques provide non-contact thin film deformation analysis^15–17, yet their effectiveness is constrained by two primary factors: the requirement for optically reflective surfaces prevents characterization of rough or diffusely scattering samples, due to Speckle noise¹⁸, while the inability to decouple substrate bending artifacts from true piezoelectric response leads to systematic overestimation of d₃₃ values by up to 40% in compliant systems¹⁶.

At the nanoscale, PFM delivers unparalleled nanostructure-level resolution (< 50 nm) through local poling analysis¹⁹. However, this approach proves impractical for device-scale evaluation due to inherent restrictions: microscopic scan windows provide limited statistical representation, while the necessity for conductive AFM tips and sensitivity to surface topography may introduce measurement artifacts in polymeric systems. Although the latter limitations have been mitigated by the introduction of non-contact piezoresponse methods²⁰, the main PFM usefulness remains limited to the characterization of the nanostructures composing the actual devices.

The widely adopted Berlincourt method, though ideal for bulk ceramics^9,21, becomes fundamentally compromised when applied to thin films. Computational studies reveal that less than 10% of applied stress actually concerns the active piezoelectric layer in substrate-supported configurations²², with additional measurement distortions arising from bending-mediated transverse piezoelectric coupling.

Based on established piezoelectric measurement principles, we developed an alternative approach to better accommodate the characterization challenges presented by flexible materials and devices. The main demand was to avoid the application of mechanical pressure on the device surface, that could possibly compromise its original structure. A typical case is that of electrospun nanofiber bundles, where global piezoelectric properties can be due the fiber arrangement in addition to the properties of individual fibers²³. Therefore, a non-contact electric polarization was adopted, with planar electrodes located at an adjustable distance from the specimen. This configuration also allowed a resonant technique to be adopted for sensing the induced mechanical stress, where the spring constant and the related resonant frequency of the sample are not spoiled by the contact of the electrodes. The developed system, named “PiezoGauge”, incorporates a number of modifications compared to conventional setups. This concept can be described as a low-load (< 1 N force range) dynamic mechanical analysis (DMA) apparatus, including a servo-controlled pre-tensioning mechanism to maintain consistent state of tensile stress during testing, combined with a mechanical resonator for measurement of extremely low piezoelectric stress, as it will be detailed hereafter.

To support measurement interpretation, particularly for more complex cases involving charged or heterogeneous materials, we also developed suitable mechanical and electrostatic models. The following sections detail the PiezoGauge structure and the related theoretical methods, followed by experimental validation demonstrating the system performance applied to different materials.

Materials and methods

The current measurement system is based on an original PiezoGauge platform, developed for polymer electrospun fiber meshes characterization¹³, and later also applied to polymeric nanocomposite films^24–26. The general grounds of the method consist in applying a transverse electric field (along the z-direction) to a sample in the form of a ribbon (length along x, width along y) or even a wire (along x), and measuring the resulting longitudinal stress (along x). The electric field is generated by applying an electric potential V_ext to a pair of planar electrodes parallel to the ribbon surface (xy-plane), positioned as close as possible to the sample without physical contact. A transverse electric field induces a longitudinal stress T_c (along the x-direction), with a magnitude proportional to the material’s piezoelectric coefficient e₃₁. One end of the sample is attached to a holder by a couple of small screws tightening two small plastic strips, typically made of Teflon or Perspex, acting as clamps for the one sample edge placed between them, and connected to a harmonic steel slab spring, that we name cantilever. The holder is superglued to the cantilever at an intermediate position, leaving around 8 mm close to the base (that we call base portion), and 30 mm leaning out (that we call free or edge portion), as depicted in Fig. 1. A red diode laser beam (wavelength 635 nm, continuous wave power 4 mW) is reflected by a mirror superglued to the free cantilever edge onto a four-quadrant split photodiode (Phresh Photonics SiQu50-M, sensing area 8 mm diameter), providing two electric currents proportional to the position of the reflected laser beam impinging on it, in the two orthogonal directions, measuring thus the cantilever bending and twisting motions. The other end of the specimen is clamped in the same way as the opposite one, and fixed to a motorized stage (M-110.1VG, with Mercury C-863 DC motor controller, Physik Instrumente, Germany), enabling precise and actively controllable pre-tensioning of the sample, as well as to record stress-strain curves. Servo control procedures were set as macro routines in the controller software.

Fig. 1.

The PiezoGauge setup for the measurement of the d₃₁ piezoelectric coefficient. (a) The sample is mounted on the setup and fixed in the holder by the Teflon clamps. (b) The motorized stage is moved until the sample results as completely tense. (c) The sample is mechanically excited by the calibrated piezo-transducer (piezo2) by inducing a known deformation value, ΔX_M, with the alternated voltage V_M, resulting in a tension T_M, depending on the sample stiffness. (d) An alternate voltage V_E is applied to the electrodes, of length lη and placed at distance η, generating an electric field inside the sample, of length l₀ and thickness η_d, resulting in a tension T_E. Cantilever bending is exaggerated.

Due to the overall constraint, the bending of the cantilever is directly proportional to T_c, and is therefore used to detect such stress. Static pre-tensioning produces bending of the base portion, while the free portion remains straight. The angle of the free portion of the cantilever is thus equal to the angle at the edge of the base portion. Therefore, the spring constant to be used for the determination of the static stress is the one of the base portion (k_b), that is around 26 kN/m.

To enhance measurement sensitivity, enabling detection of very small piezoelectric coefficients, a resonant amplification method is employed. A harmonic excitation is applied to the electrode plates, through a high-voltage amplifier (F20ADI, FLC electronics, Sweden), providing a maximum potential difference of 300 V. An oscillating stress at the sample mount (intermediate) position of the cantilever will be thus generated by the converse piezoelectric effect. The free cantilever’s dynamic behavior, being approximately that of a simple harmonic oscillator, produces an amplified bending motion of the cantilever edge, that is maximum when the excitation frequency matches the cantilever’s resonant frequency. The amplification factor equals the oscillator’s quality factor (Q). This situation in illustrated in Fig. 1c. The bending alternate signal provided by the photodiodes is sent to a dual-phase lock-in amplifier (SR830DSP, Stanford Research Systems, Sunnyvale, CA, USA) that provides the magnitude and phase of the response referenced to the excitation signal.

Fig. 2.

(a) The PiezoGauge setup for the measurement of the d₃₁ piezoelectric coefficient. (b) Close-up of the sample mount. A and B indicate the two clamping points of the sample: A is the holder attached to the cantilever, B the one attached to piezo2 and the motorized stage.

Spectra are collected by logarithmically sweeping the excitation frequency and collecting the response values by means of an acquisition software realized in LabView (National Instruments, USA).

Spectra are usually collected in the frequency range from 100 to 5000 Hz, and after the resonance frequency is located, a further spectrum is acquired in a smaller frequency range around it.

The choice to have a sectioned cantilever gives the possibility to apply rather high pre-tensioning on one side, by exploiting the base portion that has a higher spring constant (k_b), and to detect tiny piezoelectric stress at the same time, by driving at resonance the free portion, that has a much lower spring constant (k_c), that is around 1 kN/m. Along with these advantages, a complication arises since depending on the sample stiffness, the resonant modes of the cantilever may span from that of the bare free portion (when the sample stiffness is very high) to that of the full cantilever (when the sample is very compliant). Therefore, interpretation of measurements becomes nontrivial, and can be obtained by a mechanical model, that is presented in Appendix A (Supplementary Materials). Such model describes fairly well the sensitivity of the system, however it is difficult to obtain an exact description, due to the size of the holder glued on the cantilever (10 mm), that should be taken into account in more detailed calculations.

To comply with the above issues, a calibration method has been introduced to obtain quantitative determination of the piezoelectric coefficient, that addresses limitations of the approach used in the previous version, such as requiring prior knowledge of the sample’s spring constant. This method compares electrically induced piezoelectric stress with a known mechanical stress generated by a calibrated piezoelectric transducer. This element is a piezoceramic slab, here named piezo2, and mounted as in Fig. 1a, that is, connected in series with the sample.

By virtue of this calibration method, the value of d₃₁ is derived by the following formula:

1

where ΔA_E(f) is the oscillation amplitude detected when electrical excitation is applied, ΔA_M(f) is the amplitude obtained with mechanical excitation, C_P2 (in pm/V) is the piezoelectric coefficient of the piezo2 element, V_M (in V_RMS) is the ac voltage supplied to the transducer, η (in m) is the distance between the electrodes, V_ac (in V_RMS) is the ac voltage supplied to the electrodes, l_η (in m) is the length of the sample subjected to the electric field (Fig. 1d), and ε_s is a reduction factor for the electric field due to the employed geometry, that amounts to:

2

where ε_d the dielectric constant of the sample, and η_d (in m) its thickness. The derivation of Eqs. (1) and (2) is detailed in Appendix B (Supplementary Materials).

A picture of the setup is shown in Fig. 2a, with a close-up of the sample mount in Fig. 2b, the latter corresponding to that shown in Fig. 1d.

Influence of measurement conditions

In the case of some samples, a marked difference between PiezoGauge measured values just after mounting the sample and the ones measured after one or several days was evidenced, suggesting a possible role of static charges or transient polarization possibly present on the sample. Indeed, static charge neutralization protocols are sometimes used before measurements of piezoelectric performance²⁷. This has urged a better understanding of the role of experimental conditions that could be related to transient charging or polarization, like sample pre-tensioning and positioning between the electrode slabs, manipulation prior to mounting, and environmental conditions like temperature or ambient humidity. In this respect, we have concentrated here on modeling the effect of static charge present on the specimens under measurement. Such modeling turned out to provide useful indications on experimental procedures to be adopted.

Simple modeling of the electrostatic forces along z acting on a sample kept at a fixed potential V_b, as well as bearing a static charge q, are presented in Appendix C (Supplementary Materials). The results of such calculations are summarized hereafter. In the case of a sample kept at a fixed potential V_b, a force component at angular frequency Ω = 2πf could arise, proportional to V_b:

3

where V_ac is the amplitude of the applied harmonic potential at frequency Ω, A_c the area of the sample between the electrode slabs, and η_d the sample thickness. However, this cannot be the case of dielectric samples, like the piezoelectric ones, since they are expected to be insulating, therefore they cannot be kept at a given potential by a voltage generator. In the case of an insulating sample bearing a charge q, instead, the modeling provides null electrostatic force (Appendix C, Supplementary Materials).

Another important point to bear in mind is how electrostatic forces along z can to produce cantilever deflections along x. First of all, forces along z are able to produce cantilever twisting, that is, a torsion around the cantilever axis (y). This could be directly detected by the orthogonal channel of the optical lever detector. Second, it is known that, due to slight asymmetries of the cantilever system, such twisting motion is not perfectly decoupled from the bending motion, so that the bending resonance can be excited even when the crosstalk with twisting modes is minimal, similarly to what happens for cantilever sensors in atomic force microscopy²⁸. Nonetheless, the influence of static charge on the measurement results should be further strongly suppressed for this reason.

On the basis of these predictions, we have concluded that the development of robust measurement protocols for piezoelectric coefficients requires comprehensive understanding of three critical factors in the PiezoGauge system: sample positioning along z, static charge effects, and environmental conditions. We have carried out investigations to address each factor systematically, to validate and refine the emerging theoretical model.

The first experiment to assess the above results focused on positional dependence using an aluminum sheet sample electrically isolated from grounded components. Through mechanical excitation and lock-in amplifier calibration at half the resonance frequency, we established optimal alignment by minimizing the second harmonic amplitude A_2Ω. By discrete displacement of 50 μm each, in a range of ± 250 μm, a symmetric linear response in A_2Ω is found (Fig. 3), with a 180° phase shift as expected. These findings underscore the necessity for precise sample alignment to minimize electrostatic artifacts.

Fig. 3.

Amplitude of the second harmonic as a function of sample position along z.

Examination of static charge effects demonstrated the system’s sensitivity to surface potentials. Application of a dc voltage V_b (− 12 V to + 12 V, in 3 V steps) produced linearly voltage-dependent signals in first harmonic resonance amplitude A_Ω (Fig. 4). The V_b value that nullifies the first harmonic signal is due to the contact potential difference, or Kelvin potential.

Fig. 4.

Amplitude of the first harmonic as a function of applied voltage.

The role of charge on samples could be highlighted by a study of the effect of environmental conditions on signal decay dynamics. By implementing a sealed plexiglass enclosure with controlled atmosphere (high vs. low humidity levels), we observed significantly slower signal decay at lower relative humidity (10% RH by fluxing nitrogen, vs. 50% RH in ambient air, Fig. 5). This humidity-dependent behavior can be explained by surface conduction mechanisms, where water molecules facilitate charge transfer and dissipation. Additional experiments comparing open-circuit and grounded configurations revealed that the extension of electrical connections dominates over environmental factors when discharge paths exist.

Fig. 5.

First harmonic force decay in different configurations and environmental conditions. Decay time constants are: 3.6 s for the air-wire connected case, 16.9 s for the air case, 34.4 s for the nitrogen case.

These last results are in contrast with the expectations for a sample disconnected from the voltage generator, where static charges should provide no influence (Appendix C, Supplementary Materials). The reasons for this discrepancy are currently under investigation.

These findings validate key aspects of the theoretical model while establishing practical guidelines for measurement optimization. The results on dependence from z-position of the sample helps the establishment of alignment protocols, the charge sensitivity findings mandate pre-measurement neutralization procedures for the samples, and the environmental studies demonstrate the importance of controlled measurement conditions—particularly for insulating materials, as the ones presenting piezoelectricity. Together, these insights significantly improve reliability of measurement across diverse material systems and experimental conditions. Future model refinements will incorporate quantitative relationships between these factors, to enable predictive corrections for measurement artifacts.

Measurement procedure

The optimized measurement procedure to be adopted consists of the following steps:

1. The sample is mounted on the setup and fixed at the holder by the Teflon clamps.

2. The motorized stage is moved until the photodiode detects an initial tensile force, indicating proper sample clamping. The photodiode is then centered, corresponding to nearly zero force. This procedure ensures the sample is held tight between the clamps in a nearly unstressed initial state. The following measurements will be related to differences with respect to this zero reference value.

3. Centering of the sample by adjusting the z-position as well as the mutual distance of the electrodes is performed visually, checking that the sample is not contacting the electrodes, in such a way that it is free to vibrate.

4. The sample is mechanically excited by the calibrated piezo-transducer (piezo2), thus inducing a known deformation value, ΔX_M, with the alternated voltage V_M in a range of frequencies (usually from 100 to 1000 Hz). The lock-in amplifier is set to detect the cantilever bending signal at the fundamental frequency Ω. The related spectrum of the cantilever oscillation A_M(f) is acquired, and the resonant frequency Ω_res is found.

5. The mechanical excitation is turned off, and the alternated voltage V_E is sent to the electrodes in the same frequency range (from 100 to 1000 Hz). The excitation frequency is set to Ω_res/2, and the lock-in amplifier is set to detect the signal at the second harmonic frequency 2Ω . The electrode plates’ z-position is adjusted, centering the sample until the second harmonic signal is minimized. If no second harmonic is detected, then the sample charging is likely small and is not anticipated to influence the piezoresponse measurements, therefore the previous centering is maintained. If, instead, the second harmonic is too high to be nulled out exactly, sample neutralization procedures could be necessary. Such procedures should be envisaged for each kind of sample, and could also be performed in situ in some cases. We adopt a standard method (EN 779:2012) as also done in literature²⁷.

6. The lock-in amplifier is set to detect the signal at the fundamental frequency Ω. The related spectrum of cantilever oscillation A_E(f) is acquired.

7. The two spectra are divided by each other, obtaining a constant value corresponding to the piezoelectric coefficient, according to Eq. (1). Since the signal-to-noise ratio is much higher at resonance, the value of the ratio at the resonance frequency Ω_res is usually employed, especially in the case of small piezoelectric efficiency. Estimation of the PiezoGauge sensitivity based on analysis of noise sources is provided in Appendix D (Supplementary Materials).

Examples of application

To demonstrate the functionality and capabilities of the PiezoGauge system, a series of measurements were performed on compliant electrospun nanofiber meshes, specifically based on polyacrylonitrile (PAN). This material is of particular interest due to its inherent flexibility, potential for bio-compatibility, and relevance in wearable or implantable piezoelectric devices.

The PiezoGauge system was employed to quantitatively determine the transverse piezoelectric coefficient (d₃₁) of these nanostructured meshes without the need for metallization or direct electrical contact. By utilizing our non-contact electric field excitation and resonant mechanical amplification, the system successfully detected very low piezoelectric coefficients, in the range of a few pm/V, typically challenging for conventional techniques to resolve.

Importantly, the PiezoGauge revealed significant variability in measured piezoelectric response depending on experimental conditions. In particular:

• Pre-tensioning sensitivity Mechanical pre-tensioning was found to significantly affect measurement stability, particularly by preventing drift or sagging during excitation. The servo-controlled stage ensured consistent and reproducible sample tensioning, highlighting the importance of precise mechanical preparation in achieving reliable results.

• Time dependence and charging effects A noteworthy observation was the time-dependent variation in d₃₁ values, particularly for randomly aligned fiber meshes. Measurements taken immediately after mounting differed from those acquired after 1 to 5 days, entailing the role of static charge neutralization. These effects were further modulated by environmental conditions such as relative humidity, highlighting the system’s sensitivity to static charge induced artifacts. The PiezoGauge built-in capability to detect second harmonic electrostatic signals enabled the identification and mitigation of such artifacts, either through alignment correction or sample neutralization protocols.

• Mechanical resonance handling Due to the compliance of the nanofiber meshes, resonance modes varied widely based on sample stiffness and geometry. The portioned cantilever design of the PiezoGauge allowed for high-sensitivity detection via the free cantilever end. This architecture allowed reliable measurement across a broad range of mechanical properties.

• Effect of fiber alignment Aligned meshes displayed more consistent and higher piezoelectric responses compared to randomly oriented ones, as the collective alignment of molecular dipoles and mechanical axis contributed to enhance the effective d₃₁. Conversely, randomly aligned meshes exhibited broader variance, reinforcing the system’s ability to detect subtle structural influences on macroscopic piezoelectric behavior.

These findings not only validate the robust measurement protocols outlined in "Measurement procedure" section, but also emphasize the PiezoGauge diagnostic power in uncovering hidden variables affecting piezoelectric performance. By capturing environmental and structural influences on real devices, the system proves essential for the characterization and optimization of next-generation compliant piezoelectric materials.

Piezoelectricity and mechanical properties of PAN electrospun meshes

Electrospun PAN meshes were tested as model systems to explore the capabilities of the PiezoGauge in resolving piezoelectric and mechanical properties in devices made of compliant materials. Measurements confirmed the presence of significant piezoelectricity in PAN fibers, with some samples exhibiting d₃₁ values even higher than those reported in recent literature¹⁴.

A key finding was the high variability in the measured piezoelectric response, particularly in unaligned meshes. The variability depended on both pretensioning and time, (Figs. 6 and 7), indicating transient polarization or charging effects, and the role of mechanical stabilization in signal consistency. Aligned PAN meshes demonstrated greater signal consistency, and higher average d₃₁​ values compared to randomly aligned ones, underscoring the influence of fiber orientation on electromechanical behavior.

Fig. 6.

Measurements of d₃₁ on randomly aligned meshes, as a function of the measurement time (in days) and the pretension σ_pt exerted on the sample.

Fig. 7.

Measurements of d₃₁ on aligned mesh. Average ± standard deviation of several measurements as a function of measurement day are reported.

From a mechanical standpoint, stress–strain analysis revealed pronounced differences between aligned and unaligned configurations. Aligned meshes showed greater elongation and approximately double the stress values under comparable conditions. Hysteresis analysis indicated that aligned meshes exhibited a more pronounced elastic response with reduced internal rearrangement and slippage, likely due to fiber alignment restricting degrees of freedom. In contrast, randomly aligned meshes demonstrated broader hysteresis loops, consistent with relaxation and reorganization effects during loading (Fig. 8).

Fig. 8.

Estimation of stress vs. elongation (reported as l/l₀) of aligned and random (not aligned) meshes, during the first loading/unloading cycle.

Notably, aligned meshes exhibited significantly lower thickness (~ 8 μm) compared to randomly aligned ones (~ 20 μm), despite identical electrospinning durations. This suggests that alignment promotes denser packing and potentially contributes to the enhanced mechanical and piezoelectric performance.

Together, these results highlight the importance of fiber alignment and controlled mechanical preparation in optimizing the performance of PAN-based piezoelectric devices. The PiezoGauge system successfully detected these nuanced differences, validating its application in the structural and functional analysis of soft piezoelectric nanomaterials.

Piezoelectricity and mechanical properties of PAN electrospun yarns

Polymeric yarns fabricated via electrospinning are alternative geometries inspired to conventional ropes, to obtain high tensile stiffness²⁹. Figure 9 shows an example of polymeric yarns fabricated in our group³⁰. The preferential orientation of the fibers along the longitudinal direction is evident, with smaller fibers twisted around the core.

Fig. 9.

SEM micrographs of polymeric yarns at different magnifications. (A) 2300X, (B) 13000X; scale bars: (A) 30 microns, (B) 5 microns.

Figure 10 shows a summary of d₃₁ coefficients measured on different PAN yarns. Most of the yarns exhibit very low global coefficients, probably due to averaging out of piezoeffect due to fiber twisting. This result shows the broad range of piezoelectric coefficients measurable by our setup, even smaller than 1 pm/V.

Fig. 10.

Measurements of d₃₁ coefficients of eight different PAN yarns. Average ± standard deviation of several measurements are indicated.

Piezoelectricity of solution-cast chitosan films

There is renewed interest in application of chitosan as a low-cost, bio-derived, and bio-degradable polysaccharide material, in the fields of energetics and sensors. Chitosan can be easily produced by a deacetylation reaction from natural chitin, the most abundant biopolymer after cellulose, extracted mainly from marine crustaceans. Recently, chitosan has attracted growing attention due to its piezoelectric properties, in the form of solution-cast film³¹. Characterization of transverse piezoelectricity of these films, in addition to the longitudinal one, is still to be reported, that could be performed by means of PiezoGauge. Our samples were produced as described in Ref³², by starting from solutions in acidic solutions of both formic and acetic acid. A standard neutralization protocol by immersion in 1 M NaOH for increasing times (30′, 60′, 90′) was applied, that leads to stabilization of the polymer structure. Values of d₃₁ piezoelectric coefficients for the different films and annealing conditions are compared in Fig. 11. For as-procuced films, neutralization time increase from 30′ to 60′ seems to decrease performance, that increases again, to a lower extent, for 90′ neutralization. However, after thermal annealing, the trend is inverted: annealing decreases the performance of films neutralized for 30′, but it increases the performances of films neutralized for 60′, as well as that of the 90′ neutralized film from acetic acid, while that from formic acid remains stable. The best result in transverse piezoelectricity was obtained for the chitosan sample obtained from acetic acid solution, neutralized for 60′, and thermally annealed. Since PiezoGauge measurements were conducted in ambient atmosphere, so that a similar residual water content (around 10%) is expected in all measurements, the observed differences in film’s piezoelectric performances due to thermal annealing are only assumed to derive from the possible modification of its crystalline structure. The reported data are preliminary, since measurements were performed once for each sample, and only shown to demonstrate the capability of PiezoGauge to detect piezoelectric coefficients even lower than 1 pm/V. Statistics on several specimens should be applied to obtain more reliable results. Up to now, PiezoGauge in its progressive development stages has been applied to PVDF composite nanofiber meshes and films, PCL nanofiber meshes, PAN nanofiber meshes, and PHB nanocomposite films, namely: PVDF nanofiber meshes in Ref²³, nanofibers with inclusion of BaTiO₃ nanoparticles in Ref¹³, films with inclusion of boron nitride nanotubes (BNNT) in Ref²⁴, and with inclusion of BaTiO₃ nanoparticles in Ref²⁶, PCL nanofiber meshes in Ref³³, PAN nanofiber meshes in the present paper as well as in Ref³³, and PHB films with inclusion of BaTiO₃ nanoparticles in Ref²⁵.

Fig. 11.

Measurements of d₃₁ coefficients of six different chitosan films. As-produced films are compared to those thermally annealed at 140 °C for 1 h. F stands for formic acid, A for acetic acid, while 30, 60 and 90 stand for the neutralization times.

Conclusions

The PiezoGauge system offers a novel and robust platform for the quantitative measurement of the transverse piezoelectric coefficient d₃₁​ in compliant materials, particularly electrospun polymeric nanofiber meshes. Its non-contact configuration, based on electric field excitation and mechanical resonance amplification, enables high-sensitivity detection of piezoelectric responses without requiring metallization or electrical contact, which is particularly advantageous for soft or bio-integrated devices.

The apparatus includes a servo-controlled pre-tensioning stage to ensure mechanical consistency, and a portioned cantilever structure to separate pretensioning force application and sensing resonant vibrations. This design enhances both the sensitivity and reliability of the measurement.

Experimental investigations conducted so far confirmed the system’s ability to detect extremely low piezoelectric coefficients and revealed the critical influence of sample alignment, pretensioning, time-dependent effects, and environmental conditions on the measured response. These capabilities establish the PiezoGauge as a powerful tool for the comprehensive characterization of soft piezoelectric materials, enabling accurate performance assessment and guiding material design in emerging applications such as flexible electronics and biomedical devices.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

L.S.: Investigation, data curation, visualization, writing—original manuscript, writing—review and editing; L.Z.: Investigation, data curation, writing—review and editing; G.S.: Investigation, writing—review and editing; M.M.: Visualization, formal analysis, writing—review and editing; S.D.: Supervision, funding acquisition, resources, writing—review and editing ; M.L.: Conceptualization, funding acquisition, resources, investigation, formal analysis, visualization, writing—original manuscript, writing—review and editing.

Funding

This work was partially funded by European Union–Next Generation EU via the Italian Ministry of University and Research (MUR), PRIN 2022 program (PROMISE project, CUP 153D23004700006).

Data availability

Data will be made available upon written request to the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.