Electric Breakdown of Dielectric Polymers is Strongly Correlated to Mechanical Toughness

ABSTRACT

Dielectric energy storage is critical for technologies demanding ultrafast discharging and pulse power, and preventing electric failure is paramount to the design and engineering of dielectric materials. Under high voltages current traverses the dielectric leading to electric breakdown, which is the primary failure mode of dielectrics. While intrinsic breakdown strength in perfect dielectrics can be predicted from quantum mechanics, failures in dielectric materials often occur under an electric field well below their intrinsic theoretical strengths, and the mechanism is still poorly understood. Here we show that electric breakdown of dielectric polymers is strongly correlated to their mechanical toughness. We reveal through in situ experiments that breakdown of polymers proceeds through nucleation and growth of cracking channels, suggesting a close connection between electric and mechanical failures. We demonstrate that the breakdown strength of polymers can be modulated by their tensile toughness, and there is a universal relationship between electric toughness and mechanical toughness. As a result, the breakdown strength for a wide range of polymers with mechanical and dielectric properties spanning two orders of magnitude can be reliably predicted, uncovering a dominant electromechanical breakdown mode that unifies mechanical and electric failures. Toughening strategies in enhancing dielectric strength can therefore be explored.

This work resolves the longstanding challenge of dielectric breakdown in polymers, revealing through in situ and ex situ experiments that tensile toughness governs dielectric failure under electric fields far below theoretical limits. This work offers a fresh understanding on breakdown mechanism while suggests a new paradigm for enhancing dielectric strength.

1. Introduction

Dielectric energy storage has received much attention due to its ultrafast charging‐discharging rate and superior power density [1, 2, 3]. They are ideal for delivering pulse power that is highly sought after in many important technologies, including fusion energy [4], electromagnetic forming [5, 6], electric propulsion [7], and defibrillation [8]. Great efforts have been devoted to developing dielectric materials with outstanding energy storage performance, resulting in revolutionary ideas in polymer‐based nanocomposites [9, 10], oxide‐based thin films [11, 12, 13], and high‐entropy ceramics [14] showing order of magnitude enhancement in energy density. Many of the progresses are built upon ingenious design and manipulation of polar structures of the dielectrics at the nanoscale [12, 15] while the underlying mechanism responsible for the electric breakdown failure remains poorly understood. In 2024, a previously unknown type of electric tree was discovered with propagation speed exceeding 10⁷ m s⁻¹ [16], highlighting substantial gap existing in the understanding of dielectric breakdown. Since dielectric energy density scales with the square of breakdown strength, a good grasp on the dielectric failure is imperative to translate the scientific advances in dielectric energy storage from laboratories to device applications. In fact, such insight is paramount to the design and engineering of a wide range of dielectric materials found in capacitors, transistors, transformers, and transmission lines that are indispensable for modern commerce [2, 16, 17, 18].

Under high operating voltages, current traverses the dielectric, leading to permanent damage. This destructive process is known as electric breakdown [16, 19, 20], the primary failure mode of dielectrics. Modern theory of dielectric breakdown started with the pioneering works of Zener [21] and von Hippel [22] in the 1930s, who analyzed intrinsic breakdown in a perfect dielectric with quantum mechanical theoretical strength [21, 22, 23, 24]. Materials in services, however, often contain defects and fail under an electric field much smaller than the theoretical limit [25, 26]. In 1950s, Stark and Garton discovered a new mode of breakdown based on electromechanical instability arising from Maxwell stress [18], which occurs in soft dielectrics with the breakdown strength scaling with the square root of Young's modulus. Subsequent researches have noted further correlation between Young's modulus and breakdown strength, even for stiffer materials that are far away from electromechanical instability [27]. Failure criterion based on yielding strength has also been proposed [28], while facture mechanics theories assuming preexisting cracks [28, 29] or conducting filaments [27] have been developed. These works were successful in explaining breakdown behavior of a certain class of dielectrics but lack generality for polymers with diverse mechanical and electrical characteristics [18, 25, 30, 31]. In fact, the universal mechanism governing electric breakdown in dielectric polymers is yet to be uncovered.

The tensile toughness of polymers depends on how much energy is necessary to break molecular chains without the assumption of preexisting defects [32], while electric breakdown involves similar breaking as well [33]. Previous experiments have shown that high voltage in dielectrics can induce conductive gas channels [34], leading to dielectric breakdown, and the process does involve mechanical fracture. Therefore, a connection between the two may exist, and we seek to establish such connection in this work to unify mechanical and electric failures. Through both in situ and ex situ experiments in combination with comprehensive data analysis, we demonstrate that electric breakdown is strongly correlated to tensile toughness for a wide range of dielectric polymers, with which the breakdown strength of both hard (high Young's modulus, low dielectric constant) and soft (low Young's modulus, high dielectric constant) dielectrics can be reliably predicted. Toughening strategies [35, 36] in enhancing dielectric strength can therefore be explored.

2. Results

2.1. In Situ Visualization of Electrical Breakdown Process

In order to better understand the electric breakdown mechanism of dielectric polymers, we design an experimental setup as schematically shown in Figure 1a for in situ visualization of the breakdown process. The polymer specimen, here polyacrylic acid (PAA) with dimensions of 75 mm × 25 mm × 4 mm, is immersed in silicone oil and monitored via an optical microscope from above. A needle made of tungsten alloy is used as the high voltage electrode at one side of the polymer specimen, either inserting into the polymer for clear visualization, or barely touching its surface without creating a preexisting crack to confirm the underlying process. Tungsten alloy is selected because of its high hardness, which helps maintain a sharp and stable tip geometry during experiments. The opposite side of the polymer is taped with copper as the grounding electrode, which provides compliant contact with the specimen and helps reduce interfacial gaps or pores. The copper electrode is connected in series with a resistor, and the current, especially the breakdown current, is measured using an oscilloscope [37]. The external bias is applied through a high‐voltage source. Under a constant voltage of 15 kV applied via a ramp rate of 500 V s⁻¹ (Figure S1a) with the needle electrode inserting into the PAA specimen, we clearly observe in Figure 1b the initiation and growth of a cracking channel as time increases. At 0th second before the voltage is applied, no defect is observed in the specimen. At 30th second when the voltage reaches 15 kV, a small channel is found to form at the tip of the needle electrode. The channel grows toward the counter electrode as time passes by, becoming longer and longer at 50th, 60th, and 63th second. The three‐dimensional morphology of the channel cross‐section is measured using a digital optical microscope, confirming it as a crack (Figure S2a–h). At 64th second, the channel extends to the counter electrode, generating a bright breakdown current between the positive and negative electrodes that rises to ∼60 A in just 28 nanoseconds (Figure 1d) and permanently damages the sample. The time scale is consistent with that of electric tree propagation [16], and the entire breakdown process is captured in Video S1. Under cyclic charging and discharging with peak voltage of 15 kV (Figure S1b), similar process is observed (Figure 1c), that the channel grows with increasing cycles. Upon discharging at each cycle, the channel contracts significantly as evident at the first and sixth discharging shown, exhibiting clear self‐healing characteristics. At 10th cycles, the channel reaches the counter electrode, again resulting in a fast‐rising breakdown current (Figure 1e) that damages the sample. The entire process is presented in Video S2. If the needle electrode barely touches the specimen without inserting into it, the process is similar (Figure S3; Videos S3; S4), though the breakdown occurs at higher voltage of 20 kV and longer cycles of 26. Notable local deformation underneath the needle is also observed due to Maxwell stress (Videos S3 and S4), since PAA is very soft with a Young's modulus around 1 MPa. Nevertheless, the breakdowns still occur through initiation and propagation of cracking channel, which is confirmed by 3D topography (Figure S2i–l). In all these experiments before final breakdown, we did not observe any heating, arcing, or generation of bubbles in the oil bath, excluding the possibility of polymer melting. This is consistent with previous observation in biaxially oriented polypropylene (BOPP) wherein temperature only rises after breakdown due to Joule heating [37].

FIGURE 1.

In situ observation of the electrical breakdown process. (a) Schematic diagram of the experimental setup; (b,c) Growth of breakdown channel in PAA under (b) constant voltage and (c) charging‐discharge cycling; (d,e) The corresponding current measured at breakdown with nanosecond resolution.

2.2. Modulating Electric Breakdown via Mechanical Toughness

The set of in situ experiments clearly reveal that the electric breakdown of polymers proceeds through nucleation and growth of cracking channels, making us postulate if it is possible to analyze their breakdown strength based on mechanical failure. The fracture of materials is governed by their fracture toughness, yet measuring fracture toughness requires creating preexisting cracks, which is problematic if we are interested in the breakdown strength of polymers without obvious defects. On the other hand, the tensile toughness, or the work necessary to break a polymer specimen under uniaxial tensile test, correlates well with fracture toughness [38]. Therefore, we seek to determine if the electric breakdown strength can be modulated by tensile toughness. Tensile test is carried out on a BOPP specimen of dimension 50 mm × 20 mm × 10 µm (Figure 2a) utilizing a flexible film stretching system (Figure S4) at room temperature of 25°C. Typical loading‐unloading stress–strain curves are presented in Figure S5, showing Young's modulus of 1.4 GPa and yield strength of 43.4 MPa. After loading beyond the yielding, the unloading and reloading curves exhibit some hysteresis, demonstrating viscoelastic characteristics. The key point is that after loading and unloading, the tensile toughness is reduced, which is evident from stress–strain curves in Figure 2b for BOPP specimen after various pre‐stretching strain (ε  =  Δl/l) ranging from 0% to 73%. We then carry out breakdown measurement as schematically shown in Figure S6 at room temperature, wherein flat instead of needle electrode is used to ensure good consistency for quantitative analysis, and we obtain breakdown strength of pre‐stretched BOPP based on Weibull distribution (Figure 2c). It is clearly observed that the breakdown strength of BOPP is reduced after pre‐stretching, while its linear dielectric characteristic is not affected (Figure S7a). Similar behavior is also observed at elevated temperatures of 40°C and 60°C (Figure S8), while no significant change in dielectric constants occur with rising temperature (Figure S7b,c). Dielectric loss does increase with pre‐stretching, indicating possible internal damage. The electric work done for breakdown can be evaluated as, which we refer to as electric toughness, and very interestingly, a linear relationship is observed between electric toughness and tensile toughness for BOPP pre‐stretched to various extents within the temperature range investigated (Figure 2d). This supports our hypothesis that electric breakdown may be related to mechanical failure.

FIGURE 2.

Modulating electric breakdown of BOPP films via mechanical stretching. (a) Schematic diagram of pre‐stretching experiment of BOPP; (b) The corresponding stress–strain curves after pre‐stretching, measured at 25°C; (c) Weibull distributions of dielectric breakdown, measured at 25°C; and (d) relationship between tensile toughness and electric toughness at breakdown, with data measured at 25°C, 40°C, and 60°C all included.

The relationship between electric toughness and tensile toughness can be further verified by polyethylene terephthalate (PET) films of various thicknesses, which exhibit very different mechanical properties (Figure 3a) because of specific draw ratios used during fabrication process [39], yet their linear dielectric characteristics are almost identical (Figure S9a). In particular, thicker PET films possess higher tensile toughness, which translates into higher breakdown strength based on Weibull distribution (Figure 3b). The variation of breakdown strength versus thickness follows closely the variation of tensile toughness versus thickness (Figure 3c), and similar behavior is also observed at elevated temperature of 40°C–80°C (Figure S10), while no significant change in dielectric constants (Figure S9b,c). Again, a clear linear relationship is observed between electric toughness and mechanical toughness (Figure 3d) within the temperature range considered, demonstrating such correlation in two different polymer systems and confirming that the electric breakdown of polymers can be mechanically modulated.

FIGURE 3.

Modulating electric breakdown of PET films with varying thicknesses having different tensile toughness. (a) Stress–strain curves of PET with various thickness, measured at 25°C; (b) Weibull distributions of dielectric breakdown, measured at 25°C; (c) Variation of tensile toughness and breakdown strength for PET of different thicknesses at 25°C; and (d) relationship between tensile toughness and electric toughness at breakdown, with data measured at 25°C, 40°C, 60°C, and 80°C all included.

2.3. Predicting Breakdown Strength by Mechanical Toughness

To better understand the correlation, we characterized the crystalline size and crystallinity of BOPP and PET via x‐ray diffraction (XRD) (Figure S11) and Differential Scanning Calorimetry (DSC) (Figure S12). No significant change is found in BOPP after various stretching and in PET of various thicknesses. SEM images of BOPP films before and after 73% pre‐stretching also show no obvious surface cracks, voids, or defects (Figure S13). Furthermore, DSC analysis identifies the glass transition temperature of −5°C for BOPP and 78°C for PET, suggesting that the correlation is not affected by the glass transition. Since both BOPP and PET are semicrystalline, we also chose amorphous polyimide (PI), polyetherimide (PEI), polymethyl methacrylate (PMMA) as well as semicrystalline polypropylene (PP), poly(hexamethylene terephthalamide) (PA6T), polyphenylene sulfide (PPS), and polyetheretherketone (PEEK) for testing (Figure S14). We have then assembled all the data for these nine types of polymers in Figure 4a, and summarized their properties in Table S1. It confirms the linear relationship between electric toughness and tensile toughness for these polymers, regardless of the crystallinity of the polymer, with a fitting equation of W_elec =  0.02W_tensile + 4.3e6. This correlation makes it possible to predict the electric breakdown strength of dielectric polymers from their tensile toughness, $E_b={(\frac{0.04W_{tensile}+8.6e6}{{\epsilon }_0{\epsilon }_r})}^{0.5}$, which also recovers empirical inverse relationship between breakdown strength and dielectric constant [40]. To demonstrate this predictive power, we have not only included our own experimental data as presented in Figure 4a, but also a wide range of data reported in literature for amorphous Polycarbonate (PC), Fluorinated Polyimide (FPI), PEI, PI, PMMA as well as semicrystalline polyvinylidene difluoride (PVDF), polyethylene (PE), BOPP, and PP, with their properties summarized in Table S2. Excellent agreement between predicted breakdown strength and experimentally measured ones are observed in Figure 4b. Note that these polymers have relative dielectric constant varying by one order of magnitude (from 2.2 for BOPP to 24.1 for PVDF) and Young's modulus varying by two orders of magnitude (from 0.038 GPa for PE to 5.5 GPa for PI), yet they all falls in the same linear curve relating electric toughness and tensile toughness (Figure S15). Detailed data on their diverse mechanical and electrical characteristics are summarized in Table S3.

FIGURE 4.

Predicting breakdown strength via mechanical toughness. (a) Correlation between electric toughness for breakdown and tensile toughness for 9 types of polymers we tested; (b) Predicted breakdown strength for a wide range of polymers versus experimental values; (c) Poor correlation between breakdown strength and Young's modulus; (d) Predicted breakdown strength based on electromechanical instability.

Many previous works proposed that breakdown strength of polymers is correlated with their Young's modulus [18, 27]. For certain materials this may work, yet for the wide range of polymers we have considered, such a correlation clearly does not exist (Figure 4c). If we use the electromechanical instability criterion proposed by Stark and Garton [18] instead, then breakdown strengths are overestimated by more than 10 times (Figure 4d). Clearly, for vast majority of polymeric dielectrics, the breakdown is not governed by electromechanical instability but related to mechanical toughness. For softer dielectric with a Young's modulus on the order of 1 MPa, then electromechanical instability is expected to take over. For example, PAA has Young's modulus measured to be 1.5 MPa (Figure S16a), and the measured breakdown strength of 100 MV m⁻¹ (Figure S16b) agrees reasonably well with 112 MV m⁻¹ predicted based on Stark and Garton [18]. Nevertheless, when a needle electrode is used as in Figure 1, which induces strong field concentration, then breakdown in PAA occurs through nucleation and propagation of a cracking channel instead, as we have observed.

2.4. Phase‐Field Model of Dielectric Breakdown

To appreciate the correlation between mechanical toughness and dielectric breakdown, we developed a phase‐field model (Figure S17) for coupled evolution of crack (d) and electric tree (s), one governed by fracture energy (G _f) [41] while the other governed by double‐well potential [42]. In addition, electric energy and elastic energy as well as their coupling through the Maxwell stress are considered. It is found from simulation in Figure 5a that the crack initiates at 0.3030 ms and grows gradually afterward. Electric tree, on the other hand, initiate at much later time of 1.0355 ms followed by rapid propagation, resulting in complete breakdown at 1.0360 ms. The entire process is captured in Video S5. The damage areas in terms of crack and electric tree versus time are presented in Figure 5b, showing the sequences, and the trend can be understood from Figure 5c, where it is observed that the driving force for crack growth increases much faster than that for electric tree until very late in the breakdown process. Increasing the fracture G _f elevates the critical voltage for crack initiation (Figures S18 and S19a), though it does not fundamentally change the dynamics. In fact, we have carried out simulations for a series of values of G _f, and a linear relationship between electric and mechanical toughness emerges from simulations (Figure 5d; Figure S19b,c), recovering what we uncovered in the experiments. These results confirm that electric breakdown of polymers is strongly correlated to mechanically toughness.

FIGURE 5.

Phase‐field simulation of electric breakdown incorporating crack and an electric tree. (a) Initiation and growth of crack and electric tree; (b) Corresponding damage area evolution versus time; (c) evolution of driving forces during electric breakdown; (d) electric toughness versus tensile toughness simulated under different G _f.

3. Discussion

Dielectric breakdown and mechanical failure were long thought to be two different processes governed by distinct mechanisms. Yet here we show that they are intimately related to each other for a wide range of polymers, enabling accurate prediction of dielectric strength from mechanical toughness. In previous works, Fothergill [27], Schneider [43] and Wang [44] have proposed that the propagation of a breakdown channel can be understood in terms of energetic balance between electromechanical energy release and material resistance to damage growth. Our work builds on such idea but does not require prescribing an initial crack or defect. Instead, we use tensile toughness as an experimentally measurable descriptor of the energy required for a polymer to resist damage, and our in situ experiment, comprehensive data analysis, as well as phase‐field simulations overwhelmingly support such a theoretical proposal. Interestingly, the electric work done for breakdown is only a small fraction of tensile toughness, or the energy necessary to mechanically break the polymers. The microscopic mechanism underpinning such scaling worths further investigation and may be related to the fact that the fracture surface is two‐dimensional in nature, while breakdown path is one‐dimensional (1D) instead. The dimensionality is important here, and for bulk polymers wherein electric tree forms [16] instead of 1D channel, we expect that the pre‐factor coefficient between electric toughness and mechanical toughness will be different yet the underlying mechanism remains the same. Our study thus unifies electric and mechanical failures and enables a new paradigm in engineering the breakdown strength without compromising their dielectric constant.

4. Experimental Section

4.1. Polymer Bulks and Films

The sample used for the in situ dielectric breakdown test is polymer polyacrylic acid (PAA, Deli Group Co., Ltd., China) measuring 75 mm × 25 mm × 4 mm. The polymer films used for subsequent electromechanical testing are tabulated in Table S1.

4.2. In Situ Observation of Electrical Breakdown Device

The in situ observation (Figure 1a) for electrical breakdown uses a DC high voltage source (PolyK, USA) to apply a load, a microscope (6745‐HK830, China) to observe and take photographs, and a 100 Ω resistor connected in series in the circuit to measure the breakdown current passing through it with an oscilloscope (RIGOL DS1102E). The cross‐sectional morphology of the cracking channel is measured using a digital microscope system (VHX‐6000).

4.3. Mechanical Toughness Test

The film stretching experiment in this paper uses a flexible film stretching system (PURI Materials, China, Figure S4). The film sample size is 50 mm × 20 mm × h (‘h’ is the thickness of films), and the stretching speed is 0.2 mm s⁻¹.

4.4. Surface Morphology Test

The surface morphology of the polymer film was examined using a scanning electron microscope (SEM, Quattro S).

4.5. Dielectric Properties Test

The ferroelectric test (TF3000, DE) was used to test the hysteresis loop of the films, with a circular electrode having a diameter of 6 mm.

The dielectric properties were evaluated using an Agilent 4980A LCR meter at an AC voltage of 0.5 V over a frequency range of 10²–10⁶ Hz. Temperature control was managed by a Partulab DMS‐2000 system. The electrodes of the test samples were 6 mm in diameter.

4.6. Crystal Structure Characterization

Differential Scanning Calorimetry (DSC25, USA) was employed to measure the T _g, T _m, and crystallinity of the polymers. All tests were conducted at a heating rate of 10°C min⁻¹. The degree of crystallinity (X _c) was calculated as follows:

$$X_c=\frac{\mathrm{\Delta }{H}_m-\mathrm{\Delta }{H}_c}{\mathrm{\Delta }{H}_m^0}\times 100\%$$ (1)

where ΔH_m is the enthalpy of fusion, ΔH_c is the enthalpy of cold crystallization, and $\mathrm{\Delta }{H}_m^0$ is the standard enthalpy of fusion.

X‐ray diffraction (XRD) was performed on Smartlab 3 KW, Japan equipped with Cu Kα radiation (λ = 1.54 Å). Based on XRD results combined with the Scherrer Formula, the crystalline size (t _hkl) of the polymer film can be obtained, where the calculation formula is [45]:

$$t_{hkl}=\frac{K\lambda }{\beta cos\theta }$$ (2)

where K is Scherrer constant, typically 0.9 for polymers; λ is the x‐ray wavelength, with λ = 0.15406 nm used for a copper target; β is the full width at half maximum of the crystalline peak; θ is the corresponding Bragg angle at the peak position.

4.7. Phase‐Field Simulation

For specific details of the phase field model, please refer to the Supporting Information section.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File 1: adma74050‐sup‐0001‐SuppMat.docx.

Supporting File 2: adma74050‐sup‐0002‐VideoS1.mp4.

Supporting File 3: adma74050‐sup‐0003‐VideoS2.mp4.

Supporting File 4: adma74050‐sup‐0004‐VideoS3.mp4.

Supporting File 5: adma74050‐sup‐0005‐VideoS4.mp4.

Supporting File 6: adma74050‐sup‐0006‐VideoS5.mp4.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.