Insights of 3D-printed dielectric elastomer layers: Electrical and mechanical properties, and prospects for artificial muscle applications

Summary

3D printing of dielectric elastomers (DEs) opens new possibilities for next-generation soft actuators, offering greater flexibility. Additive manufacturing (AM) enables complex, customizable geometries that traditional fabrication methods cannot achieve. In this study, the potential of Elastic 50A as a candidate material for DE development is explored. It is demonstrated that dielectric constant of Elastic 50A increases with decreasing thickness, reaching a maximum value of 8.09 at 0.66 mm. The highest Maxwell stress is observed at 0.50 mm thickness, confirming thinner elastomer layers have better actuation performance. Additionally, Elastic 50A-polylactic acid (PLA) bilayers were fabricated to evaluate the influence of substrate coupling. Compared with the pure Elastic 50A samples, the bilayers exhibited enhanced electric breakdown strength and energy at break. However, reduction in some electrical and mechanical parameters was observed. These findings emphasize that further optimization of interfacial properties is essential for achieving efficient and reliable 3D-printed DE systems.

Graphical abstract

Highlights

• •3D-printed Elastic 50A achieves a maximum dielectric constant of 8.09 at 0.66 mm thickness
• •Dielectric constant show non-monotonic thickness dependence arising from the printing process
• •Irreversible structural changes in Elastic 50A occur between 38°C and 40°C
• •Elastic 50A-PLA structures show enhanced electric breakdown strength and energy at break

applied sciences; engineering; devices.

Introduction

Artificial muscles represent a significant advancement in materials science, mimicking the functionality of biological muscles through innovative materials and designs.^1,2 Recent findings highlight the potential of various types of artificial muscles, including hydraulic and pneumatic actuators, shape memory alloys (SMAs), ionic polymer-metal composites (IPMCs), and dielectric elastomers (DEs).^3,4

Dielectric elastomer actuators (DEAs) are sandwich structured flexible capacitors, which consist of electroactive elastomer covered with electrodes.⁵ DEs convert applied electrical voltage into Maxwell stress leading to mechanical motion. The key factors to consider for attaining high effectiveness includes large actuation strain and high energy density.⁶ The thickness strain (S_z) is inversely proportional on Young’s modulus (Y), directly proportional to the permittivity of free space (ε₀) and the dielectric constant (k) of the elastomer and applied electrical field square (E²) (Equation 1)⁷;

$$s_z=-\frac{k{\epsilon }_0{E}^2}{Y}$$ (Equation 1)

On the other hand, DEs act as soft capacitors, consisting of a thin elastomeric film sandwiched between two compliant lectrodes. When a voltage V is applied, an electric field E = V/d develops across the elastomer. The interaction between the electric field and the dielectric medium gives rise to an electrostatic pressure, commonly referred to as Maxwell stress (details in section “frequency-dependent electric properties”). This Maxwell stress compresses the elastomer in the thickness direction, while, due to incompressibility of the material, a lateral expansion in area occurs. As a result, the DE film undergoes a voltage-induced thickness reduction and surface strain, which can be harnessed as mechanical actuation. The magnitude of this electromechanical response depends on the dielectric constant, film thickness, applied voltage, and the mechanical stiffness of the elastomer.

Thus, to achieve large actuated deformation at low electrical field, the polymer should have high dielectric constant and low Young’s modulus. Additionally, the low viscoelasticity, high breakdown strength and stable actuation performance are of high importance.⁸ Earlier it was achieved high dielectric constant of 10.23 at 1 kHz and Young’s modulus of 0.09 MPa showing exceptional high specific power using polar fluorinated polyacrylate⁹․ in another manuscript they used polydimethylsiloxane (PDMS) dielectric layer of 6 μm thick to prepare an insect sized legged robot with operating voltage less than 450 V.¹⁰ Stabilization of actuation performance was achieved by interpenetrating polymer networks.^11,12 Network structure and combination of materials can lead to stability of actuation performance and better mechanical properties.¹³ Addition 50% of epoxy aliphatic acrylate (EAA) to aliphatic urethane diacrylate (AUD) leaded to increase of breakdown strength from 29.7 to 40.9 V μm⁻¹ (Table 1) and decrease of hysteresis loss from 40.8% to 12.8%.²³ Multilayer DEAs were also prepared to improve the actuation performance.²⁴ Multilayer DEAs has potential to improve actuation stress and strain.^25,26 Additionally, multilayer DEA was prepared by 3D printing technology achieving good mechanical and electrical properties.²⁷

Table 1.

Dielectric and mechanical properties of DEs from literature

Reference	Material	Dielectric constant (AC field freq., Hz)	Young’s modulus (MPa)	Tensile strength (MPa)	Actuation strain in % at V/μm voltage	DC Electric breakdown (V/μm)	Key features for applications in AM
Dijkshoorn et al.9 and Zhou et al.14	polar fluorinated polyacrylate	10.23 (103)	0.09	–	253% at 46	similar polymer: 700	specific energy/mass energy density: 225 J kg−1 high specific power/mass power density: 2,245 W kg−1 @ 40 MV m−1
Qian et al.15 and Kochetov et al.16	polyurethane (PU)	5.99 (103)	6.76	4.89	0.3% at 2	91.03	dielectric loss (DL) (103 Hz): 0.07 electromechanical sensitivity: 0.89 MPa−1
Natori et al.17 and He et al.18	thermoplastic polyurethane (TPU)	15.0 (1), 8.2 (102, 103)	3.4	24.6	0.6% at 25	225	electrical conductivity (EC): 10−11 S m−1 breakdown strength DL (103 Hz): 0.03
Natori et al.17	TPU—10 phr PEG	222.0 (1), 12.0 (102), 8.7 (103)	1.7	14	3.5% at 16	16	EC: 10−9 S m−1 DL (103 Hz): 0.42
Natori et al.17	TPU—50 phr PEG	3500.0 (1), 20.0 (102, 14.0 (103)	0.3	0.64	<2.3% at 42	5.26	EC: 10−7 S m−1 DL (103 Hz): 0.03
Zhang et al.,19 Rahman et al.,20 and Simaite et al.21	PVDF	14–15 (1) 11 (103)	1200	–	0.6% at 0.018	172	DL (1 Hz): ∼0.1 DL (103 Hz): ∼0.2
Zhang et al.19 and Taine et al.22	polydimethylsiloxane (PDMS)	∼2 (1–105)	2.0	2.8-6.3	0.04% at 60	140	DL (1 Hz): ∼0.05 DL (103 Hz): ∼0.1
Huang et al.23	aliphatic urethane diacrylate (AUD)	10․3 (103)	4.21	–	–	29.7	DL: 0.090 hysteresis loss: 40. 8%
Huang et al.23	AUD:EAA (epoxy aliphatic acrylate) = 5:5	7.3 (103)	0.58	–	–	40.9	DL: 0.059 hysteresis loss: 12. 8%
This study	Elastic 50A	8.1 (105), 6.1 (106)	5.6	0.61	–	≈10	electrical conductivity: 1.7∗10−6 S m−1
This study	PLA-Elastic 50A	6.8 (105), 4.9 (106)	13.2	0.63	–	>10	electrical conductivity: 1.3∗10−6 S m−1

The 3D printing enhanced the DEA fabrication process and opens new possibilities for preparation of complex biomimetic soft actuators.^{23,27,28,29,30,31,32} Innovative printing techniques and materials for DE fabrications remains challenging. A system that integrates 3D printing with a UV-curable elastomer creates conductive designs on printed layers, would yield completely operational DE actuators and sensors through automated methods.

The continuous research and development of artificial muscles are aimed at improving the material, performance, actuation mechanism, efficiency, movement freedom, controllability, and manufacturability. Such innovations propel the market overall, which itself brings new challenges to researchers.

Recently, the investigations showed that the integrated smart architectures can increase the effectiveness of artificial muscles in motion freedom and handling stresses.^33,34,35 These architectures not only save the space and weight, but also achieve higher functionality, strength, and stiffness. Smart materials, manufacturing advancements, and actuation concepts are also essential for reaching top-tier products. The choice of materials depends on the actuation mechanism, functional requirements to the system and manufacturing technology.

This research is focused on finding electrical properties of Elastic 50A and Elastic 50A-PLA laminate structures, as well as their variation tendencies with changing thickness, increasing temperature and dependence on AC frequency. Elastic 50A Resin is a soft, translucent elastomer with a Shore durometer of 50A, designed for 3D printing applications that requires flexibility and elasticity.³⁶ It belongs to the class of thermoplastic polyurethane (TPU)-based elastomers, can be characterized by its segmented polymer structure, combining soft elastomeric segments with hard thermoplastic domains, which provide a balance between elasticity, mechanical robustness, and processability. Although it shows characteristics close to some DEs,^8,37 including the capacity to bend, stretch, and compress, we have found no explicit evidence in the literature suggesting that Elastic 50A resin can act as a DE. Additionally, in order to provide superior adhesion to the elastomeric layers, ensuring structural integrity and minimizing delamination risks, while its rigidity contributed to enhanced mechanical stability and repeatable deformation behavior in the laminates polylactic acid (PLA) was selected as a second layer to print the elastomer on. Strong interfacial bonding occurs during polymerization process of the elastomer printed on PLA layer, leading to high quality adhesion and prevents early delamination and contributes to the mechanical stability of the laminates.

The dielectric constant, mechanical properties and energy density of the 3D printed elastomer demonstrates that it has relatively high dielectric constant and thus it has the potential to be used as DE, if its electric properties are adopted for AM applications. In general, DEs are among the most promising material classes for artificial muscle applications due to their intrinsic compliance, large reversible deformation, fast response, and high energy density. In artificial muscle systems, DE-based actuators are actively explored for use in soft robotics, adaptive grippers, bio-inspired locomotion systems, wearable assistive devices, and haptic interfaces, where lightweight construction, silent operation, and muscle-like deformation are essential. Their capacitor-like architecture enables straightforward electrical control, while their soft mechanical response allows safe interaction with humans and delicate environments. Importantly, recent advances in multilayer designs, material compounding, and additive manufacturing (AM) have significantly improved actuation stress, durability, and scalability, bringing DE-based artificial muscles closer to practical deployment. Within this context, elastomers exhibiting moderate dielectric constants combined with sufficient mechanical robustness and printability are particularly attractive, as they enable integration into complex architectures and scalable fabrication routes. Therefore, materials such as Elastic 50A, which demonstrate dielectric properties comparable to established DEs and are also intended for 3D printing technologies, represent promising candidates for future artificial muscle systems, provided that their electrical performance is further optimized toward high-field, low-loss actuation regimes. Benchmarking intrinsic electrical properties (dielectric constant, conductivity, and breakdown-related parameters) against existing DE systems helps judge the potential of a material for actuation and energy-conversion applications. Device-level figures of merit such as dielectric–mechanical coupling or electrically induced actuation strain require actuator testing (including electrode type, device geometry, etc.) and therefore cannot be directly obtained from capacitor-style measurements presented here. Nevertheless, mapping how dielectric constant k, conductivity and k/d² depend on film thickness, AC frequency and temperature provides the necessary inputs to (1) estimate attainable Maxwell pressures in a device model, and, (2) prioritize material modifications (e.g., fillers, network chemistry, or multilayer stacking) to increase actuation at fields below breakdown.^38,39,40

Results

Thickness-dependent electronic properties

The thickness of each sample was carefully measured across all surfaces in 15 points, using a micrometer suited for soft materials, to determine thickness variation and consistency. It was projected to fluctuate within a maximum range of 16%. Capacitance measurements vary within a 3% margin from the average for samples of each thickness. All the measured and calculated data are compiled in Table S1 of the supplemental material. According to the well-known parallel plate capacitor formula (II), where k is the dielectric constant of the material, ε₀ is vacuum permittivity, A = 1.65 cm² is the electrode area, and d is the insulator thickness,³⁹ a decrease in thickness is expected to result in an increase of capacitance. This can be seen in Elastic 50A films (Table S1 SM; Figure 2A), supporting the classic insulating characteristics of printed Elastic 50A films.

$$C=\frac{k{\epsilon }_0{\rm A}}{d}$$ (Equation 2)

Figure 2.

Electric properties of 3D printed Elastic 50A

Thickness dependence of (A) capacitance, (B) conductance, (C) conductivity, and (D) dielectric constant for Elastic 50A measured in 1 mHz harmonic field.

Electric breakdown assessments were performed at three distinct spots on each sample (right side of Figure 1): the center, deep in the corner, and close to the edge. For every sample, irrespective of thickness, the initial two locations showed an electric breakdown voltage greater than 5 kV (Table S1, SM). However, for samples with a thickness of ≤0.8 mm, the measurements taken near the edge sometimes revealed reduced breakdown voltages (3.8–4.9 kV). A thorough inspection shows that the edges were typically thinner. Nonetheless, the thin printed samples, which had central areas thinner than the edges of the thick printed samples, still show greater electric breakdown voltages. This implies that structural defects occur more frequently near the edges compared to the deeper areas of the samples. Furthermore, as anticipated, a reduction in thickness leads to a decrease in resistance (R ∝ d) and a corresponding increase in conductance (G = 1/R). These trends are clearly evident in Figure 2B, where the relationships can be visually distinguished.

Figure 1.

Parallel plate capacitor scheme along with the capacitor system picture with Elastic 50A as an insulating material in the middle and scheme of samples with their dimensions, and the positions where electric breakdown was measured

Ideally, the conductivity and dielectric constant of a material should remain constant regardless of thickness, as they are intrinsic material properties rather than object-specific features. However, thickness dependence is observed for these parameters (Figures 2C and 2D). Interestingly, this dependence is non-monotonic, showing a maxima in conductivity and dielectric constant around a thickness of 0.66 mm. These findings suggest anisotropy in the material, likely resulting from the layer-by-layer printing process. The layered structure of the films may introduce unexpected bulk effects, as observed here. The increase in conductivity due to capacitor losses could be attributed to slight variations between layers’ electric properties, leading to the generation of additional free charge carriers.^9,17 However, the subsequent decrease with greater dielectric thickness suggests opposing electrical tendencies between adjacent layers, which may trap free charge carriers in the middle layer of the dielectric film.

Furthermore, the non-monotonic behavior of the dielectric constant may arise from the combined effects of trapped charge carriers due to the Maxwell-Wagner effect and perpendicular interfacial polarization caused by anisotropy (detected in Figure 7C) in the row-by-row printed layers. Specifically, as the film thickness increases up to approximately 0.63 mm, the Maxwell-Wagner effect—resulting from interfacial anisotropy parallel to the electrodes, dominates, leading to a rise in the dielectric constant. However, with a further increase in thickness, other factors become more significant: the bulk material becomes less polarized, and perpendicular interfacial polarization disrupts charge transport while also reducing conductivity. These effects collectively reduce the dielectric constant, creating a maximum at around 0.63 mm leading to the idea, that this may be the potentially best thickness for later artificial muscle applications. Weather it is so or no, can be checked calculating thickness dependence of k/d², taking into account actuation effective pressure relationship with thickness and dielectric constant (checked in paragraph 3.3).

Figure 7.

Microstructural characterization of the cross-section of 0.5 mm Elastic 50A samples

(A) Low magnification, (B) high magnification, and (C) other angle, SEM where layers perpendicular to the surface are shown.

Temperature-dependent electric properties

Considering that layer effects is proposed to be minimized for the thinnest films, this paper also examines the temperature dependence specifically of thin samples. As the temperature of the sample rises, its capacitance, dielectric constant, and conductivity also increase (Figure 3; Table S2, SM). The increase in capacitance and dielectric constant with rising temperature can be explained by the enhanced reorientation rate of dipole molecules.⁴⁰ Particularly, the increasing conductivity can be attributed to two main factors.

• (1)Thermal excitation of charge carriers: in dielectrics, a small number of charge carriers are typically present due to impurities or defects. As temperature rises, more electrons gain enough energy to jump from trap states or localized defect states into the conduction band, increasing conductivity.
• (2)Increase in bulk conductivity: the conductivity (σ) of many dielectrics follows an exponential dependence on temperature, often described by an Arrhenius-like equation.⁴¹ This relationship indicates that higher temperatures facilitate charge transport, reducing resistivity and increasing conductivity (σ = 1/ρ).

Figure 3.

Hysteresis of electric properties due to temperature variance

Temperature dependence of (A) capacitance, (B) dielectric constant, and (C) conductivity for Elastic 50A in 1 MHz AC field.

This behavior aligns with the initial data showing a dielectric with high molecular mass of the polymer. This indicates that these complex molecules cannot track high frequencies (1 MHz), resulting in incomplete reorientation; however, a rise in temperature causes quicker reorientation for high-frequency AC power sources. Meanwhile, when the temperature is as high as 38°C abnormal behavior of the parameters is observed: the capacity, and dielectric constant start to decrease, while the conductivity still increases, and then all of them reach saturation. The samples were heated until 40°C and cooled back, monitoring the electric properties all the way. Although the capacitance and dielectric constant return to their original values, huge hysteresis is observed and they go beyond already being as cooled as 35°C. Furthermore, the conductivity of the samples during cooling exhibits a significantly different behavior compared to its changes during heating. It also never returns to its initial value. Such extraordinary behavior of conductivity and inconsistency of capacitance and dielectric constant clearly indicate irreversible changes in polymer structure and its possible structural modifications within the range of 38°C–40°C.⁴² Hence, the pure Elastic 50A may be used in AM in temperatures lower than 38°C.

Frequency-dependent electric properties

To assess the frequency dependence of electrical properties and verify consistency with temperature dependence, measurements were performed with a 100 kHz AC power supply. As expected for polymer-based materials with long molecular chains, a clear frequency dependence was observed. Capacitance and dielectric constant increased by approximately 30% in all samples (Figure 4; Table S3, SM). These results align with temperature-dependent trends, confirming that dipole reorientation is more effective at lower frequencies, allowing molecules sufficient time to realign before the electric field direction changes. Consequently, this suggests that increasing temperature should have little to no effect on capacitance in a 100 kHz AC field. Experimental verification confirmed this prediction, as no changes in capacitance were observed with temperature variations; therefore, no additional data are provided.

Figure 4.

Behavior of Elastic 50A electric properties for various thickness values

Thickness dependence of (A) capacitance, (B) dielectric constant, and (C) dielectric constant ratio on squared thickness for Elastic 50A in 1 and 0.1 MHz frequencies of AC field.

The results for dielectric constant exhibited a non-monotonic dependence on thickness across both AC frequencies, with higher values observed at lower frequencies. Since dielectric constant is an intrinsic material property and capacitance varies with frequency, this behavior at lower frequencies is expected. A high dielectric constant is essential for generating a stronger actuation force—Maxwell stress. Based on Figure 4B, the optimal thickness appears to be in the range of 0.65–0.75 mm. However, the dependence of actuation effective pressure on dielectric properties, as described previously,⁴³ adheres to Equation 3:

$$P={k{\epsilon }_0\left(V/d\right)}^2$$ (Equation 3)

where V is the applied actuation voltage, and other parameters are defined in Equation 1.

This equation highlights that effective pressure is influenced by both the dielectric constant and sample thickness. Therefore, selecting optimal parameters requires considering the thickness dependence of the derived parameter (Figure 4C). The figure clearly shows that thinner layers result in greater Maxwell stress for the same applied voltage and it almost reaches saturation near 0.50 mm thickness.

Additionally, two-layer samples composed of Elastic 50A and PLA were prepared, and their electrical properties were measured under AC fields at 1 MHz and 100 kHz: electrical breakdown, conductivity, dielectric constant, and k/d² (Figure 5). Electrical breakdown exceeded 5 kV in all samples across various regions (measured using the same method as described previously in Figure 1), suggesting higher quality compared to the single-layer structures.

Figure 5.

Behavior of Elastic 50A-PLA double layer system electric properties for various thickness values

Thickness dependence of (A) conductivity, (B) dielectric constant, and (C) k/d² for Elastic 50A-PLA samples in 1 and 0.1 MHz frequencies of AC field.

Raman spectroscopy characterization

The obtained Raman spectra (Figure 6A) show differences after 37° heating. It can be observed that the peaks at 394 and 512 cm⁻¹ are increased in intensity, which are associated with out-of-plane and in-plane bending vibrations of the aromatic ring. Such results may be a consequence of kinetic energy gained by the aromatic ring, which influences out-of-plane vibrations in increasing manner. Furthermore, the ratio of peak intensities at 394, 512, 571, 627, and 652 cm⁻¹ remains the same (C-H out-of-plane bending vibrations at 571 cm⁻¹, C-H in-plane bending vibrations at 627 cm⁻¹, and ring deformation vibrations at 652 cm⁻¹), in this region only the noise from the backbone vibrations is increased. On the other hand, the peaks at 1,000, 1,566, and 1,610 cm⁻¹ increased in intensity. These peaks are mostly associated with the aromatic ring chain vibrations. Additionally, the peaks at 627 and 652 cm⁻¹ were merged before 37°C of heating and separated at higher temperatures. The cause of this behavior could be the activation of the aromatic groups and their reorientation in the structure of the molecule. The small gap between 627 and 652 cm⁻¹ peaks suggests that the aromatic groups were very close to each other after and stronger interaction between them occurred in 37°C with each other. Thus, on the spectra, it was observed as one peak. During heating the groups had more kinetic energy, reorientation could be the cause of the peak separation. The fact that the intensity of the 1,000, 1,566, and 1,610 cm⁻¹ increased indicates that the aromatic groups are absorbing a significant amount of energy. However, significant changes occur starting from 50°C. The disappearance of the 394 and 512 cm⁻¹ peaks at temperatures starting from 50°C, with no reappearance after cooling, indicates that an irreversible reorientation has taken place.

Figure 6.

Influence of temperature treatment on the structure of Elastic 50A

(A) Temperature-dependent structural changes of Elastic 50A films visualized with Raman spectroscopy.

(B) Temperature-dependent energy flows measured with a differential of DSC (DDSC).

Electric measurements and Raman spectroscopy results indicate the need for detailed temperature analysis of the material. Hence, DSC technique was applied for further study. As the amount of heat released during conformational changes of the molecule is too small, there is no visual change on the DSC curve. In order to address this problem the differential of DSC was used (DDSC). The DDSC curve on Figure 6B shows a small peak at 39.1°C, which starts at 39°C and finishes at 39.4°C. This may represent the point of irreversible change, as observed in the Raman spectra between 37°C and 50°C, confirming the temperature-dependent behavior of the electrical parameters. The bell shape of the DDSC and DSC curves (Figures 6B and S1) is a result of two factors: the relatively high thermal capacity of the polymer (indicated both at the start and the end of the heating on Figure S1) and the non-linear heating at first several degrees of the analysis (Figure S2).⁴⁴

Mechanical properties of Elastic 50A

The mechanical properties of films have been evaluated. Stress-strain curves for studied materials can be viewed in Figure S3 in supplemental information, and the tensile properties of the studied films are presented in Table 2.

Table 2.

Tensile test properties of the studied films

Sample	Tensile stress (MPa)	Young’s modulus (MPa)	Energy at break (J)	Tensile strain at break (%)
Elastic-50	0.61 ± 0.08	5.6 ± 0.6	0.06 ± 0.01	13.0 ± 1.9
Elastic-50-PLA	0.63 ± 0.06	13.2 ± 1.9	0.07 ± 0.01	11.0 ± 1.4

The Young’s modulus of Elastic-50 is lower than it was reported previously: 8.73 ± 0.85 MPa, for the same material.³⁸ This can be caused by the printing parameter difference and curing effect. In fact, the effect of the environment, such as humidity and temperature were reported to have a great impact on Elastic 50A.³⁸ When Elastic-50 was printed on a thin layer of PLA, the Young’s modulus increased 2.4 times. The Young’s modulus of PLA depends on the degree of crystallinity.⁴⁵ The pristine PLA films have Young’s modulus of ∼2 GPa, tensile strength of 44 MPa and elongation at break of 3.1%.^46,47 This may be a reason the thin layer of PLA, which is ∼12% of the thickness of Elastic-50-PLA film had large impact on the mechanical properties of this layered composite.

Microstructural characterization

The cross-sectional analysis of the samples using scanning electron microscopy (SEM) reveals slight non-uniformities in the layers (Figure 7). Focusing on the cross-sectional surface (Figure 7A) indicates appearance of three main layers: highly porous left layer, split into two middle layer, and smooth right layer. Middle layer, on its own turn, contains a smoother middle-left and slightly porous right layers (Figure 7B). Such a structure confirms earlier electric results: non-monotone behaviors, explained trapped charges and saturation of parameters in the range of 0.7–0.9 mm. Additionally, Figure 7C demonstrates layered structure perpendicular to the electrodes: which is a manufacturing effect. This structure is discussed above to badly influence the dielectric properties of the material for AM applications. Observed variations in electric properties of the samples likely result from both micro-scale defects between layers presented on SEM pictures and nanoscale defects that are not visible under SEM.

Discussion

Discussions on: dielectric constant, mechanical properties, electric breakdown, frequency dependence, evaluation of Maxwell stress, mechanical properties, and morphology.

Electrical properties

The 3D printed Elastic 50A shows a maximum permittivity k ≈ 8.09 (0.1 MHz) and the PLA-Elastic 50A bilayer k ≈ 6.8 (0.1 MHz). These values exceed typical commercial VHB and natural-rubber values reported in the literature: specifically, several studies report that commercial VHB 4910 has a dielectric constant of about 4.3 at 1 kHz, while natural rubber is around 3.8 at 1 kHz, and our results are comparable with previously reported high-k filled elastomer composites: PU/BaTiO₃ (PU/BT) with k ≈ 8.3 at 1 Hz,^38,48 and PU/BT-MDI with k ≈ 8.4 at 1 kHz.^49,50 Although, high dielectric constant values are obtained for elastomers with additives, in case of Elastic 50A we have reached relatively high dielectric constant just by manufacturing it through 3D printing method. However, the breakdown field for Elastic 50A and Elastic 50A-PLA materials (near 10 V/μm) remains lower than the very large breakdown strengths reported for other elastomers or chemically modified systems (examples: breakdown fields reported up to hundreds of V/μm in the literature under specific conditions).^11,38,51 Thus, the permittivity we obtain for 3D-printed Elastic 50A is substantially higher than typical unfilled commercial elastomers and comparable with some engineered filled composites-remarkably achieved here by 3D printing rather than filler addition. Taken together, our measurements indicate that (1) the relatively high permittivity of 3D-printed Elastic 50A is promising, (2) the current breakdown limits will constrain the maximum usable field unless modifications are made, and (3) the dataset (thickness, frequency, and temperature dependence) provides a rational basis for selecting material modification strategies and the conditions (e.g., field frequency, temperature range, additives, etc.) to pursue AM applications.^50,52

The temperature and frequency dependence tendencies of capacitance, dielectric constant, and conductivity found in sections “temperature-dependent electric properties” and “frequency-dependent electric properties,” help to optimize operating conditions for artificial muscles, demonstrating that using a low-frequency AC power supply can minimize temperature influence and prevent additional losses. Furthermore, it can be inferred that the AC field applied in the future to control the expansion and contraction of the material for use as an artificial muscle should not exceed 100 kHz.

The increase in the dielectric constant observed at 1 MHz with rising temperature, in contrast to the nearly temperature-independent behavior at 100 kHz, suggests that molecular polarization processes are able to fully respond to the electric field at lower frequencies. At 100 kHz, dipolar polarization can follow the applied field within each cycle, resulting in stable dielectric values over the investigated temperature range. In contrast, at 1 MHz the polarization mechanisms cannot fully keep pace with the rapidly oscillating field, leading to the observed temperature-dependent increase in the dielectric constant.

Based on this behavior, it can be expected that measurements performed at even lower frequencies (below 100 kHz) would exhibit dielectric responses similar to those obtained at 100 kHz. To verify this assumption, additional measurements were conducted using an LCR meter (Rohde & Schwarz HM8118 LCR Meter) under an AC harmonic field with frequencies down to 2.5 kHz. Measurements at lower frequencies were not feasible due to instrumental limitations. Nevertheless, the obtained results were consistent with the higher-frequency measurements, showing a maximum deviation of approximately 3 pF.

The dielectric breakdown, on the other hand, occurs near 5 kV in the geometry and thicknesses tested (see “results” and Figure 1). This breakdown magnitude constrains the maximum usable field and so the maximum attainable electrostatic pressure and actuation for a device built from the present films. Literature shows that some elastomers (modified and non-modified) can achieve much higher breakdown strengths (reports of order 10²–10³ V/μm under particular sample preparation and testing protocols are present), enabling very large electrically induced area strains.¹¹ Conversely, silicone systems with high-k fillers have demonstrated significant strain (e.g., ≈11% transverse strain around 9–10 V/μm in certain filled silicones) but also show that increasing voltage commonly approaches breakdown,⁵³ so raising permittivity without compromising breakdown strength is crucial. The present combination—relatively high permittivity, 13% elastic strain but breakdown near 10 V/μm—indicates that to realize substantial actuation at safe voltages we must either (1) further increase permittivity while maintaining breakdown, or (2) adopt device strategies that reduce the required field (multilayer stacking, mechanical pre-strain, or compliant geometries that convert small thickness change to larger displacement), or implement both strategies.

We observe higher k at 0.1 MHz than at 1 MHz in Elastic 50A samples (Figures 4B and 5B). Several studies emphasize that measured k depends strongly on frequency in low-frequency regimes and on electrode/sample interfaces.^38,54 This suggests a design strategy in which device driving frequency is chosen to align with the material’s higher-permittivity window (i.e., lower frequencies in our measurements), provided that device loss and heating remain acceptable.

In addition the results concerning the conductivity measurements of Elastic 50A-PLA samples (Figure 5A), closely align with the electric breakdown results for the same samples and show significantly lower conductivity—by more than 1 μS/m compared to single-layer samples. In fact, the conductivity of the thin, double-layer polymer structure reached values as low as approximately 0.9 μS/m, thereby bringing it within the range suitable for soft muscle applications. However, this does not imply that it is already suitable for such applications; rather, we demonstrate that it has the potential to become so with further modifications.

Conversely, the dielectric constant and k/d² values were lower for the Elastic 50A-PLA samples, indicating that further material optimization is necessary to enhance their suitability for AM applications. However, it is noteworthy that all three parameters (Figure 5) exhibit monotonic trends, suggesting that the films on PLA are more uniform. Overall, while improvements are still needed, the double-layer structure demonstrates clear advantages and presents a promising direction for future development in soft muscle fabrication.

Mechanical properties

According to the section “mechanical properties of Elastic 50A,” Elastic-50-PLA possesses greater rigidity and strength in the film. Furthermore, it demonstrates improved toughness due to its higher energy at break values. However, the tensile strain at break for this sample is comparable to Elastic-50, falling within the range of experimental error. On the other hand, according to the manufacturer’s data-sheet, the Elastic 50A resin exhibits a maximum elongation at break in the range of 100%–160%. In contrast, our experiments yielded much lower values—approximately 13% tensile strain at break for single-layer Elastic 50A films and about 11% for PLA-Elastic 50A double-layer structures. This deviation can be attributed to the aging process, as the samples were stored at room temperature for 30 days.

Meanwhile, non-uniformity found on cross-sectional surface of Elastic 50A samples (microstructural characterization) explains the non-monotone behavior of electric properties, and the layered structure of the polymer in the direction perpendicular to the electrodes may negatively influence the dielectric constant of the material for AM applications, hence suggesting improvement of manufacturing method to obtain uniformity in the mentioned direction, e.g., making sure slower polymerization process during 3D printing process to avoid the layered structure. Thus, findings in microstructural characterization confirm explanations and basic understanding for the obtained electrical properties.

On the other hand, recent advances in AM of elastomers highlight the potential for achieving far higher stretchability than observed in Elastic 50A films in current study. For instance, recent studies^55,56 employed a pneumatic-based direct pellet printing method with a propylene-based thermoplastic elastomer (Vistamaxx 6202) and, through parametric optimization using the Taguchi method, reported high elongations, along with tensile strengths of 5.22 MPa and Young’s modulus of 1.7 MPa. The optimized printing parameters yielded parts with excellent interlayer adhesion and cohesive fusion, in contrast to poorly optimized samples that suffered from weak bonding and cavities. These results demonstrate that, with appropriate process optimization, 3D printed elastomers can combine superior stretchability and satisfactory mechanical integrity in the future, thereby expanding their applicability in areas such as soft robotics, stretchable sensors, and biomedical devices.

Moreover, in Figure 4C, we plot the quantity k/d² (where k is the measured relative permittivity and d the sample thickness) as a convenience for readers because, under constant applied voltage V, the Maxwell (electrostatic) stress is determined by Formula 3. We emphasize that the Maxwell stress was not directly measured in this work; Figure 4C provides a derived quantity that enables readers to estimate the electrostatic pressure that would be produced at any chosen voltage using the measured permittivity and thickness values reported here. For example, at V = 5 kV, k ≈ 5.5, and d = 0.60 mm, the above formula gives p(Maxwell) ≈ 3.4 kPa, illustrating the order of magnitude of the pressure that can be expected under our experimental voltage limit.

Several important caveats must be noted when interpreting Figure 4C. First, the dielectric constant of 3D-printed elastomers depends on multiple factors (frequency, morphology, porosity, printing parameters, and interfaces with any electrode and coating/PLA layer), and these factors will modulate the true electrical and mechanical response and actuation strain. Second, the plotted quantity is therefore only a relative indicator of expected Maxwell pressure under constant voltage—it does not include mechanical boundary conditions, pre-strain, electrode compliance, or field non-uniformity, all of which influence the actual actuation.

Thickness influence on dielectric properties and mechanical compliance

Despite these limitations, the derived plot is useful for design decisions because it allows to (1) compare candidate material/stack combinations reported here and (2) compute the expected Maxwell pressure for any chosen operating voltage. In our samples, the PLA-Elastic 50A bilayer series shows a clear saturation of k/d² near d ≈ 0.60 mm, indicating an effective thickness window for maximizing electrostatic pressure without further benefit from thicker reductions in this range. By contrast, Elastic 50A single-layer films do not show saturation within the thickness range accessible here (0.55–0.91 mm), which we attribute to constraints in our 3D printing process that prevented reliably fabricating thinner samples. This observation suggests that further reduction of Elastic 50A thickness (for example, to ∼0.50 mm or below) could increase k/d² and the expected Maxwell pressure; we therefore identify fabrication of thinner films and direct actuation measurements as clear priorities for future work. Although direct actuation measurements and cyclic electromechanical testing are essential to evaluate the quality, applicability, and durability of the material under repeated actuation, these experiments are currently underway as part of our ongoing work. In this study, we focus on the fundamental mechanical, electrical, and structural properties of Elastic 50A, which provide the necessary foundation for future optimization and cyclic performance evaluation.

Limitations of the study and future perspectives

As a result, our study provides an initial insight into the fundamental limitations and strengths of Elastic 50A in laminate structures, which is a necessary step before material optimization. One of the most important outcomes is that future developments should focus on incorporating functional additives to increase the dielectric constant and enable larger actuation strains at safe electric fields. Thus, rather than directly advancing the state of the art, our results establish a perspective and guide future material modifications that could allow this system to be realistically applied in soft actuator applications.

At the present stage, the electrical breakdown field is lower than the estimated actuation field, and the elasticity of the films decreases with aging. Therefore, as a next step, we plan to modify the polymer formulation and optimize the printing parameters for the modified Elastic 50A. Actuation experiments will be performed only after achieving a breakdown field exceeding the required actuation field. To ensure smaller actuation field the dielectric constant of the material needs to be increased, which will on its turn lead to increased Maxwell stress. Therefore, as a next step, in line with above-mentioned strategies, we plan to incorporate high-permittivity fillers such as barium titanate to improve the electromechanical performance of Elastic 50A and PLA-Elastic 50A double-layer structures for AM systems.⁵⁷

Such achievements will allow the first attempts of Elastic 50A and Elastic 50A-PLA layers to be tested for AM applications Specifically, future modifications will include the incorporation of barium titanate nanoparticles into the liquid Elastic 50A prior to printing, in order to enhance the dielectric permittivity and thereby improve the potential performance for artificial muscle applications, in line with previous reports.⁵⁸ In addition, to mitigate physical aging and chain relaxation, the UV curing dose will be reduced to avoid excessive crosslinking, and polyethylene glycol (PEG) will be introduced to increase chain mobility, lower the effective crosslink density, and improve elastic recovery, leading to more stable long-term performance.^59,60

In summary: to achieve optimized DE actuators, the following strategies will be pursued in future work.

• -Increase dielectric constant: incorporate high-permittivity fillers such as Si, BaTiO₃ nanoparticles (at concentrations of 1–20 wt %) or low-concentration conductive nanofillers (e.g., carbon black at <1 vol %) into the liquid Elastic 50A resin prior to printing, targeting a dielectric constant exceeding 15 at 100 kHz and lower frequency fields to enhance actuation performance at safe electric fields.
• -Reduce elastic modulus: blend Elastic 50A with softer elastomeric components and systematically adjust printing parameters—including UV curing dose and layer thickness—to reduce the Young’s modulus below 1 MPa, enabling larger electromechanical deformation at voltages below the current breakdown threshold (∼5 kV).
• -Improve tensile strength: reinforce the polymer matrix with low concentrations of graphene nanoplatelets or carbon nanotubes (CNTs), and optimize bilayer or multilayer PLA-Elastic 50A stacking to improve tensile strength while preserving elongation at break above the currently observed ∼13%.
• -Minimize dielectric loss: control filler dispersion through sonication or surface functionalization to ensure homogeneous distribution within the resin, and optimize the polymerization uniformity during 3D printing to suppress interfacial charge accumulation and reduce dielectric loss tangent.
• -Optimize architecture: investigate multilayer stacked DEA configurations to amplify output displacement, integrate compliant electrode materials (e.g., carbon grease or ionic hydrogels), and explore novel geometries such as origami-inspired or corrugated designs to convert small thickness strains into large macroscopic displacements.

These approaches aim to balance electrical, mechanical, and structural properties to produce safe, efficient, and high-performance artificial muscles.

In this work, the suitability of 3D-printed Elastic 50A for DE and artificial muscle applications was systematically investigated. The study focused on thickness-dependent dielectric behavior, frequency- and temperature-dependent electrical response, and the influence of PLA substrate coupling in bilayer configurations. Electrical, mechanical, Raman spectroscopy, and DDSC analyses were performed to evaluate both intrinsic material properties and operational limitations.

The results demonstrate that Elastic 50A exhibits a relatively high dielectric permittivity (k = 5–8), with the dielectric constant increasing as thickness decreases, reaching a maximum value of 8.09 at 0.66 mm. The highest Maxwell stress was observed near 0.50 mm thickness, confirming that thinner elastomer layers provide improved actuation capability. Frequency analysis revealed temperature-dependent behavior in a 1 MHz AC field, including irreversible structural changes at 38°C–40°C, whereas stable dielectric performance was maintained at 100 kHz. Bilayer Elastic 50A-PLA structures showed enhanced breakdown strength and energy at break, although some electrical and mechanical parameters were reduced due to interfacial and stiffness effects.

These findings establish both the potential and the present limitations of Elastic 50A in its commercial form and provide quantitative guidance for further material optimization.

• -The obtained relatively high dielectric constant values (ranging from 5 to 8) suggest that Elastic 50A holds significant potential for use in artificial muscle applications. The presence of large polymer chains within the material and the corresponding electrical properties indicate that lower frequencies, such as 100 kHz AC field, are preferable for optimal performance.
• -Although the electrical parameters of Elastic 50A exhibit temperature dependence in 1 MHz AC field, irreversible changes were observed in the range of 38°C–40°C and confirmed by Raman spectroscopy and DDSC, hence the material may be exposed to temperatures ≤38°C to be functionalized in AM in the future.
• -On the contrary, no temperature dependence of the capacitance and dielectric constant was detected in the 100 kHz AC field. Therefore, to ensure stability, it is ideal to operate under temperature-independent conditions, such as using an AC field at 100 kHz.
• -Additionally, a sample thickness of ≤0.5 mm is recommended to achieve optimal performance in artificial muscles, balancing both structural uniformity and electrical characteristics.
• -The Young’s modulus of the Elastic-50 is two times lower than Elastic-50-PLA. However, in both cases the Young’s modulus should be further optimized to achieve good actuation deformation.²³

Resource availability

Lead contact

All detailed data are provided in https://github.com/AsatryanArevik/Elastic-50A_AM_2025. Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Arevik Asatryan (arevik.asatryan@ichph.sci.am).

Materials availability

This study did not generate new unique reagents. The ones used during the study: Elastic 50A and PLA films can be purchased from Formlabs Inc. (USA) and Bleher Folientechnik GmbH (Germany) correspondingly.

Data and code availability

• •The authors declare that the data supporting the findings of this study are available in https://github.com/AsatryanArevik/Elastic-50A_AM_2025. Should any raw data files be needed in another format they are available from the corresponding author upon reasonable request.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper are available from the lead contact upon request.

Acknowledgments

We thank Gagik Karapetyan for technical support, Vahan Nikoghosyan for his advices and valuable discussions, and Gurgen Kolotyan for the statistical analysis. This research is funded by the Higher Education and Science Committee of MESCS RA under grant number 24FP-2F023.

Author contributions

A.A., preparation of the manuscript, measurements of the electrical properties, and analysis of the results; N.P., system construction, methodology, and supervision of electric measurements; M.T., characterization of the polymer and its behavior under Raman spectroscopy and differential scanning calorimetry; E.T., characterization of mechanical properties; M.A., additive manufacturing of polymer, optimization of manufacturing parameters, reviewing the manuscript, funding acquisition, project management, supervision, conceptualization. Conceptualization, M.A.; investigation, A.A. and E.T.; methodology, M.A., N.P., and A.A.; formal analysis, A.A. and M.A.; writing – original draft, A.A.; writing – review and editing, A.A., N.P., and M.A.

Declaration of interests

The authors declare no competing interests.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT in order to polish the language appearance. After that the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
Elastic 50A	Formlabs Inc., USA	https://formlabs.com/store/materials/elastic-50a-resin-v2/
PLA film	Bleher Folientechnik GmbH, Germany	https://www.bleher.com/de/?gad_source=1&gad_campaignid=14048776765&gbraid=0AAAAADtPo2ltO_MX-7kVIqPhRDTR-nTFv&gclid=Cj0KCQjwzqXQBhD2ARIsAKrIeU8tlyEEn7daMS1Bv0wJhFqVw-sHPD1j2KJUfFhIhUu9rHZXaojJXQ8aAlxmEALw_wcB
Isopropyl alcohol (post-processing wash) lab. Grade	N/A	N/A
Deposited data
All the data have been deposited at github repository and are publicly available as of the date of publication.		https://github.com/AsatryanArevik/Elastic-50A_AM_2025
Software and algorithms
PreForm slicing software	Formlabs Inc., Somerville, USA	https://formlabs.com/software/preform/
Instron Bluehill (or equivalent analysis software)	Instron	N/A
Statistical Analysis	Python	https://www.python.org
Other
Formlabs Form 3B printer	Somerville, Massachusetts, United States	https://formlabs.com/3d-printers/form-3b/
Digital L, C, R measuring E7-12 device	instrumentation factories, Soviet Union	https://zapadpribor.com/en/e7-12/
Tesla RLCG Bridge-Voltmeter BM 559	TESLA, Praha Czechoslovakia	https://www.radiomuseum.org/r/tesla_rlcg_bridge_voltmeter_bm5.html#google_vignette
HORIBA XploRA PLUS equipment	HORIBA France SAS	https://www.horiba.com/int/scientific/products/detail/action/show/Product/xploratm-plus-1528/
NETZSCH STA 449 F3 Jupiter	NETZSCH-Gerätebau GmbH, Germany	https://analyzing-testing.netzsch.com/en/footer/legacy-products/sta-449-f3-jupiter
SEM-Zeiss, Evo 10	Carl Zeiss Microscopy, Germany	https://www.zeiss.com/microscopy/en/products/sem-fib-sem/sem/evo.html
Instron machine 5866	Illinois Tool Works - ITW, United States	https://www.instron.com/en/products/testing-systems/out-of-production-systems/electromechanical/
Rohde & Schwarz HM8118 LCR Meter	Rohde & Schwarz GmbH, Munich, Germany	https://www.rohde-schwarz.com/au/products/test-and-measurement/rs-essentials-meters-and-analyzers/rs-hm8118-lcr-bridge-meter_63493-44101.html

Materials

Elastic 50A from Formlabs Inc., USA was used for 3D printing of thin films in the range of 0.5–0.9 mm. According to early study³⁸ Elastic 50A resin consist of 3,3,5-TrimethylCyclohexyl Methacrylate (10–20%), Methacrylate Ester Monomer (70–90%), Diurethane dimethacrylate (<5%), and Phenylbis (2,4,6-TrimethylBenzoyl) Phosphineoxide (BAPO) (<2%).

The 3D printing of Elastic 50A samples was carried out on original platform of Form 3B (Formlabs Inc., Somerville, USA) printer. To print Elastic 50A-PLA samples, the platform of Form 3B was covered with PLA film (Bleher Folientechnik GmbH, Germany) with 20 ± 10 μm in thickness (details below). All the samples have been aged for 30 days at RT.

Method details

3D printing process

In general, 3D printing technology enables manufacturing of customized parts with lower cost, reduces material waste, enhances on-demand and local production. This technology is important for DEA fabrication, as it enables to enhance the performance via improvement of design parameters and fabrication of multi-material components in a single stage.⁶¹ Although 3D printing has a list of advantages over traditional manufacturing technologies, the physico-mechanical properties of the printed parts suffer.⁶² In this work, we employed standard 3D printing techniques to emphasize their accessibility and potential for future use in soft actuators.

Samples were fabricated using a Formlabs Form 3B printer with the manufacturer’s default optimized parameters, which included an XY layer resolution of 25 μm, a laser spot size of 85 μm, a layer height of 0.1 mm, an infill speed of 50 mm/s, and an operating temperature of 35°C. The 3D model was sliced at a layer height of 0.05 mm. Post-fabrication: only the manufacturer-recommended post-processing procedures were applied.

The novelty of our approach lies in printing Elastic 50A films on PLA substrates to create double-layer structures with distinct mechanical and functional properties.

When printing Elastic 50A- PLA samples, the platform of the printer was covered with PLA film. The PLA film has 20 ± 10 μm in thickness (Bleher Folientechnik GmbH, Germany). When printing Elastic 50A, the process was carried out directly on the metallic platform. A rectangular sample 3D model was designed and printed. The printer utilizes a layer-by-layer approach with a 0.1 mm layer thickness. The number of layers depends on the layer thickness. The samples are printed horizontally, and it is crucial to uphold a high-touch surface throughout the printing procedure for successful results. The printing parameters are as follows: the layer thickness was 0.100 mm, the temperature of the slurry - 35°C, laser wavelength - 405 nm, printing orientation - 0°.

The printed samples were washed with isopropyl alcohol to remove any not polymerized slurry and then cured in Form Cure (2nd Generation) (Formlabs Inc., USA) at 35°C, 405 nm light for 60 min.

Electrical measurements

Electric properties of the films were investigated on Digital L, C, R measuring E7-12 device for f = 1 MHz harmonic signal AC frequencies and on Tesla RLCG Bridge-Voltmeter BM 559 for f = 100 kHz harmonic signal AC frequencies. The conductivity and capacitance were measured and used to calculate dielectric constant, resistance, conductivity and resistivity of the material depending on its thickness. The measurements were carried out using a parallel plate capacitor system (Figure 1). Various thickness films were studied in comparison, as well as frequency dependance and temperature dependence of the electric properties.

Four different thickness films were printed with the same surface area dimensions: d₀ = 0.9 mm, d₁ = 0.8 mm, d₂ = 0.65 mm, d₃ = 0.5 mm, a = b = 20 mm (Figure 1). The capacitor has an electrode area of A = 1.65 cm², allowing the polymer films to extend beyond the electrode edges and thereby minimizing edge effects.

The Raman spectroscopy was carried out on HORIBA XploRA PLUS equipment, with ×100 objective and 785 nm laser. DSC investigation was performed on NETZSCH STA 449 F3 Jupiter. The aluminum crucibles were used for analysis, in the air atmosphere, with the heating rate of 10°C/min, in the range of 37–200°C. Microstructural characterization was performed by scanning electron microscope (SEM), (Zeiss, Evo 10, Carl Zeiss, Oberkochen, Germany) equipped with an EDS detector (Carl Zeiss, Oberkochen, Germany). Samples were coated with a 30 nm layer of gold to ensure enough conductivity.

Mechanical measurements

The tensile tests were performed with Instron machine 5866 at 23°C and 30% humidity for all the samples. The Elastic 50A film, with a thickness of 1.20 mm, and Elastic 50A - PLA, with a thickness of 1.37 mm, were cut into ribbons measuring 90 x 10 mm. For each sample, 7–10 ribbon specimens were tested, and the values of elastic modulus, strain at break, stress at break, and energy were averaged. Tensile tests were performed at a crosshead speed of 2 mm/min, which corresponds to a quasi-static strain rate, in order to minimize viscoelastic rate effects and effectively compare various sample performances. The Young modulus values were calculated using the standard relation E = stress/strain in the linear elastics region and subsequently averaged across all tested samples.

Quantification and statistical analysis

A Pearson correlation analysis was performed to examine relationships between film thickness, dielectric constant and conductivity. The analysis yielded a weak negative correlation between dielectric constant and thickness (r = − 0.260) and a moderate negative correlation between conductivity and thickness (r = − 0.513). No obvious correlation is observed in the first relationship (Figure S5). The weak apparent dependence is most likely an artifact caused by the non-monotonic variation of the dielectric constant as a function of film thickness. A moderate inverse relationship for conductivity versus thickness indicates increased charge entrapment in thicker films. In contrast, conductivity and dielectric constant show a strong positive correlation (r = + 0.766). In addition to non-monotone relationship discussed above (Figures 2C and 2D), these dependences show general trends and point to an intrinsic link between dielectric response and charge transport in our films. Correlation plots and statistical summary diagrams are provided in the Supplementary Material (Figure S5).

Software and algorithms

Python (statistical analysis and data visualization) | Python Software Foundation | https://www.python.org.