Field-dependent nonlinear electrical response characteristics in polymer dielectrics with sodium alginate scaffold

Abstract

Polymer-based self-adaptive dielectrics are considered promising materials to meet the growing insulation needs of flexible electronic devices and high-voltage DC cables. However, the temperature-sensitive electrical performance and poor thermal management ability of polymer dielectrics are bottlenecks that limit their further development. Here, we report a novel three-dimensional microstructure, i.e., nonlinear silicon carbide (SiC) micromaterials loaded on sodium alginate (SA) aerogel, exhibiting satisfactory non-linear electric conductivity with ultra-high thermal conductivity (3.86 W m⁻¹ K⁻¹, compared to 0.21 W m⁻¹ K⁻¹ of the pure epoxy resin). The SA aerogel, rich in high-density pores, is conductive to SiC forming a highly interconnected network structure under low loading, which endows polymer composites with the ability to quickly disperse charges under high electric field. In addition, the three-dimensional interconnected SiC network can disperse the Joule heat from local currents generated by nonlinear behavior, preventing thermal breakdown caused by the adverse effect of heat accumulation on the electrical properties of the material. In combining the advantages of nonlinear electrical conductivity characteristics, high thermal management ability, and low load capacity, this strategy expands the application scenarios of electric field self-adaptive polymer materials under high-temperature conditions.

Graphical abstract

We report a novel three-dimensional microstructure dielectric composite with self-assembly SiC on sodium alginate aerogel. Due to the high interconnectivity and porous structure of SA aerogel, efficient construction of conducting paths is achieved at a low filler content (1 vol%), which endows the composite with satisfying nonlinear conductivity and thermal management capacity.

1 Introduction

Power electronic devices and high-voltage insulation, with the surge of power density and highly integration, bring up more severe challenges to the insulation performance and intelligence of insulation packaging materials [1,2,3,4]. Among them, electrostatic discharge and local electric field distortion caused by defects are the main factors causing insulation failure of packaging materials [5,6,7,8]. In addition to improving the insulation performance of polymer materials, an intelligent nonlinear polymer material has emerged, i.e., self-adaptive dielectric (SAD) materials, which can maintain high insulation at low voltage but quickly evacuate charges at high voltage to prevent insulation failure caused by local high-field strength enhancement [9].

SAD materials are composed of polymers as insulation matrices and semiconductive fillers as electrical nonlinear carriers. In the past decade, many reports have proved that doped wide bandgap semiconductor functional fillers (such as silicon carbide (SiC) or zinc oxide (ZnO) microvaristors) can enable insulating polymers to achieve electric field–dependent nonlinear electrical properties at a load above percolation threshold [10, 11]. Unfortunately, this type of composite material typically requires a relatively high-volume content of fillers (~ 25 vol%) [12, 13], which seriously degrades the processing and mechanical properties [14, 15].

Many efforts have been made to reduce the loading of fillers in SAD materials, such as using high aspect ratio nanostructures (e.g., nanowires and nanosheets) to replace micro-nano spherical particles [16,17,18]. For example, the SAD with the lowest filler concentration is a sheet-like graphene oxide (GO)/polydimethylsiloxane (PDMS) composite, which exhibits excellent nonlinear behavior when the filler concentration is only 3 vol% [19]. Recently, He et al. arranged functional fillers through alternating current (AC) electric fields to form a bridge-type conductive path [20]. In this case, when using fillers with high aspect ratios (such as Bi/Co oxide coated ZnO nanowires), the concentration can be significantly reduced to 0.5 vol%. However, nanostructures with high aspect ratios often bring about high economic costs and low yields, and complex process conditions will put higher demands on large-scale production. Therefore, there is an urgent need for an economical, low-content of fillers, and outstanding nonlinear SAD material for the protection of electronic devices.

Another noteworthy issue is that SAD will generate Joule heat during the process of high-field charge evacuation, while the thermal conductivity of polymer-based materials is usually below 0.5 W m⁻¹ K⁻¹ [21]. The accumulation of heat that cannot be quickly evacuated will cause temperature gradients in insulation components, which will further lead to electric field distortion, and in severe cases affect equipment safety [22]. In addition, high-temperature nonlinear electrical properties should be emphasized due to the temperature-sensitive thermal activation and transport processes of carriers [23]. Therefore, while paying attention to the nonlinear performance of SAD, it is also necessary to consider the thermal management ability of the material, which cannot be achieved in previous material strategy.

Herein, we report the fabrication of a series of epoxy based SADs supported by a sodium alginate aerogel that exhibit adjustable nonlinear electrical conductivity and excellent thermal management capacity. We investigate the nonlinear conductive behaviors of these composites at different concentrations of micron SiC and analyze the correlations between loading structure and transport of electrons. With the filler loading increasing, the relative structure between the SiC particles and the aerogel presents different characteristics. We categorize the composites into three cases: light-, quasi-, and over-loading, then explore the mechanism of microstructure affecting switching electrical field. Meanwhile, the interconnected scaffold assists in the construction of thermal percolation networks. The fabricated 15 vol% loading composite exhibits a high thermal conductivity of 3.856 W m⁻¹·K⁻¹, which is a significant enhancement of 2000% compared to epoxy polymers. Our results indicate that tailoring the SA scaffold and SiC filler concentration can regulate the nonlinear conductive properties, offering promise for the use of SAD in practical high-voltage insulation and electrostatic discharge protection.

2 Experimental section

2.1 Materials

All the chemicals purchased are analytical grade and used as received without further purification. The SiC micron particles with an average diameter of 5 μm are supplied by Bole Metal Material Co., Ltd. The epoxy resin used in this work is a cycloaliphatic epoxy resin (S-06E, > 95%) obtained by Synasia (Nanjing) Co., Ltd, China. The epoxy equivalent is 130–135 g·eq⁻¹ and the viscosity is 220–250 mPa‧s at 25℃. The curing agent methylhexahydrophthalic anhydride (MHHPA, 98%), the accelerator 2-ethyl-4-methylimidazole (EMI, 96%), and sodium alginate with a purity of 90% (SA, viscosity of 200 ± 20 mPa·s) are purchased from Macklin Biochemical (Shanghai) Co., Ltd China.

2.2 Fabrication of SA-SiC scaffold and EP/SA-SiC composites

First, specific weights of SiC particles are dispersed in deionized water by sonication for 45 min. The dispersion is mixed with sodium alginate powder. Homogenous SA-SiC solution with concentration of 3 wt% is prepared by intensive stirring overnight at 70℃, then places for 4 h to degassing. Finally, the SA-SiC solution is freeze-dried for 48 h to obtain the SA-SiC scaffold. The EP/SA-SiC composites are fabricated through vacuum-assisted impregnation according to our previous work [24]. The curing agent (MHHPA) and catalyst (EMI) are added into cycloaliphatic epoxy resin for continuously stirring for 1 h at room temperature. The mixture is degassed in a vacuum for further treatment. Then, the 3D SA-SiC scaffolds are immersed into the epoxy mixture until thoroughly infiltrated with epoxy resin. The scaffolds are transferred into a vacuum for continuous degassing at room temperature for 12 h. Finally, the epoxy composites are placed in a mold and cured at 100℃ for 2 h, 110℃ for 1 h, and 120℃ for 30 min. The fabricated composites are marked as EP/SA-SiC_n where n is the volume fraction of SiC, and EP/SiC_n series composites with randomly distributed SiC in epoxy matrix are also fabricated in the same curing process for comparison. The approach for determining the volume fraction of SiC is detailed in supporting information.

2.3 Characterization

Microstructural observations of the prepared SA-SiC network with different volume fractions of SiC loading and EP/SA-SiC composites are performed using a scanning electron microscope (SEM, Merlin, Zeiss, German). Observations are conducted to study the spatial structure of SiC and sodium alginate skeletons at different volume fractions and their conductive pathways constructed in composites.

A dielectric temperature spectrometer (DMS-500, Partulab, Wuhan, China) is carried out to obtain the dielectric constant and loss of the composites at frequencies ranging from 10 to 10⁶ Hz. The thermal conductivity is obtained by Thermal Interface Material Tester (TIM Tester 1300/1400), which conforms to the test method ASTM D-5470. The surface temperature distribution and variation of the EP/SA-SiC composites after heating and cooling are measured by the thermal infrared imager (SAT-G96P).

3 Results and discussion

3.1 Preparation and morphology of the SA-SiC scaffold and EP/SA-SiC composites

In order to endow the polymer dielectric with satisfying nonlinear electrical properties and high thermal conductivity, theoretically as many conduction paths as possible should be constructed per unit volume fraction of filler. Constructing the conduction path along a three-dimensional scaffold is a potential and feasible method, and the scaffold should have as high connectivity and suitable porosity in this case [25]. Sodium alginate (SA) is a natural polysaccharide polymer extracted from seaweed that is widely used for hydrogel and aerogel fabrication due to its excellent processability and environmental sustainability [26, 27]. Owing to the abundant O-containing functional groups in alginate, such as − COO, − OH, and O − , hydrogen bonding is easily formed, which makes them more tightly bound to the filler particles and polymer matrix [28]. As a result, constructing efficiently percolated nonlinear conduction paths through SA scaffold is theoretically possible, achieving SAD with a combination of nonlinear electrical conductivity and high thermal conductivity at a low filling content.

The porous SA aerogel scaffold can be obtained by simple dissolution and freeze drying, as shown in Fig. 1a. The SEM image shows that the SA aerogel presents a highly interconnected network structure with elliptical pores all over the surface, and independent branches and fractures are barely seen. Pores with a width of 50–100 µm facilitate the uniform loading of the micron SiC particles (around 5 µm) onto the SA scaffold. SiC is a promising semi-conductor filler to prepare electric field grading materials because it has not only a wide band gap but also high breakdown strength. SiC is a promising semi-conductor filler widely used in various electromagnetic materials, because it has not only a wide band gap but also high breakdown strength [29,30,31,32].

Fig. 1

Schematic of fabrication and SEM images of a SA scaffold, b SA-SiC scaffold, and EP/SA-SiC composite

More crucially, the SiC particles, rich in hydroxyl groups on the surface, are easy to form hydrogen bonding with SA aerogels, which tightly load on the scaffold to form a long-range continuous SiC pathway (Fig. 1b). Finally, the EP/SA-SiC composites are prepared by vacuum-assisted impregnation of epoxy resin. It can be seen from the SEM image that the SiC paths (yellow lines) along the surface of aerogel fiber have been successfully constructed in epoxy matrix, which has a strong attraction for lowering the switching electrical field and thus enhancing the nonlinear coefficient of composites [33].

Figure 2a, b and c presents the cross-section SEM images of SA-SiC₁, SA-SiC_7.5, and SA-SiC₁₅ scaffolds, respectively. The general morphology of the SA-SiC is consistent with that of the SA scaffold, which suggests that the loading of SiC does not affect the aerogel structure. SiC fillers are uniformly distributed and tightly bound together on the SA scaffolds, which indicates that undesirable deposition barely occurs during static defoaming and freeze-drying of the SA-SiC solution [34]. Therefore, the loading SiC efficiently constructs the spatial conduction paths. In the locally enlarged SEM image shown in Fig. 2d, e and f, arrangement patterns of SiC on the scaffold can be easily distinguished for different loading volume fractions. Specifically, at a loading volume fraction of 1 vol%, most SiC particles are isolated and uniformly dispersed on the SA skeleton, accompanied by a few interconnected aggregates. After increasing the loading to 7.5 vol%, SiC particles, closely arranged on the surface of the scaffold, are physically contacted with each other to form a long-range interconnected scale-like structure, and the stacking phenomenon is barely observed. While the loading further reaches 15 vol%, SiC particles are tightly stacked in multiple layers on the surface of the scaffold, which may cause unnecessary performance surplus. Based on the above results, the loading volume fraction of 7.5 vol% is defined as the quasi-loading case, while below or above this volume fraction is defined as the light-loading case and over-loading case, respectively.

Fig. 2

Cross-section SEM images of a SA-SiC₁, b SA-SiC_7.5, c SA-SiC₁₅ scaffolds and the locally enlarged morphology of d SA-SiC₁, e SA-SiC_7.5, f SA-SiC₁₅ scaffolds

3.2 Nonlinear conductive performance

The nonlinear electrical conductivity is obtained by a self-built typical 3-electrode system according to the IEC 62631 standard. The Picoammeter Keithley 6485 monitored the steady-state conduction current after applying different voltages for 15 min at different temperatures. Then, the electrical conductivity σ can be calculated as follows [35]:

$$\sigma =\frac{I}{V}\cdot \frac{4L}{\pi {\left(d+g\right)}^{2}}$$

(1)

where I and V are the detected conduction current and applied voltage, respectively. L is the thickness of the sample, d is the diameter of the high voltage electrode, and g is the shielding electrode gap.

The log (σ) of EP/SiC and EP/SA-SiC composites versus log (E) is shown in Fig. 3. Notably, the EP/SA-SiC₁ exhibits a typical characteristic of nonlinear electrical conductivity, that is, the current density grows rapidly as the electric field increases. It can be attributed to the fact that the surface of the SiC is surrounded by a thin layer of SiO₂, leading to surface charging and band bending when the voltage is applied upon the particle–particle contact, similar to Schottky barriers in conventional semiconductors [7], as presented in Figure S1. The bending band results in a nonlinear transport behavior for carriers passing from one particle to the next [36]. By contrast, EP/SiC₂₀ composite with randomly distributed SiC remains a linear material without nonlinear electrical conductivity, until the volume fraction of SiC reaches 25 vol% before exhibiting nonlinear performance. However, the nonlinear switching electric field of EP/SiC₂₅ is still significantly higher than that of EP/SA-SiC₁. This is attributed to the presence of numerous thin epoxy layers between the isolated SiC particles, resulting in the nonlinear conduction behavior occurring at higher electric field. The above research highlights the significant advantages of SA aerogel in the construction of SiC conductive path, which can achieve a relatively low threshold filtration level.

Fig. 3

Nonlinear electrical conductivity and fitting result of a EP/SiC and EP/SA-SiC under b light-loading, c quasi-loading, and d over-loading cases. FEM simulation results of e spatial cross-section and f central axial electric field distributions in 2 SiC, 3 SiC, and 4 SiC particles conditions. g Dielectric constant and h loss tanget of EP/SA-SiC₁, EP/SA-SiC_7.5, and EP/SA-SiC₁₅. i The relationship between ln (J/R·T²) and E^1/2 for EP/SA-SiC composites with different volume loading of SiC

For SADs with nonlinear electrical conductivity, the nonlinear switching electrical field E_b (abbreviated as switching field in this paper) and nonlinear coefficient α are usually used to describe the nonlinear electrical conducting behaviors, playing an important role in the potential application range and field-grading effect. The E_b and α can be obtained by fitting the Eq. (2) [37]:

$${\sigma }_{dc}={\sigma }_{0}\left(1+{\left(E/{E}_{b}\right)}^{a-1}\right)$$

(2)

where σ_dc is the electrical conductivity, σ₀ is the low field electrical conductivity, and E is the electric field strength, respectively. The fitting results are listed in Table 1.

Table 1 The switching field E_b and nonlinear coefficient α of the EP/SA-SiC composites

In the light-loading case, the E_b of the EP/SA-SiC series composite decreases from 1.57 to 1.03 kV mm⁻¹ with the increasing volume fraction from 1 to 5 vol%. This can be attributed to the fact that the SiC particles are not in direct contact in the light-loading case and adjacent particles are kept at a distance from each other. Frenkel suggested an electrical field assisted hopping mechanism for electron transport according to the following [38]:

$${J}_{hopping}={A}_{R}\cdot{T}^{2}\cdot exp\left(\frac{K\cdot {E}^{1/2}\Phi }{{k}_{B}\cdot T}\right)$$

(3)

where A_R and k_B is the Schottky-Richardson constant and Boltzmann constant, respectively, Φ is the work function of the filler material, and T and E are the temperature and applied electric field strength. It can be seen from above equation that the hopping ability is significantly affected by the electric field strength. Here, a brief FGM model is adopted to explain the effect of filler particle spacing on the local electric field (details of model are shown in Support Information S2). From the results shown in Fig. 3e, f, the shorter the distance between SiC particles, the stronger the electric field in the localized region on the SiC surface. This is because the relative permittivity of the epoxy matrix (4) is smaller than that of the SiC (7), resulting in a significant enhancement of the distortion of the electric field at the interface. When the distance between SiC particles decreases rapidly with the increasing loading volume fraction, the distortion of the surface electric field becomes more severe. Thus, the electrons are more prone to hopping between neighboring SiC particles, leading to a lower switching field at higher volume fraction.

As the loading case switches from quasi- to over-loading, there is a further decrease of E_b, e.g., from 0.96 kV mm⁻¹ of EP/SA-SiC_7.5 to 0.64 kV mm⁻¹ of EP/SA-SiC₁₀. It should be noted that the variation of switching field here is distinct from the sharp decrease in the light-loading case. Considering the aerogel is not subjected to oriented freeze-drying, a connected spatial structure is formed in random directions. This leads to the fact that the SiC particles loaded on the scaffold do not follow the shortest path (vertical material-electrode interface) to form the conducting paths. In this situation, a larger amount of filler concentration makes the shortest path more prone to be constructed, resulting in a decrease in switching field. Therefore, the decrease of switching field in quasi- and over-loading cases can be attributed to the larger possibility of the shortest path achieved with increasing filler concentration. After the loading reaches over 10 vol%, the switching field decreases less and stabilizes at 0.6 kV mm⁻¹, indicating that the optimal conduction pathway is already formed. At the same time, the multilayer SiC structure also brings more charge transport pathways, like the parallel structure of circuits. The volume current increases with filler concentration, which agrees with the gradual increase of the nonlinear coefficient in Table 1. Based on the findings, we can easily tailor the switching field and the volume current growth rate to suit the requirements of various applications.

On this basis, we further investigate the potential barrier of interconnected SiC particles and the nonlinear mechanism of the EP/SA-SiC. The Schottky barrier is derived through the theory of Schottky mechanism (electrode limited conduction), and the empirical equations under the Schottky mechanism can be defined as Eq. (4) [39] (due to the large distance between SiC particles at filler concentration below 5 vol%, the light-loading case is not suitable for the Schottky mechanism to carry out the study):

$$ln\left(\frac{J}{{R}_{i}{T}^{2}}\right)=\left(\frac{\beta }{{k}_{B}T}\right){E}^{1/2}-\frac{{\Phi }_{B}}{{k}_{B}T}$$

(4)

where R_i is the Richardson constant and k_B is the Boltzman constant, β is a potential barrier width relating constant, and Φ_B is the height of the potential barrier formed at the grain boundary. The relation between the ln(J/R_iT²) and E^1/2 and the fitting results obtained from Eq. (4) are shown in Fig. 3g and Table 1. The barrier height is positively correlated with the loading volume fraction, and the growth of the potential barriers slows down at higher loading. It can be assumed that once the shortest path is completed, the carriers transport along the optimal path to realize the nonlinear conductive behavior as the electric field energy is higher than the potential barrier.

The effect of the spatial structure of SiC on the electrical properties is also reflected in the broad