Permittivity Research Articles

Dielectric behaviour, impedance and conductivity studies of YBaYbSiO oxy-apatite compounds

This paper reports the dielectric behaviour and electrical conduction properties of Y6-xBa4Ybx(SiO4)6O2 (YBaSiO: xYb) compounds. The Scanning Electron Microscopy (SEM) was utilized to obtain the surface microstructure of the compound. The micrographs showed both the circular and elongated shape of grains and their random distribution. The Fourier Transform Infrared Spectroscopy (FTIR) was used to confirm the presence of bond formations in the compounds. From the spectra, it was observed that the peaks at 690 cm−1 and a band from 850 cm−1 to 998 cm−1 are due to the stretching frequency of Y-O molecules and Si-O molecules, respectively. The peak centred at 1464 cm−1 is of vibration modes of Ba2+ions. These peaks confirmed the formation of oxy-apatite compounds. Both the dielectric permittivity and dielectric loss, decreases with increasing values of frequency due to reduction in the polarization effects on the higher side of frequency. This is because the dipole orientation lags with the rapidly reversing alternating current (ac) field. The value of dielectric loss was found to range between, 0 – 3.5 in frequency ∼ 100 Hz and 0 – 0.5 in frequency ∼ 100,000 Hz, up to temperature 500 °C. The impedance value decreases and hence a. c. conductivity increases, at higher frequencies. The increment in ac values followed the universal power law. The Nyquist plot showed that the area under the curves reduces and hence indicates negative temperature coefficient of resistance i.e., NTCR behaviour of compounds. The obtained results suggest the utilization of compound in electrical devices as power loss component, solid oxide fuel cells, and capacitors etc.

Enhancing the dielectric and piezoelectric properties of Pb0.99Gd0.01Zr0.53Ti0.47O3 ferroelectric ceramics by Sr-doping

Recently, high-performance lead zirconate titanate (Pb([Formula: see text]Tix)O3, PZT) ferroelectric ceramics have attracted intensive attention due to their wider operating temperature range, better temperature stability, as well as larger piezoelectric properties and higher energy conversion efficiency. In this study, the perovskite-type ferroelectric ceramics with a chemical formula of [Formula: see text][Formula: see text]Srx[Formula: see text][Formula: see text]O3 ([Formula: see text] and 0.02, abbr. PGZT and PGSZT, respectively) were prepared by the traditional solid-state reaction route. The influences of Sr-doping on the phase structure, dielectric properties, ferroelectric properties and piezoelectric properties of the PGZT ceramics were comprehensively investigated. The field-dependent P–E hysteresis loops of PGSZT were measured in the frequency range of 0.05–10[Formula: see text]Hz and temperature range of 20–100∘C. The results show that Sr-doping not only enhances the dielectric permittivity and piezoelectric coefficient of PGZT, but also decreases its dielectric loss tangent, with the [Formula: see text] value of 473[Formula: see text]pC/N, [Formula: see text] value of 1586 and [Formula: see text] value of 0.016 found in PGSZT. Also, PGSZT shows a high Curie temperature ([Formula: see text]) of [Formula: see text]C. The underlying mechanisms of the property enhancement were identified as that the introduced [Formula: see text] replaces the volatile [Formula: see text] located at the A-site of the perovskite structure, thereby reducing the concentration of lead vacancies and promoting the grain growth of the ceramics, consequently enhancing the dielectric and piezoelectric properties of PGZT. On the other hand, the frequency change in the low-frequency range ([Formula: see text][Formula: see text]Hz) played a significant impact on the remanent polarization ([Formula: see text]) and internal biased electric field ([Formula: see text]) of PGSZT, but the frequency dependence of coercive field ([Formula: see text]) tends to diminish in the high-frequency range ([Formula: see text][Formula: see text]Hz).

Density dependence for the dielectric permittivity of simple gases and liquids

The present work is devoted to the analysis of polarization effects in atomic systems of the argon type. Special attention is given to the manifestation of the polarizabilities of two particles in the density dependence of the dielectric permittivity of a system and its effective molecular polarizability. It is shown that the effective polarizability of a molecule in the liquid state of a system is mainly caused by deviation of the molecular distribution in the first coordination layer from the spherical one. Due to this, the atomic polarizability inherent to rarefied gas increases practically twice near the triple point. The interconnection between the atomic polarizability and the proper volume of an atom is discussed in detail. It is established that the optimal size of an atom follows from the kinematic shear viscosity measurements.

Mixing Rules for Left-Handed Disordered Metamaterials: Effective-Medium and Dispersion Properties.

Left-handed materials are known to exhibit exotic properties in controlling electromagnetic fields, with direct applications in negative reflection and refraction, conformal optical mapping, and electromagnetic cloaking. While typical left-handed materials are constructed periodic metal-dielectric structures, the same effect can be obtained in composite guest-host systems with no periodicity or structural order. Such systems are typically described by the effective-medium approach, in which the components of the electric permittivity tensor are determined as a function of individual material properties and doping concentration. In this paper, we extend the discussion on the mixing rules to include left-handed composite systems and highlight the exotic properties arising from the effective-medium approach in this framework in terms of effective values and dispersion properties.

New Short-Circuited Coaxial Method Implementation for Complex Permittivity Measurement of Power Transformer Oils

The investigation into the dielectric properties of transformer oils has been a focal point in both historical and contemporary electric insulation technology as high-voltage applications have greatly benefited from the continuous research efforts in this field. The dielectric permittivity is one of the factors to be negotiated when discussing the electric insulation of any material. This work aims to showcase a new short-circuited coaxial cable method to evaluate the complex dielectric permittivity of palm, sunflower and rapeseed oil and review other previously used measurement techniques. Mainly, the test was performed using a sample holder that represents a short-ended coaxial cable filled with the test material which is connected to one port of a vector network analyser. The measurements of the input impedance for various oil samples were conducted at frequencies ranging from 1 MHz to 10 MHz. The technique uses the value of the input impedance which depends on the reflected signals from the test sample to the network analyser, consequently, the value of the dielectric permittivity and dielectric loss have been calculated using the short circuit impedance formula which involves numerical methods to get the results which shows that this method can be used as an alternative to investigate the oils insulation parameters as it provides smooth results for permittivity without any divergence, ensuring more reliable and consistent measurements as well as providing high accuracy in determining the permittivity of materials.

Magnetization and magnetodielectric effect in Cr3+-doped Ca3Co2-xCrxO6 compounds

In one dimensional Ca3Co2O6, the magnetic frustration could result in partially disordered antiferromagnetic state. The Ca3Co2O6 thus presents spin freezing and slow relaxation at low temperature. In this investigation, magnetic Cr3+-dopants were chosen to substitute the Co3+ cations and a series of Ca3Co2-xCrxO6 ceramics were synthesized. Their magnetoelectric properties were characterized. The results manifest that the introduced Cr3+ cations situate in the CoO6 octahedral centers and they could increase the lattice volume slightly. The antiferromagnetic coupling between Cr3+ and the adjacent Co3+ could reduce the frustration. The doped-Ca3Co2-xCrxO6 compounds display a slower magnetic dynamic behavior. The Cr3+ substitution also has great impact on the dielectric properties of Ca3Co2O6. The slower response of the freezing spin in Cr3+ doped-Ca3Co2O6 makes the dielectric anomaly (anomaly Ⅰ) around the freezing temperature weakens with increasing Cr3+. Additionally, the introduced Cr3+ dopant not only increases the dielectric permittivity but also decreases the dielectric loss greatly. Cr3+ cation is a good candidate for improving the dielectric properties of Ca3Co2O6. Magnetodielectric measurement reflects the effectiveness of magnetic field on manipulating the electric dipole of Ca3Co2O6. For spin frustrated materials, electric measurement is proved to be an effective method on characterizing the subtle variation of the magnetic structure.

On the optimization of Maxwell's eigenvalues as functions of the electric permittivity in a cavity

We formulate an optimization problem for the dependence of the eigenvalues of Maxwell's equations in a cavity with perfect electric conducting boundary upon variation of the electric permittivity, and we prove a corresponding Maximum Principle.

High dielectric breakdown strength of antipolar CaTiGeO5 ceramics sintered at optimized temperature

Titanite CaTiSiO5 (CTS) is considered to be a promising dielectric material for preparing high-voltage multilayer ceramic capacitors because it exhibits a positive bias dependence of the dielectric permittivity due to its antipolar crystal structure. In this study, we investigated the dielectric response and breakdown strength of CaTiGeO5 (CTG), a structural analog of CTS, inspired by its higher low-field dielectric permittivity. Particular attention was paid to the sintering temperature to reveal the effect of the microstructure and loss of volatile Ge on the electrical properties of CTG. Dense CTG ceramics with relative densities above 97 % and grain sizes between 1.3 and 3.4 μm were obtained through a conventional solid-state reaction route at sintering temperatures between 1150 and 1250 °C. A secondary phase of CaTiO3 was formed in the ceramics sintered at 1200 and 1250 °C due to Ge loss, but this phase was easily removed by surface polishing alone. The sintering temperature largely affected the dielectric breakdown strength through microstructural development, resulting in the highest breakdown strength of 1190 kV cm−1 for a sample sintered at 1200 °C, while it did not change the low-field dielectric properties of the samples. Furthermore, the sample retained high breakdown strength of >900 kV cm−1 at elevated temperatures up to 150 °C and exhibited a nonlinear polarization response, resulting in the positive electric field dependence of the dielectric permittivity.

Understanding the grain size dependence of functionalities in lead-free (Ba,Ca)(Zr,Ti)O3

Grain size effects in ferroelectric ceramics have long been exploited to tailor their functional properties. However, the underlying mechanism for the grain size effects is not yet fully understood. Here, we study the grain size dependence of domain wall activities in a lead-free piezoceramics system, (Ba,Ca)(Zr,Ti)O3, with grain sizes in the range of 4 − 22 μm. The dielectric permittivity is highest at intermediate grain sizes (∼12 μm) where there are moderate lattice distortion and the most active domain wall motion under low voltages. Despite the larger fraction of switched domains in the material with larger distortion (∼22 μm), as revealed by in situ electric-field synchrotron X-ray diffraction, time-resolved characterizations demonstrate an easier and faster domain wall dynamics in the sample with moderate lattice distortion. Our analysis and phase-field simulations show that the grain size dependence of the domain wall dynamics of polycrystalline ferroelectrics is dictated by the interaction between an external electric field and the grain size-related change in intergranular stress, and this interaction is most effective in stimulating the movement of non-180° domain wall at intermediate grain sizes during the initial phase of polarization reversal. Our results provide a new fundamental understanding to guide the future design of materials for improving functionalities.

Dislocation Density-Mediated Functionality in Single-Crystal BaTiO3.

Unlike metals where dislocations carry strain singularity but no charge, dislocations in oxide ceramics are characterized by both a strain field and a local charge with a compensating charge envelope. Oxide ceramics with their deliberate engineering and manipulation are pivotal in numerous modern technologies such as semiconductors, superconductors, solar cells, and ferroics. Dislocations facilitate plastic deformation in metals and lead to a monotonous increase in the strength of metallic materials in accordance with the widely recognized Taylor hardening law. However, achieving the objective of tailoring the functionality of oxide ceramics by dislocation density still remains elusive. Here a strategy to imprint dislocations with {100}<100> slip systems and a tenfold change in dislocation density of BaTiO3 single crystals using high-temperature uniaxial compression are reported. Through a dislocation density-based approach, dielectric permittivity, converse piezoelectric coefficient, and alternating current conductivity are tailored, exhibiting a peak at medium dislocation density. Combined with phase-field simulations and domain wall potential energy analyses, the dislocation-density-based design in bulk ferroelectrics is mechanistically rationalized. These findings may provide a new dimension for employing plastic strain engineering to tune the electrical properties of ferroics, potentially paving the way for advancing dislocation technology in functional ceramics.

Analytical Modeling of Wave Absorption Performance in Gradient Graphene/Polymer Nanocomposites.

Due to the low impedance matching caused by the high dielectric permittivity of graphene, the strong absorption of electromagnetic waves by graphene/polymer nanocomposites is challenging. In this paper, an analytical model for microwave absorption based on Maxwell's equation and the effective medium theory, considering the interface effect, was constructed to explore the effect of the gradient distribution of graphene in the polymer matrix on its microwave absorption performance. The outcome indicated that the impedance of the composites matched well with the air, and its attenuation ability for electromagnetic waves was obviously improved as the graphene concentration was distributed in a gradient form. For instance, when the thickness of the material is 10 mm, based on the optimal concentration of the homogeneous composites being 0.7 wt%, the graphene concentration range of the gradient composites is set to 0.7-0.9 wt% and distributed in three gradient forms of linear, parabolic, and 0.5 power. The results show that the microwave absorption performance is significantly improved compared with the homogeneous composites. Among them, the effective bandwidth on the 0.5 power distribution is 5.2 GHz, 0.5 GHz higher than that of the homogeneous composites. The minimum reflection loss (RL) is as low as -54.7 dB, which is 26.26 dB lower than that of the homogeneous composites. This paper contributes to the design and application of gradient absorbing structures.

Frequency-Dependent Dielectric Permittivity and Water Permeability in Ordered Mesoporous Silica-Grafted Fluorinated Polyimides.

Polymers with a low dielectric constant (Dk) are promising materials for high-speed communication networks, which demand exceptional thermal stability, ultralow Dk and dissipation factor, and minimum moisture absorption. In this paper, we prepared a series of novel low-Dk polyimide films containing an MCM-41-type amino-functionalized mesoporous silica (AMS) via in situ polymerization and subsequent thermal imidization and investigated their morphologies, thermal properties, frequency-dependent dielectric behaviors, and water permeabilities. Incorporating 6 wt.% AMS reduced the Dk at 1 MHz from 2.91 of the pristine fluorinated polyimide (FPI) to 2.67 of the AMS-grafted FPI (FPI-g-AMS), attributed to the free volume and low polarizability of fluorine moieties in the backbone and the incorporation of air voids within the mesoporous AMS particles. The FPI-g-AMS films presented a stable dissipation factor across a wide frequency range. Introducing a silane coupling agent increased the hydrophobicity of AMS surfaces, which inhibited the approaching of the water molecules, avoiding the hydrolysis of Si-O-Si bonds of the AMS pore walls. The increased tortuosity caused by the AMS particles also reduced water permeability. All the FPI-g-AMS films displayed excellent thermooxidative/thermomechanical stability, including a high 5% weight loss temperature (>531 °C), char residue at 800 °C (>51%), and glass transition temperature (>300 °C).

Core-shell engineering of graphite nanosheets reinforced PVDF toward synchronously enhanced dielectric properties and thermal conductivity

Polymer composites integrating high dielectric permittivity (ε′) but low loss, large breakdown strength (Eb) and thermal conductivity (TC), have attracted widespread attention in electronic devices and power systems. To simultaneously achieve these properties in graphite nanosheet (GNS)/poly(vinylidene fluoride, PVDF), the GNS were first encapsulated by a layer of aluminum oxide (Al2O3), and then incorporated into PVDF, and the resulting PVDF nanocomposites’ dielectric properties and TC were explored in terms of the Al2O3 shell thickness and filler loading. The insulating Al2O3 shell serves as a barrier layer for the formation of leakage current and long-distance electron migration thus resulting in much lower dielectric loss and conductivity of the GNS@Al2O3/PVDF. It effectively mitigates the dielectric mismatch between the filler and host matrix, further introduces more traps that can capture charge carriers, and increases the barrier height for electron detrapping subsequently preventing the growth of electric trees and elevating the Eb. Moreover, the Al2O3 interlayer alleviates both the phonon density state and phonon impedance mismatches between the filler and matrix and facilitates the interfacial phonon transport thus leading to improved TC. The dielectric parameters and TC of the GNS@Al2O3/PVDF can be simultaneously modulated by optimizing the Al2O3′s thickness. This work offers an effective approach for designing and fabricating the polymeric nanodielectrics concurrently integrating high ε′ but low loss, enhanced Eb, and TC for prospective applications in power equipment and microelectronic devices.

Development, Dielectric Response, and Functionality of ZnTiO3/BaTiO3/Epoxy Resin Hybrid Nanocomposites

In the present work, hybrid nanocomposites of an epoxy resin reinforced with ZnTiO3 and BaTiO3 nanoparticles, at various filler contents, were fabricated and studied. The successful integration of ceramic nanofillers and the fine distribution of nanoparticles were confirmed via X-ray Diffraction patterns and Scanning Electron Microscopy images, respectively. Dielectric properties and related relaxation phenomena were investigated via Broadband Dielectric Spectroscopy in a wide range of frequencies and temperatures. Data analysis showed that dielectric permittivity increases with filler content, although optimum performance does not correspond to the maximum ZnTiO3 content. Four relaxation processes were observed and attributed to interfacial polarization (IP) (at low frequencies and high temperatures), glass-to-rubber transition (α-relaxation) of the epoxy matrix (at intermediate frequencies and temperatures), and local rearrangements of polar side groups of the macromolecules (β-relaxation) and small flexible groups of the main polymer chain (γ-relaxation) occurring at low temperatures and high frequencies. The ability of hybrid nanocomposites to store and retrieve energy was studied under dc conditions by employing a charging/discharging sequence. The stored and retrieved energy increases with filler content and charging voltage. The optimum ability of energy recovering, shown by the epoxy/7 phr ZnTiO3/7 phr BaTiO3 nanocomposite, ranges between 30 and 50 times more than the matrix, depending on the time instant. The employed nanoparticles induce piezoelectric properties in the nanocomposites, as found by the increase in the piezoelectric coefficient with filler content.

Excellent thermal conductivity and electrical insulation in polyimide/graphene oxide/carbon nanotubes composites

AbstractPolymer composites with heat resistance, good thermal conductivity, and insulation properties can meet the special needs of electronics and electrical appliances. In this work, graphene oxide (GO) and carbon nanotubes (CNTs) are coated by polydopamine (PDA). 4,4′‐diaminodiphenyl ether (ODA), pyromellitic dianhydride (PMDA), and 4,4′‐oxydiphthalic anhydride (ODPA) in‐situ polymerize to prepare poly(amide acid) (PAA) containing thermally conductive yet insulating fillers (PDA@GO, PDA@CNTs). As the concentration of fillers in PI composites increases, the thermal conductivity rises, but the insulation property decreases. Keeping the filler content constant and varying the ratio of PDA@GO and PDA@CNTs, the thermal conductivity increases and then decreases. When PDA@GO and PDA@CNTs have a mass ratio of 10:1, the significant synergistic effect affects the thermal conductivity. The PI/PG10C1–25 sample has a thermal conductivity of 1.46 W/(m·K), which is 6.9 times greater than the pure PI. Additionally, the volume resistivity, dielectric permittivity, and dielectric loss (100 kHz) of PI/PG10C1–25 are 2.8 × 1013 Ω cm, 5.4 and 0.28, respectively. The heat resistance of PI composites is almost the same as that of pure PI. Given these outstanding attributes, the developed PI composites offer vast applications in many fields.Highlights Synergistic PDA@GO and PDA@CNTs (10:1) optimize thermal conductivity. PI/PG10C1–25 achieves 6.9 times higher thermal conductivity than pure PI. Volume resistivity of PI/PG10C1–25 reaches 2.8 × 1013 Ω·cm. Dielectric permittivity of PI/PG10C1–25 reaches 5.4 at 100 kHz. Developed PI composites maintain excellent heat resistance.

Ca doped Y2/3Cu3Ti4O12: Structure and dielectric properties

In this study, we systematically examined the structure and dielectric properties of Y2/3-xCa3x/2Cu3Ti4O12 (x = 0.0, 0.05, 0.10, 0.15, and 0.20). X-ray diffraction (XRD) analysis revealed that the structure of all ceramics conformed to the CaCu3Ti4O12 ceramics database, specifically with JCPDS No. 75–2188, and no impurity phases were detected. The conducted experiments revealed a notable rise in the dielectric constant at elevated concentrations of Ca doping, ranging from 104 to 105. Conversely, the loss tangent values, lower than those of Y2/3Cu3Ti4O12, exhibited a decrease from 0.533 to 0.333 as x increased from 0 to 0.20. Synchrotron radiation, based on X-ray photoelectron spectroscopy, was employed to investigate the valence states of Ti and Cu ions. This observation is directly linked to the presence of oxygen vacancies within the lattice. Impedance spectroscopy analysis unveiled two distinct electrical states within the Ca-doped Y2/3Cu3Ti4O12 system. The first part corresponds to the semiconductive nature exhibited by the grain, while the subsequent part pertains to the insulative characteristics observed at the grain boundary. The remarkable dielectric permittivity observed in Ca-doped Y2/3Cu3Ti4O12 system ceramics can be attributed to the existence of a heterogeneous microstructure comprising semiconducting grains and insulating grain boundaries. The presence of Cu+ and Ti3+ ions could potentially account for the semiconductive state observed within the grains of Y2/3Cu3Ti4O12 ceramics.

Influence of particle size on the magnetic and microwave absorption properties of magnetite via mechano-mechanical methods for micro-nano-spheres

The demand for innovative electromagnetic wave absorbers stems from the pressing need to mitigate electromagnetic interference and pollution emanating from electronic devices and communication technologies, which pose risks to human health and disrupt the functionality of electronic equipment. This study investigates how particle size influences the magnetic and microwave absorption properties of magnetite micron-nano-spheres. Utilizing ball milling (BM) and mechanochemical alloying (MA), particle sizes were controlled by varying the milling times, resulting in a reduction of magnetite's average particle size from 3 µm to 43 nm. The research uncovers the unique effects of blending micron and nano-sized particles, a phenomenon previously undocumented. It was observed that saturation magnetization and coercivity increase with larger particle sizes due to the small size effect. The complex permittivity, dielectric loss and attenuation constant of the magnetite nanocomposites were influenced by the larger interface area and increased defects in smaller-sized nano-filler composites. Decreasing the magnetite particle size leads to a lower frequency shift and a broader bandwidth of the reflection loss (RL) peak in the fixed absorber, with maximum RL achieved for thinner absorber layers. Notably, the mixed micron-nano magnetite composite exhibits promising microwave absorption capabilities, achieving a maximum RL of −35.36 dB at 16.8 GHz with a 1 mm thickness, making it suitable for lightweight microwave absorption. Resonance frequencies corresponding to RL below −20 dB extend to 3.63 GHz, meeting the 99 % wave absorption requirement due to the high loss tangent of antiferromagnetic resonance and significant magnetic relaxation peak over the 8–18 GHz frequency range. This study underscores the significant impact of adjusting the particle size on microwave absorption properties, where decreasing the size broadens the absorption bandwidth, shifts the RL peak to lower frequencies and maximizes RL with thinner thicknesses. Increasing the nano-filler content enhances the absorption bandwidth and microwave absorber performance by augmenting the dielectric loss, attenuation constant and impedance matching. Overall, controlling the particle size proves effective in tailoring microwave absorption, highlighting the potential of magnetite composites as ultra-thin, lightweight materials capable of absorbing a wide range of microwave frequencies. These composites find applications in microwave absorption, stealth technology and managing electromagnetic interference, leveraging the magnetic properties of ferrites and exploiting super-exchange interactions in microparticles-sized materials. Moreover, they benefit from the amplified dielectric or/magnetic losses resulting from the characteristics of nanoparticle-sized materials, including high surface area, greater surface atoms and multiple reflections, resulting in exceptional microwave absorption performance exceeding 99 % across an exceptionally broad bandwidth.

Sol–gel derived ceramic nanoparticles as an alternative material for microstrip patch antenna in WLAN applications

In the fast-evolving realm of communication technology, microstrip patch antennas (MPAs) are in high demand owing to their compact size, lightweight, inexpensive, ease of integration, and compatibility with modern electronic devices. This research focuses on the synthesis of ZnAl2O4Ca (ZAC) ceramic nanoparticles using an economical sol–gel method suitable for microstrip patch antenna applications. The structural analysis study of ZAC nanoparticles confirmed the polycrystalline nature with 8.1 nm of crystallite size whereas an investigation of functional groups showed the corresponding vibration modes. Morphological investigation revealed the spherical grains having their mean diameter of 12.32 nm. The dielectric property’s examination, revealed the dielectric permittivity of 13, loss tangent of 0.02, and conductivity of 67 μΩ−1 cm−1. Furthermore, a prototype patch antenna fabricated using ZAC ceramics demonstrated a dual-band performance at frequencies 2.8 GHz and 4.8 GHz, with return losses of − 25.78 dB and − 28.5 dB, respectively. This work suggests the suitability of ZAC ceramic nanoparticles for use in WLAN applications.

Scaling behavior of the localization length for TE waves at critical incidence on short-range correlated stratified random media

We theoretically investigate the scaling behavior of the localization length for s-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro–Loginov formula of differentiation, we accurately compute the localization length ξ of s waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter σ2 and the disorder correlation length lc. Away from the critical angle, ξ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber k, kξ depends on the single parameter klcσ2, satisfying a universal equation kξ≈1.3717klcσ2−1/3 across the entire range of parameter values. Additionally, we find that ξ scales as λ4/3 for the entire range of the wavelength λ, regardless of the values of σ2 and lc. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence.

Elastomers based on polynorbornene with polar polysiloxane brushes for soft transducer applications

Elastomers based on cross‐linked bottlebrush polymers combine an extreme softness at low strains with a strain‐stiffening effect, which makes them attractive as active components in dielectric elastomer actuators (DEA). Their main disadvantage concerns the small relative permittivity, which lies in the range of 3.5, requiring relatively high driving voltage in actuators. We synthesized a bottlebrush polymeric elastomer with polar brushes, which exhibit an enhanced dielectric permittivity of 4.4. Anionic ring‐opening polymerization of a polar cyclosiloxane afforded telechelic polar brushes, while ring‐opening polymerization of a norbornene macromonomer gave a bottlebrush polymer which was cross‐linked to elastomers by a thiol‐ene reaction. Elastomers with a small elastic modulus below 100 kPa, strain at break exceeding 100%, attractive elasticity, and small mechanical loss factors (tanδ) were achieved. Temperature‐dependent impedance measurements revealed a transition temperature of ‐95 °C and an interfacial polarization. The multigram scale synthesis demonstrates the potential for scaling up, which opens the door to broader applications of these materials beyond actuators, such as capacitive sensors, batteries, and electroluminescent devices. Notably, these devices operate at extremely low voltages where the dielectric breakdown does not limit their functionality, but still, the softness and the increased dielectric permittivity are a plus.