Permittivity Measurements Research Articles

On the measurement of skeletal muscle anisotropic permittivity property with a single cross-shaped needle insertion

Application of minimally invasive methods to enable the measurement of tissue permittivity in the neuromuscular clinic remain elusive. This paper provides a theoretical and modeling study on the measurement of the permittivity of two-dimensional anisotropic tissues such as skeletal muscle with a multi-electrode cross-shaped needle. For this, we design a novel cross-shaped needle with multiple-electrodes and analyse apparent impedance corresponding to the measured impedance. In addition, we propose three methods of estimate anisotropic muscle permittivity. Compared to existing electrical impedance-based needle methods that we have developed, the new needle design and numerical methods associated enable estimating in vivo muscle permittivity values with only a single needle insertion. Being able to measure muscle permittivity directly with a single needle insertion could open up an entirely new area of research with direct clinical application, including using these values to assist in neuromuscular diagnosis and to assess subtle effects of therapeutic intervention on muscle health.

Frequency-Variation Sensors for Permittivity Measurements Based on Dumbbell-Shaped Defect Ground Structures (DB-DGS): Analytical Method and Sensitivity Analysis

It is shown in this paper that a microstrip line loaded with a dumbbell-shaped defect ground structure (DB-DGS) is useful for complex permittivity measurements. The working principle of the sensor is the variation in the notch (resonance) frequency and depth caused by the material under test (MUT), when it is put in contact with the sensitive region of the device, i.e., the capacitive slot. It is demonstrated that the relative sensitivity of the sensor, defined as the variation of the resonance frequency of the DB-DGS with the dielectric constant of the MUT relative to the resonance frequency of the bare structure, does not depend on the geometry of the DB-DGS, provided the substrate is thick enough. The relative sensitivity, the key figure of merit, is dictated by the equivalent dielectric constant of the substrate, and it increases as the substrate permittivity decreases. Using the circuit model of the sensing structure, simple analytical expressions providing the dielectric constant and the loss tangent of the MUT are derived. Such analytical formulas depend on the notch frequency and depth of the sensor with and without MUT in contact with it, i.e., easily measurable quantities. The analysis carried out is corroborated through full-wave electromagnetic simulation and experiments.

Dielectric properties of hot-pressed Poly(vinylidene fluoride)/Functionalized carbon nanotube composites

This work reports the structural and dielectric properties of poly(vinylidene fluoride) (PVDF) composites with functionalized carbon nanotube (FCNT) prepared by the hot pressing method. XPS, SEM, TEM, and TGA techniques were employed to understand the extent of functionalization of CNT with acid treatment. Permittivity, Electric Modulus, and AC conductivity measurements of hot pressed samples are compared with samples prepared by the solvent casting method. It was found that the PVDF-FCNT composites were formed with more γ phases. Hot pressing the samples increases the overall polar phases, especially the β phase. The permittivity, electric modulus, and AC conductivity studies reveal the dielectric behavior and conductivity changes with hot pressing samples.

Effectiveness of Electrostatic Shielding in High-Frequency Electromagnetic Induction Soil Sensing.

High-frequency electromagnetic induction (HFEMI) sensors, operating in the frequency range from 300 kHz to 30 MHz, have been proposed for the measurement of soil electrical conductivity and dielectric permittivity that are related to the physical and chemical properties of soil. Because of the high-frequency operation, the capacitive coupling between the sensor transmitter and receiver coils is comparable to inductive coupling, creating the need for electrostatic shielding. The remnant capacitive coupling after the implementation of shielding can lead to significant difficulties in the sensor signal interpretation, because both coupling mechanisms are highly dependent on the geometry of the HFEMI sensor and applied shield. In this paper, we introduce the discussion on the relationship between the sensor geometry, shielding and the coupling mechanisms for HFEMI soil sensing. We theoretically and experimentally evaluate a typical HFEMI sensor and its shielding in the frequency range of up to 20 MHz and propose a method for evaluating the effectiveness of a shield configuration. In the case study, we experimentally analyze the HFEMI sensor above a saline solution for two shield configurations. The results agree well with the results of a finite element method analysis.

Local Response and Barrier Recovery in Elderly Skin Following the Application of High-Density Microarray Patches.

The high-density microneedle array patch (HD-MAP) is a promising alternative vaccine delivery system device with broad application in disease, including SARS-CoV-2. Skin reactivity to HD-MAP applications has been extensively studied in young individuals, but not in the >65 years population, a risk group often requiring higher dose vaccines to produce protective immune responses. The primary aims of the present study were to characterise local inflammatory responses and barrier recovery to HD-MAPs in elderly skin. In twelve volunteers aged 69–84 years, HD-MAPs were applied to the forearm and deltoid regions. Measurements of transepidermal water loss (TEWL), dielectric permittivity and erythema were performed before and after HD-MAP application at t = 10 min, 30 min, 48 h, and 7 days. At all sites, TEWL (barrier damage), dielectric permittivity (superficial water);, and erythema measurements rapidly increased after HD-MAP application. After 7 days, the mean measures had recovered toward pre-application values. The fact that the degree and chronology of skin reactivity and recovery after HD-MAP was similar in elderly skin to that previously reported in younger adults suggests that the reactivity basis for physical immune enhancement observed in younger adults will also be achievable in the older population.

Permittivity of wood as a function of moisture for cultural heritage applications: a preliminary study

Abstract In this work, the evaluation of moisture content in historic wooden objects starting from permittivity measurements is investigated. For this purpose, a WR430 waveguide with a 1.7-2.6 GHz range was used to estimate the complex permittivity correlated to different moisture levels. Experimental tests were carried out on poplar (Populus nigra L.), a wood typically used in central Italy in the thirteenth-sixteenth centuries as a painting support. For the considered measurement system, experimental results and calibration curves are reported.

Measurement of the broadband complex permittivity of soils in the frequency domain with a low-cost Vector Network Analyzer and an Open-Ended coaxial probe

The performance of a handheld Vector Network Analyzer (VNA), the nanoVNA, a low-cost, open-source instrument, was evaluated. The instrument measures the complex permittivity of dielectric media from 1-port reflection parameters in the 1 – 900 MHz bandwidth. We manufactured an open-ended coaxial probe using a SMA-N coaxial adapter to perform dielectric measurements. The accuracy of the nanoVNA was comparable to that of a commercial VNA between 1 and 500 MHz according to tests in reference organic liquids, while a lack of stability was found beyond 700 MHz. The self-manufactured open-ended coaxial probe was subjected to a Finite Element Method (FEM) analysis and its electromagnetic (EM) field penetration depth was determined to be 1.5 mm at 100 MHz, being reduced to 1.3 at 900 MHz and thus demonstrating a frequency-dependent support volume. The broadband complex permittivity of three mineral soils of varied textures was obtained for a range of bulk densities and water contents from dry to water-saturated conditions. The dielectric response of the soils approximated the well-known Topp et al. (1980) equation at high frequencies. At lower frequency however, higher permittivities were exhibited due to dielectric dispersion, which emphasizes the importance of EM-based soil moisture sensor operating frequency when considering sensor calibration or comparing the response of different sensors.

Lithium-ion transport in covalent organic framework membrane

The traditional form of covalent organic framework (COF) is solid powder, which greatly limits its practical application. Besides, owing to the restricted chain dynamics in its highly crystalline regions, polyethylene glycol (PEG)-based electrolytes generally suffer from low ionic conductivity that poses a huge obstacle to its practical applications in solid-state batteries. In this contribution, we developed a confinement-driven strategy to confine PEG into the one-dimensional nanochannels of covalent organic framework membrane, dramatically slashing the crystalline phase and improving ion coupled chain dynamic. The composite electrolyte acquires remarkable ionic conductivity of 2.2 × 10−5 S cm−1 at 20 °C and 1.9 × 10−3 S cm−1 at 120 °C, which is much higher than bulk PEG (only 4.5 × 10−6 S cm−1 at 20 °C and becomes liquid state at elevated temperature). Dielectric permittivity and electric modulus measurement indicated that the ion pairs dissociation, Li-ion coupled chain motion and ion cooperation caused by the confinement effect were all reinforced, bringing out apace Li+ moving from short distance to long distance. Thanks to the flexibility of electrolyte membrane together with excellent thermal and electrochemical stability, the assembled Li-ion battery can operate normally even at 100 °C, obtaining high specific discharge capacity of 135.7 mAh g−1 after 80 cycles and stable interface evolution between electrodes and electrolyte. This work paved the way for the further application of COF membranes as high-performance electrolytes to the construction of high-energy–density solid-state energy storage devices.

Fast and Robust Characterization of Lossy Dielectric Slabs Using Rectangular Waveguides

Waveguide characterization of dielectric materials is a convenient and broadband approach for measuring dielectric constant. In conventional microwave measurements, material samples are usually mechanically shaped to fit the waveguide opening and measured in closed waveguides. This method is not practical for millimeter-wave and sub-millimeter-wave measurements where the waveguide openings become tiny, and it is rather difficult to shape the sample to exactly the same dimensions as the waveguide cross-section. In this paper, we present a method that allows one to measure arbitrarily shaped dielectric slabs that extend outside waveguides. In this method, the measured sample is placed between two waveguide flanges, creating a discontinuity. The measurement system is characterized as an equivalent Pi-circuit, and the circuit elements of the Pi-circuit are extracted from the scattering parameters. We have found that the equivalent shunt impedance of the measured sample is only determined by the material permittivity and is rather insensitive to the sample shape, position, sizes, and other structural details of the discontinuity. This feature can be leveraged for accurate measurements of permittivity. The proposed method is very useful for measuring the permittivity of medium-loss and high-loss dielectrics from microwave to sub-terahertz frequencies.

Dielectric Measurement of Agricultural Grain Moisture-Theory and Applications.

Moisture content is a critical variable for the harvesting, processing, storing and marketing of cereal grains, oilseeds and legumes. Efficient and accurate determination of grain moisture content even with advanced nondestructive techniques, remains a challenge due to complex water-retaining biological structures and hierarchical composition and geometry of grains that affect measurement interpretation and require specific grain-dependent calibration. We review (1) the primary factors affecting permittivity measurements used in practice for inferring moisture content in grains; (2) develop novel methods for estimating critical parameters for permittivity modeling including packing density, porosity, water binding surface area and water phase permittivity and (3) represent the permittivity of packs of grains using dielectric mixture theory as a function of moisture content applied to high moisture corn (as a model grain). Grain permittivity measurements are affected by their free and bound water contents, chemical composition, temperature, constituent shape, phase configuration and measurement frequency. A large fraction of grain water is bound exhibiting reduced permittivity compared to that of free water. The reduced mixture permittivity and attributed to hydrophilic surfaces in starches, proteins and other high surface area grain constituents. The hierarchal grain structure (i.e., kernel, starch grain, lamella, molecule) and the different constituents influence permittivity measurements due to their layering, geometry (i.e., kernel or starch grain), configuration and water-binding surface area. Dielectric mixture theory offers a physically-based approach for modeling permittivity of agricultural grains and similar granular media.

Improved open-ended coaxial probe for temperature-dependent permittivity measurements of foodstuff at radio frequencies

Accurate determination of permittivity is a crucial factor for successfully developing new food processing technologies at radio frequencies. An improved measurement test fixture based on an open-ended coaxial probe was developed to determine the permittivity of lossy food products at radio frequencies as a function of temperature. In order to increase the sensitivity of the permittivity measurements at these frequencies, especially when using a vector network analyzer as a measuring device, the dimensions of the coaxial cell were carefully modeled to consider the range of dielectric losses estimated for food materials. The electromagnetic model was used to retrieve permittivity values from reflection measurements where the entire geometry of the test fixture was considered assuming there was no open radiation or infinite flanges and without the need of reference materials to calibrate the probe. The new cell was validated through permittivity measurements of six saline solutions and then, employed to determine the dielectric properties of cheese sauces and commercial milk samples at 40.68 MHz up to 120 °C. The ionic content and temperature had a limited influence on the dielectric constant but highly determined the loss factor. • A test fixture was developed for improved temperature-dependent permittivity measurements of foodstuffs at radio frequencies. • It used an open-ended coaxial probe achieving more than 6 times the response of previous designs reported in the literature. • Permittivity of milk and cheese food sauces were measured at 40.68 MHz up to 120 °C.

Dual-band measurement of complex permittivity in a microwave waveguide with a flexible, thin and sensitive metamaterial-based sensor

A dual-band metamaterial-based sensor is proposed to determine the complex dielectric constant of ethanol-methanol mixtures. The original sensor structure incorporates one connected dual H-shaped slot resonators at the center and one H-shaped slot resonator at the left and right sides of a rectangular copper patch to provide two distinct resonance frequencies. Polycarbonate is chosen as the substrate material due to its lightness, flexibility, robustness and transparency. Full-wave simulations of electric field distributions reveal that the dual resonances at 3.7 GHz and 4.6 GHz stem from different parts of the metamaterial. Measurements are carried out with a WR-229 microwave waveguide and the electromagnetic simulation results are confirmed with good agreement. A first-order equation that relates the complex dielectric constant to the shift of resonance frequency and peak attenuation is used to determine the complex dielectric constant of ethanol-methanol mixtures in the vicinity of 3.3 GHz and 4.4 GHz frequencies. A good agreement with the literature values is obtained validating the accuracy of the used model. Experimental results revealed that the frequency detection resolution and sensitivity parameter values of the proposed sensor are 25.3 MHz and 0.73% for the lower-frequency band and 9.6 MHz and 0.22% for the higher-frequency band, respectively. In addition to being able to operate at dual frequencies, the proposed metamaterial-based sensor has high sensitivities for the two resonance frequencies. Moreover, the advantages of the proposed sensor, as being electrically-small, flexible, noncontact and reusable, provide a good option for discrimination of binary liquid mixtures at multiple frequencies.

Standoff High-Frequency Electromagnetic Induction Response of Unsaturated Sands: A Tank-Scale Feasibility Study

Standoff electromagnetic induction (EMI) measurements of complex conductivity and complex permittivity for engineering soil properties have the potential to revolutionize the way the US Army handles route planning and infrastructure assessment. An unmanned aerial system (UAS) based EM platform for soil interrogation would have wide reaching impact in a variety of applications including: civil infrastructure inspection, in-theater ingress and egress routing, reduction of false positives in IED detection, and permafrost mapping, among many others. Traditional frequency domain EMI instruments assess conductivity at low-frequencies, generally in the range of 1–20 kHz; however, recent advancements have resulted in instrumentation targeting a broadband range of frequencies, from 10 kHz through 20 MHz. This advancement, known as high-frequency electromagnetic induction (HFEMI) allows the potential to evaluate frequency domain relaxation effects in soils by acquiring both the in phase and quadrature response of the secondary field from the soil. Relaxation phenomena such as induced polarization and dielectric permittivity are related to important soil properties that can potentially be exploited using this HFEMI system. While conductivity measurements using the quadrature component of the EMI response are well established in EMI instrumentation, understanding of the relationship between direct electrical measurements and standoff HFEMI measurements is lacking. In an effort to illuminate this relationship between various electrical and electromagnetic methods at a scale suitable for soil property estimation, we perform side-by-side measurements using galvanic geoelectrical methods (ERT, IP), electromagnetics, time-domain reflectometry (TDR) and ground penetrating radar (GPR). We compare HFEMI obtained quadrature and in-phase responses to ERT, IP, TDR and GPR measurements. A tank-scale test cell was developed for comparison of the above methods and allowed assessment of sand at varying saturation levels. Further, the HFEMI response at varying heights above the sand surface was also assessed. Qualitative observations are reported in an initial attempt to relate the HFEMI response to important soil parameters.

Broadband Complex Permittivity and Electric Modulus Spectra for Dielectric Materials Research

Measurement of the complex permittivity of a substance in a wide frequency range, for example, from 10 mHz to 100 kHz, provides useful information on the dielectric properties of the substance. In this regard, some of such dielectric properties can be analyzed more clearly if we pay attention to the frequency spectra of electric modulus, which is a reciprocal of complex relative permittivity. Especially, the imaginary part of the electric modulus can be a powerful tool for dielectric materials research. In this paper, this fact is demonstrated clearly by showing abundant examples acquired by the author's laboratory. First, the equations of electric modulus that hold for various dielectric relaxation processes, including their derivation, are shown in an easy‐to‐understand manner. After that, for several insulating polymers, actual measurement examples of broadband complex permittivity spectra are shown, up to frequencies of about 100 kHz and a much broader range up to several THz. In the first example of showing permittivity spectra, polyamide exhibits an incredibly high relative permittivity value of 106 at high temperatures such as 200 °C at a frequency as low as 10 mHz. This is a result of the phenomenon often called electrode polarization. In other words, if electric charge carriers accumulate in an insulator facing a nearby electrode and have the polarity opposite to that of the electrode, the permittivity of the insulator goes up. In such a case, the dielectric loss factor usually shows a very high value in the low‐frequency range and decreases in inverse proportion to the frequency. This reflects the fact that the charge carriers are transported, and the conductivity can be derived from this frequency dependence much more easily with apparently higher reliability than measuring the dc leakage current. Furthermore, it is shown that the coefficient of thermal expansion can be estimated from the permittivity spectra relatively accurately for several polymers that satisfy the necessary condition. Next, taking examples in electric modulus spectra measured in important insulating polymers such as engineering ones, it is demonstrated that the processes of dielectric polarization and relaxation, which are difficult to see in permittivity spectra, can be recognized obviously. Moreover, the effects of the addition of nanosized or microsized fillers to epoxy resin on its thermal property and filler‐induced inhomogeneity are analyzed using the electric modulus spectra measured in these samples. The effects of thermal aging treatment and simultaneous aging treatment with heat and radiation on the degradation of cross‐linked polyethylene are also analyzed by paying attention to the frequency spectra of its imaginary electric modulus. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Multifrequency Inversion of Complex Electrical Conductivity Measurements for Simultaneous Assessment of Wettability, Porosity, and Water Saturation

Summary Multifrequency complex electric measurements are influenced by the joint effects of mineralogy, spatial distribution of fluids and solids, properties of fluids and minerals, and interfacial polarization mechanisms. The interpretation of multifrequency electrical conductivity and dielectric permittivity dispersion can yield information about the dominant dielectric polarization mechanisms. The dielectric polarization mechanisms detected in sedimentary rocks are linked to grain size, shape, and orientation relative to the externally applied electric field, electrochemical adsorption/desorption complexation reactions, wettability, porosity, and fluid saturations. In this work, we introduce a new workflow for multifrequency interpretation of complex permittivity measurements. The introduced workflow enables simultaneous assessment of dominant wettability, porosity, and hydrocarbon reserves. These properties are estimated by minimizing a cost function using a combination of downhill gradient-descent and an evolutionary algorithm. The cost function quantifies the difference between measured and numerically calculated multifrequency complex dielectric permittivity through a recently introduced rock-physics model. We successfully applied the new interpretation workflow to multifrequency electrical resistivity/permittivity measurements obtained from two water-wet and two hydrocarbon-wet sandstone core samples. Simultaneous estimates of wettability, water saturation, and porosity obtained by applying the new interpretation workflow were in agreement with experimental measurements. Assessment of hydrocarbon reserves, porosity, and dominant wettability solely from the interpretation of multifrequency complex-valued electrical measurements is a unique contribution of the introduced workflow. Additionally, the new workflow honors rock fabric and, thus, it minimizes the necessity of extensive calibration efforts. All the parameters needed as inputs to the new interpretation workflow are associated with physical mechanisms at microscopic- and pore-scale domains or realistic and quantitative pore geometry features of the rock.

Observation of chiral solitons in LiCuVO4

Quantum spin liquids represent a magnetic ground state arising in the presence of strong quantum fluctuations that preclude ordering down to zero temperature and leave clear fingerprints in the excitation spectra. While theory bears a variety of possible quantum spin liquid phases their experimental realization is still scarce. Here, we report experimental evidence for chiral solitons in the S = 1/2 spin chain compound LiCuVO4 from measurements of the complex permittivity ε* in the GHz range. In zero magnetic field our results show short-lived thermally activated chiral fluctuations above the multiferroic phase transition at TN = 2.4 K. In ε* these fluctuations are seen as the slowing down of a relaxation with a critical dynamical exponent νξz ≈ 1.3 in agreement with mean-field predictions. When using a magnetic field to suppress TN towards 0 K the influence of quantum fluctuations increases until the thermally activated fluctuations vanish and only an excitation can be observed in the dielectric response in close proximity to the phase transition below 400 mK. From direct measurements we find this excitation’s energy gap as ESE ≈ 14.1 μeV, which is in agreement with a nearly gapless chiral soliton that has been proposed for LiCuVO4 based on quantum spin liquid theory.

Measurement of the electric permittivity using Bleustein–Gulyaev wave sensor

We present a novel compact electric permittivity sensor that exploits Bleustein–Gulyaev waves propagating along the surface of shear-poled piezoelectrics. We formulate the dynamic nonlinear electromechanical partial differential equations of motion governing wave propagation under electromagnetically quasistatic conditions. The permittivity of the medium-under-test was found to influence the sensor eigenvalues, enabling the implementation of a frequency-shift permittivity sensor. Solution of the equations of motion demonstrates resonance of the first and third modes when excited using an interdigitated transducer. We fabricated two sensor prototypes on shear-poled PZT4 and LiNbO3 substrates and used a Vector Network Analyzer to observe the shift in their fundamental natural frequency in the presence of various media-under-test. S 11 measurements show deterministic and repeatable shifts in the resonant frequency of the first mode of the LiNbO3 sensor measured at MHz for ethanol and MHz for deionized water where the bare surface frequency was initially at MHz.

High-Resolution Detection of Rock-Forming Minerals by Permittivity Measurements with a Near-Field Scanning Microwave Microscope.

The identification of the minerals composing rocks and their dielectric characterization is essential for the utilization of microwave energy in the rock industry. This paper describes the use of a near-field scanning microwave microscope with enhanced sensitivity for non-invasive measurements of permittivity maps of rock specimens at the micrometer scale in non-contact mode. The microwave system comprises a near-field probe, an in-house single-port vectorial reflectometer, and all circuitry and software needed to make a stand-alone, portable instrument. The relationship between the resonance parameters of the near-field probe and the dielectric properties of materials was determined by a combination of classical cavity perturbation theory and an image charge model. The accuracy of this approach was validated by a comparison study with reference materials. The device was employed to determine the permittivity maps of a couple of igneous rock specimens with low-loss and high-loss minerals. The dielectric results were correlated with the minerals comprising the samples and compared with the dielectric results reported in the literature, with excellent agreements.

Self‐Poled Heteroepitaxial Bi(1−x)DyxFeO3 Films with Promising Pyroelectric Properties

AbstractPyroelectric materials are very promising for thermal energy harvesting applications. To date, lead‐based systems are the foremost studied materials in this field. A facile and simple metal organic chemical vapor deposition route is applied for the fabrication of lead‐free, high quality, epitaxial Bi(1−x)DyxFeO3 (x = 0, 0.06, 0.08, 0.11) thin films deposited on conductive SrTiO3:Nb (100) single crystal substrates. The films are studied by structural, morphological, compositional, and functional characterization. The correlation between the Dy‐doping amount and the dielectric properties is thoroughly investigated. Unipolar polarization–electric field loops and permittivity measurements show the important impact of Dy on ferroelectric, dielectric, and pyroelectric properties. Dy doping increases considerably the dielectric response, but much more the pyroelectric coefficient, up to a concentration of 8% Dy. The films are self‐poled, which is an ideal situation for pyroelectric applications. The best figure of merit for pyroelectric energy harvesting, FE, is 82 J m−3 K−2, showing a factor increase of 2.6 as compared to the undoped film of the sample series. It constitutes a factor 4.5 improvement as compared to previous results obtained on BiFeO3 based thin films.

Atomically dispersed cobalt anchored on N-doped graphene aerogels for efficient electromagnetic wave absorption with an ultralow filler ratio

The widespread application of high-frequency electronic and communication devices has caused increasingly severe electromagnetic pollution. It is highly desirable but challenging to develop ultralight electromagnetic wave (EMW) absorbers with strong absorption performance to eliminate the negative effects of electromagnetic pollution. Herein, a secondary ion adsorption and defect-anchoring strategy was proposed to construct ultralight N-doped graphene aerogels containing isolated single cobalt atoms (Co-SAs/GAs) with a tunable content of Co-SAs from 1.13 to 2.58 wt. %. The optimal Co-SAs/GAs with a matching thickness of 1.5 mm and an ultralow filler ratio of 5 wt. % attenuated about 99.999% electromagnetic energy and exhibited specific EMW absorption performance (SMAP) of 37 220 dB cm2 g−1, which was 15 000 dB cm2 g−1 higher than that of the best reported absorber in literature. Permittivity and electrical conductivity measurements indicated that the introduction of Co-SAs significantly increased the conduction and polarization losses of the GAs, which was confirmed by simulation results based on the Havriliak–Negami equation. Theoretical calculations demonstrated that the Co–N4 moiety exhibited obvious polarization behavior, which could be further tuned by defective sites in its vicinity. This comprehensive investigation of the relationships between single-atom structure and electromagnetic wave absorption property provides an efficient route toward the rational design of ultralight absorbers with metal single-atoms.