Journal articles: 'Dynamic dielectric properties'

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Zhuravlev, V. I., and T. M. Usacheva. "Dynamic dielectric properties of butanediols." Moscow University Chemistry Bulletin 65, no. 2 (April 2010): 70–74. http://dx.doi.org/10.3103/s0027131410020033.

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Cosby, Tyler, David P. Durkin, Robert A. Mantz, and Paul C. Trulove. "Interplay of Local Dynamic Heterogeneity, Mesoscale Aggregate Dynamics, and Transport Properties of Imidazolium Ionic Liquids." ECS Meeting Abstracts MA2022-02, no. 55 (October 9, 2022): 2099. http://dx.doi.org/10.1149/ma2022-02552099mtgabs.

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Ion dynamics and charge transport in 1-methyl-3-octylimidazolium ionic liquids with chloride, bromide, tetrafluoroborate, tricyanomethanide, hexafluorophosphate, triflate, tetrachlorodialuminate, bis(trifluoromethylsulfonyl)imide, and heptachlorodialuminate anions are investigated by broadband dielectric spectroscopy, rheology and viscometry. A detailed analysis reveals anion and temperature-dependent separation of characteristic relaxation rates extracted from various representations of the dielectric spectra. The degree of separation is interpreted as an experimental signature of significant heterogeneity of the local ion dynamics associated with the structural glass transition, viscosity, and dc ion conductivity. It is found that the degree of dynamic heterogeneity correlates closely with the strengths of slow dielectric and mechanical relaxations previously attributed to the dynamics of mesoscale solvophobic aggregates. Increasing local dynamic heterogeneity correlates with an increase in the strength of the slow, aggregate dielectric relaxation and a decrease in the strength of the slow, aggregate mechanical relaxation. Accordingly, the local dynamic heterogeneity correlates with an increase in the static dielectric permittivities and a decrease in the contribution of aggregate dynamics to the zero-shear viscosities. These results are presented within a broader framework of current understanding of dynamics in ionic liquids and the interplay of dynamics, solvophobic aggregation, and charge transport in these technologically important systems.

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Saad, A., U. Becker, M. Stockhausen, and Y. Barakat. "Notiz: Dynamic Dielectric Properties of Some Alkylamino Ethoxylates." Zeitschrift für Naturforschung A 50, no. 11 (November 1, 1995): 1083–84. http://dx.doi.org/10.1515/zna-1995-1116.

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Abstract Nine ethoxylated (EO) alkyl amines, (CnH2n + 1) N(EO)x; H(EO)y H, with n = 10 to 16 and p = x + y = 7.6 to 14.5, were studied as pure liquids with respect to their dielectric relax ation behaviour over the frequency range 5 MHz to 36 GHz at 20 °C. The broad and structureless dielectric loss spectrum is similar for all samples. It can be described by a main lower frequency spectral component of Havriliak-Negami type plus two minor, higher frequency Debye type components. The relaxation parameters are reported. Dynamic Dielectric Properties of Some Alkylamino Ethoxylates

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Zakharov, A. V., and L. V. Mirantsev. "Dynamic and dielectric properties of liquid crystals." Physics of the Solid State 45, no. 1 (January 2003): 183–88. http://dx.doi.org/10.1134/1.1537433.

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CUI, LIAN, HAIYING CUI, CHUNMEI WU, GUIHUA YANG, ZELONG HE, YULING WANG, and JIXIN CHE. "DYNAMIC PROPERTIES OF DIELECTRIC SUSCEPTIBILITY IN FERROELECTRIC THIN FILMS." Surface Review and Letters 23, no. 03 (May 3, 2016): 1650010. http://dx.doi.org/10.1142/s0218625x16500104.

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In this paper, frequency, temperature, film thickness, surface effects, and various parameters dependence of dielectric susceptibility is investigated theoretically for ferroelectric thin films by the modified Landau theory under an AC applied field. The dielectric susceptibility versus AC applied field shows butterfly-shaped behavior, and depends strongly on the frequency and amplitude of the field and temperature. Our study shows that the existence of the surface transition layer can depress the dielectric susceptibility of a ferroelectric thin film. These results are well consistent with the phenomena reported in experiments.

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Chakraborty, Sudhangshu. "Frequency-dependent dielectric properties of sodium silicate." Modern Physics Letters B 32, no. 33 (November 30, 2018): 1850411. http://dx.doi.org/10.1142/s0217984918504110.

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The dielectric properties of sodium silicate (Na2SiO3) (SS) have been investigated in a wide range of frequencies and temperatures. A strong dielectric dispersion is found to exist in low-frequency region. The frequency-dependent dielectric properties of SS follow the universal dynamic response proposed by Jonscher. The measured dielectric data strongly depends on dielectric dispersion and controls the basic relaxation property. However, the parameters that control the frequency-dependent dielectric properties such as coupling of ions or polarizability are found to have peak values at the frozen out condition or critical point.

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Baklanov, Mikhail R., and Karen Maex. "Porous low dielectric constant materials for microelectronics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1838 (November 29, 2005): 201–15. http://dx.doi.org/10.1098/rsta.2005.1679.

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Materials with a low dielectric constant are required as interlayer dielectrics for the on-chip interconnection of ultra-large-scale integration devices to provide high speed, low dynamic power dissipation and low cross-talk noise. The selection of chemical compounds with low polarizability and the introduction of porosity result in a reduced dielectric constant. Integration of such materials into microelectronic circuits, however, poses a number of challenges, as the materials must meet strict requirements in terms of properties and reliability. These issues are the subject of the present paper.

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Rabii, Sanaa, Ayoub Lahmidi, Samir Chtita, Mhammed El Kouali, Mohammed Talbi, and Abdelkbir Errougui. "Molecular dynamics modelling of the structural, dynamic, and dielectric properties of the {LiF - ethylene carbonate} energy storage system at various temperatures." Journal of the Serbian Chemical Society, no. 00 (2024): 61. http://dx.doi.org/10.2298/jsc240205061r.

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Lithium-ion batteries (LIBs) play a vital role in advancing the hybrid industry, especially in electric vehicles, as clean and sustainable electrochemical energy sources. However, the prevalent use of organic solvents in the liquid electrolytes of these energy storage systems raises environmental concerns. In this study, we investigated the impact of a polar aprotic solvent, Ethylene Carbonate (EC), on the structural, dynamic, and dielectric properties of the LiF electrolyte using molecular dynamics simulations. By employing the CHARMM 36 force field, our goal was to comprehend the various physicochemical phenomena occurring in this electrolytic system across different temperatures within the saturation region. The structural properties were analyzed through the computation of the radial distribution function (RDF) for various pairs, while the dynamic and dielectric behaviors were elucidated by simulating the self-diffusion coefficient (D) and the dielectric constant (?).

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Pascariu, Petronela, Mihaela Homocianu, Loredana Vacareanu, and Mihai Asandulesa. "Multi-Functional Materials Based on Cu-Doped TiO2 Ceramic Fibers with Enhanced Pseudocapacitive Performances and Their Dielectric Characteristics." Polymers 14, no. 21 (November 4, 2022): 4739. http://dx.doi.org/10.3390/polym14214739.

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In this work, pure TiO2 and Cu (0.5, 1, 2%)-doped TiO2 composites prepared by electrospinning technique followed by calcination at 900 °C, and having high pseudocapacitive and dielectric characteristics were reported. These nanocomposites were characterized by scanning electron microscopy, X-ray diffraction, and dynamic water sorption vapor measurements. The structural characterization of these nanostructures highlighted good crystallinity including only the rutile phase. The electrochemical characteristics were investigated by cyclic voltammetry and galvanostatic charge–discharge measurements, which were performed in a KOH electrolyte solution. Among the Cu-doped TiO2 nanostructures that were prepared, the one containing 0.5% Cu exhibited superior electrochemical properties, including high specific gravimetric capacitance of 1183 F·g−1, specific capacitance of 664 F·g−1, energy density of 45.20 Wh·kg−1, high power density of 723.14 W·kg−1, and capacitance retention of about 94% after 100 cycles. The dielectric investigation shows good dielectric properties for all materials, where the dielectric constant and the dielectric loss decreased with the frequency increase. Thus, all the interconnected studies proved that these new materials show manifold ability and real applicative potential as pseudocapacitors and high-performance dielectrics. Future work and perspectives are anticipated for characterizing electrochemical and dielectric properties for materials including larger amounts of Cu dopant.

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Czechowski, Grzegorz, and Jan Jadżyn. "Static and Dynamic Dielectric Properties of Mesogenic n-Nonyloxycyanobiphenyl (9OCB)." Zeitschrift für Naturforschung A 62, no. 1-2 (February 1, 2007): 61–66. http://dx.doi.org/10.1515/zna-2007-1-209.

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The dielectric properties of n-nonyloxycyanobiphenyl in the isotropic (I), nematic (N) and smectic A (SA) phases were investigated. The dielectric relaxation spectra, recorded in the frequency range 50 kHz - 100 MHz, were analyzed with use of the Cole-Cole equation. An anomalous temperature behavior of the static permittivity, the rotational diffusion exponent and the activation energy of mesogenic molecules rotating around their short axis, observed in the vicinity of the phase transitions, are discussed.

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Czub, Joanna, Roman Dąbrowski, Stanisław Urban, and Dorota Ziobro. "Dielectric Properties of Strongly Polar Nematogens." Zeitschrift für Naturforschung A 65, no. 3 (March 1, 2010): 221–30. http://dx.doi.org/10.1515/zna-2010-0311.

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Results of the static and dynamic dielectric investigations of four liquid crystalline compounds consisting of two or three phenyl rings with n-alkoxy and cyano terminals, carboxylic bridging groups, and fluoro lateral substituents in pure state and in the solution of low polar liquid crystalline medium, are presented. These compounds form the nematic phase being a monotropic one in the case of two ring compounds. The dielectric parameters are analyzed in relation to the dipolar structures of the molecules. The dielectric properties of pure substances are strongly influenced by conductivity and dimerization effects, while extracted from the data for solutions are consisted well with the structures. In the nematic phase the compounds exhibit a crossover of the principal permittivity components among the kilo and megahertz frequency range

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Li, Peng, Jiajun Yu, Shaohua Jiang, Hong Fang, Kunming Liu, and Haoqing Hou. "Dielectric, mechanical and thermal properties of all-organic PI/PSF composite films by in situ polymerization." e-Polymers 20, no. 1 (June 5, 2020): 226–32. http://dx.doi.org/10.1515/epoly-2020-0020.

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AbstractAll-organic high dielectric materials are highly required in the field of modern electronic industry and energy storage. In this work, all-organic polyimide/polysulfone composite films with different amounts of PSF (PI/PSF-X) were prepared by in situ polymerization followed by film casting and thermal treatment. The dielectric, mechanical and thermal properties of these PI/PSF-X composite films are characterized by dielectric measurement, tensile test, thermogravimetric analysis and dynamic mechanical analysis. The results suggest that the PI/PSF-X composite films have good dielectric properties, good mechanical properties and excellent thermal properties, which are suitable for applications in electronic devices in harsh environments, especially in high-temperature environments.

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Kovaleva, L. A., R. R. Zinnatullin, V. N. Blagochinnov, A. A. Musin, Yu I. Fatkhullina, and Yu S. Zamula. "Destruction of water-in-oil emulsions in electromagnetic fields in a dynamic mode." Proceedings of the Mavlyutov Institute of Mechanics 9, no. 1 (2012): 110–15. http://dx.doi.org/10.21662/uim2012.1.021.

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Some results of experimental and numerical studies of the influence of radio-frequency (RF) and microwave (MW) electromagnetic (EM) fields on water-in-oil emulsions are presented. A detailed investigation of the dependence of the dielectric properties of emulsions on the frequency of the field makes it possible to establish the most effective frequency range of the EM influence. The results of water-in-oil emulsion stability in the RF EM field depending on their dielectric properties are presented. The effect of the MW EM field on the emulsion in a dynamic mode has been studied experimentally. In an attempt to understand the mechanism of emulsion destruction the mathematical model for a single emulsion droplet dynamics in radio-frequency (RF) and microwave (MW) electromagnetic fields is formulated.

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Buyong, Muhamad Ramdzan, Farhad Larki, Celine Elie Caille, Norazreen Abd Aziz, Ahamad Ghadafi Ismail, Azrul Azlan Hamzah, and Burhanuddin Yeop Majlis. "Dynamic dielectric properties characterization of tapered dielectrophoresis microelectrodes for selective detection and rapid manipulation of cells." Microelectronics International 37, no. 4 (September 4, 2020): 189–98. http://dx.doi.org/10.1108/mi-03-2020-0015.

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Purpose This paper aims to present the dielectrophoresis (DEP) force (FDEP), defined as microelectrofluidics mechanism capabilities in performing selective detection and rapid manipulation of blood components such as red blood cells (RBC) and platelets. The purpose of this investigation is to understand FDEP correlation to the variation of dynamic dielectric properties of cells under an applied voltage bias. Design/methodology/approach In this paper, tapered design DEP microelectrodes are used and explained. To perform the characterization and optimization by analysing the DEP polarization factor, the change in dynamic dielectric properties of blood components are observed according to the crossover frequency (fxo) and adjustment frequency (fadj) variation for selective detection and rapid manipulation. Findings Experimental observation of dynamic dielectric properties change shows clear correlation to DEP polarization factor when performing selective detection and rapid manipulation. These tapered DEP microelectrodes demonstrate an in situ DEP patterning efficiency more than 95%. Research limitations/implications The capabilities of tapered DEP microelectrode devices are introduced in this paper. However, they are not yet mature in medical research studies for various purposes such as identifying cells and bio-molecules for detection, isolation and manipulation application. This is because of biological property variations that require further DEP characterization and optimization. Practical implications The introduction of microelectrofluidics using DEP microelectrodes operate by selective detecting and rapid manipulating via lateral and vertical forces. This can be implemented on precision health-care development for lab-on-a-chip application in microfluidic diagnostic and prognostic devices. Originality/value This study introduces a new concept to understand the dynamic dielectric properties change. This is useful for rapid, label free and precise methods to conduct selective detection and rapid manipulation of mixtures of RBC and platelets. Further, potential applications that can be considered are for protein, toxin, cancer cell and bacteria detections and manipulation. Implementation of tapered DEP microelectrodes can be used based on the understanding of dynamic dielectric properties of polarization factor analysis.

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Dong, Kim, and Choi. "Graphene Oxide and Its Inorganic Composites: Fabrication and Electrorheological Response." Materials 12, no. 13 (July 7, 2019): 2185. http://dx.doi.org/10.3390/ma12132185.

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Composite particles associated with graphene oxide (GO) and inorganic materials provide the synergistic properties of an appropriate electrical conductivity of GO with the good dielectric characteristics of inorganic materials, making them attractive candidates for electrorheological (ER) materials. This review paper focuses on the fabrication mechanisms of GO/inorganic composites and their ER response when suspended in a non-conducting medium, including steady shear flow curves, dynamic yield stress, On-Off tests, and dynamic oscillation analysis. Furthermore, the morphologies of these composites, dielectric properties, and sedimentation of the ER fluids are covered.

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Dmitrikov, Vladimir F., Alexander Yu Petrochenko, Vyacheslav M. Isaev, and Dmitriy V. Shushpanov. "Features of designing line radio interference filter in a wide frequency range, taking into account equivalent circuits for capacitors and inductors." Physics of Wave Processes and Radio Systems 23, no. 4 (February 11, 2021): 85–96. http://dx.doi.org/10.18469/1810-3189.2020.23.4.85-96.

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Based on the phenomenological equations describing the dynamic processes of magnetization of ferromagnets of inductors and polarization of capacitor dielectrics, taking into account complex frequency-dependent dielectric constants e(jw) of capacitor dielectrics and magnetic permeabilities m(jw) of inductor cores, equivalent electrical structural-parametric and capacitor replacement circuits were obtained. The connection of parasitic elements of equivalent electric circuits of capacitors and inductors with the electrophysical characteristics of the material of the dielectric of the capacitor and the inductor core, which determine their frequency properties, structure and parameters of the elements of the equivalent circuit, is established. The features of the design of line radio interference filter taking into account the parasitic parameters of the inductors and capacitors of line radio interference filter, found as a result of the synthesis of equivalent electric circuits of the inductors and capacitors in a wide frequency range of 150 kHz 30 MHz.

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HUDAK, MATEJ, and ONDREJ HUDAK. "DYNAMIC SUSCEPTIBILITY IN A PARAELECTRIC PHASE IN A SMALL PARTICLE, BOUNDARY EFFECTS." International Journal of Modern Physics B 27, no. 09 (April 10, 2013): 1350015. http://dx.doi.org/10.1142/s021797921350015x.

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The dielectric dynamic susceptibility of a particle is studied numerically using the exact susceptibility expression in other to understand particle physical properties. There exist one peak in the imaginary part and two peaks in the real part of the susceptibility. Constant behavior of peaks width and height is found in the imaginary and real part of the susceptibility going from the center. A decrease of peaks to zero is an effect of boundary. Our results are in contrast with behavior of susceptibility behavior found variationally where there is no constant behavior of the susceptibility peaks changing r. These results are new in literature of dielectrics.

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Zuo, Yuchen, Yuxi Ding, Junshi Zhang, Mingliang Zhu, Lei Liu, and Jianwen Zhao. "Humidity Effect on Dynamic Electromechanical Properties of Polyacrylic Dielectric Elastomer: An Experimental Study." Polymers 13, no. 5 (March 4, 2021): 784. http://dx.doi.org/10.3390/polym13050784.

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In this research, by utilizing the Very-High-Bond (VHB) 4905 elastomer, we carry out an experimental examination on the humidity effect on dynamic electromechanical performances of dielectric elastomers, including the dynamic response and viscoelastic creeping. Firstly, we experimentally analyze effects of the pre-stretch, peak voltage, waveform and frequency of the dynamic response of VHB 4905 elastomer under several ambient humidities. In general, the amplitude of dynamic deformation gradually adds up with the increasing humidity. Besides, it is found that the amplitude affected by different parameters shows diverse sensitivity to humidity. Subsequently, effect of humidity on the viscoelastic creeping of VHB 4905 is explored. The results demonstrate that, subject to different ambient humidities, the viscoelastic creeping under Alternating Current (AC) voltage is similar to that under Direct Current (DC) voltage. Furthermore, the equilibrium position of dynamic viscoelastic creep enlarges gradually with the humidity, regardless of voltage waveforms. For the dielectric elastomer with a pre-stretch ratio of 3, when the humidity increases from 20% to 80%, the increase of average equilibrium position of dynamic viscoelastic creep is larger than 1599%.

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Foschini, C. R., P. C. Joshi, J. A. Varela, and S. B. Desu. "Properties of BaBi2Ta2O9 thin films prepared by chemical solution deposition technique for dynamic random-access memory applications." Journal of Materials Research 14, no. 5 (May 1999): 1860–64. http://dx.doi.org/10.1557/jmr.1999.0250.

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We report on the properties of BaBi2Ta2O9 (BBT) thin films for dynamic random-access memory (DRAM) and integrated capacitor applications. Crystalline BBT thin films were successfully fabricated by the chemical solution deposition technique on Pt-coated Si substrates at a low annealing temperature of 650 °C. The films were characterized in terms of structural, dielectric, and insulating properties. The electrical measurements were conducted on Pt/BBT/Pt capacitors. The typical measured small signal dielectric constant and dissipation factor, at 100 kHz, were 282 and 0.023, respectively, for films annealed at 700 °C for 60 min. The leakage current density of the films was lower than 10−9 A/cm2 at an applied electric field of 300 kV/cm. A large storage density of 38.4 fC/μm2 was obtained at an applied electric field of 200 kV/cm. The high dielectric constant, low dielectric loss and low leakage current density suggest the suitability of BBT thin films as dielectric layer for DRAM and integrated capacitor applications.

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Taha, E. O., and G. M. Nasr. "Dielectric and dynamic mechanical properties of Rochelle salt / PVA composites." IOP Conference Series: Materials Science and Engineering 1046, no. 1 (February 1, 2021): 012008. http://dx.doi.org/10.1088/1757-899x/1046/1/012008.

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Uchida, Giichiro, Kosuke Takenaka, Atsushi Miyazaki, Kazufumi Kawabata, and Yuichi Setsuhara. "Dynamic Properties of Helium Atmospheric Dielectric-Barrier-Discharge Plasma Jet." Journal of Nanoscience and Nanotechnology 15, no. 3 (March 1, 2015): 2324–29. http://dx.doi.org/10.1166/jnn.2015.10232.

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Zhang, Yi-He, Zhi-Min Dang, Shao-Yun Fu, John H. Xin, Jian-Guo Deng, Juntao Wu, Shiyong Yang, Lai-Feng Li, and Qing Yan. "Dielectric and dynamic mechanical properties of polyimide–clay nanocomposite films." Chemical Physics Letters 401, no. 4-6 (January 2005): 553–57. http://dx.doi.org/10.1016/j.cplett.2004.11.084.

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Hsiue, Ging-Ho, Wen-Kuei Huang, and Wei-Hsin Hou. "Dynamic mechanical and dielectric properties of epoxidized SBS triblock copolymer." Journal of Polymer Science Part A: Polymer Chemistry 27, no. 12 (November 1989): 4119–28. http://dx.doi.org/10.1002/pola.1989.080271219.

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Zhang, Yongjian, Fan Yang, Shuiping Ouyang, Bo Cai, Chao Zhao, Hehuan Peng, Bin Li, and Xiaomin Ma. "Dynamic dielectric properties of biomass fractionation system using ethylene glycol." Industrial Crops and Products 222 (December 2024): 119639. http://dx.doi.org/10.1016/j.indcrop.2024.119639.

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Burton, L. C., K. Hwang, and T. Zhang. "Dynamic Electrical and Electromechanical Properties of Carbon-Black Loaded Rubber." Rubber Chemistry and Technology 62, no. 5 (November 1, 1989): 838–49. http://dx.doi.org/10.5254/1.3536278.

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Abstract 1. Low-frequency resistance can be dominated by contacts. It was found that silver paint contacts were roughly equivalent to metal contacts bonded during vulcanization. 2. Three electrical regimes are clearly evident, determined by loading: dielectric, percolation, and conducting. 3. Resistance and dielectric constant dispersion for loading above 30 phr agree with Kawamoto's model. 4. Each carbon-black loading results in a distinctive dispersion signature. 5. Dynamic conductivity can be used to delineate persistent and transient carbon-black-structure changes versus composition, DSA, frequency, and potentially other parameters (temperature, stress waveform, etc.). 6. The remaining conductive network during stress is represented by gmin; Δg is determined by network fracture and reformation; gmin−gα is proportional to the amount of remaining transient structure; g0−gα is proportional to the total transient structure; normalized conductivity Z is the remaining-to-total transient-structure ratio. 7. The Δgm=0.525(g0−gα) relation indicates that maximum reformation occurs when approximately half the transient structure is broken down and confirms the correlation between conductivity parameters and transient carbon-black structure.

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Alam, Mohd, Labanya Ghosh, Supriyo Majumder, Prajyoti Singh, Satya Vijay Kumar, Srishti Dixit, Dheeraj Kumar, et al. "Multifunctional behaviour in B-site disordered double perovskite EuPrCoMnO₆." Journal of Physics D: Applied Physics 55, no. 25 (April 1, 2022): 255003. http://dx.doi.org/10.1088/1361-6463/ac5fd4.

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Abstract We report magnetic, transport, dielectric, and complex impedance of polycrystalline double perovskite EuPrCoMnO6 which crystallizes in disordered orthorhombic phase with space group Pnma. The DC magnetization shows two successive ferromagnetic transitions around 146 K and 138 K. The temperature and magnetic field variation of DC-susceptibility suggest the existence of Griffith phase and spontaneous exchange bias. AC susceptibility measurement shows a glassy dynamic behaviour near ferromagnetic transition. Further, a re-entrant glassy dynamic state is seen at a low temperature around 40 K. Temperature-dependent resistivity shows semiconducting/insulating nature, which gets increased under the application of magnetic field, showing positive magnetoresistance. The dielectric study shows usual frequency-dependent step-like behaviour with a colossal dielectric constant near room temperature. The complex impedance study shows both grain and grain boundary contribute to the electrical properties. The observed properties suggest the material can be used for spintronic devices and high dielectric applications.

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Li, Chi-Ping, and Chih-Min Chuang. "Thermal and Dielectric Properties of Cyanate Ester Cured Main Chain Rigid-Rod Epoxy Resin." Polymers 13, no. 17 (August 30, 2021): 2917. http://dx.doi.org/10.3390/polym13172917.

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Thermal and dielectric properties of rigid-rod bifunctional epoxy resin 4,4-bis(2,3-epoxypropoxy) biphenyl epoxy (BP) and commercial epoxy resin diglycidyl ether of bisphenol A (DGEBA) were studied using differential scanning calorimeter (DSC), thermogravimetric analyzer (TGA), dynamic mechanical analyzer (DMA), thermal mechanical analyzer (TMA) and dielectric analyzer (DEA). These two epoxies were cured with cyanate ester hardener 2,2’-bis(4-cyanatophenyl) propane (AroCy B10). The BP/B10 system consisting of a rigid-rod structure exhibited better thermal properties than the DGEBA/B10 system with a flexible structure. Anisotropic BP/B10 (2:1) had the highest 5% weight loss temperature, the highest amount of residue and a smaller thermal expansion coefficient than the commercial DGEBA/B10 system. The BP/B10 system, which cured at the LC phase temperature, had higher Tg than the commercial DGEBA/B10 system, as found from dynamic mechanical analysis. The BP/B10 system also demonstrated better dielectric properties than the commercial DGEBA/B10 system when enough curing agent was provided.

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Lei, Yangxue, Mingzhen Xu, Mingli Jiang, Yumin Huang, and Xiaobo Liu. "Curing behaviors of cyanate ester/epoxy copolymers and their dielectric properties." High Performance Polymers 29, no. 10 (October 20, 2016): 1175–84. http://dx.doi.org/10.1177/0954008316672291.

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The curing behavior and dielectric properties of cyanate ester/epoxy (EP) with a latent initiator imidazole was investigated as a function of blend composition. Differential scanning calorimetry (DSC) was used to investigate the dynamic cure behavior of the blends. Multiheating rate DSC, peak fitting, and iso-conversion method were applied to analyze the curing kinetic parameters. Two distinct peaks were fitted from the dynamic DSC curve and the activation energies of each reaction varied with the increase of curing degrees. Fourier transform infrared spectra revealed that several reactions coexisted during the curing processes of cyanate and EP, resulting in the coexistence of the polymers and copolymers in the final composites. The dielectric properties of the composites were studied and the phenomenon that the dielectric constants for all of the composites are independent of frequency was observed. The thermal decomposition characteristics of the blends were investigated using thermogravimetric analysis. By increasing the content of EP, the thermal properties of the cured blends were improved to a small extent, while the char yield markedly decreased.

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Shi, Min Xian, Ming Zhang, Zhi Xiong Huang, and Yan Qin. "Effects of Silane Coupling Agent Treatment on Properties of PMN/EP Composites." Advanced Materials Research 160-162 (November 2010): 359–63. http://dx.doi.org/10.4028/www.scientific.net/amr.160-162.359.

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The PMN/EP composites were prepared by resin casting method from PMN powder pretreated with silane coupling agent KH-550. The microstructure of the PMN/EP composite was observed by SEM, the damping property and dielectric property of the composite were investigated by dynamic mechanical analyzer and impedance analyzer respectively. In the composite prepared with PMN powder pretreated by 1.5% silane coupling agent, much epoxy resin fragment is attached in the surface of PMN particles. When the silane coupling agent concentration is 1.5%, the composite shows the best damping property. Dielectric analyses suggest that the dielectric constant of the PMN/EP composite decreases with the increase of silane coupling agent content, however the dielectric loss increases with the increase of silane coupling agent content.

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Mkrtchian, Vanik E., and Hamlet G. Badalyan. "Dynamic dielectric and magnetic properties of a spontaneously polarized single layer of the polar dielectric." Physics Letters A 381, no. 41 (November 2017): 3580–83. http://dx.doi.org/10.1016/j.physleta.2017.09.019.

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Stephen, Ranimol, Sabu Thomas, K. V. S. N. Raju, Siby Varghese, Kuruvilla Joseph, and Zachariah Oommen. "Dynamic Mechanical and Dielectric Properties of Nanocomposites of Natural Rubber (NR), Carboxylated Styrene Butadiene Rubber (XSBR) Latices and their Blends." Rubber Chemistry and Technology 80, no. 4 (September 1, 2007): 672–89. http://dx.doi.org/10.5254/1.3548187.

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Abstract The viscoelastic and dielectric properties of nano structured layered silicates reinforced natural rubber (NR), carboxylated styrene butadiene rubber (XSBR) and their blends have been analyzed. The viscoelastic properties such as storage modulus, loss modulus, damping behavior and glass transition temperature of nano filled latices have been investigated. Upon the addition of filler, the storage modulus of nanocomposites was found to increase due to the enhancement in stiffness of the material. Due to the restricted mobility of polymer chain segments, the damping values decreased as a function of filler loading. An investigation of the viscoelastic properties revealed that there was a strong interaction between the polymer and the filler. Latex nanocomposites was characterized by X-ray diffraction technique. The enhanced d values indicated the intercalation of polymer chain into the layers of silicates. The dielectric properties of nanocomposites have been investigated as a function of frequency in the range of 50Hz–100KHz. The effect of frequency on dielectric permittivity (Ε′), dielectric loss (Ε″), dissipation factor (tan δ) and volume resistivity (ρv) of latex nanocomposite have been measured under alternating current. The dielectric permittivity of the samples was found to be higher upon the incorporation of nano fillers. The volume resistivity decreased due to the enhanced conductivity of filled samples.

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Xing, Zhaoliang, Chong Zhang, Haozhe Cui, Yali Hai, Qingzhou Wu, and Daomin Min. "Space Charge Accumulation and Decay in Dielectric Materials with Dual Discrete Traps." Applied Sciences 9, no. 20 (October 11, 2019): 4253. http://dx.doi.org/10.3390/app9204253.

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Charge trapping and de-trapping properties can affect space charge accumulation and electric field distortion behavior in polymers. Dielectric materials may contain different types of traps with different energy distributions, and it is of interest to investigate the charge trapping/de-trapping dynamic processes in dielectric materials containing multiple discrete trap centers. In the present work, we analyze the charge trapping/de-trapping dynamics in materials with two discrete traps in two cases where charges are injected continuously or only for a very short period. The time dependent trapped charge densities are obtained by the integration of parts in the case of continuous charge injection. In the case of instantaneous charge injection, we simplify the charge trapping/de-trapping equations and obtain the analytical solutions of trapped charge densities, quasi-free charge density, and effective carrier mobility. The analytical solutions are in good agreement with the numerical results. Then, the space charge dynamics in dielectric materials with two discrete trapping centers are studied by the bipolar charge transport (BCT) model, consisting of charge injection, charge migration, charge trapping, de-trapping, and recombination processes. The BCT outputs show the time evolution of spatial distributions of space charge densities. Moreover, we also achieve the charge densities at the same position in the sample as a function of time by the BCT model. It is found that the DC poling duration can affect the energy distribution of accumulated space charges. In addition, it is found that the coupling dynamic processes will establish a dynamic equilibrium rather than a thermodynamic equilibrium in the dielectric materials.

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Drozd-Rzoska, Aleksandra, Jakub Kalabiński, and Sylwester J. Rzoska. "Critical Model Insight into Broadband Dielectric Properties of Neopentyl Glycol (NPG)." Materials 17, no. 16 (August 21, 2024): 4144. http://dx.doi.org/10.3390/ma17164144.

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This report presents the low-frequency (LF), static, and dynamic dielectric properties of neopentyl glycol (NPG), an orientationally disordered crystal (ODIC)-forming material important for the barocaloric effect applications. High-resolution tests were carried out for 173K<T<440K, in liquid, ODIC, and solid crystal phases. The support of the innovative distortion-sensitive analysis revealed a set of novel characterizations important for NPG and any ODIC-forming material. First, the dielectric constant in the liquid and ODIC phase follows the Mossotti Catastrophe-like pattern, linked to the Clausius–Mossotti local field. It challenges the heuristic paradigm forbidding such behavior for dipolar liquid dielectrics. For DC electric conductivity, the prevalence of the ‘critical and activated’ scaling relation is evidenced. It indicates that commonly applied VFT scaling might have only an effective parameterization meaning. The discussion of dielectric behavior in the low-frequency (LF) domain is worth stressing. It is significant for applications but hardly discussed due to the cognitive gap, making an analysis puzzling. For the contribution to the real part of dielectric permittivity in the LF domain, associated with translational processes, exponential changes in the liquid phase and hyperbolic changes in the ODIC phase are evidenced. The novelty also constitutes tgδ temperature dependence, related to energy dissipation. The results presented also reveal the strong postfreezing/pre-melting-type effects on the solid crystal side of the strongly discontinuous ODIC–solid crystal transition. So far, such a phenomenon has been observed only for the liquid–solid crystal melting transition. The discussion of a possible universal picture of the behavior in the liquid phase of liquid crystalline materials and in the liquid and ODIC phases of NPG is particularly worth stressing.

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Drozd-Rzoska, Aleksandra, Jakub Kalabiński, and Sylwester J. Rzoska. "Preliminary Broadband Dielectric Spectroscopy Insight into Compressed Orientationally Disordered Crystal-Forming Neopentyl Glycol (NPG)." Materials 18, no. 3 (January 31, 2025): 635. https://doi.org/10.3390/ma18030635.

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This report presents the first results on broadband dielectric spectroscopy insights into ODIC-forming neopentyl glycol (NPG) under compression up to the GPa domain. Particular attention was paid to the strongly discontinuous phase transition: orientationally disordered crystal (ODIC)–solid crystal. The insights cover static, dynamic, and energy-related properties, namely evolutions of the dielectric constant, DC electric conductivity, and dissipation factor. Worth stressing are results regarding the pressure-related Mossotti catastrophe-type behavior of the dielectric constant, the novel approach to non-Barus dynamics, and the discussion on fundamentals of dissipation factor changes in NPG. The results presented in the given report also introduce new experimental evidence and model discussions regarding the nature of ODIC mesophase and discontinuous phase transitions. Notable is the significance of understanding the nature of the colossal barocaloric effect in NPG.

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35

Mozur, Eve M., and James R. Neilson. "Cation Dynamics in Hybrid Halide Perovskites." Annual Review of Materials Research 51, no. 1 (July 26, 2021): 269–91. http://dx.doi.org/10.1146/annurev-matsci-080819-012808.

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Hybrid halide perovskite semiconductors exhibit complex, dynamical disorder while also harboring properties ideal for optoelectronic applications that include photovoltaics. However, these materials are structurally and compositionally distinct from traditional compound semiconductors composed of tetrahedrally coordinated elements with an average valence electron count of silicon. The additional dynamic degrees of freedom of hybrid halide perovskites underlie many of their potentially transformative physical properties. Neutron scattering and spectroscopy studies of the atomic dynamics of these materials have yielded significant insights into their functional properties. Specifically, inelastic neutron scattering has been used to elucidate the phonon band structure, and quasi-elastic neutron scattering has revealed the nature of the uncorrelated dynamics pertaining to molecular reorientations. Understanding the dynamics of these complex semiconductors has elucidated the temperature-dependent phase stability and origins of defect-tolerant electronic transport from the highly polarizable dielectric response. Furthermore, the dynamic degrees of freedom of the hybrid perovskites provide additional opportunities for application engineering and innovation.

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36

Cohen, N., A. Greenbaum, Y. Feldman, and G. Marom. "Dynamic dielectric properties and the γ transition of bromine doped polyacrylonitrile." Express Polymer Letters 1, no. 10 (2007): 704–9. http://dx.doi.org/10.3144/expresspolymlett.2007.96.

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Zhang, Hongda, Hong Zhou, Guolong Liu, Jing Ge, and Liguo Jin. "Mechanical, dielectric, and dynamic mechanical properties of Al2O3–ATP/EP composites." Journal of Materials Science: Materials in Electronics 32, no. 23 (October 10, 2021): 27871–81. http://dx.doi.org/10.1007/s10854-021-07169-7.

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Cadène, A., B. Rotenberg, S. Durand-Vidal, J. C. Badot, and P. Turq. "Dielectric spectroscopy as a probe for dynamic properties of compacted smectites." Physics and Chemistry of the Earth, Parts A/B/C 31, no. 10-14 (January 2006): 505–10. http://dx.doi.org/10.1016/j.pce.2006.04.002.

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Wang, Rui, Congzhen Xie, Bin Gou, Huasong Xu, Shoukang Luo, Jiangang Zhou, and Leilei Zeng. "Preparation and properties of carbon‐based epoxy nanocomposites: Dynamic mechanical, dielectric, and thermal properties." Polymer Composites 41, no. 12 (August 13, 2020): 4974–82. http://dx.doi.org/10.1002/pc.25767.

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40

Berselli, Giovanni, Rocco Vertechy, Mitja Babič, and Vincenzo Parenti Castelli. "Dynamic modeling and experimental evaluation of a constant-force dielectric elastomer actuator." Journal of Intelligent Material Systems and Structures 24, no. 6 (August 28, 2012): 779–91. http://dx.doi.org/10.1177/1045389x12457251.

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Constant-force actuators based on dielectric elastomers can be obtained by coupling a dielectric elastomer film with particular compliant frames whose structural properties must be carefully designed. In any case, the practical achievement of a desired force profile can be quite a challenging task owing to the time-dependent phenomena, which affect the dielectric elastomer’s electromechanical response. Within this scenario, a hyperviscoelastic model of a rectangular constant-force actuator is reported. The model, based on the bond graph formalism, can be used as an engineering tool when designing and/or controlling actuators that are expected to work under given nominal conditions. Simulations and experimental results are provided, which predict the system response to fast changes in activation voltage and actuator position as imposed by an external user.

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Mir, Showkat H., Sharad B. Pillai, Narayan N. Som, Prakash C. Jha, and Prafulla K. Jha. "First Principles Study of Electronic, Lattice Dynamic, and Thermal Properties of Single Layer Phosphorene." Advanced Materials Research 1141 (August 2016): 210–14. http://dx.doi.org/10.4028/www.scientific.net/amr.1141.210.

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Heat removal is a fundamental issue for continuous progress in the electronic industry and for the thermal management in electronic devices. Materials with high thermal conductivity may help in the elimination of excess heat more efficiently which is necessary for improving the device performance. Phosphorene is a 2D material that has been recently exfoliated mechanically. Using density functional theory, we presented the electronic, lattice dynamic, thermal and dielectric properties of phosphorene. It is found that sound velocity is larger along the zigzag direction signifying anisotropic thermal behaviour. The macroscopic dielectric constant calculated is also found to be anisotropic in nature. Finally, the variation of entropy and specific heat with temperature is obtained.

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Wang, Huihui, Ling Wang, Hui Xie, Chenyue Li, Shumeng Guo, Meng Wang, Cheng Zou, Dengke Yang, and Huai Yang. "Electrically controllable microstructures and dynamic light scattering properties of liquid crystals with negative dielectric anisotropy." RSC Advances 5, no. 42 (2015): 33489–95. http://dx.doi.org/10.1039/c5ra02516h.

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Pawlaczyk, Czesław, and Ryszard Jakubas. "On the Dynamic Dielectric Behaviour of (CH3NH3)3Sb2Br9(MABA)." Zeitschrift für Naturforschung A 58, no. 4 (April 1, 2003): 189–93. http://dx.doi.org/10.1515/zna-2003-0401.

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The complex electric permittivity of ferroelectric (CH3NH3)3Sb2Br9 (MABA) single crystals has been measured in the frequency range 1 kHz - 3 GHz between 15 and 300 K. The dynamic dielectric behaviour of MABA is determined by the properties of high frequency relaxation of Cole-Cole type. It is thermally activated and characterised by a relatively small activation energy. The phase transitions at 168 and 134 K influence the amplitude of the relaxation (Δε) without any important changes in the relaxation frequency.

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Chueangchayaphan, Wannarat, Piyawadee Luangchuang, and Narong Chueangchayaphan. "High Performance of Titanium Dioxide Reinforced Acrylonitrile Butadiene Rubber Composites." Polymers 14, no. 23 (December 2, 2022): 5267. http://dx.doi.org/10.3390/polym14235267.

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Recently, dielectric elastomer actuators (DEA) have emerged as one of the most promising materials for use in soft robots. However, DEA needs a high operating voltage and high mechanical properties. By increasing the dielectric constant of elastomeric materials, it is possible to decrease the operating voltage required. Thus, elastomeric composites with a high dielectric constant and strong mechanical properties are of interest. The aim of this research was to investigate the effect of titanium dioxide (TiO2) content ranging from 0 to 110 phr on the cure characteristics, and physical, dielectric, dynamic mechanical, and morphological properties of acrylonitrile butadiene rubber (NBR) composites. The addition of TiO2 reduced the scorch time (ts1) as well as the optimum cure time (tc90) but increased the cure rate index (CRI), minimum torque (ML), maximum torque (MH), and delta torque (MH − ML). The optimal TiO2 content for maximum tensile strength and elongation at break was 90 phr. Tensile strength and elongation at break were increased by 144.8% and 40.1%, respectively, over pure NBR. A significant mechanical property improvement was observed for TiO2-filled composites due to the good dispersion of TiO2 in the NBR matrix, which was confirmed by scanning electron microscopy (SEM). Moreover, incorporating TiO2 filler gave a higher storage modulus, a shift in glass transition temperature (Tg) to a higher temperature, and reduced damping in dynamic mechanical thermal analysis (DMTA). The addition of TiO2 to NBR rubber increased the dielectric constant of the resultant composites in the tested frequency range from 102 to 105 Hz. As a result, TiO2-filled NBR composite has a high potential for dielectric elastomer actuator applications.

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Špitalský, Zdenko, Ján Kratochvíla, Katarína Csomorová, Igor Krupa, Manuel P. F. Graça, and Luis C. Costa. "Mechanical and Electrical Properties of Styrene-Isoprene-Styrene Copolymer Doped with Expanded Graphite Nanoplatelets." Journal of Nanomaterials 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/168485.

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The molecular dynamics of a triblock copolymer and of expanded graphite nanoplatelets were investigated. Composites were prepared using the solution technique. The effects of filler addition and of filler-matrix interactions were investigated using dielectric relaxation spectroscopy (DRS) and dynamic mechanical analysis (DMA). Only one relaxation was observed by DRS, which was associated with the relaxation of the main polymer chain. Both DRS and DMA demonstrated that the addition of the filler does not cause a significant change in either the temperature of the relaxation or its activation energy, which suggests the presence of weak interactions between the filler and matrix. The storage modulus of the composites increased with increasing filler content. The composite containing 8% filler exhibited a storage modulus increase of approximately 394% in the rubber area. Using the DC electrical conductivity measurements, the electrical percolation threshold was determined to be approximately 5%. The dielectric permittivity and conductivity in the microwave region were determined, confirming that percolating behavior and the critical threshold concentration.

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Lecoublet, Morgan, Mohamed Ragoubi, Nathalie Leblanc, and Ahmed Koubaa. "Investigation of Thermomechanical and Dielectric Properties of PLA-CA 3D-Printed Biobased Materials." Journal of Composites Science 8, no. 6 (May 23, 2024): 197. http://dx.doi.org/10.3390/jcs8060197.

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Renewable dielectric materials have attracted the attention of industries and stakeholders, but such materials possess limited properties. This research focused on studying polylactic acid (PLA)/cellulose acetate (CA) blends produced by 3D printing to facilitate their integration into the electrical insulation field. The dielectric findings showed that a blend containing 40% of CA by weight had a dielectric constant of 2.9 and an electrical conductivity of 1.26 × 10−11 S·cm−1 at 100 Hz and 20 °C while exhibiting better mechanical rigidity in the rubbery state than neat PLA. In addition, it was possible to increase the electrical insulating effect by reducing the infill ratio at the cost of reduced mechanical properties. The differential scanning calorimetry, broadband dielectric spectroscopy, and dynamic mechanical analysis results showed that the PLA plasticizer reduced the energy required for PLA relaxations. These preliminary results demonstrated the benefits of using a combination of PLA, CA, and 3D printing for electrical insulation applications.

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Hu, Xiaofeng, Jianping Zhang, Ming Wei, and Yingying Wang. "Research on the Induced Electrostatic Discharge of Spacecraft Typical Dielectric Materials under the ESD Pulse Irradiation." Materials 15, no. 6 (March 13, 2022): 2115. http://dx.doi.org/10.3390/ma15062115.

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Based on polyimide (PI), epoxy resin (EP), polytetrafluoroethylene (PTFE) typical dielectric materials used in spacecraft, a research platform for charge-discharge experiment under strong field was established. The influence of irradiation field strength, beam energy, dielectric thickness, etc., on electrostatic discharge characters of dielectric materials were studied and summarized. The results show that with the increase of field strength, the frequency of induced electrostatic discharge increases, the accumulated charge on the dielectric surface decreases, and the dielectric surface potential decreases; Under the same conditions, PI has the lowest discharge frequency and the highest surface dynamic balance potential. The thicker the dielectric material, the lower the discharge frequency, the higher the surface dynamic equilibrium potential; The shape and size of the background electrodes also affect the discharge frequency. When the area is the same, the sharper the electrode edge, the higher the discharge frequency. When the shape is the same, the larger the grounding area, the higher the discharge frequency. By proposing the induced discharge test method, the function mechanism of spatial environmental factors on the electrostatic discharge of typical dielectric materials are obtained. Comparative analysis on electrostatic properties of different dielectric materials can provide data reference and technical support for spacecraft electrostatic safety and protection.

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Blatsi, Chryssanthi, Anastasios C. Patsidis, and Georgios C. Psarras. "Dielectric Properties and Energy Storage of Hybrid/Boron Nitride/Titanium Carbide/Epoxy Nanocomposites." Journal of Composites Science 6, no. 9 (September 7, 2022): 259. http://dx.doi.org/10.3390/jcs6090259.

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In this study, hybrid boron nitride (BN)/titanium carbide (TiC)/epoxy resin composite nanodielectrics were manufactured and characterized. Their morphological and structural characterization was conducted via scanning electron microscopy (SEM) images and X-ray diffraction (XRD) patterns, whereas the dielectric behavior was studied by means of broadband dielectric spectroscopy (BDS). Dielectric measurements were carried out from 30 to 160 °C and from 10−1 to 106 Hz, respectively. The dielectric results revealed the existence of three relaxation mechanisms, which from high to low frequencies, at constant temperature, refer to re-arrangement of polar-side groups (β-relaxation) of the macromolecular chains, transition from glassy to rubbery state of the amorphous polymer matrix (α-relaxation) and interfacial polarization (IP) between the polymer matrix and the nanofillers. It was found that, in general, nanodielectrics exhibited enhanced dielectric properties mainly due to the high dielectric permittivity of TiC and the fine dispersion of the fillers, confirmed also by the SEM images. Dynamic analysis conducted for the α-relaxation showed a Vogel–Fulcher–Tammann dependence on temperature. The ability of energy storing of the nanocomposites was examined via their energy density. Optimum performance is exhibited by the 5 phr TiC/1 phr BN/epoxy nanocomposite, reaching an energy storing ability nine times greater than the unfilled matrix.

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Shareef, S. Noormohammad, Boya Palajonnala Narasaiah, W. Madhuri, K. Vagdevi, and Ramnarayan. "Carbon Quantum dots doped Chitosan/HPMC nano composites and their Functional, Structural, Morphological, Dielectric and Tensile properties." E3S Web of Conferences 430 (2023): 01149. http://dx.doi.org/10.1051/e3sconf/202343001149.

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Carbon Quantum Dots (CQDs) were prepared from modified hydrothermal method using Citric acid and ethane diamine as a source material. The synthesized CQDs were characterized by UV-Vis spectroscopy, Fluorescence Studies (FL), Atomic force microscopy (AFM). The particle size is conformed from Dynamic Light Scattering (DLS) analysis. The synthesized CQDs were doped in polymer blend with various weight percentages and the further characterizations were carried out for X-Ray Diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), dielectric properties, and tensile properties at room temperature and higher temperatures with the help of Universal Testing Mission (UTM). The dielectric behavior of Chitosan/HPMC/CQDs polymer nanocomposites (PNCs) were studied in the range of 50 Hz to 5 MHz frequency and the temperature ranging from 30-100 °C, using LCR meter. The dielectric constant (ε'), dielectric loss (ε') are found with different wt% of CQDs in the PNCs.

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Fortes, Santiago P., Robert P. Lipton, and Stephen P. Shipman. "Sub-wavelength plasmonic crystals: dispersion relations and effective properties." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (February 10, 2010): 1993–2020. http://dx.doi.org/10.1098/rspa.2009.0542.

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We obtain a convergent power series expansion for the first branch of the dispersion relation for sub-wavelength plasmonic crystals consisting of plasmonic rods with frequency-dependent dielectric permittivity embedded in a host medium with unit permittivity. The expansion parameter is η = kd =2 πd / λ , where k is the norm of a fixed wavevector, d is the period of the crystal and λ is the wavelength, and the plasma frequency scales inversely to d , making the dielectric permittivity in the rods large and negative. The expressions for the series coefficients (also called dynamic correctors) and the radius of convergence in η are explicitly related to the solutions of higher order cell problems and the geometry of the rods. Within the radius of convergence, we are able to compute the dispersion relation and the fields and define dynamic effective properties in a mathematically rigorous manner. Explicit error estimates show that a good approximation to the true dispersion relation is obtained using only a few terms of the expansion. The convergence proof requires the use of properties of the Catalan numbers to show that the series coefficients are exponentially bounded in the H 1 Sobolev norm.

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Journal articles on the topic 'Dynamic dielectric properties'

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