Lichtenecker Equation Research Articles

Effect of BaTiO3 Filler Modification with Multiwalled Carbon Nanotubes on Electric Properties of Polymer Nanocomposites.

Two ranges of dielectric permittivity (k) increase in polymer composites upon the modification of BaTiO3 filler with multiwalled carbon nanotubes (MWCNTs) are shown for the first time. The first increase in permittivity is observed at low MWCNT content in the composite (approximately 0.07 vol.%) without a considerable increase in dielectric loss tangent and electrical conductivity. This effect is determined by the intensification of filler-polymer interactions caused by the nanotubes, which introduce Brønsted acidic centers on the modified filler surface and thus promote interactions with the cyanoethyl ester of polyvinyl alcohol (CEPVA) polymer binder. Consequently, the structure of the composites becomes more uniform: the permittivity increase is accompanied by a decrease in the lacunarity (nonuniformity) of the structure and an increase in scale invariance, which characterizes the self-similarity of the composite structure. The permittivity of the composites in the first range follows a modified Lichtenecker equation, including the content of Brønsted acidic centers as a parameter. The second permittivity growth range features a drastic increase in the dielectric loss tangent and conductivity corresponding to the percolation effect with the threshold at 0.3 vol.% of MWCNTs.

Dielectric Properties of Polytetrafluoroethylene/CaCu3Ti4O12 Composites

Polymer-based composite was investigated by embedding calcium copper titanate (CaCu3Ti4O12; CCTO) fillers into polytetrafluoroethylene(PTFE) matrix. The dielectric performances of the composite were investigated within the frequency range from 100 Hz to 1 MHz. It is indicated that dielectric permittivity (e) and dielectric loss (tanδ) increase gradually as the filler content increases. Dielectric permittivity for the composite with 50 vol% CCTO filler loading is 33.5, approximately 16 times higher than that of pure PTFE (e = 2.1) at 100 Hz. As the frequency increases, the dielectric loss decreases rapidly and reaches stability, and then remains low when the frequency rises to 1 MHz. The values for dielectric permittivity and dielectric loss in the microwave frequency (8-13 GHz) are lower than that in low frequency of 10 kHz for the composites because of different polarization modes. Several theoretical models were implemented to compare the experimental results with the theoretical calculations and the modified Lichtenecker equation was found to fit the best.

The dielectric properties and dielectric mechanism of perovskite ceramic CLST/PTFE composites

Polytetrafluorethylene (PTFE) composites filled with perovskite (Ca,Li,Sm)TiO3 (CLST) dielectric ceramic of various volume fractions filler up to 60% were prepared. The effects of volume fraction of ceramic filler on the microstructure and dielectric properties of the composites have been investigated. A comparative study of dielectric properties of experiment and modeling analysis has been carried out at high frequencies for the CLST/PTFE composites. The results indicate that both the dielectric constant and the dielectric loss increase with the filler. The CLST/PTFE composite with 40% ceramic has exhibited good dielectric properties: e r = 7.92 (~10 GHz), tan δ = 1.2 × 10−3 (~10 GHz), and τ f = −45 ppm/°C. The dielectric properties are obviously better than most composites reported previously at high frequencies in the aspects of dielectric loss and thermal stability. The dielectric constant and dielectric loss of composites predicted by the Rother–Lichtenecker equation and the general mixing model are in good agreement with the experiment data when the volume fraction of ceramic is less than 40%. When the volume fraction of the ceramic is more than 40%, the deviation occurs. By introducing the correction factor, the theoretical values of the dielectric constant agrees well with the experimental values.

Investigation of the composites of epoxy and micro-scale BaTi4O9 ceramic powder as the substrate of microwave communication circuit

BaTi4O9 (BT4) ceramic was sintered at 1270 °C and ground into fine ceramic powder with average particle size of about 3 μm. After that, the micro-scale BT4 ceramic powder with different concentrations (from 5 to 70 wt%) was mixed with O-Cresol Novolac (OCN) epoxy resin to form flexible epoxy-BT4 composites. The dielectric constant of epoxy-BT4 composites was first measured from 100 kHz to 100 MHz at room temperature by using the “plate method”. The measured dielectric constants of epoxy-BT4 composites were compared with the values predicted by Lichtenecker equation. We would show that the measured results were well fitted with the predicted values. In order to investigate the composites of epoxy and micro-scale BT4 ceramic powder for the application of microwave communication, the dielectric constants of epoxy-BT4 composites were also measured from 1 to 10 GHz at room temperature by using a “square cavity resonator” method. As the measured frequencies were at the range of GHz, the dielectric constants of epoxy-BT4 composites were almost unchanged with the increase of frequency. It conjectured that epoxy-BT4 composites could be used as the flexible substrates to fabricate the microwave filters and antennas.

Dielectric properties of PTFE loaded with micro- and nano-Sm2Si2O7 ceramics

The present study compares the dielectric and thermal properties of PTFE loaded with Sm2Si2O7 filler of varying filler size. The composites were prepared by powder processing technique followed by hot pressing. The variation of the dielectric properties with filler content (0–0.25 vf) was studied at 1 MHz and 9 GHz. The microstructural study using scanning electron microscopy showed that the nano size fillers were uniformly dispersed in the matrix as compared to that of the micron size. The PTFE loaded with 0.25 vf micro Sm2Si2O7 composites showed a relative permittivity and dielectric loss of 3.51, 0.00155 whereas for nano Sm2Si2O7 composites with same volume fraction the values were 4.35, 0.04861 respectively at 1 MHz. The experimental values of relative permittivity were compared with various theoretical models, and the modified Lichtenecker equation and Effective Medium Theory were found to be in good agreement for both the composites even for higher filler content. Furthermore, the comparison of thermal expansion coefficient of the PTFE/Sm2Si2O7 composites implies a much lower CTE value for nano fillers.

Room-temperature fabrication of microwave dielectric Li2MoO4–TiO2 composite ceramics

This paper presents the incorporation of large amounts of insoluble additives into a Li2MoO4 ceramic matrix fabricated with a room-temperature densification method. Li2MoO4–TiO2 composite ceramics were fabricated by a method based on the water-solubility of Li2MoO4, where the densification occurs at room temperature during sample pressing and is followed by further post-processing at 120°C to remove residual water. As the amount of added rutile TiO2 rose from 10 to 30vol%, relative permittivity and loss tangent values at ~9GHz increased from 6.9 to 10.1 and from 1.1×10−3 to 3.8×10−3, respectively, and thermal coefficient of permittivity decreased from 180ppm/°C to −170ppm/°C. The Lichtenecker equation used in the analysis of relative permittivity was applicable in this study for Li2MoO4–TiO2 composite ceramics with up to 20vol% of TiO2. However, with 25 and 30vol% additions of TiO2, correspondence decreased due to increased porosity in the composites. The low post-processing temperature made this material feasible for Ag electrode integration without formation of unwanted extra phases.

Core–Shell Approach to Control Acid–Base Properties of Surface of Dielectric and Permittivity of Its Composite

Abstract Hybrid organic–inorganic composites comprising cyanoethyl ester of poly(vinyl alcohol) (CEPVA) and submicron-sized barium titanate with a core–shell structure are studied. For the first time, the permittivity of obtained composites was studied in correlation with the acid–base properties of the filler and controlled via the filler surface modification by the formation of core–shell structures using sol–gel and plasma processes. The permittivity is found to grow with the increase in the content of Brønsted basic centers on the filler surface due to enhanced interactions with acid groups of polymer. This effect is especially prominent in the case of silica nanocoating deposited onto BaTiO3 surface. The permittivity of the studied composites is approximated by a modified Lichtenecker equation based on permittivity values of individual components, their concentrations, and a specific parameter characterizing their acid–base interaction.

Preparation and wide-frequency dielectric properties of (Ba0.5Sr0.4Ca0.1)TiO3/poly(vinylidene fluoride) composites

Poly(vinylidene fluoride) (PVDF) and (Ba0.5Sr0.4Ca0.1)TiO3 (BSCT) are used as matrix and fillers, respectively, to prepare polymer functional composites by solution casting with N,N-dimethyl formamide as a solvent. It is found that the addition of BSCT has significant influence on the crystallization, melting, and glass transition behaviors of the PVDF matrix. The dielectric properties of the BSCT/PVDF composites are studied over a wide frequency range from 100 Hz to 1 GHz and a wide temperature range from −50 °C to 100 °C to explore the dependences of frequency and temperature. High dielectric constant (ɛ) up to 132 at 100 Hz and low dielectric loss (tan δ) down to 0.0045 at 1 GHz are achieved for the BSCT/PVDF composites. The obtained data of ε are also theoretically fit by different models, and the modified Lichtenecker equation and Jayasundere-Smith equation show the best match.

Thermal and dielectric behavior of flexible polycarbonate/lead zirconate titanate composite system

ABSTRACTPolycarbonate (PC)/Lead Zirconate Titanate (PZT) composites were prepared using solution mixing method followed by hot pressing. The volume fraction of PZT particles was varied from 0 to 27.5%. SEM showed good dispersion of PZT in the PC matrix. XRD confirmed the perovskite structure of PZT and amorphous structure of polycarbonate. The dielectric constant of the composites measured at 1 kHz, increased ∼3.5‐fold compared with pure PC. The modified Lichtenecker equation agreed well with the experimental data. There was no dispersion in the dielectric constant of the composites for the frequency range of 1 kHz to 10 MHz. However, at frequencies higher than 10 MHz significant drop in dielectric constant was observed. The dissipation factor of the composites was found below 0.02. However, above 1 MHz, an abrupt increment in the dissipation factor was observed. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 39913.

Dielectric properties of 0.25(BZT–BCT)–0.75[(1−x)PVDF–xCCTO] (x=0.02, 0.04, 0.06, 0.08 and 0.1) composites for embedded capacitor applications

Abstract 0.25{0.5[Ba(Zr 0.2 Ti 0.8 )O 3 ]–0.5[(Ba 0.7 Ca 0.3 )TiO 3 ]/[BZT–BCT]}–0.75[(1 − x )(PVDF)– x CaCu 3 Ti 4 O 12 /(CCTO)] 0–3 composites (where x = 0.02, 0.04, 0.06, 0.08 and 0.1 volume fractions) were prepared by two step mixing and uniaxial hot-press method. The structural, micro structural and dielectric properties have been investigated and discussed in detail. There was an increase in relative permittivity ( e r ) of the composites with the increase in the volume fractions of the CCTO ceramics up to x = 0.08, and beyond it there was a decrease in e r . At room temperature (RT) and at 1 kHz frequency, [0.25(BZT–BCT)–0.69(PVDF)–0.06(CCTO)] composite showed a highest e r ∼ 90, making it suitable for embedded capacitor applications. Experimental data were fitted to several theoretical equations to find the equation useful for the prediction of the effective dielectric constant of the studied composites. The Lichtenecker equation, Yamada model and EMT models were found to be useful for the prediction of the effective dielectric constant of studied composites.

Measuring the frequency-dependent dielectric properties of microwave composites using simple measurement methods

BaTi4O9 (BT4) ceramic was sintered at 1270°C and ground into fine ceramic powder with an average particle size of 3μm, then the BT4 powder was mixed with O-Cresol Novolac (OCN) epoxy resin to form epoxy-BT4 microwave composites. Using the plate method, the dielectric constants of the epoxy-BT4 microwave composites were measured from 100kHz to 100MHz at room temperature, then from 20°C to 140°C at 1MHz. The measured dielectric constants were fitted to the values predicted by the Lichtenecker equation. The dielectric constants of the epoxy-BT4 microwave composites were also measured from 1GHz to 10GHz at room temperature using the “square cavity resonator” method. In the GHz range, the dielectric constants of the composites were almost unchanged. It is conjectured that in both measurement frequency ranges, dielectric relaxation was nonexistent in both the BT4 ceramic powder and the epoxy-BT4 composites.

Dielectric, mechanical and thermal properties of polymer/BaTiO3 composites for embedded capacitor

Barium titanate (BaTiO3) filled polymethylmethacrylate (PMMA) composites were prepared using the simple solution method followed by hot pressing. The content of BaTiO3 was varied from 0 to 65vol.%. Scanning electron microscopy showed good dispersion and adhesion of BaTiO3 with the PMMA matrix. The dielectric constant of the composites increased significantly. There was weak dispersion in the dielectric constant of the composites (up to 45vol.%) with frequency between 100Hz and 15MHz. The dissipation factor of the composites increased from 0.021 for pure PMMA to 0.029 for 45vol.% composites. However, 65vol.% composite showed dispersion in dielectric constant with increasing frequency and higher dissipation factor. The Lichtenecker equation agreed well with the experimental data. The microhardness and the glass transition temperature of the composites increased approximately 4.7-fold and 42°C, respectively, compared to pure PMMA. The CTE of the 65vol.% composite is close to that of copper.

THE USE OF DIELECTRIC MIXTURE EQUATIONS TO ANALYZE THE DIELECTRIC PROPERTIES OF A MIXTURE OF RUBBER TIRE DUST AND RICE HUSKS IN A MICROWAVE ABSORBER

A change in the relative proportions of a mixture of rubber tire dust and rice husks will cause a change in the mixture's electrical permittivity and its ability to absorb electromagnetic energy. An open- ended coaxial probe was used in conjunction with three dielectric mixture equations (the Kraszewski equation, the Landau equation and the Lichtenecker equation) to obtain the dielectric properties of a mixture of rubber tire dust and rice husks (RTDRH) over the frequency range of 7GHz to 13GHz. Lichtenecker's equation for dielectrics proved to be a useful practical formulation for determining the efiective permittivity of homogeneous dielectric mixtures. The efiectiveness of these dielectric mixture equations in determining the efiective permittivity of RTDRH was investigated in this study. A newly developed mixture equation was derived based on these dielectric

Fabrication and Properties of Novel Polyetheretherketone/Barium Titanate Composites with Low Dielectric Loss

Dielectric, thermal, and microhardness properties of high-performance barium titanate (BaTiO3)-filled polyetheretherketone (PEEK) composites were studied. BaTiO3 was varied from 0 vol.% to 67 vol.% in the PEEK matrix. The dielectric constant of the composites measured at 1 MHz increased approximately 14-fold. There was no dispersion in the dielectric constant with frequency between 10 kHz and 15 MHz. The Lichtenecker equation and modified Lichtenecker equation agreed well with the experimental data. The dissipation factor of the composites varied from 0.0056 to 0.0096. Scanning electron microscopy showed uniform dispersion of BaTiO3 in the matrix. The microhardness of the composites increased by more than 2.5-fold compared with pure PEEK. The coefficient of thermal expansion measured below and above the glass-transition temperature was reduced by up to 56%. These results make these composites promising candidate high-temperature organic substrates.

Photoacoustic measurement of thermal properties of polystyrene metal oxide composites

Thermal properties (diffusivity, effusivity and conductivity) of polystyrene filled with low content of metal oxide (ZnO and MnO) particles are measured using heat transmission configuration of photoacoustic technique. The results show that ZnO changes thermal transport properties of polymer more effectively than MnO. The obtained data of the thermal conductivity are well explained by Lichtenecker's equation for thermal conductivity of two phase system. The experimental values of thermal conductivity of the composites have been used to estimate thermal conductivity of metal oxides. The data presented here show that this method is sensitive enough to detect variations in thermal properties of polymers due to addition of slight amount of particulate solids.

A comparative approach to predicting effective dielectric, piezoelectric and elastic properties of PZT/PVDF composites

Abstract The present study addresses the problem of quantitative prediction of effective relative permittivity, dielectric loss factor, piezoelectric charge coefficient, and Young's modulus of PZT/PVDF diphasic ceramic–polymer composite as a function of volume fraction of PZT in the different compositions. Theoretical results for effective relative permittivity derived from several dielectric mixture equations like those of Knott, Rother–Lichtenecker, Bruggeman, Maxwell–Wagner–Webmann–Skipetrov or Dias–Dasgupta, Furukawa, Lewin, Wiener, Jayasundere–Smith, Modified Cule–Torquato, Taylor, Poon–Shin and Rao et al. were fitted to the experimental data taken from previous works of Yamada et al. Similarly, the results for effective piezoelectric coefficient and Young's modulus, derived from different appropriate equations were fitted to the corresponding experimental data taken from the literature. The study revealed that only a few equations like modified Rother–Lichtenecker equation, Dias–Dasgupta equation and Rao equation for dielectric and piezoelectric properties while the four new equations developed in the present study of elastic property (Young's modulus) well fitted the corresponding experimental results. Further, the acceptable data put to various regression analyses showed that in most of the cases the third order polynomial regression analysis provided more acceptable fits.

The development of prediction method for the permittivity of epoxy/(Ba0.9Sr0.1)(Ti0.9Zr0.1)O3 composites

The relative permittivity of O-cresol Novolac epoxy resin/(Ba0.9Sr0.1)(Ti0.9Zr0.1)O3 (epoxy/BSTZ) composites with various contents of BSTZ ceramic powder was measured at 10 kHz to 1 MHz. As the content of BSTZ ceramic powder increases from 0 to 70 wt%, the permittivity increases from 5.72 to 25.23. Four different mixing rules are used to predict the variation of permittivity of epoxy/BSTZ composites, and the Lichtenecker equation fits the measured results. The permittivity of epoxy/BSTZ composites slightly increases as the measured temperature increases, and is unchanged when the measured temperatures are higher than the Curie temperature of BSTZ ceramic. This research proves that we can develop the epoxy/BSTZ composites with characteristics of stable temperature and frequency dependence.

Measuring the relative permittivity of polyetherimide/(Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 composites from 10 kHz to 12 GHz

The relative permittivity of polyetherimide-(Ba0.8Sr0.2)(Ti0.9Zr0.1)O3 (PEI-BSTZ) composites is measured from 10 kHz to 1 MHz using plate method. As the content of BSTZ filler is less than 18 vol %, the experimental values are fitted to the values predicted by Lichtenecker equation. As the content is more than 18 vol %, the measured relative permittivity of PEI-BSTZ composites is higher than the predicted values. The relative permittivity of PEI-BSTZ composites is measured at 1–12 GHz using “square cavity resonator” method. Measured at gigahertz, the relative permittivity of PEI-BSTZ composites is almost unchanged.

Analysis of bread dielectric properties using mixture equations

Breads are prone to rapid microbial spoilage, particularly mold growth. In order to develop in-package pasteurization treatments based on radio frequency or microwave energy, a combined open-ended coaxial probe and mixture equation method was used to obtain bread dielectric properties over the frequency range of 1-1800 MHz and the temperature range of 25 °C–85 °C. Influences of frequency, moisture content and temperature on bread dielectric properties were analyzed. The Lichtenecker Equation (LE) was suited for calculating dielectric constant, and the Landau and Lifshitz, Looyenga Equation (LLLE) for dielectric loss factor of bread. Penetrations of both RF and microwave energies decrease with increasing temperature and moisture content. Overall, RF energy has several times the penetration in white bread than microwave energy.

Microwave Dielectric Properties of Rutile Filled PEEK Composites

Ceramic-filled PEEK composites were prepared by sigma mixing followed by thermolamination. Rutile-grade titanium dioxide, particle size less than 5 μm, was used as the particulate filler in the PEEK matrix to tailor the dielectric properties of the composite matrix. The dispersion of the particular filler in the PEEK matrix was studied using scanning electron microscopy. The dielectric properties of the PEEK/TiO2 composite materials were measured in the low frequency region up to 13 MHz using an impedance analyzer. Dielectric properties in the microwave region were measured using cavity perturbation technique to evaluate the use of the composites as packaging material. Experimental results were compared with theoretically predicted values using the Lichtenecker equation. The present study shows that temperature-stable packaging materials can be realized in the PEEK/TiO2 systems by judiciously controlling the ceramic filler concentration.