Nicola Bowler

Designing dielectric loss at microwave frequencies using multi-layered filler particles in a composite

Microwave-absorbing materials find application in telecommunications, microwave heating and for representing the behavior of biological tissue in the presence of microwave radiation. Commonly, such materials are formed using ferromagnetic filler particles and rely on the phenomenon of ferromagnetic resonance for absorption of microwaves. Dielectric loss at microwave frequencies can be engineered through creating a phase lag, with respect to the applied electric field, of the movement of free charges in a composite formed using metal-coated filler particles. These materials can be engineered to be less dense and, therefore, more lightweight than those formed with ferromagnetic fillers, which is an advantage in some applications. Furthermore, theory shows that the frequency of maximum absorption can be tailored by selecting the conductivity and thickness of the particle coating although, in practice, it may be difficult to fabricate particles with tightly controlled physical parameters. In this work, theories for calculating complex permittivity of composites with layered filler particles are reviewed, and experimental observations of dielectric relaxation in composites formed by dispersing tungsten-coated glass bubbles in paraffin wax are shown

Electrical conductivity measurement of metal plates using broadband eddy-current and four-point methods

Electrical conductivity of metal plates is measured by two distinct methods and the uncertainty associated with each method is evaluated. First, the impedance of an air-cored eddy-current coil is measured in the frequency range 100 Hz to 20 kHz. Corrections are made to account for the fact that the coil is not a pure inductor but exhibits finite resistance and capacitance in and between the windings. Then, the conductivity of brass and stainless steel plates is determined with 3 and 2% uncertainty (68% confidence level) by seeking the best fit (least-mean-square error) between experimental measurements of coil impedance and values calculated theoretically. The residual error in the fitting process is found to be the main indicator of uncertainty in the conductivity measurement. Second, four-point alternating current potential drop measurements are made on the same samples in the frequency range 1–100 Hz. Conductivity is determined from these measurements by means of a simple analytic formula, valid in a quasi-static regime, with an uncertainty approximately 0.5%. The main source of uncertainty in the four-point conductivity measurement is scatter in the voltage measurements. Both of these techniques give rise to smaller uncertainties in the measurement of conductivity than a MIZ-21A eddy-current instrument (2% and 40% for brass and stainless steel, respectively) and without the need for calibration specimens. In addition, the four-point approach is independent of magnetic permeability below a certain characteristic frequency and can be used to measure conductivity of ferrous metals. As an example, the conductivity of a spring steel plate is also determined.

Dielectric relaxation in metal-coated particles: the dramatic role of nano-scale coatings

Insulating materials filled with conducting particles permit tailoring of electrical, electromagnetic and thermal properties of the resulting composite. When the filler particles are small and metallic, a dielectric relaxation due to interfacial polarization is commonly observed at optical or smaller wavelengths. Here, experimental results are presented in which the dielectric relaxation is shifted to microwave frequencies as a result of using metal-coated dielectric particles with a nano-scale coating thickness. The results are analysed in the context of effective medium theory adapted for multi-layer particles. Such a large shift in relaxation frequency, compared with that for a similar composite with solid metal filler particles, is shown to be a function of both the coating geometry and a thin-film-related reduction in the conductivity of the metal. The observed broadening of the relaxation peak is attributed to non-uniformity of the coating thickness and a consequent distribution of coating conductivity.

Frequency-Dependence of Relative Permeability in Steel

A study to characterize metal plates by means of a model‐based, broadband, four‐point potential drop measurement technique has shown that the relative permeability of alloy 1018 low‐carbon steel is complex and a function of frequency. A magnetic relaxation is observed at approximately 5 kHz. The relaxation can be described in terms of a parametric (Cole‐Cole) model. Factors which influence the frequency, amplitude and breadth of the relaxation, such as applied current amplitude, sample geometry and disorder (e.g. percent carbon content and surface condition), are considered.

Theory of four-point alternating current potential drop measurements on a metal half-space

An analytic expression describing the complex voltage measured between the pickup points of a four-point probe, in contact with the surface of a half-space conductor, is derived. The driving current is assumed to be time harmonic. There are two contributions to the measured voltage. One arises from the potential drop due to electric current flowing in the conductor. The other arises from induction in the loop of the pickup circuit. Both terms are obtained by integrating analytic expressions for the electric field, derived previously, along appropriate paths. Theory is compared with experimental data for co-linear and rectangular arrangements of the probe points, and very good agreement is obtained.

Theory of four-point alternating current potential drop measurements on conductive plates

Measurements of alternating current potential drop (ACPD) made at the surface of a conductive plate can be used to determine, non-destructively, the parameters of the plate such as its thickness, electrical conductivity and linear effective magnetic permeability. In order to invert the measured potential drop to yield values for these parameters, a theoretical model is needed. In this work, closed form analytical expressions are derived for the ACPD measured between the two voltage electrodes of a four-point probe. Alternating current is injected and extracted by two current electrodes. The problem is formulated in terms of a single, transverse magnetic, potential. The exact solution for the electromagnetic field is expressed in terms of a Greens function for a plate via the method of images. The ACPD is also expressed as a sum of contributions from multiple images. Two series representations are given: one converges more rapidly for plates which are somewhat thicker than the probe dimensions and the other for plates which are somewhat thinner. Theoretical expressions for the ACPD in special cases of thick (half space) and thin conductors are shown to agree with the results presented previously. In this paper, calculated ACPD values are compared with the experimental data taken on a titanium plate, in the regime in which the plate thickness is similar to the probe length and excellent agreement is obtained.

Block copolymer/ferroelectric nanoparticle nanocomposites

Nanocomposites composed of diblock copolymer/ferroelectric nanoparticles were formed by selectively constraining ferroelectric nanoparticles (NPs) within diblock copolymer nanodomains via judicious surface modification of ferroelectric NPs. Ferroelectric barium titanate (BaTiO3) NPs with different sizes that are permanently capped with polystyrene chains (i.e., PS-functionalized BaTiO3NPs) were first synthesized by exploiting amphiphilic unimolecular star-like poly(acrylic acid)-block-polystyrene (PAA-b-PS) diblock copolymers as nanoreactors. Subsequently, PS-functionalized BaTiO3 NPs were preferentially sequestered within PS nanocylinders in the linear cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymer upon mixing the BaTiO3 NPs with PS-b-PMMA. The use of PS-b-PMMA diblock copolymers, rather than traditional homopolymers, offers the opportunity for controlling the spatial organization of PS-functionalized BaTiO3 NPs in the PS-b-PMMA/BaTiO3 NP nanocomposites. Selective solvent vapor annealing was utilized to control the nanodomain orientation in the nanocomposites. Vertically oriented PS nanocylinders containing PS-functionalized BaTiO3 NPs were yielded after exposing the PS-b-PMMA/BaTiO3 NP nanocomposite thin film to acetone vapor, which is a selective solvent for PMMA block. The dielectric properties of nanocomposites in the microwave frequency range were investigated. The molecular weight of PS-b-PMMA and the size of BaTiO3 NPs were found to exert an apparent influence on the dielectric properties of the resulting nanocomposites.

Analysis of a concentric coplanar capacitive sensor for nondestructive evaluation of multi-layered dielectric structures

A concentric coplanar capacitive sensor is analyzed for the quantitative characterization of material properties for multi-layered dielectrics. The sensor output signal, transcapacitance CT, is related to the thickness and dielectric constant of each layer of the material under test. Electrostatic Greens functions due to point charges over different dielectric structures are derived utilizing the Hankel transform given the cylindrical symmetry of the proposed sensor. Numerical implementations based on the Greens functions are presented. The sensor electrodes are divided into a number of circular filaments, and the sensor surface charge distribution is then calculated using the method of moments (MoM). From the sensor surface charge, CT is calculated. Numerical calculations on sensor optimization are conducted and show that normalized CT as a function of sensor configuration is determined solely by its own relative dimensions, regardless of the overall dimensions of the sensor. In addition, calculations indicate how the sensor can be optimized for sensitivity to changes in core permittivity of a three-layer test-piece such as an aircraft radome. Benchmark experiment results are provided for one, two-, and three-layer test-pieces and very good agreement with calculated CT is observed. The sensor is also applied to water ingression measurements in a sandwich structure resembling the aircraft radome, in which the water-injected area can be successfully detected from the sensor output signal.

Effects of lossy, layered filler particles on the bulk permittivity of a composite material

The ability to control the frequency at which a dielectric material exhibits maximum loss (the relaxation frequency) is of interest in telecommunications and radar absorption. A theoretical investigation of the behaviour of the complex bulk permittivity of a composite material with coated, spheroidal filler particles is presented. In the model, the filler particles are replaced mathematically by electric multipole sources located at their centres (Harfield N 2000 J. Mater. Sci. 35 5809–16). It is shown how factors such as particle shape, orientation with respect to the applied electric field, thickness of coating and permittivity value of the individual phases influences the bulk permittivity of the composite material. For a composite with coated filler particles, one or two relaxation frequencies may be observed. Employing the theory of Pauly and Schwan (Hanai T 1968 Electrical properties of emulsions Emulsion Science ed P Sherman (London: Academic)), particular attention is paid to the way in which the relaxation frequencies are affected by the material parameters.

Analytical solution for the electric field in a half space conductor due to alternating current injected at the surface

An analytical expression for the electric field in a half space conductor, due to alternating current injected at the surface, is derived. Assuming that the injected current flows in wires perpendicular to the surface of the test piece, the problem can be formulated in terms of a single, transverse magnetic, potential. Considering at first one wire, the cylindrical symmetry permits simplification of the calculation by use of the Hankel transform. The final result for a system with two current-carrying wires is obtained by superposition.