A Pair of Perfectly Conducting Disks in an External Field

A pair of non-overlapping perfectly conducting equal disks embedded in a two-dimensional background was investigated by the classic method of images, by Poincar´e series, by use of the bipolar coordinates and by the elliptic functions in the previous works. In particular, successive application of the inversions with respect to circles were applied to obtain the field in the form of a series. For closely placed disks, the previous methods yield slowly convergent series. In this paper, we study the local fields around closely placed disks by the elliptic functions. The problem of small gap is completely investigated since the obtained closed form solution admits a precise asymptotic investigation in terms of the trigonometric functions when the gap between the disks tends to zero. The exact and asymptotic formulae are extended to the case when a prescribed singularity is located in the gap. This extends applications of structural approximations to estimations of the local fields in densely packed fiber composites in various external fields

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Effective transport and optical properties of composite materials

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Imaging Channel Connectivity in Proton and Hydroxide Conducting Membranes for Fuel Cells

Proton exchange membrane (PEM) fuel cells offer an alternative as an efficient power source with low environmental impact. The heart of the fuel cell is the membrane, which conducts protons through an aqueous channel network. Proton transport is critically tied to the channel connectivity – disconnected channels do not participate in the overall electrochemical activity of the cell. Nafion, the current benchmark PEM, is a random statistical copolymer, characterized by a percolating network of cylindrical channels. In previous work, conductive-probe atomic force microscopy (cp-AFM) was used to image the conductance of Nafion. Although cp-AFM provides relevant information on which channels are connected, it provides no information on the disconnected “dead-end” channels at the surface. Electrostatic Force Microscopy (EFM) was used to analyze the structure and frequency of the “dead-end” channels. Applying a simple parallel plate model allowed us to assign differences in the EFM signal to particular channel shapes: connected cylindrical channels, “dead-end” cylinder channels, and bottle-neck channels. Anion exchange membranes (AEMs), which conduct hydroxide, have attracted recent interest due to improved reaction kinetics in alkaline media, yet suffer from low conductivity and easily degrade. To this end, our AFM methodology was applied to analyze the channel connectivity of a commercial FumaTech AEM was investigated in its hydroxide form over a wide range of relative humidity (RH) by combining phase imaging and cp-AFM. At high RH, our AFM data indicates significant surface swelling. Lastly, we investigated a class of phosphonium-containing diblock copolymer AEMs that formed ordered morphologies. Although channels were observed to be well-connected in the bulk by TEM, channels aligned parallel at the surface leading to many “dead-end” channels shown by EFM. Correlating these findings with bulk measurements could offer insight toward AEMs with improved conductivity and chemical stability