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We report the effect of electron-beam patterning on the water uptake and ionic conductivity of Nafion films using a combination of x-ray photoelectron spectroscopy, quartz crystal microbalance studies, neutron reflectometry, and AC impedance spectroscopy. The aim was to more fully characterize the nature of the nanoscale patterned Nafion structures recently used as a key element in novel ion-to-electron transducers by Gluschke et al. To enable these studies, we develop the electron beam patterning process for large areas, achieving patterning speeds approaching 1 cm$^{2}$/hr, and patterned areas as large as 7 cm$^{2}$ for the neutron reflectometry studies. We ultimately show that electron-beam patterning affects both the water uptake and the ionic conductivity, depending on film thickness. We see Type-II adsorption isotherm behaviour for all films. For thick films (~230 nm), we see a strong reduction in water uptake with electron-beam patterning. In contrast, for thin films (~30 nm), electron-beam patterning enhances water uptake. Notably, we find that for either thickness the reduction in ionic conductivity arising from electron-beam patterning is kept to less than an order of magnitude. We propose mechanisms for the observed behaviour based on the known complex morphology of Nafion films to motivate future studies of electron-beam processed Nafion.

Starting from an applicative problem related to the modeling of an element of a cable-stayed bridge, we compute the elasticity solution for a hollow cylinder loaded at the end faces with axial loads. We prove results of symmetry for the solution and we expand it in proper Fourier series; computing the Fourier coefficients in adapted power series, we provide the explicit solution. We consider an engineering case of study, applying the corresponding approximate formula and giving some estimates on the error committed with respect to the truncation of the series., Comment: 36 pages, 7 figures