Electrical and dielectric properties of uncoated and coated wood-free paper for electrophotography

The print substrate influences the print result in dry toner electrophotography, which is a widely used digital printing method. The influence of the substrate can be seen more easily in color printing, as that is a more complex process compared to monochrome printing. However, the print quality is also affected by the print substrate in grayscale printing. It is thus in the interests of both substrate producers and printing equipment manufacturers to understand the substrate properties that influence the quality of printed images in more detail. In dry toner electrophotography, the image is printed by transferring charged toner particles to the print substrate in the toner transfer nip, utilizing an electric field, in addition to the forces linked to the contact between toner particles and substrate in the nip. The toner transfer and the resulting image quality are thus influenced by the surface texture and the electrical and dielectric properties of the print substrate. In the investigation of the electrical and dielectric properties of the papers and the effects of substrate roughness, in addition to commercial papers, controlled sample sets were made on pilot paper machines and coating machines to exclude uncontrolled variables from the experiments. The electrical and dielectric properties of the papers investigated were electrical resistivity and conductivity, charge acceptance, charge decay, and the dielectric permittivity and losses at different frequencies, including the effect of temperature. The objective was to gain an understanding of how the electrical and dielectric properties are affected by normal variables in papermaking, including basis weight, material density, filler content, ion and moisture contents, and coating. In addition, the dependency of substrate resistivity on the electric field applied was investigated. Local discharging did not inhibit transfer with the paper roughness levels that are normal in electrophotographic color printing. The potential decay of paper revealed that the charge decay cannot be accurately described with a single exponential function, since in charge decay there are overlapping mechanisms of conduction and depolarization of paper. The resistivity of the paper depends on the NaCl content and exponentially on moisture content although it is also strongly dependent on the electric field applied. This dependency is influenced by the thickness, density, and filler contents of the paper. Furthermore, the Poole-Frenkel model can be applied to the resistivity of uncoated paper. The real part of the dielectric constant ε’ increases with NaCl content and relative humidity, but when these materials cannot polarize freely, the increase cannot be explained by summing the effects of their dielectric constants. Dependencies between the dielectric constant and dielectric loss factor and NaCl content, temperature, and frequency show that in the presence of a sufficient amount of moisture and NaCl, new structures with a relaxation time of the order of 10-3 s are formed in paper. The ε’ of coated papers is influenced by the addition of pigments and other coating additives with polarizable groups and due to the increase in density. The charging potential decreases and the electrical conductivity, potential decay rate, and dielectric constant of paper increase with increasing temperature. The dependencies are exponential and the temperature dependencies and their activation energies are altered by the ion content. The results have been utilized in manufacturing substrates for electrophotographic color printing.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.