The dynamic equilibrium of space charge in insulators such as ceramics, molecular crystals, or high polymers, is considered from the thermodynamic point of view with quantum-mechanical boundary conditions. The treatment constitutes the opposite extreme from the usual ohmic; conduction equations; in the first paper, only the zero-current equilibrium of charge is considered. Applications are"made to the observed charging of high polymers during molding...
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Rapid breaks of metal-polymer-metal adhesive specimens have shown the presence of a charge density on the metallic surface, provided the break occurs at the metal-polymer interface, and a much smaller charge if it occurs in the interior of the polymer. This is analyzed in terms of the electron atmosphere existing external to the metal in a dielectric region of low barrier. The barrier values in certain cases are otherwise known to be of appropriate order of magnitude. Measured experimental surface charge densities permit estimation of the maximum limit of barrier height. Because of the presence of the charge distribution in the polymer, there is an electrostatic force on the adherend metal directed toward the dielectric polymer, which represents a contribution to the total adhesive forces opposing break. Such electrostatic contributions to adhesion have not previously been considered; their order of magnitude and their relation to the thickness of the adhesive are discussed. The qualitative agreement between the theory and a number of previously unexplained experimental results in the literature is shown.
The discussion of the thermodynamic equilibrium of an electron atmosphere in a dielectric is extended to the current-carrying steady state. Under the assumption that the experimental behavior at zero current is continuous with that when there are finite electrical currents, it is found that forward and reverse currents show distinct behavior. Expressions are developed for the electrostatic potential, field, charge density, the current-applied voltage relation, and the capacity and rectifying behavior of dielectric layers. The non-ohmic conduction exhibits rectification, and departures from the Wagner relation are predicted, of the type observed experimentally, including turnover voltages. The contact charging of a dielectric is the zero-current limit of the non-ohmic behavior which causes rectification.
In treating film lubrication, Reynolds and Sommerfeld confined themselves to surfaces of infinite width, for mathematical reasons. Michell obtained the solution for a plane surface of finite width; the importance of this lies in the fact that leakage of lubricant through the lateral edges of a finite bearing reduces considerably the load supportable by the bearing. Solutions are obtained here for general cases of rectangular bearings with surfaces curved in both directions; for the Michell sector type of thrust bearing plate, in a case which allows consideration of the effect of the variation of film thickness with the radial distance from the center of rotation; and for the fitted finite journal bearing. General methods are exhibited suitable for handling other cases. In particular, the equations for the finite journal bearing in the general case are partially developed. Solutions for the journal bearing are shown to require laborious computation, so that an approximation to the film thickness is preferable; such an approximation, which can be handled relatively easily, is treated, and the solution obtained.
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