Volume Conductivity of Borosilicate Glass

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Abstract
Through use of circuitry of variable RC time constants it has been shown that the slow exponential rise and decline of the charging current of the glass condenser between metal plates that do not exchange ions with the glass, in the past assumed to be characteristic of the glass, is an instrumental RC-conditioned time constant. The previously unexplained linear decline, sometimes called the ``anomalous'' charging current, in consequence represents the migration of the mobile alkali ions to create a cathode potential fall establishing the steady-state conduction current. While temperature variation of resistance follows the previously assumed pattern, the steady-state current is limited by the rate of recombination of the alkali ions in the space-charge sheath close to the cathode with O− ions created by electrons from the metal electrode. Near the anode, loss of alkali ions through accumulation of O− ion space-charge fields provides the electron current to the anode. From the alkali atom density, measurement of the time constant of the linear decline, measurement of the steady-state current density, and measurement of the activation energy, one can estimate the dissociation energy, the depth of the ionic potential well, the alkali-ion density, and the ionic mobility. The mobility is in fortuitously good agreement with that calculated from logically assumed basic constants. The data yield an ``effective'' ion-electron surface recombination coefficient responsible for steady-state current flow. The theory of the linear current indicates limits to the superposition principle. Current passage, at room temperatures at high current density, on the order of hundreds of hours reduces the alkali-ion concentration near the anode and changes the resistance. Thus, there is achieved a unified self-consistent theory for the bulk conductivity, the constants of which are directly determinable from the measurements, with minimum assumptions of arbitrary nature.

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