Dielectric polarization in non-uniform fields

Abstract

A fluid system containing non-polarizable molecules with a general charge distribution interacting with a static non-uniform field is investigated. The invariance of the dielectric polarization to the arbitrary choice of molecular origin is demonstrated. Generalizing Kirkwood's theory of dielectric polarization, statistical mechanical expressions for the multipole densities are derived which are determined by the Lorentz field and short-range correlation integrals. The multipole susceptibilities in respect of the Maxwell field are independent of the sample shape, but depend on the choice of the molecular origin. It is shown that in homogeneous fluids the difference between the dielectric displacement and the Maxwell field is due to the dipole density only. The other multipole densities, however, contribute to the free energy of the capacitor if the field is non-uniform, so that the value of the “dielectric constant” determined experimentally from the capacitance may depend on the geometry of the capacitor.