Polarization and alignment in polar fluids

The classical statistical mechanical approach to the theory of dielectric polarization due to Kirkwood is examined. Kirkwood derived a rigorous expression for the mean value in the presence of a uniform electric field of the cosine of the angle between the permanent dipole moment of a molecule and the field. This result can be generalized to provide an equation for the mean value in the field of a α i , the cosine of the angle between any molecule-fixed α axis and a space-fixed i axis. For a fluid in a static electric field gradient a rigorous expression is deduced relating the mean value of the product of any pair of direction cosines, a α i a β i , to the average quadrupole moment of a molecule and its neighbours in a large microscopic sphere centred on a fixed molecule, in the absence of the external field gradient.