Kinetic Yvon-Born-Green theory of the linear dielectric constant and complex permittivity of isotropic polar fluids

The theory of the linear static dielectric constant and linear complex permittivity of isotropic polar fluids is formulated starting from the coupled Langevin equations describing the rototranslational dynamics of longrange interacting molecules with thermal agitation and subjected to external forces and torques. To this aim, adequate reduced densities are introduced and equations governing their dynamics derived. In the equilibrium zero frequency limit, integral expressions for the Kirkwood correlation factor g(K) are given, transparently showing that the popular method consisting in comparing g(K) with 1 in order to deduce pair dipolar ordering has no serious theoretical grounding. In the dynamical situation, the complex permittivity spectrum of a simple liquid is shown to exhibit an infinite discrete set of relaxation times, some of which may have thermally activated behavior. The theory is also shown to contain all previous results derived in the area provided molecular inertial effects are ignored, so restricting the range of validity of the theory to frequencies much below the far-infrared region. Finally, the theory can be adapted without much effort to relaxation of interacting magnetic nanoparticles for which macroscopic magnetic anisotropy arising from the assembly of nanoparticles is neglected.

Automated summary

The theory presents a formulation of the linear static dielectric constant and linear complex permittivity for polar fluids. It introduces reduced densities and derives equations governing their dynamics. The theory provides integral expressions for the Kirkwood correlation factor g(K), revealing the limitations of comparing it with 1 to deduce pair dipolar ordering. In the dynamical situation, the theory shows the complex permittivity spectrum of a simple liquid exhibits an infinite set of relaxation times, some of which may have thermally activated behavior. The theory encompasses previous results while ignoring molecular inertial effects, making it valid at frequencies below the far-infrared region. Additionally, it can be applied to the relaxation of interacting magnetic nanoparticles with neglected macroscopic magnetic anisotropy arising from nanoparticle assembly.