The Dielectric Behavior of Colloidal Particles with an Electric Double-Layer

The dielectric behavior of colloidal particles is treated mathematically. The particles are assumed to be spheres and the electric double-layer is represented by a concentric conducting shell. Assuming that the conductivity of the shell is large compared with that of the particle and that its thickness is small compared with the radius of the particle, the relaxation time in sec. is given by $\frac{3\epsilon \alpha }{8\pi c^2{\lambda }_{2}d}$ where $\epsilon$ is the dielectric constant of the material of the particle, $a$ its radius in cm, $c$ the ratio of the e.m.u. to the e.s.u., ${\lambda }_2$ the conductivity of the shell in e.m.u., and $d$ its thickness in cm. A distribution of particle size is assumed, and by the use of Wagner's treatment of non-homogeneous media expressions are obtained for the capacity and power factor as functions of the frequency. It is thus shown that the dielectric behavior predicted by Wagner for an assemblage of spheres having different specific conductivities may also result from an assemblage of colloidal particles of non-uniform size.