The electric birefringence of polyelectrolytes: an electrokinetic approach

We discuss the Kerr constant of a polyelectrolyte solution in the dilute regime. We show that the birefringence induced in a suspension of nonspherical polyelectrolytes by an external electric field probes the electrokinetic properties of the suspension. This is because the Kerr constant is directly connected to the electric torque exerted on the particles, and therefore contains information on the induced dipole, similarly to the other electrokinetic techniques. The article is a guideline for the development of an electrokinetic theory of the electric birefringence of polyelectrolytes. We compare two different methods to derive the Kerr constant of the polyelectrolyte solution. The first method uses an expression for the electric torque which is obtained through electrostatics, and yields a Kerr constant which has the same frequency dependence as the anisotropy of the real part of the polarizability of the dressed particle (that is, of the particle plus surrounding ions). The second method assigns an effective value of the induced electric dipole per particle by using the theory of the dielectric enhancement, and gives a Kerr constant proportional to the anisotropy of the real part of the dielectric constant of the suspension. The two methods give a considerably different frequency dependence of the Kerr constant: we suggest that the expression obtained by the second method is more capable of correctly describing the main features of the experimental results obtained with polyelectrolytes having small shape anisotropy.