Transient electric birefringence of flexible polymers: Orientation and relaxation dynamics

The orientation and relaxation dynamics of flexible polymers in an electric field is analyzed by following the change in electric birefringence with time. The polymer chain is represented by two beads (dipole) connected by a Hookean spring and interacts with the electric field through a local induced dipole which is proportional to the end-to-end distance between the beads. Equations of motion are written for the beads taking into account (a) the hydrodynamic drag force, (b) the Brownian force, (c) the spring force, and (d) the electric force acting on the molecule. The electric field produces a strong anisotropic orientation of the polymer chain. Thus, equations are derived and analytically solved to yield the time dependence of the rise of birefringence in the electric field, the relaxation of the birefringence from a nonequilibrium state, and the change in the mean-squared end-to-end distance of the molecule with time. The dynamics are found to be governed by the dimensionless number μ0E2/H, where μ0 is a constant related to the polarizability of the molecule, E is the electric field strength, and H the Hookean spring constant. A merit of this analysis lies in the fact that expressions for the time course of the birefringence rise in the presence of an orienting field of strength E as well as relaxation in the presence of a reduced electric field, Er (Er<E) can be readily derived; hence cases other than the field-free decay (Er=0) can be interpreted. Moreover, for a biological system, a state of equilibrium with Er=0 may never be reached. Finally, the field dependence of the birefringence and the orientation and relaxation time constants has been obtained using the model and comparison of the steady state and relaxation behavior of Hookean and finitely extensible nonlinear elastic (FENE) polymer chains has been carried out.