Electric birefringence and dichroism of DNA fragments in aqueous solution

A major task in this work is to study the mechanisms of orientation of DNA fragments in dilute solution in presence of an electric field. The DNA fragments are modeled as charged and polarizable bent rods. Considering the participation of electrophoresis and electric moments in the orientation of particles, we first obtain the Fokker–Planck equation for the system in the local coordinate system and finally arrive to the Smoluchowski equations for the steady state in the laboratory system. We here demonstrate that the solution of this equation, the orientational distribution function of molecules, is independent from the location of the origin of the molecule coordinate system. This property is based on the fact that the drift vector in the Fokker–Planck equation is also invariant to this change. This characteristic enables us to state that when the bent rods move by electrophoresis, wherever the bent rod coordinate system is located, the orientation of the ensemble always results in a translation–rotation coupling of particles with the origin of the molecule coordinate system in their center of charge. We analyze the orientation characteristics of the particles due to an electric moment mm that appears when the origin of the coordinate system is located in a different point from its center of charge and we compare it with the electric dipole moment μμ, originated by the charge distribution with null net electric charge.