Polarization of nanorods submerged in an electrolyte solution and subjected to an ac electrical field

Recently, there has been growing interest in utilizing electrical fields to position and separate rod-shaped particles such as DNA molecules, actin filaments, microtubules, viruses, bacteria, nanotubes, and nanorods. The polarization of the electrical double layer, enveloping the rod, plays a critical role in determining the magnitude and direction of the rod's dipole moment. We consider noninteracting, rod-shaped (spherocylinder) particles and calculate the induced dipole moment as a function of the electrical field frequency, the rod's aspect ratio (length/radius), the rod's free surface charge, and the double-layer thickness. To this end, we solve the Poisson-Nernst-Planck (PNP) equations for the ions' migration, diffusion, and convection. When the surface charge is small and the rod is short, the dipole moment is negative. As the rod's length increases, the dipole moment increases and eventually changes sign from negative to positive. The dipole coefficient of a rod, whose length is greater than some critical value, increases linearly with length. This latter observation simplifies the estimation of the dipole moment of particles with large aspect ratios (length/radius). The theoretical predictions are compared and favorably agree with experimental data for double-stranded, short DNA molecules.