Vibration of DNA polymer in viscous solvent

The problem of viscous damping of vibrating DNA polymer in solution is solved in the low‐amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. Analytic solutions are obtained for a model describing the DNA polymer as a smooth circular cylinder. Numerical solutions are presented for a model describing the DNA polymer as a twisted cylinder of elliptical cross section. The amount of mass loading is determined for both models and the damped spectrum for the mass‐loaded oscillator is calculated. The viscous damping is found to be a strong function of frequency, singular at very low frequencies for all modes except the torsional mode of the circular cylinder. All acoustic modes are overdamped, implying that the observation of well‐defined resonances in DNA requires either highly structured water on the molecular level or very dry material.