Unzipping DNA by a periodic force: Hysteresis loop area and its scaling

Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency ($\omega$) and amplitude ($G$). For the static force, i.e., $\omega \to 0$, the DNA is in equilibrium with no hysteresis. On increasing $\omega$, the area of the hysteresis loop initially increases and becomes maximum at frequency $\omega^{*}(G)$, which depends on the force amplitude $G$. If the frequency is further increased, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscillatory component. The height of subsequent peaks decrease and finally the loop area becomes zero at very high frequencies. The number of peaks depends on the length of the DNA. We give a simple analysis to estimate the frequencies at which maxima and minima occurs in the loop area. We find that the area of the hysteresis loop scales as $1/\omega$ in high-frequency regime whereas, it scales as $G^{\alpha} \omega^{\beta}$ with exponents $\alpha =1$ and $\beta = 5/4$ at low-frequencies. The values of the exponents $\alpha$ and $\beta$ are different from the exponents reported earlier based on the hysteresis of small hairpins.