Pulling a polymer out of a potential well and the mechanical unzipping of DNA

Motivated by experiments on DNA under torsion, we consider the problem of pulling a polymer out of a potential well by a force applied to one of its ends. If the force is less than a critical value, then the process is activated, and has an activation energy proportional to the length of the chain. Above this critical value, the process is barrierless and will occur spontaneously. We use the Rouse model for a description of the dynamics of the peeling out, and study the average behavior of the chain by replacing the random noise by its mean. The resultant mean-field equation is a nonlinear diffusion equation, and hence rather difficult to analyze. We use physical arguments to convert this to a moving boundary value problem, which can then be solved exactly. The result is that the time $t_{\mathrm{po}}$ required to pull out a polymer of N segments scales like $N^2.$ For models other than the Rouse model, we argue that $t_{\mathrm{po}}\sim N^{1+\nu }.$