Force Induced Unzipping

Delocalization may arise as a result of the action of an external force. This is motivated by several real experiences, we mention in particular some recent experiments on mechanically induced unbinding (or unzipping) of a double strand of DNA via experiments at a molecular level (see Section 1.10 for literature and further details). From the arguments in Section 1.4 it is clear that we can directly look at the reduced model of pulling a polymer out of an attractive defect line. The model is the following  

Theorem 1.7 The free energy Fpuii(/ , F), that is the limit of the sequence (1/A ) logZjy l, exists. Moreover we have the formula 

Before proving this result, we observe that for fixed / 0 it is natural 

Since f(-) is analytic outside of 0 and since Funzip(-) is analytical on (0, oo), then Fpuii (0, oo) R is analytical on (0, oo) (/3, F) F = Fd/S). Moreover the contact density, d Fpuu(/3, F), is zero if F Fc (3) and it is positive if F Fc f3), so this is clearly a localization-delocalization transition. And this transition is of first order, since the contact density is independent of the value of F as long as it is smaller than Fc(/3). 

By taking the derivative of Fpun(/3, ) one readily sees that 

---

For force induced unzipping or delocalization in model systems, but motivated by biopolymer experiments, we signal [Marenduzzo et al. (2001)] and [Lubensky and D. R. Nelson (2000)], even if our approach is rather different. An example of application of the same models outside of the biopolymer context can be found in [Kafri et al. (2006)]. Formula (1.41) extends easily to disordered cases, see [Giacomin (2004), Ex. 2.3] and from it a number of conclusions can be easily drawn. 

---