Entropic force on a Polymer

 Several micro-manipulation techniques, such as Atomic Foce Microscopy, measure forces required to unravel specific (mostly bio-) polymers.

     

   

 What is the entropic force on a uniform (phantom or self-avoiding) polymer?

 The answer depends on whether the bounding surfaces are attractive or repulsive:

Attractive Surface and Repulsive tip   

The polymer exerts an attractive force, equal to the free energy gain per unit length:

The free energy gain vanishes at the depinning transition. Close to this transition:

      

The coefficient A' depends on the shape of the tip, and is universal for scale free shapes.

Repulsive Surface and tip         

 Dimensional analysis suggests:

 Work done in moving the tip (with polymer attached) away from the surface is

=>

 This work can be related to the difference in free energies, as

 Comparing the two expressions yields

"Entropic force of polymers on a cone tip," M. F. Maghrebi, Y. Kantor, M. Kardar, EPL 96, 66002 (2011)