ABSTRACT
Numerous practical problems involve the deformation (and the subsequent relaxation) of single polymer chains by external factors (forces, fields, confinement, etc.) [1]. Although this fully justifies why scientists study the statistical properties of single-polymer chains under various constraints, such investigations are also important for fundamental reasons. First, single-molecule studies represent a strong test of our understanding of basic physics; for instance, we can access microscopic information such as molecular conformations and trajectories, not only ensemble averaged values. Second the simplicity of such problems suggests that it should be possible to develop models with fewer approximations, thus leading to exact solutions. Third, current computing power makes it possible to simulate many single-molecule problems with atomistic or united-atom molecular dynamics algorithms [25]. Finally, current experimental techniques such a single-molecule fluorescence microscopy allow us to visualize single-polymer molecules for long periods of time, thus allowing us to test our models and simulations in great detail [6]. It should also be mentioned that our understanding of many-chain problems implicitly relies on our knowledge of the behavior of single-polymer chains in various environments [7-10].
