ABSTRACT
When a polymermolecule is initially directed to the nanopore, its chain ends are not necessarily at the entrance of the pore. As described in the preceding chapters and introduced in Figure 1.9c (Section 1.5.3), the entropic costs associated with the search by chain ends to be localized at the pore mouth and the reduction in chain conformations to be squeezed further into the pore are manifest as a free energy barrier. Once the free energy barrier is surmounted, subsequent transport of the chain along the nanopore is a favorable process, when the translocation is facilitated with a driving force. As a result, the combination of barrier crossing and the subsequent downhill process associated with the translocation event by a single polymer molecule can be treated as the classical nucleation and growth, which is of common occurrence in many phenomena such as the kinetics of phase transitions. We therefore import the technology of nucleation and growth mechanism to the translocation phenomenon. After introducing a few representative experimental results on the threading kinetics of polymers through nanopores and channels, and a few key ideas from computer simulations, we present the model of nucleation and growth for translocation. Based on the background materials developed in Chapters 5 and 6, in terms of entropic barriers and the Fokker-Planck formalism, we shall derive explicit formulas for the translocation time and its distribution function. We shall then return to the experimental contexts and discuss the progress that has been made with such theoretical concepts and the challenges that still remain for a better understanding.
