Entropic trapping of a flexible polymer in a fixed network of random obstacles

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Abstract
Using Langevin dynamics simulations, we model the dynamics of a polymer in a fixed network of random obstacles containing a spherical cavity. We define the partition coefficient K as the time-averaged ratio of the number of monomers inside/outside the cavity and calculate this quantity as a function of polymer length N. Our results show that ln K(N) increases with N until the polymer’s radius of gyration is approximately equal to the size of the cavity L h . Further increase of N leads to a decrease in ln K. The linear regime of this curve can be understood by comparing the free energy of a polymer confined through the spherical cavity to the corresponding free energy of the polymer in the mesh of the random network (this is the origin of the phenomenon of entropic trapping). The decrease in ln K when N is large results from imperfect confinement of the polymer inside the cavity. The number of monomers confined inside the cavity is limited by the size of the cavity and thus ln K decreases with N, roughly logarithmically, when N is very large.