Statistics of tethered self-avoiding chains under spherical confinement and an external force.

We compute the partition function of self-avoiding chains tethered inside a confining sphere using Monte Carlo simulations on a three-dimensional lattice. Two cases are considered: (i) single-tethered chains with one end anchored and one end free and (ii) double-tethered chains where both ends are tethered at a distance equal to the diameter of the sphere. The self-avoidance, confinement, and tethering constraints dramatically decrease the number of allowed configurations when compared with an unconstrained random coil, thereby affecting the sampling method used in the Monte Carlo procedure. The effect of an external applied force and the bias it introduces in the partition function are also investigated. Our method involves a decomposition of the partition function into the product of several terms that can be evaluated independently. For short chains, we demonstrate the validity of our approach through a direct evaluation of the partition function using an exact enumeration of the appropriate paths on the lattice. In the case of long chains, scaling laws for the behavior of the partition function are identified.