Monte Carlo Simulations of Free and Confined Walks in Reflecting Statistics

Abstract

The entropy of confined walks in reflecting statistics has been estimated through Monte Carlo simulations and compared with the corresponding entropy in usual absorbing statistics. This comparison is primarily viewed as one involving two distinct problems in combinatorial analysis. However, the authors believe reflecting statistics may also find applications in physics, physical chemistry, or other fields. Arguments, e.g., are given in the Discussion, tending to show that for severely confined polymer chains usual absorbing statistics cannot apply, and therefore that reflecting statistics might be followed instead.

Confined Space and Effective Interactions of Multiple Self-Avoiding Chains

“…A more intuitive approach is that of stacking ''blobs'' [ Fig. 2(a)] [3,19,20], where the size of each blob is the correlation length aD 3 =a 3 N =3ÿ1 in an equivalent semidilute solution. We note that Eq.…”

“…The basic idea is similar to that of the RW analysis described above: Each ''independent'' subchain is a series of connected blobs [19], which percolates and connects two points on the confining walls as illustrated by the gray (red online) blobs in Fig. 2(a).…”

“…Within the stacking-blob picture (not to be confused with the stacking-sphere picture), we can view a long chain with excluded volume confined in a spherical cavity as a system of overlapping multiple chains. The basic idea is similar to that of the RW analysis described above: Each "independent" subchain is a series of connected blobs [19], which percolates and connects two points on the confining walls as illustrated by the red blobs in Fig. 2(a).…”