From Modeling Free Chains with the Rosenbluth Algorithm to Modeling Rigid, Compact, and Overlapped Chains with Our Developed Algorithm

In 1955, Rosenbluth developed a chain-growth technique for Self-Avoiding Random Walk (SARW) with a set of weights that allows one to approximate all possible configurations of a real chain in a cubic or square lattice. We incorporate the Boltzmann factors for intermolecular bending energy into the monomer growth direction choice in the Rosenbluth algorithm to model chains of arbitrary nearest-neighbor rigidity. This allows for the consideration of compact, free, or extended chains. We validate against, and compare to, various other results, showing very good agreement with known results for short chains and demonstrate the ability to model chains up to 500 segments long, far beyond the length at which the normal Rosenbluth method becomes unstable for reasonable non-zero bending energies. Furthermore, we incorporate the Boltzmann factors for finite overlap energy to model chains that allow only two segments to overlap, Single-Overlapped Random Walk (SORW), into our algorithm. Again, we validate our results with a complete set of SORW for short chains. Our developed algorithms can be easily modified to model any configuration, stiff, free, compact, or overlapped, of polymer-like molecules in biological and non-biological systems.