Elastic behavior of short compact polymers

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance R(2) and the ratio of R(2)/S(2) increase with lambda. However, when the elongation ratio becomes larger, the curves of R(2)/S(2) become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90 degrees, 180 degrees, and 270 degrees). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio lambda. In the meantime, the elastic force per bond (f ) also increases with elongation ratio lambda, and the energy contribution to the elastic force (f(U)) increases first and then drops, and there exists the maximum of f(U) in the region of lambda=1.40-1.80 for different sequences. The entropy contribution to force (f(S)) is close to zero at a small elongation ratio lambda and then increases with lambda. Some comparisons with different sequences (including nonfolding and folding sequences) are also made.