Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness $\epsilon_{\rm b}$. In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first-order as long as $\epsilon_{\rm b}$ is positive [H. Zhou {\em et al.}, Phys. Rev. Lett. {\bf 97}, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a 2D lattice polymer. The system's phase-diagram at zero force is obtained. Depending on $\epsilon_{\rm b}$ and the temperature $T$, the polymer can be in one of three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous, the globule-coil transition is continuous. At moderate or high values of $\epsilon_{\rm b}$ the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.