The Computer Simulation Of Restricted Single Polymer Chain Conformation

The conformation of restricted single polymer chain on oriented lattice and non-oriented lattice was systematically studied using computer simulation.The Manhattan lattice was an oriented lattice. The total number of self-avoiding walks terminally attached to a surface on both two-dimensional Manhattan lattice and three-dimensional Manhattan lattice, their mean square end-to-end distance, and their mean square radius of gyration, were exactly enumerated. The analysis of exact enumeration data using the ratio method and Dlog Fade approximate gave the connective constant and the critical exponents of conformation and end-to-end distance. At the same time, we got the same kinds of properties of free self-avoiding walks on three-dimensional Manhattan lattice. The length of free SAW and tail SAW on three-dimensional Manhattan lattice was up to 31 and 30 steps, which is the longest up to now.On the non-oriented simple cubic lattice, the self-avoiding walks were confined to the half-space (z>0) with the origin vertex in the plane (z=0). In the adsorption model the self-avoiding walks interacted with the plane zr=0 and contributed an additional energy term. At the same time the steps had nearest-neighbor interactions within the walk and contributed an additional energy term for the collapse model. The thermodynamic properties for self-avoiding walks on simple cubic lattice with both surface-interacting and nearest-neighbor interacting were calculated using multiple Markov chains method and histogram technique. These results gave the location of transition in the phase diagram of this r'odel. The phase diagramindicated that there were four kinds of phases. They are AE (adsorbed-expanded), DE (desorbed-expanded), AC (adsorbed-collapsed) and DC (desorbed-collapsed). It was found that both adsorption and collapse transitions were existed.We discussed the problem of polymer chains near an impenetrable plane. The conformational properties of NRW and SAW on square lattice and simple cubic lattice were studied by means of the equation, the exacted enumeration and the Monte Carlo simulation. It was shown that both NRW and SAW contracted rapidly and then extended slowly when the distance between the surface and the origin vertex of chain increased.