Conformational statistics of polymer chain terminally attached to wall (III) —NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface, the polymer chain forms the “loop” conformation. Investigation has been made on the conformational statistics of a model loop chain by the normal random walk (NRW) on a lattice confined in the half-infinite space. Based on the conformational distribution function of the NRW model tail chain, it is easy to deduce an analytical formula expressing the conformational number of the model loop chain. It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power functionN ^-2/3 when the chain lengthN→οο. The same result -was obtained by means of the recursion equation. The ratio of the mean square end-to-end distanceh ² for the model loop chain to its mean square bond lengthl ² is 2N/3. Compared with the free chain with the same lengthN, the mean square end-to-end distance of the model loop chain contracts to a certain extent. The basic relationships deduced were supported by the exact enumeration and Monte Carlo simulations. Project supported by the National Natural Science Foundation of China.