Monte Carlo Study On Conformation Statistics Of Polymer Chain

In this paper, based on off-lattice model, according to conditional probability of real macromolecular chains, a Monte Carlo model, rotational isometric state simulation scheme (RISMO) was presented. In the RISMO model, the real bond length, real bond angle and the conditional probabilities of a certain segment staying in one or another rotational isometric state under Θ conditions were used to built the sample polymer chains, so the statistics average was simply replaced by sample average and high precision could be achieved even with few samples.Because of the limitation of the exact enumeration method and Flory's matrix method in the study of statistics of macromolecular conformation, our RISMO method worked as a supplement as well as an improvement of above methods. This paper included the following: The rotational isometric state Monte Carlo model was systematically established and the feasibility of this Monte Carlo model was theoretically verified. The simulation results of unperturbed chains of polyethylene and polyoxyethylene calculated by using the presented method were compared with that of the Flory's matrix method as well as the exact enumeration method. The precision of using our model as showed by the comparison of the above resultsproved that our method was suitable and accurate even if fewer samples were taken. Secondly, the conformation statistics of unperturbed chains under different confined conditions (tail chain, polymer chains confined to tube, two parallel planks and nano-global) were studied, the mean square end-to-end distance, its component, and the gyration radius were calculated, and the scaling law was also discussed. At the same time, the mean square end-to-end distance distributions were studied and the space shape of polymer chain was discussed. In addition, the conformation statistics of real chains (both free real chains and confined real chains) were studied thoroughly. While considering of the excluded volume, the effect of real chain structure imposed on conformation statistics was investigated, and the scaling law of real chains was also elaborately discussed. Lastly, the space shape of polymer chain was studied according to the ratio of components of the gyration radius tensor. The temperature coefficients were also calculated. In addition, a further improved model was proposed while the number of the successfully confined sample real chains decreased dramatically with the increase of chain segments.