金刚石格点上自避行走尾形链的构象统计理论

CONFIGURATIONAL STATISTICS OF POLYMER TAIL CHAIN SIMULATED BY SELF AVOID WALK ON DIAMOND LATTICE

研究了金刚石格点上自避随机行走（ＳＡＷ）尾形链，采用精确计数和ＭｏｎｔｅＣａｒｌｏ模拟方法求得该ＳＡＷ尾形链的构象数Ｃ（Ｄ）１（Ｎ）和均方末端距［ｈ（Ｄ）１（Ｎ）］２及其分量随链长Ｎ的变化关系．发现它们与自由ＳＡＷ链一样都服从标度律，从这些量的计算机实验数据拟合求出了金刚石格点上ＳＡＷ尾形链的临界指数和格点指数．计算结果还表明短链ＳＡＷ在壁的法向与ＮＲＷ尾形链一样有所伸展，均方末端距的法向分量几乎是平行分量的２倍；但随Ｎ→∞，链自回避效应对壁的作用有所屏蔽．这些都与简立方格子模型上得到的结果一致．

The self avoiding walk(SAW) tail chain on diamond lattice was studied in this work.The permitted conformational number C (D) 1(N) and the mean square end to end distance h (D) 1(N) 2 as function of the chain length N for such a model tail chain were obtained by the computer simulations including the exact enumeration and Monte Carlo method.These two basic quantities obeyed the relations deduced from the scaling law.The critical exponents and the lattice indexes obtained from C (D) 1(N) and h (D) 1(N) 2 were given by fitting the data of the computer experiments.It was shown that there is a certain extension in the size in the direction normal to the wall for the SAW tail chain as well as for the normal random walk tail chain.The normal component of the mean square end to end distance is almost as twice as the parallel component of the short chain SAW.However,as N→∞ ,the effect of the wall on the chain conformation becomes weak because of the self avoiding behavior for the model.It was identical with the result obtained from the SAW on the simple cubic lattice.