端基附壁模型聚合物环形链的构象统计理论

CONFIGURATIONAL STATISTICS OF MODEL POLYMER LOOP CHAINS ATTACHED TO A SURFACE

环形链定义为两个端基均附壁的线形聚合物链所得的环 .采用精确计数和蒙特卡罗模拟方法 ,研究了自回避行走 (SAW)模型表示的环形链的构象 ,求得构象数和均方回转半径随链长的变化 .对于二维和三维SAW环形链 ,精确计数的最大链长分别为N =2 9和 1 9.用标度理论处理了数值结果 ,所得的标度指数和其他参数与理论预示值进行了比较 .模拟结果表明 ,SAW环形链限制壁平行方向的尺寸大于垂直方向的尺寸 ,与SAW尾形链尺寸的变化正好相反 .

The polymer loop discussed in this paper was defined as a polymer chain,both ends of which are attached to a surface of impenetrated wall.In order to obtain the configurational statistics of this polymer loop,the exact enumeration and Monte Carlo methods were applied to the model of self\|avoiding walk(SAW) on two\| and three dimensional lattices.For the SAW on the simple cubic or square lattice,the maximum length of the model chain loop was 29 and 19,respectively.The numerical results based on the simulations were fitted to the scaling theory,by which the scaling exponents and other parameters were obtained and compared with the corresponding theoretlal values.It was shown in the simulations that for these SAW loops the parallel components of their sizes with respect to the surface of the confined wall were larger than the perpendicular ones.It was interesting to notice that these results are contrary to those for the corresponding model tail chains,only one end of which is attached to the surface.