嫁接于平行板的受限紧密高分子链末端距分布函数的研究

DISTRIBUTION OF END-TO-END DISTANCE OF A GRAFTED COMPACT POLYMER CHAIN CONFINED IN TWO PARALLELS

采用剪除增加Rosenbluth方法(Pruned-enriched-Rosenbluth method,PERM)算法计算了嫁接于平行板的受限紧密高分子链的末端距分布函数.由于受限紧密高分子链具有各向异性,重点研究了平行板方向x轴上的分布函数P(x),发现P(x)可以表示为ln[P(x)/Pm(x)]/ND-5/3=a0+a1u+a2u2+a3u3(其中u=x/ND-2/3).这里N为链长,Pm(x)为分布函数P(x)的最大值,两平行板的间距为D+1.通过计算P(x)的Shannon熵发现末端距分布函数P(x)的Shannon熵可以用来描述高分子链受限的程度,Shannon熵对平行板间距的变化非常敏感,对于同一链长N,P(x)的Shannon熵会随着D的增大而迅速减小,超过临界值Dc会趋向一个定值,即当D≥Dc时Shannon熵将趋于稳定,也说明了此时受限条件对紧密高分子链影响非常小.同时临界值Dc与链长N有关,Dc^Nλ,其中λ=0.543,并进行了一定的理论分析.

The end-to-end distance distribution of a grafted compact polymer chain confined between two parallels is studied by using the PERM （pruned-enriched-Rosenbluth method）algorithm. Because of the difference in different directions of confined polymer chains, in this paper we just consider the distribution function P （ x ） in the x-axis direction,and it can be expressed as In[ P（ x ）/ Pm （ x ） ]/ ND^-2/3 = a0 ＋ a1 u ＋ a2 u^2 ＋ a3 u^3, here u = x/ ND^-2/3, N is the chain length, P m （x） is the maximum value of P （ x ）, D ＋ 1 is the distance between the two parallels. On the other hand, we calculate the Shannon entropy according to P （ x ）, which is very sensitive to the variation of the distance of two parallels, and it can be used to describe the restriction of the polymer chain. With a given chain length N, the Shannon entropy of the distribution P （ x ） decreases rapidly first and then tends to a fixed value with increasing D ,by which we can find a transition point Dc .When D 〉 Dc the Shannon entropy tends to a constant, and at the same time the restriction of polymer chain performed by the two parallels can be ignored. We also find that the relationship between Do and N as Dc-N^λ , here λ = 0.543.