A modified gambler's ruin model of polyethylene chains in the amorphous region

被引：5

作者：

Duan, ZH ^{[1
]}

Howard, LN ^{[1
]}

机构：

[1] FLORIDA STATE UNIV,DEPT MATH,TALLAHASSEE,FL 32306

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 1996年 / 93卷 / 19期

关键词：

semicrystalline polymers; random walk; difference equations;

D O I：

10.1073/pnas.93.19.10007

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks, They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M(2) + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M(3) + O(M(2)), the variance of the tie length 28/45M(4) + O(M(3)), and the variance of the walk length 2M(3) + O(M(2)).

引用

页码：10007 / 10011

页数：5