Extent of the correlation between the squared radius of gyration and squared end‐to‐end distance in random flight chains
Extent of the correlation between the squared radius of gyration and squared end‐to‐end distance in random flight chains
复制标题
随机飞行链中回转半径平方与端到端距离平方之间的相关程度
DOI：
10.1063/1.456037
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发表时间：
1989
影响因子：
4.4
通讯作者：
K. Sienicki
中科院分区：
文献类型：
--
作者：
W. Mattice;K. Sienicki
通过处理生成矩阵方程，可以求出由n个L键组成的自由连接链<r4>、<s4>和<r2s2>的精确闭合解析表达式。指定构象的平方末端距和平方旋转半径分别由R2和S2表示。<R4>的表达式和<S4>的极限与文献中用其他方法得到的结果一致。所得结果用于计算自由连接链中S2和R2的相关系数所必需的三个无量纲比：<R4>/<R2>2、<S4>/<S2>2和<r2s2>/<R2><S2>。这三个无量纲比的渐近极限分别为5/3、19/15和4/3。当n从2增加到无穷大时，相关系数的值从1减小到(5/8)1/2。在n趋于无穷大的极限下，S2与R2之间的最佳线性关系为S2=(R2+R2)/12。
Manipulation of generator matrix equations permits the evaluation of exact closed‐form analytical expressions for 〈r4〉, 〈s4〉, and 〈r2s2〉 for freely jointed chains comprised of n bonds of length l. The squared end‐to‐end distance and squared radius of gyration for a specified conformation are denoted by r2 and s2, respectively. The expression for 〈r4〉, and the limit for 〈s4〉, agree with results in the literature that were obtained by other methods. The results are used to formulate the three dimensionless ratios, 〈r4〉/〈r2〉2, 〈s4〉/〈s2〉2, and 〈r2s2〉/〈r2〉〈s2〉, that are necessary for evaluation of the correlation coefficient for s2 and r2 in a freely jointed chain. The three dimensionless ratios have asymptotic limits of 5/3, 19/15, and 4/3, respectively. The value of the correlation coefficient decreases from 1 to (5/8)1/2 as n increases from 2 to infinity. In the limit as n goes to infinity, the best linear relationship between s2 and r2 is s2=(〈r2〉+r2)/12. The nature of the deviation of s2 and r2 for specif...