ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
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 specified conformations from the best straight line is documented by an illustrative numerical calculation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.456037
Permalink