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.

A theoretical model for diffusion-controlled excimer formation in the presence of excimer dissociation is presented. We assume that the rate coefficient for excimer formation k1(t) has the form k1(t)=a+bt−1/2. The equations obtained for monomer and excimer fluorescence decays are given in terms of Laplace transforms. Numerical analysis of monomer and excimer fluorescence decays are given in order to show the influence of dissociation, diffusion, and solution concentration on fluorescence decays. It has been shown that dissociation leads to exponentialization of decay curves. Two different methods of calculation quantum yields of monomer and excimer fluorescence are given in the case of time-dependent excimer formation and dissociation.