Dynamics of helical worm-like chains. VIII. Higher-order subspace approximations to dielectric and magnetic relaxation and fluorescence depolarization for flexible chains

Abstract

Following the general scheme developed in the preceding paper (paper VII), dielectric and magnetic relaxation and fluorescence depolarization for flexible chain polymers in dilute solution are reinvestigated on the basis of the discrete helical worm-like chain in the higher-order subspace approximation. A comparison of theory with experiment is made with respect to the dielectric correlation time τD, the spin-lattice relaxation time T1, the spin–spin relaxation time T2, the nuclear Overhauser enhancement (NOE), the fluorescence emission anisotropy r(t), the average fluorescence anisotropy r̄, and the fluorescence correlation time τF. It is found that there is agreement between the diameters of the chains determined from these dynamic properties and those from chemical structures, better than in the previous crude subspace approximation, indicating that the theory is remarkably improved in the present approximation. The magnetic correlation time τM is in general not an observable, and therefore an empirical equation to be used for its determination from the observed T1 is constructed. It is then found that there is good correlation between the dynamic chain stiffness τX/τ0X and the static chain stiffness λ−1, where τ0X is the correlation time of the isolated subbody (monomer unit) with X=D, M, and F; τX/τ0X is a monotonically increasing function of λ−1 nearly independent of X as far as perpendicular dipoles are concerned. An explanation of this result is given. However, the dependence of τX on temperature cannot be explained very satisfactorily.