Dynamics of helical worm-like chains. V. Nuclear magnetic relaxation

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Abstract
Nuclear magnetic relaxation of both flexible and stiff chain polymers in dilute solution is studied on the basis of the discrete helical worm-like chain. For most cases, only the dipolar interaction is considered by attaching a spin–spin (internuclear) vector rigidly or with a rotational degree of freedom to each of the subbodies composing the chain. For some cases of stiff chains, both the dipolar interaction and the anisotropic chemical shift are considered by affixing also a shielding tensor. The spectral densities are formulated by the use of the L=2 time-correlation functions derived previously. Then, the behavior of the five branches of the eigenvalue spectrum and the amplitudes is examined, and a mode analysis of each branch is also made. With these results, the behavior of the spectral densities is examined with a comparison with those from other theories. A comparison of theory with experiment is made with respect to the spin-lattice relaxation time T1, the spin–spin relaxation time T2, and the nuclear Overhauser enhancement NOE for various chains. For flexible chains, the agreement between theory and experiment is as good for T1 as for the dielectric correlation time τD but not for T2 and NOE, especially for T2, except for the extreme narrowing case. However, there is correlation between the static stiffness parameter λ−1 and the dynamic stiffness as defined as the ratio of a properly defined magnetic correlation time τM to that of the isolated subbody. For stiff chains, the agreement is rather good. Specifically, the molecular weight dependences of T1 and T2 can be explained semiquantitatively, and a reasonable estimate of the torsional constant of, e.g., DNA can be obtained. Finally, the defect of the theory and its improvement are discussed.