Spin-diffusion approach for relaxation in bi-spaced periodic one-dimensional systems

A theoretical model for 1H-1H dipolar nuclear spin relaxation for a bi-spaced periodic one-dimensional array of spin 1/2 nuclei has been developed. A diffusion equation is formed for such a system by assuming nearest-neighbor interaction and isotropic random molecular reorientations. Under spin-diffusion conditions (ωτc ≫ 1), this equation has been solved using Laplace transform for an infinite chain. The results are presented for the boundary conditions described for truncated driven Nuclear Overhauser effect experiments. The solution is further generalized by making the inter-spin spacing as a random variable with a Gaussian distribution.