Theory of nuclear spin relaxation in disordered systems: comparison of Bloembergen-Purcell-Pound models and Monte Carlo simulations

Two Bloembergen-Purcell-Pound (BPP) models for analysing nuclear spin relaxation data for translational diffusion in disordered systems are compared with Monte Carlo simulations. One model (the a-BPP model. 'a' standing for average) is commonly used for disordered systems and the other (the Cameron-Sholl BPP model) is more rigorously based and can distinguish between site- and barrier-energy disorder. Simulated relaxation data produced using Gaussian distributions of energy disorder are analysed using the models. and the parameters obtained from the fits are compared with the values used for the simulations. It is found that both models can give reasonable fits to the data. Both models also give reasonable agreement with the simulation parameters provided that the standard deviation of the energy distribution for the a-BPP model is interpreted as the average of the site- and barrier-energy standard deviations. Quantitative estimates are given of the accuracy of the parameters from the fits.