Nuclear spin relaxation in aqueous paramagnetic ion solutions

TL;DR

This paper introduces a Brownian shell model for nuclear spin relaxation in aqueous paramagnetic ion solutions, accurately fitting experimental NMR relaxation data and improving upon previous models by incorporating detailed distance dependence.

Contribution

The paper presents a novel Brownian shell model that provides a closed-form expression for NMR relaxation rates, enhancing the accuracy of modeling rotational dynamics in paramagnetic solutions.

Findings

The model accurately fits experimental T1 relaxation dispersion curves.

Distance parameters and time constants agree with independent data.

The model improves upon previous particle-particle models.

Abstract

An angular time-dependent probability density function describing Brownian or anomalous rotational dynamics of fixed-length atom-to-atom vectors is presented. The probability density function, which fully incorporates angular boundary conditions, is applied to aqueous ion complexes. The rotational dynamics of ion-$^1$H vectors are shown by molecular dynamics (MD) simulation to be Brownian. A Brownian shell model is presented which yields a closed form expression for the frequency-dependent nuclear-magnetic-resonance spin-lattice relaxation rate $T_1^{-1}(\omega)$ based on a distance parameter and time constant. Appropriate combinations of shell and/or continuum models are shown to provide excellent fully-quantitative fits to experimental $T_1^{-1}(\omega)$ dispersion curves from aqueous manganese(II), iron(III) and copper(II) chloride solutions. The distance parameters and time constants obtained from the fits are in good agreement with independent experimental and MD data in the literature. The Brownian shell model is a significant enhancement to existing particle-particle models that describe the rotational correlation function as a single exponential and are unable to provide the correct distance dependence for a shell of $^1$H spin density preventing a match to experiment without an arbitrary scaling factor.