The theory and methodology of nuclear spins diffusing through porous media

Abstract

The internal architecture of porous media is often a mystery, which poses an issue for diffusional studies aimed at surveying structural parameters. Across many fields, NMR has excelled in determining parameters such as tortuosity and porosity: vital variables that can influence the efficiency of batteries or the proliferation of 3D cell cultures. Yet the technique is hindered by the inhomogeneous magnetic fields introduced when the heterogeneous system is placed within an external field. Any diffusing spins will therefore experience fluctuating fields, contributing to an exceedingly short T2. Mitigation techniques include the use of long-lived states, magnetically silent states with lifetimes exceeding T1 and T2 by orders of magnitude, or transferring to low field at the cost of resolution. Yet there was no defined and proven numerical reasoning behind the effect of diffusion due to internal field gradients (DDIF), which was previously approximated to idealistic linear solutions. This unquantified effect abolishes the possibility of performing diffusion-NMR in some cases unless one can understand and therefore manage it. This thesis details the derivation of a numerical theory that incorporates Brownian dynamics and average Hamiltonian theory to produce a framework capable of calculating DDIF. Through understanding the phenomenon, a field-cycling technique is adopted, utilising a custom-built low-field probe to minimise magnetic susceptibility mismatches but increase sensitivity. The methodology is then applied to 3D cell cultures to provide a means of testing scaffold design for tissue growth.

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Identifiers

ORCID for Giuseppe Pileio: orcid.org/0000-0001-9223-3896

ORCID for Marcel Utz: orcid.org/0000-0003-2274-9672

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