Heuristic Algorithm for the Analysis of Fast Field Cycling (FFC) NMR Dispersion Curves

Abstract

Evaluation of nuclear magnetic relaxation dispersion (NMRD) curves obtained by the fast field cycling nuclear magnetic resonance (FFC-NMR) relaxometry technique is a valuable tool for analyzing the microscopic dynamics of condensed matter systems. However, quantitative data analysis involves several conceptual and practical issues. Moving forward from previous literature approaches, we propose a new analysis method, relying on the elaboration of the inverse integral transform of the NMRD curve. Our approach results in a true heuristic method, able to unambiguously individuate the dynamic domains in the system, thereby avoiding the possible introduction of any element of discretion. The analysis of some data sets relevant to real samples suggests the possibility that the results obtained with the heuristic method may be actually led back to some distinct physical/chemical features of the systems.

Changes in Physicochemical Properties of Biochar after Addition to Soil

“…Results revealed not only changes in porosity but also in the hydrophilic character of the biochar surface, thereby confirming the relatively fast oxidation following its application to soil, as described in the literature [21]. Nevertheless, an additional aim of the present study consists in the testing of the mathematical models pointed out in previous papers from Conte's group [30][31][32][33][34] for the evaluation of the experimental data from fast field cycling NMR relaxometry experiments carried out on both hard and soft materials.…”

“…The heuristic algorithm was recently introduced by Lo Meo and co-workers [34] to simplify the plethora of different mathematical models which have been developed in the past for the investigation of organic and inorganic systems having different nature and provenience. A list of all the possible models is reported in references [20,28].…”

“…A list of all the possible models is reported in references [20,28]. The algorithm, whose details are reported below, appeared to be suitable for the evaluation of the chemical-physical characteristics of β-cyclodextrins, nano sponges, cheese, and cellulose [34].…”

“…where R 0 is an offset term accounting for very fast dynamic components (τ c < 1 ns), R HH describes the homonuclear relaxation as a sum of three BPP-like terms, and R NH is a complex ad hoc term to take into account the effect (i.e., the "quadrupolar peaks" in the NMRD profiles) of the quadrupolar interactions with nitrogen nuclei. In order to overcome the conceptual difficulties arising from the degree of discretionarily in the choice of Lorentzian or BPP components typical of model-free approaches, very recently Lo Meo et al [34] proposed a heuristic analysis method, based on the assumption that, in principle, a complex system may be viewed as a continuum of virtual dynamic domains, each describable in terms of a BPP-like function with a proper τ c value. Hence, the second term of Equation ( 18) can be transformed into an integral form:…”

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

“…Lo Meo et al [14] developed a heuristic algorithm to model the NMRD profiles R 1 (ω) based on the model-free approach, where the profiles are defined as a combination of two terms:…”