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Fast Field-Cycling Nuclear Magnetic Resonance relaxometry is a non-destructive technique to investigate molecular dynamics and structure of systems having a wide range of applications such as environment, biology, and food. Besides a considerable amount of literature about modeling and application of such technique in specific areas, an algorithmic approach to the related parameter identification problem is still lacking. We believe that a robust algorithmic approach will allow a unified treatment of different samples in several application areas. In this paper, we model the parameters identification problem as a constrained $L_1$-regularized non-linear least squares problem. Following the approach proposed in [Analytical Chemistry 2021 93 (24)], the non-linear least squares term imposes data consistency by decomposing the acquired relaxation profiles into relaxation contributions associated with 1H-1H and 1H-14N dipole-dipole interactions. The data fitting and the L1-based regularization terms are balanced by the so-called regularization parameter. For the parameters identification, we propose an algorithm that computes, at each iteration, both the regularization parameter and the model parameters. In particular, the regularization parameter value is updated according to a Balancing Principle and the model parameters values are obtained by solving the corresponding $L_1$-regularized non-linear least squares problem by means of the non-linear Gauss-Seidel method. We analyse the convergence properties of the proposed algorithm and run extensive testing on synthetic and real data. A Matlab software, implementing the presented algorithm, is available upon request to the authors.

In the last years, the development of nano-formulations for cancer treatment represents one of the major challenges of the scientific research. The prodrug strategy, that combines chemotherapeutic agents with nanocarriers such as halloysite nanotubes (HNTs), is a promising strategy both to improve the biological activity of the drug molecules and to reduce the side effects of drugs. Herein we report the synthesis and characterization of a HNTs prodrug based on 1,2,3-triazole units covalently linked to HNTs external surface, bearing different positively charged moieties, which could present interesting pharmacological activities.

Different cyclodextrin-calixarene nanosponges (CyCaNSs) have been characterized by means of FFC-NMR relaxometry, and used as sorbents to remove Pb2+ ions from aqueous solutions. Considering that the removal treatments may involve polluted waters with different characteristics, the adsorption experiments were performed on solutions without and with the addition of background salts, under different operational conditions. The adsorption abilities and affinities of the nanosponges towards Pb2+ ions were investigated by measuring the metal ion concentration by means of Inductively Coupled Plasma Emission Spectroscopy (ICP-OES) and Differential Pulse Anodic Stripping Voltammetry (DP-ASV). The acid-base properties of nanosponges and of metal ion as well as their interactions with the other interacting components of the systems have been considered in the evaluation of adsorption mechanism. Recycling and reuse experiments on the most efficient adsorbents were also performed. On the grounds of the results obtained, post-modified CyCaNSs appear promising materials for designing environmental remediation devices.