Enhanced Resolution Analysis for Water Molecules in MCM-41 and SBA-15 in Low-Field T2 Relaxometric Spectra

Abstract

Mesoporous silica materials are the subjects for relaxometric NMR studies in which we obtain information on the properties of molecules in confined geometries. The signal analysis in such investigations is generally carried out with the help of the Inverse Laplace Transform (ILT), which is accompanied by a regularization procedure. The appropriate selection of the regularization method may positively affect the resolution of the spectrum and the essence of the final conclusions. In this work, we examined the MCM-41 and SBA-15 model systems in various saturation states, using L-Curve regularization for relaxation spectra based on our own version of the fast fast ILT implementation. In a single relaxometric spectrum, the water contributions from the internal volume in the pores and between the silica particles were identified, which allowed us to trace the dynamics of the corresponding drying trends during the removal of water from the sample as a function of total water saturation.

Non-negative Least Squares via Overparametrization

“…Large scale applications in which (NNLS) appears include NMR relaxometry [62], imaging deblurring [4], biometric templates [40], transcriptomics [42], magnetic microscopy [50], sparse hyperspectral unmixing [26], and system identification [14]. The formulation in (NNLS) is also closely related to non-negative matrix factorization [19] and supervised learning methods such as support vector machines [67].…”