Research On Some Numerical Approaches Applied To Chemometric Analysis Of NMR Spectroscopy Data

Nuclear Magnetic Resonance (NMR) spectroscopy plays an important role in today’s research fields of physics, chemistry, biology, medicine, materials, etc. The measurements of diffusion coefficients and relaxation times via the application of NMR provide useful information for exploring structural and dynamical properties of the sample. Meanwhile, these techniques are also powerful tools for component analysis of organic compounds and biomacromolecules.To improve the processing of NMR data and extract information as much as possible, Chemometric methods for data analysis need to be implemented. In this thesis, in-depth research is conducted in the processing of NMR diffusion/relaxation data. Principles and performances of mainstream numerical approaches in the field, including their advantages and deficiencies, are also illustrated. To overcome major numerical flaws of these methods while possessing their merits, some improvements and new approaches are presented. The main achievements are listed below.1. Deficiency of the conventional monoexponential fitting strategy when applied to diffusion data of complex samples (e.g. polymers, biomacromolecules) is studied and discussed. Numerical analysis and simulations demonstrate that a deviation between the obtained diffusion coefficient and the statistical mean value is introduced by the conventional method. The deviation is proportional to the square of distribution width and the proportionality factor is determined by experimental presets. The main purpose of this work is to remind researchers to employ appropriate techniques for difusion data analysis, especially for polydisperse samples.2. A new numerical approach is presented for the inversion of diffusion NMR data, i.e. for the calculation of diffusion coefficient distributions. The new approach differs from prevalent direct regularization methods. It is an iterative approach on the basis of the trust-region algorithm. This approach overcomes major numerical flaws of the mainstream methods and shows significant advantages as illustrated by numerical tests and experimental verifications. It improves the accuracy of diffusion data analysis and is expected to become regularly used in the field of diffusion NMR.3. Some improvements are presented with respect to multivariate analysis methods applied to the matrix resolution of solid-state NMR relaxation data, including the optimization of initial guess and the separation of non-relaxational components. Besides, the advantages and feasibility of the application of artificial intelligence algorithms to the field are also discussed and a new numerical approach based on the simulated annealing algorithm is presented. Numerical tests and experimental verifications illustrate that when applied to data sets with relative noise levels larger than0.5%, the results obtained by the new approach are relatively more accurate.Since the mixed exponential process commonly exists in all kinds of signals and experimental data, the improvements and numerical approaches presented in this thesis are applicable to the analysis of data acquired from NMR spectroscopy as well as other fields.