Methodological Development and Applications of Transverse Relaxation in NMR

Chakraborty, Ipsita (2019) Methodological Development and Applications of Transverse Relaxation in NMR. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

This thesis aims to describe methodological development and the applications of the transverse relaxation in Nuclear Magnetic Resonance (NMR). The first part of the thesis shows the applications of the transverse relaxations aim to qualitatively monitor the morphological changes of the smart polymers using solvent relaxation method. The later part of the thesis aims to measure the efficiencies of various decoupling (DD) pulse sequences in the presence of the field noise and tries to identify the optimal DD sequence to extract the longest or the best T₂ values of molecules in solutions. This dissertation contains total five chapters. Chapter 1 covers the theoretical preliminaries required for the experimental works described in the rest of the thesis. At the beginning, a brief history of the NMR spectroscopy has been presented. Subsequently, a brief discussion on principles of NMR and the main techniques for the detection of NMR signal (FT- and CW-NMR) have been given. The first part of the following section describes the phenomenological equations of Bloch. Then the semi-classical theory of Redfield on spin relaxation has been developed starting from von Neumann-Liouville equation of motion. The role of the time correlation functions and resulting auto- and cross-correlated spectral densities have also been discussed. Specifically the expressions of the auto-correlated spectral density functions arising from two different relaxation mechanisms have been given. Next, different pulse sequences used to measure the transverse relaxation rate – from spin-echo to CPMG have been presented in detail. The role of the dynamic decoupling (DD) sequences developed for the suppression of low- frequency fluctuations has been briefly discussed. In the following section, a brief note on the effect of chemical exchange on transverse relaxation rate is given and the names of several techniques commonly used to measure the chemical exchange rate are mentioned. In the same context, the CPMGbased Relaxation Dispersion (RD) technique has been explained in detail. Also, the derivation of the Luz-Meiboom equation which is used to extract the exchange information from the CPMG-RD experiment is briefly shown. Subsequently, a discussion on the solvent relaxation and its variety of applications have been introduced. The last section contains the outline of the rest of the thesis. Chapter 2 focuses on exploring a new yet simple method to understand the macro structural changes of an amphiphilic pH-responsive polymer in aqueous medium as a function of pH using solvent relaxation method. In the introduction, the structural and ionization features of the pH-responsive polymers are discussed. Then their applications, the mechanisms behind the formation of micelle and the micellar aggregates in the aqueous medium are shown. Later, it has been argued that why NMR could be useful to probe the structural changes of the pH-responsive polymers. In the following section, the protocol of the measurement of the exchange rate has been discussed. In the ‘Theory’ section, the Luz-Meiboom model and a new method to calculate the average diameter of the micellar aggregates using the exchange information have been introduced. The following section is experimental which has three parts, namely i) brief description of the synthesis of the polymer, ii) the design and parameters of CPMG-based RD experiment and iii) confirmatory experiments using other techniques, UV-Visible, Dynamic Light Scattering (DLS) and Scanning Electron Microscopy (SEM). Finally, with the help of the proposed model and from the measured exchange rates using the Luz-Meiboom model the detailed mechanism of the aggregation of the micelles has been investigated and also the average diameter of the aggregates are calculated. The next section elaborately discusses the principal results obtained by the above method (with pictures and plots). At the end, the advantages and disadvantages of this method are discussed and potential applications of this method are highlighted. Chapter 3 aims to monitor the coil-globule phase transition of a N-isopropylacrylamide (NIPAM) based thermoresponsive polymer using the solvent relaxation method and to quantitatively estimate the hydrogen bonds participation across the phase transition. The introductory section contains the general features of the coil-globule transition of the NIPAM-based polymers. It also includes the details on previous experiments on the volume-phase transition of this class of thermoresponsive polymers using solvent relaxation. Later, a small review on some theoretical and experimental findings on the solvent dynamics reported by other scientific groups have been provided. Finally, a discussion on the motional time-scales of the solvent molecules taking part in the phase-transition is described. At the end of this section, the equation which has been commonly used to explain the experimental behavior of the solvent proton relaxation has been introduced. In the following section, the construction of a new phenomenological model taking the cues from the previous theories and experimental studies is presented in detail. The section on the experimental details describes the synthesis of polymers used, and the methods used experiments in NMR and UV-visible spectroscopes. In the ‘Result and discussion’ section the experimental data and corresponding fit using our model for the different NIPAM polymers in different solvent mixtures have been presented. Also, a discussion on the physical significance of the different fitting parameters has been provided. Our results also conjectured with previous demonstrated experiments and theories. In the ‘Conclusion’ section the advantages of our proposed model along with the other scope of work using this method have been pointed out. Chapter 4 focuses on finding an optimal pulse sequence to measure T₂ of a solute in a solution in the presence of field noise. In the ‘Introduction’, the greater importance of transverse relaxation rate measurement, the different sources of decoherences and very briefly the advantages of spin-echo and CPMG have been discussed. Then a qualitative discussion on a recently developed Uhrig’s dynamic decoupling (UDD) sequence has been introduced. The motivation for choosing this sequence is discussed. The detailed description of UDD and its one of its derivative sequence, Realistic UDD (RUDD) have been given in the subsequent sections. In the next section, the concept of field noise is introduced and how it affects the decay rate of the transverse magnetization is shown mathematically. In the ‘Experiment’ section the experimental designs, protocols, parameters, and the model chemical compounds are described. The method of extraction of spectrometer noise from a free induction decay (FID) recorded for CHCl₃ has also been discussed. Subsequently, the experimental results are presented with error in tabulated form. In the next section, the results are analyzed with greater detail and the justification of the consistence of our result for various system has been provided in the light of field noise. In the same section, the limitations and the advantages of the new DD sequences are mentioned. In the final section, the advantages of using the optimal sequence for measurement of T₂ in the presence of the field-noise are mentioned. Chapter 5 is a summary of all the works done on the contrast agents needed in Magnetic Resonance Imaging (MRI). In the first section, the properties of contrast agents, the description of two methods – Relaxivity and 1D NMR imaging, which are used to characterize a newly synthesized metal complex as a contrast agent have been provided. In the following two sections, theoretical aspects of spatial encoding and relaxivity have been discussed respectively. Subsequently, for each contrast agent a section is devoted which contains a small introduction of a metal complex, synthesized by our collaborators, then experimental detail on the measurement of relaxivity constants or recording of T₁ or T₂ weighted 1D NMR images and corresponding setup of the sample followed by a concluding remark. Finally, a summary of all relaxivity and 1D-NMR based works on these contrast agents is written.

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