The Applications Of Dynamic NMR Spectra On Quantitative Analysis

This thesis includes two themes:(1)The correction of the systematic bias in NMR diffusion measurement Molecular diffusion coefficients(MDCs)are always related to the molecular size,the surrounding temperature,and the solution concentration From the measurement of MDCs,one can obtain the information about molecular dynamics and molecular radius.This is important for people to understand materials in nature.The MDC measurement using the Nuclear Magnetic Resonance(NMR)technique can be retrospected to the Spin-Echo(SE)pulse sequence which was developed by Hahn in the 1950s.The MDC value can be gained through a pair of the Pulsed Field Gradients(PFGs)which encode the spatial position of the molecule and the diffusion decay profile which are made of the SE signals.After that,Stejskaland Tanner et al.modified the SE pulse sequence and proposed their so-called Stimulated Spin-Echo(SSE)pulse sequence which avoided the effects of spin-spin relaxation in the SE pulse sequence.This enhanced the signal-to-noise ratio,and so it has a wide range of application in the MDC measurement.For most small molecules,the MDC value can be easily obtained via least-squares fitting on the Stejskal-Tanner equation.However,due to the complication of the molecular structure in many polymers and bio-macromolecules and the distribution of the MDCs in these molecules,the result which gained from the fitting of the Stejskal-Tanner equation no longer represents the real average MDC value of these macromolecules.There exists a systematic error between the fitting result and the real average MDC value,which influences the accurate estimation of molecular radius and molecular dynamics.In this paper,the theoretical research and the numerical simulation were both applied according to the above problem in order to study the NMR diffusion experiment.The MDCs are trend to give a normal distribution in most macromolecules.In this paper,we assumed a normal distribution of the MDCs and substituted the distribution function into the Stejskal-Tanner equation,after that,we have solved this equation.Through the precise mathematical reasoning,we obtained the analytical form of this systematic bias which caused by the distribution of the MDCs.Meanwhile,we have done the numerical simulation of the diffusion experiment on macromolecules and,we demonstrated that under the existence of the distribution of MDCs there would always come out a systematic bias in both linear and non-linear least-squares fitting of the Stejskal-Tanner equation The result obtained from the numerical simulation matches well with our theoretical analytical solution.We also provided the revised form of this bias under both linear and non-linear fitting.By means of theoretical analysis and numerical simulation here we conclude that(1)under the existence of the distribution of MDCs,the fitting result obtained from Stejskal-Tanner equation has a systematic bias with the real MDC value;(2)this bias is proportional to the square of the distribution half-width;(3)to those experiment data which contain quite big noises,the linear fitting will magnify the noises so that the fitting result will be impacted,while the non-linear fitting can give better result;(4)with the growth of the dispersion of the distribution the bias will become bigger synchronously.In our research,the systematic bias can reach to 5%and 2%in linear and non-linear fitting,respectively.This makes the result from NMR diffusion measurement to be inaccurate.The conclusions of this paper have big significances on the data processing of the NMR diffusion experiment and,these results have reference value on quantitative analysis and accuracy of measurement of the MDCs.(2)The quantitative analysis of cross-polarization(CP)from overlapped peaksIn solid NMR,due to the limitation of motion between molecules,the dipole-dipole coupling becomes strong and this leads to a homogeneous broadening of the spectral peaks.The invention of magic-angle spinning(MAS)technique narrows the solid peaks effectively,but owning to the limitation of the spinning speed,the dipole-dipole interaction cannot be removed thoroughly.When the chemical shifts of two molecules in the sample are quite close,there always shows an overlapped peak which results in big difficulty on spectra analysis and quantitative analysis.In addition,to those nucleuses which have low natural abundance,such as 13C,the cross-polarization(CP)method should be applied to gain quite satisfied signal-to-noise ratio.However,due to the differences of the CP efficiency among different nucleuses,the CP spectra cannot reflect the quantitative information of the sample.The proposal of the reciprocal relation solves the problem about quantification in CP spectra.However,because of the difficulty in distinguishing each component in the overlapped peak,this quantification method is helpless in problems of overlapped peaks.The decomposition and quantification of overlapped peaks is always a big challenge in solid NMR.In this paper,we proposed a multivariable analysis method to distinguish the different parts contained in the overlapped peak via different spin-lattice relaxation times.Through the measurement of molecular spin-lattice relaxation time,and the data matrix decomposition together with the multivariable analysis we can obtain the information of each component in the overlapped peak and we can also gain their spin-lattice relaxation times.Further,via quantification of the CP spectra,the quantitative information of each component in the overlapped peak can be calculated.In this paper,a PEO powder sample were used and tested.The Torchia pulse sequence which are applied for measuring the spin-lattice relaxation time were optimized,and the CP pulse sequence were also optimized.After the experiments and the calculations,we obtained the quantitative spectra of the two components which each stand for the crystalline part and the amorphous part of the PEO successfully.Besides,the crystallinity of this PEO sample was derived from the quantitative information of the spectra.The method we proposed here not only can be applied to test the crystallinity of polymers but also can be used to stuy the CP dynamics of the individual components in the overlapped peaks.This method therefore has significant meaning in quantitative analysis of overlapped peaks.It has solved a big problem in the analysis of overlapped peaks.