Active Nuclei in NMR NMR and the periodical table Spin one-half Chemical Shift and Coupling Single Detection vs Quadrature Detection Relaxation
Active Nuclei in NMR Nuclei are composed of Neutrons and Protons. To be active in NMR, the nuclei need to posses a property called the Spin (Spin is represented by the letter I in quantum mechanic). When introduced in a magnetic field B0 the nuclei magnetic moment will orient in (2 n I + 1) orientations. If you look at the periodic table animation below, we can extract the general rules: · Even Mass nuclei that have Even number of neutron have I=0 (not interesting from the NMR point of view) · Even Mass nuclei that have Odd number of Neutrons have an Integer Spin quantum number · Odd Mass nuclei have half integer Spin quantum number NMR and the Periodic table You can examine the NMR properties of various nuclei (frequency, spin state, natural abundance, chemical shift...), in the following animated movie of the periodical table. (For Windows-95 5.3 Mb) ( Shockwave animation) Spin one-half This course will describe mainly spin one-half nuclei for which the magnetic moment can orient with or against the field. The energy difference between the two orientations is very small and therefore both orientations will be populated by almost the same number of nuclei (e.g. at 1.5 Tesla, out of 2 million nuclei, there is an excess of 15 nuclei in the parallel orientation). Each isotope (that is active in NMR) is characterized by a magnetogyric ratio (constant) and posses a Magnetic Moment. In the magnetic field, those magnetic moments orient and precess at the so called "Larmor Frequency". The Larmor frequency is directly proportional (the constant of proportionality is the magnetogyric ratio ) to the applied field. Increasing the field on a spectrometer will have several effects: · It does increase the Larmor frequency of the various nuclei · The energy between the two orientations is increasing as the field increases · As the energy gap becomes more important the population difference between the two orientations increases, so does the sensitivity. (The sensitivity varies as the cube of the frequency) · The chemical shift is also directly proportional to the applied field whereas the coupling constants are independent. Therefore by submitting a sample to a higher field one expect to simplify the spectra as many of the second order effect disappear. You can watch precession and the effect of the field in the following Shockwave animated movie. Chemical Shift and Coupling Chemical shift and the various parameters the NMR we can measure in NMR are discussed in the following Shockwave animation . The coupling constants are discussed in more depth in the following animation.
Single Detection vs Quadrature Detection The NMR data on modern spectrometers are usually obtained in the time domain (Free Induction Decay - FID). Fourier Transform is the mathematical process used to obtain from the time domain data the more familiar frequency domain spectra. The acquisition of the data in the time domain require that the data are digitized in order to be able to save the data in a computer. There are two ways to acquire the data in the time domain: Single detection (older) and Quadrature detection (modern). Those two methods can be examined in the following animation. In this animation you will also find discussion on the various aspects concerning the sampling of the FID (Spectral Window, sampling rate, Acquisition time, Number of points, Nyquist theorem, digital resolution ...). These terms are briefly defined in the table below.
Abbreviations Parameter Explanation SW Spectral window The frequency range being sampled. Nyquist theorem In order to sample properly a sine wave through a digitization process, at least two data points per cycle are needed. Sampling rate As SW is the maximum frequency (fastest frequency) being sampled, and following the Nyquist theorem that the sampling rate must be => 2 points/cycle, this means that the sampling rate must be 2*SW (cycles per seconds - Hz). - calculated by the spectrometer. DW Dwell Time The time interval between the acquisition of individual data points => 1/(2*SW) NP (TD) Number of Points The number of points taken on an FID will control the digital resolution. For a given number of points, one obtain (NP/2) real and (NP/2) imaginary points in the spectra. AT (AQ) Acquisition time Total time to acquire the FID. It can be calculated from the number of points and the time it takes to acquire each data point (dwell time) AT=NP/(2*SW) DR Digital Resolution The accuracy of the frequency domain depends on the number of point per frequency interval => DR=(2*SW)/NP or DR=1/AT Prior to sampling, of course, a pulse that nutate the magnetization in the XY plane, have been applied. You can learn more about the pulse in the Pulse Tools section: Pulses: Pulse Phase and Pulse Power. The pulse and the receiver can be cycled together to get rid of some artefacts. Phase cycling is described in more details in the 1D - Phase cycle section of the tool box. Relaxation Once the magnetization have been excited with a pulse, it needs to return to equilibrium. The process that returns the magnetization to the +Z axis is called the Spin-Lattice relaxation time and is abbreviated: T 1 (do not mix this term with the evolution time t1 in 2D NMR). T 1 is further discussed in the next chapter. This process can be best measured with the Inversion recovery. You can watch this experiment in the following animation. Once the magnetization is coherent in phase in the XY plane (transverse plane) after a pulse, it needs to return to equilibrium: by loosing it's phase coherence. This relaxation time is called the Spin-Spin relaxation time and is abbreviated: T2 (do not mix this term with the acquisition time t2 in 2D NMR). T2 is further discussed in the next chapter. This process can be best measured with the Spin Echo experiment. You can watch this experiment in the following animation. This experiment can also be used to measure diffusion in the NMR tube by using gradients. To have more information about the gradient version of that experiment you can consult the following animation
| Chemistry | NMR internal site | NMR on Avance spectrometer ] Basic Concepts T1 - Relaxation time
Spin-lattice Relaxation time T1 (longitudinal) The relaxation time T1 represents the "lifetime" of the first order rate process that returns the magnetization to the Boltzman equilibrium along the +Z axis. T1 relaxation time can be measured by various techniques describe in the table below. Name Pulse Sequence signal evolution vs T1 Inversion Recovery (IRFT) D1-180-tau-90
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