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Content 1.Basic Concepts of Nuclear Spins in a Magnetic Field a. Angular momentum, magnetic moments, magnetization b. Precession of the classical magnetization.

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Presentation on theme: "Content 1.Basic Concepts of Nuclear Spins in a Magnetic Field a. Angular momentum, magnetic moments, magnetization b. Precession of the classical magnetization."— Presentation transcript:

1 Content 1.Basic Concepts of Nuclear Spins in a Magnetic Field a. Angular momentum, magnetic moments, magnetization b. Precession of the classical magnetization c. RF irradiation, resonance and the rotating frame d. Concepts of quantum mechanics* e. T1 and T2 Relaxation * Extension depending on students 3. Basic Concept of Pulsed NMR a. The Bloch equations, NMR signals in the laboratory frame b. NMR signals in the rotating frame, quadrature detection c. Manipulating the magnetization and continuous wave spectroscopy d. T1 and T2 measurement, Hahn echo e. Free induction decays and Fourier transform f. FFT, data sampling, spectral width and Nyquist Theorem g. RF pulses, off-resonance effects and composite pulses h. The NMR spectrometer i. Phase cycling j. Digital filtering, pulse programming, the magnet and field inhomogeneity NMR-Primer for Chemists and Biologists Shimon Vega & Yonatan Hovav and November 2013 1

2 4. The NMR Interactions and 1D spectra a. Chemical shift, isotropic and CSA-interactions b. The vector model and two level system c. Nuclear spin-spin interactions and spectral multiplets d. INEPT and COSY e. Decoupling 5. Two dimensional NMR a. Basic principles b. 2D COSY c. Twisted peaks in 2D NMR, TPPI and STATES d. Examples of 2D experiments e. Nuclear Overhauser Effect and NOESY 6. Solid State NMR Basic principles* * Depending on time left 2

3 Some books: Modern NMR techniques for Chemistry Research by A.E Derome Nuclear Magnetic Resonance spectroscopy by R.K Harris Advanced: Spin Dynamics by M.H Levitt Understanding NMR Spectroscopy by James Keeler Principles of NMR in 1 and 2 Dimensions by R. R. Ernst, G. Bodenhausen A. Wokaun Principles Magnetic Resonance by C. P. Slichter Solid State NMR Spectroscopy by M Duer Web: 1. 2. 3

4 Born (1905-10-23)October 23, 1905 Zürich, Switzerland ZürichSwitzerland Died September 10, 1983(1983-09-10) (aged 77) Zürich, Switzerland ZürichSwitzerland CitizenshipSwiss, American NationalitySwiss FieldsPhysics Institutions University of California, Berkeley Stanford University Alma mater ETH ZürichETH Zürich and University of Leipzig University of Leipzig Doctoral advisorWerner Heisenberg Known for NMR Bloch wall Bloch's Theorem Bloch FunctionNMR Bloch wall Bloch's Theorem Bloch Function (Wave) Bloch sphere Bloch sphere Notable awards Nobel Prize for Physics Nobel Prize for Physics (1952) Born (1912-08-30)August 30, 1912 Taylorville, Illinois, USA Taylorville, Illinois USA Died March 7, 1997(1997- 03-07) (aged 84) Cambridge, Massachusetts, USA Cambridge, MassachusettsUSA NationalityUnited States FieldsPhysics Institutions Harvard University MIT Alma mater Purdue University Harvard University Doctoral advisorKenneth Bainbridge Other academic advisors John Van Vleck Doctoral students Nicolaas Bloembergen George Pake George Benedek Charles Pence Slichter Known for Nuclear magnetic resonanceNuclear magnetic resonance (NMR) Smith-Purcell effect 21 cm line Smith-Purcell effect 21 cm line Notable awards Nobel Prize for PhysicsNobel Prize for Physics (1952) Felix Bloch Edward Purcell 4

5 1920's Physicists have great success with quantum theory Quantum theory was used to explain phenomena where classical mechanics failed. This theory, proposed by Bohr, was particularly useful for the understanding of absorption and emission spectra of atoms. These spectra showed discrete lines which could be accounted for quantitatively by quantum theory. However, this theory still could not explain doublet lines found in high resolution spectra. 1921 Stern and Gerlach carry out atomic and molecular beam experiments The basis of quantum theory was confirmed by the atomic beam experiment. A beam of silver atoms was formed in high vacuum and passed through a magnetic field. 1925 Uhlenbeck and Goudsmit introduce the concept of a spinning electron The idea of a spinning electron with resultant angular momentum gave rise to the magnetic dipole moment. 1926 Schrödinger/Heisenberg formulate quantum mechanics This new branch of quantum physics replaced the old quantum theory. Quantum mechanics was successful for understanding many phenomena but still could not account for doublets in absorption and emmision spectra. 1927 Pauli and Darwin include electron spin in quantum mechanics 1933 Stern and Gerlach measure the effect of nuclear spin Stern and Gerlach increased the sensitivity of their molecular beam apparatus enabling them to detect nuclear magnetic moments. They observed and measured the deflection of a beam of hydrogen molecules. This has no contribution to the magnetic moment from electron orbital angular momentum so any deflection would be due to the nuclear magnetic moment. 5

6 1936 Gorter attempts experiments using the resonance property of nuclear spin The Dutch physicist, C.J.Gorter, used the resonance propertyresonance of nuclear spin in the presence of a magnetic field to study nuclear paramagnetism. Although his experiment was unsuccessful, the results were published and this brought attention to the potential of resonance methods. 1937 Rabi predicts and observes nuclear magnetic resonance During the 1930's, Rabi's laboratory in Columbia University became a leading center for atomic and molecular beam studies. One experiment involved passing a beam of LiCl through a strong and constant magnetic field. A smaller oscillating magnetic field was then applied at right angles to the initial field. When the frequency of the oscillating field approached the Larmor frequency of the nucleus in question, resonance occurred. The absorption of energy was recorded as a dip in the beam intensity as the magnetic current was increased. 1943 Stern awarded the Nobel prize for physics Otto Stern was awarded this prize 'for his contribution to the development of the molecular ray method and discovery of the magnetic momentum of the proton'. 1944 Rabi awarded the Nobel prize for physics Rabi was given this prize for his work on molecular beams, especially the resonance method. 6

7 1945 Purcell, Torey and Pound observe NMR in a bulk material At Harvard, Purcell, Torey and Pound assembled apparatus designed to detect the transition between nuclear magnetic energy levels using radiofrequency methods. Using about 1kg of parrafin wax, the absorbance was predicted and observed. 1951 Packard and Arnold observe that the chemical shift due to the -OH proton in ethanol varies with temperature. It was later shown that the chemical shift for this proton was also dependent on the solvent. These results were explained by hydrogen bonding. 1952 Bloch and Purcell share the Nobel prize in physics This prize was awarded 'for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith'. 1953 A. Overhauser predicts that a small alteration in the electron spin populations would produce a large change in the nuclear spin polarisation. This theory was later to be named the Overhauser effect and is now a very important tool for the determination of complex molecular structure. 1957 P. Lauterbur and C. Holm independently record the first 13 C NMR spectra. Despite the low natural abundance of the NMR active isotope 13 C,isotope the recorded spectra showed a signal to noise ratio as high as 50. 1961 Shoolery introduces the Varian A-60 high-resolution spectrometer. The Varian A-60 was used to study proton NMR at 60MHz and proved to be the first commercial NMR spectrometer to give highly reproducible results. 7

8 2. Basic Concepts of Nuclear Spins in a Magnetic Field a. Angular momentum, magnetic moments: magnetization We are dealing with the nuclei of atoms and in particular with their magnetic properties. The nuclei are characterized by their “spin values”. These spins correspond to well-defined angular momenta with values proportional to Planck’s constant: with h = 6.6260755x10 34 m 2 kg/sec and The protons and neutrons (fermions) composing the nuclei determine the nuclear spin value. A nucleus with an odd mass number M has an half-integer spin and a nucleus of an even M has an integer spin. Nuclei with an even number of protons and neutrons have nuclear spin I=0. Each nuclear spin has a magnetic moment proportional to its angular momentum-spin. Proton: g = 5.5856912 +/- 0.0000022 Neutron: g = -3.8260837 +/- 0.0000018 For each nucleus the angular momentum vector and the magnetic moment vector are related by its magnetogyric ratio  (from QM) or  magnetogyric ratio 8

9 9 General comments about angular momentum: Remember: conservation of angular momentum ! ` q = charge q/L = charge density L = 2  r v = velocity i = current A = area A =  2 r 1.The torque on the magnetic moment induced by a magnetic field B 2.Energy of a magnetic moment in a magnetic field Minimizing energy moment of inertia number of turn per second number of radians per second General comments about magnetic momentums: e Reminder: 9

10 1 H Hydrogen ½300.130 2 H Deuterium 1 46.073 3 H Tritium 1/2 320.128 3 He Helium 1/2 228.633 6 Li Lithium 1 44.167 7 Li Lithium 3/2 116.640 9 Be Beryllium 3/2 42.174 10 B Boron 3 32.246 11 B Boron 3/2 96.258 13 C Carbon 1/2 75.46 Larmor Frequencies in MHz units: with 100MHz - 2.3 T 300MHz - 7.0 T 500MHz - 11.7 T 800MHz - 18.8 T 900MHz - 21.1 Tesla (2.1 KHz - 0.5 Gauss) 1T = 10,000G Proton NMR: 10

11 Element/NameIsotope SymbolNuclear Spin Sensitivity vs. 1 H Hydrogen 1H1H1/21.000000 Deuterium 2 H or D11.44 e-6 Tritium 3H3H1/2- HeliumHelium-3 3 He-1/2- LithiumLithium-6 6 Li10.000628 Lithium-7 7 Li3/20.270175 BerylliumBeryllium-9 9 Be-3/20.013825 BoronBoron-10 10 B30.00386 Boron-11 11 B3/20.132281 CarbonCarbon-13 13 C1/20.000175 NitrogenNitrogen-14 14 N10.000998 Nitrogen-15 15 N-1/23.84E-06 OxygenOxygen-17 17 O-5/21.07E-05 FluorineFluorine-19 19 F1/20.829825 NeonNeon-21 21 Ne-3/26.3E-06 SodiumSodium-23 23 Na3/20.092105 MagnesiumMagnesium-25 25 Mg-5/20.00027 AluminumAluminum-27 27 Al5/20.205263 SiliconSilicon-29 29 Si-1/20.000367 Receptivity : (natur.abund.-%) x  x I(I+1) PhosphorusPhosphorus-31 31 P1/20.06614 SulfurSulfur-33 33 S3/21.71E-05 ChlorineChlorine-33 33 Cl3/20.003544 Chlorine-37 37 Cl3/20.000661 PotassiumPotassium-39 39 K3/20.000472 Potassium-41 41 K3/25.75E-06 CalciumCalcium-43 43 K-7/29.25E-06 ScandiumScandium-45 45 Sc7/20.3 TitaniumTitanium-47 47 Ti-5/20.00015 TitaniumTitanium-49 49 Ti-7/20.00021 VanadiumVanadium-50 50 V60.00013 Vanadium-51 51 V7/20.37895 ChromiumChromium-53 53 Cr-3/28.6E-05 ManganeseManganese-55 55 Mn5/20.174386 IronIron-57 57 Fe1/27.37E-07 CoboltCobolt-59 59 Co7/20.275439 NickelNickel-61 61 Ni-3/24.21E-05 CopperCopper-63 63 Cu3/20.064035 CopperCopper-65 65 Cu3/20.035263 ZincZinc-67 67 Zn5/20.000117 1/213/55/27/29/2 Frequency (MHz) Tesla - MHz 5 x10 -5 2.1 x10 -3 2.35 100 7.05 300 9.40 400 11.75 500 18.80 800 21.15 900 11

12 2b. The classical precession of the magnetization Suppose we apply a magnetic field on our magnetization: as a result a torque tries to rotate the direction of the angular momentum. A torque ( ) perpendicular to an angular momentum causes a precession motion: Example: top view: From Remember the motion of a top: (gravitation + top) 12

13 x y z The Larmor frequency The precession of the magnetization around the magnetic field direction is independent of the orientation of (in analogy with ) 13

14 2c. RF irradiation, resonance and the rotating frame Let Let us now consider a special time-dependent magnetic field: The equation of motion for the magnetization in an external magnetic field x y z Laboratory frame x y z How does magnetic moment respond? 14

15 To follow the response of the magnetization let us rotate the coordinate system: Then we get the equation of motion: and insertion of the original equation of motion: we get Thus the equation of motion in the rotating frame becomes: 15

16 Thus in the rotating frame the magnetic field becomes time-independent while the z-magnetic field component is reduced by the frequency of rotation x RoF y RoF z RoF On-resonance, when, there is only an x-components to the field. In such a case the magnetization performs a precession around the x-direction with a rotation frequency. rotating frame How to generate this B 1 RF irradiation field in the laboratory frame: x y x y z Ignore because it is off-resonance! Top view B0B0 16

17 Doty Scientific National High Magnetic Field Laboratory Bird cage Thus the magnetic field in the laboratory frame : Becomes in the rotating frame: Although the signal detection in the laboratory frame is along the direction of the coil: In NMR we measure the magnetization in the rotating frame: in: out: A sample with an overall the S/N voltage at the coil is: f = noise of apparatus  = filling factor  = frequency  =band width Q = quality factor V s = sample volume 17

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