Charithram
1926: Pauli’s    prediction of nuclear spin
1932: Detection of nuclear magnetic moment by Stern
1936: First the...
Nuclear spin

              Neutrons and protons have S = 1/2
                    Nucleons are fermions
                Th...
Zeeman interaction

 In the atom, the orbital angular momentum
   of the electrons gives rise to a magnetic
 dipole moment...
Precession model

    A            B              C




                           B0
D            E         F            ...
Nuclear Magnetic Resonance




          B0



Precession non-observable       Precession observable




   The process of...
Nuclear Magnetic Resonance

         For a spin-1/2 nucleus




                     RF    ~ 100 MHz




Frequency of emis...
Nuclear Magnetic Resonance

        The population deference between the high
    and low energy levels by the Boltzmann d...
Nuclear Magnetic Resonance

                  Bloch Equations:




         Transverse (spin-spin) relaxation: T2
        ...
NMR interactions


     There are five important NMR interactions


    ˆ     ˆ     ˆ    ˆ     ˆ     ˆ
    H N = H Z + HQ ...
Chemical shift
                            1H   NMR
 I feel shy..!                                   Well, I don’t..!

   ...
Chemical shift

 ppm scale:
       In a 9.4T Magnet, 1H Larmor frequency =400MHz
       In a 9.4T Magnet, 13C Larmor frequ...
J-coupling
                                                   30 MHz
               Indirect interaction
                 ...
Dipolar coupling

              Direct interaction
         ˆ = "d(3cos 2 # "1) I S
         H D IS              ˆˆ
      ...
Quadrupolar coupling

    Nuclei with Spin>1/2 have Electric Quadrupole Moments
        (non-spherical charge distribution...
Chemical shift anisotropy (CSA)

Chemical shift is dependent on the orientation of the
         nuclei in the molecule in ...
Magic Angle Spinning (MAS)
                                 Experimental MAS speed can
                                 av...
Magic Angle Spinning (MAS)

          Rotors                                Probe-head

7mm                               ...
Spin decoupling
 Liquid                                         Solid
JFH                    Combining MAS and dipolar dec...
Practical liquid state NMR
Locking:
In high-field super-conducting NMR magnets, field drift happens
often. This is of very...
Practical liquid state NMR
Shimming:
The effective magnetic field experienced by the sample should be
homogeneous all over...
Practical liquid state NMR
Tuning and Matching:
The NMR probe is an Inductor-Capacitor circuit. The capacitance
has to be ...
Practical liquid state NMR
RF pulse:




                     Advantage
                   -no freq. sweep
               ...
Practical liquid state NMR
Fourier transformation:
The observed NMR signal is in time domain, which is a very
complicated ...
NMR Magnet




             probe is introduced from the bottom
                                            24
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Nmr for friends

  1. 1. Charithram 1926: Pauli’s prediction of nuclear spin 1932: Detection of nuclear magnetic moment by Stern 1936: First theoretical prediction of NMR by Gorter 1944: Nobel Prize in Physics to Rabi 1945: First NMR of a liquid (H2O) by Bloch & solid (paraffin) by Purcell 1949: Discovery of chemical shifts 1952: Nobel Prize in Physics to Bloch and Purcell 1992: Nobel Prize in Chemistry to Ernst 2002: Nobel Prize in Chemistry to Wüthrich 2003: Nobel Prize in Medicine to Mansfield and Lauterbur 1
  2. 2. Nuclear spin Neutrons and protons have S = 1/2 Nucleons are fermions They obey Pauli (separately) Hence, there is “Nuclear Shell Model” S(4He, 16O)=0 S(11B, 23Na)=3/2 S(93Nb, 115In)=9/2 S(138La)=5 S(1H, 13C)=1/2 S(17O, 27Al)=5/2 S(10B)=3 S(50V)=6 S(2H, 14N)=1 S(45Sc, 133Sc)=7/2 S(40K)=4 S(176Lu)=7 2
  3. 3. Zeeman interaction In the atom, the orbital angular momentum of the electrons gives rise to a magnetic dipole moment which interacts with external magnetic fields In the normal Zeeman effect, electronic states with angular momentum have split energy levels in the presence of a magnetic field Similarly, a single nucleon with intrinsic angular momentum (spin) can interact with an external magnetic field, with different energy configurations 3
  4. 4. Precession model A B C B0 D E F G Low energy High energy relaxing 4
  5. 5. Nuclear Magnetic Resonance B0 Precession non-observable Precession observable The process of making precession observable is NMR 5
  6. 6. Nuclear Magnetic Resonance For a spin-1/2 nucleus RF ~ 100 MHz Frequency of emission / absorption = ΔE/h #B0 "L = 2$ 6
  7. 7. Nuclear Magnetic Resonance The population deference between the high and low energy levels by the Boltzmann distribution: "hB 0 Na =e kT Nb Population difference ∝ Signal intensity Favorites: a. High field b. Low temperature ! 7
  8. 8. Nuclear Magnetic Resonance Bloch Equations: Transverse (spin-spin) relaxation: T2 Longitudinal (spin-lattice) relaxation: T1 T2 describes the line-width of your signal T1 asks you to wait until net magnetization comes back to thermal equilibrium 8
  9. 9. NMR interactions There are five important NMR interactions ˆ ˆ ˆ ˆ ˆ ˆ H N = H Z + HQ + H D + HCS + H J Zeeman interaction ~ 100 MHz Quadrupolar interaction ~ 1-10 MHz Dipolar interaction ~ 100 kHz ! Chemical shift interactions ~ 10 kHz Scalar (J) interaction ~ 100 Hz 9
  10. 10. Chemical shift 1H NMR I feel shy..! Well, I don’t..! + chemical + information e¯ I’m de-shielded I’m well-shielded I’m observed down-field Hmm.. Up-field You need high frequencies Haha.. Low freqs are enough I’ve high chemical shifts I’ve low chemical shifts -OH -CH3 In comparison with TMS 10
  11. 11. Chemical shift ppm scale: In a 9.4T Magnet, 1H Larmor frequency =400MHz In a 9.4T Magnet, 13C Larmor frequency=101MHz In a 9.4T (400 MHz) Magnet, 1H chemical shift of 1ppm =400Hz In a 9.4T (400 MHz) Magnet, 1H chemical shift of 1Hz =1/400ppm In a 9.4T (400 MHz) Magnet, 13C chemical shift of 1ppm=101Hz In a 9.4T (400 MHz) Magnet, 13C chemical shift of 1Hz=1/101ppm 1H chem. shift of 1ppm is the same for 9.4T and 11.7T 1H chem. shift of 1Hz is 1/400ppm for 9.4T and 1/500ppm for 11.7T 11
  12. 12. J-coupling 30 MHz Indirect interaction Remember n+1 rule & Pascal’s triangle bonding 700 MHz information Through bond Travels with Fermi and Pauli. Not visible in solid state..! 12
  13. 13. Dipolar coupling Direct interaction ˆ = "d(3cos 2 # "1) I S H D IS ˆˆ z z distance information vector ! # µ0 & h) I ) S d =% ( 3 " $ 4 " ' rIS Through space ! 1 H, 1 H: 1Å: 120kHz 1 H, 13C: 1Å: 30kHz ! 1 H, 13C: 13C, 13C: 2Å: 3.8kHz 2Å: 0.95kHz Averaged in solution state..! 13
  14. 14. Quadrupolar coupling Nuclei with Spin>1/2 have Electric Quadrupole Moments (non-spherical charge distribution on nucleons) A quadrupole interacts with electric field gradients (EFG) CQ = eQVzz /h symmetry information ! P2Cosθ P4Cosθ c = 54,736°  P2(c)=0 c = 30,55° or 70,11°  P4(c)=0 Averaged in solution state..! 14
  15. 15. Chemical shift anisotropy (CSA) Chemical shift is dependent on the orientation of the nuclei in the molecule in a solid σ11, σ22, σ33 are the three asymmetry (η) principal components of the chemical shielding tensor. crystallography information #"11 0 0& % ( " PAS = % 0 " 22 0 ( %0 $ 0 " 33 ( ' ! Averaged in solution state..! 15
  16. 16. Magic Angle Spinning (MAS) Experimental MAS speed can average only the first order quadrupolar interaction and never the second order..! 1H MAS NMR 23Na MAS NMR Spinning the powder sample at magic angle rapidly with respect to the external 0kHz magnetic field averages the orientation dependent terms to zero..! 20 kHz Experimental MAS speed can often average CSA (~10kHz). But never the dipolar coupling (~100kHz)..! a) polycarbonate b) sodium citrate 16
  17. 17. Magic Angle Spinning (MAS) Rotors Probe-head 7mm in 4mm 3.2mm KEL-F BN stator ZrO2 2.5mm 1.3mm 70kHz 35kHz 8kHz 18kHz 23kHz 17
  18. 18. Spin decoupling Liquid Solid JFH Combining MAS and dipolar decoupling MAS alone reduces line-w idth from 5000 Hz to 200 Hz MAS & decoupling reduces line- w idth from 5000 Hz to 2 Hz Decoupling alone reduces line- w idth from 5000 Hz to 450 Hz Similar to liquid state sample..! δ(19F) δ(13C) 18
  19. 19. Practical liquid state NMR Locking: In high-field super-conducting NMR magnets, field drift happens often. This is of very small magnitude (eg: 5Hz per Hr), but big enough to affect liquid state NMR spectra. A frequency lock to the deuterium signal in the deuterated solvent helps to avoid this problem. Each solvent has a different lock frequency. So locking to a wrong solvent kills the spectrum. 19
  20. 20. Practical liquid state NMR Shimming: The effective magnetic field experienced by the sample should be homogeneous all over the sample volume. In other words, there should not be any field gradient. This is achieved by introducing various currents to the gradient shimming coils, so that a homogeneous magnetic field is effected on a specific sample volume. 20
  21. 21. Practical liquid state NMR Tuning and Matching: The NMR probe is an Inductor-Capacitor circuit. The capacitance has to be changed for the inductor to deliver radio waves of different frequencies. In a 9.4T magnet, if I want to observe 1H, I have to change the capacitance, so that the induction coil supplies me 400MHz RF. This process, in practice, involves Tuning, where suitable frequency is selected and Matching, where Q of circuit is matched. 21
  22. 22. Practical liquid state NMR RF pulse: Advantage -no freq. sweep -no field sweep FID 22
  23. 23. Practical liquid state NMR Fourier transformation: The observed NMR signal is in time domain, which is a very complicated piece of information. FT is done to view this in the frequency domain. Phasing: Signals obtained in NMR are having a real and an imaginary part. To observe the ‘real-only’ part, an absorptive mode is helpful. Phasing of the signal helps to achieve the absorption mode from the dispersion mode. Referencing: Usually in liquid state NMR, a standard sample with most shielded nuclei is used as an internal chemical shift reference. Eg: TMS for 1H and 13C NMR (0ppm) 23
  24. 24. NMR Magnet probe is introduced from the bottom 24
  25. 25. 25

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