Chem 355 10 Lecture 32 ESR and Molecular Motions

1. Chem 355 10 Lecture 32 ESR and Molecular Motions

2. What is being observed in an MRI scan?

3. General Information What is being observed in an MRI scan? The protons associated with mobile H2O.

4. General Information What is being observed in an MRI scan? The protons associated with mobile H2O. Why is image information obtained?

5. General Information What is being observed in an MRI scan? The protons associated with mobile H2O. Why is image information obtained? The magnetic field at which “resonance” due to a specific water “pool” is observed is dependent on where the “pool” is in a magnetic field gradient across the sample.

6. First an aside on MRI: Magnetic field gradient y x sample

7. Magnetic field gradient y y x x Bo sample

8. Magnetic field gradient y y x x Bo sample Bo(x)

9. Magnetic field gradient y y Bo x x sample Bo(x)

10. Magnetic field gradient y y Bo x x sample Bo(x) Bo(y)

11. Magnetic field gradient y y Bo x x sample Bo(x)

12. Magnetic field gradient y y Bo x x sample Bo(x) Bo(y)

13. Dipolar Hyperfine Interactions.

14. , or

16. The average dipolar hyperfine contribution averages to zero. Eint =

17. The average dipolar hyperfine contribution averages to zero. There is also a particular orientation in which Eint = 0, i.e..

18. This is referred to as the “magic angle”. q = 54.7o It is of particular relevance in solid state NMR.

19. Consider now a similar dipolar (electric) interaction between e.g H2O molecules at T = 298K. In this case the 3 orientations are not equally populated. The attractive interaction would be more heavily weighted resulting in an overall total or average – ve energy.

20. Let = e1 = e2 and = e3 Let’s calculate the average Eint for H2O molecules with this geometry at 298K, given m = 1.85D and r = 4Å

26. At 4Å separation 96% of the interacting pairs occupy the attractive low-energy state. A repeat of this calculation at a separation of 5Å reveals that a much smaller fraction of the interacting pairs are able to exist in the low-energy state.

27. In a calculation of this type with the magnetic dipolar interactions involved in the hyperfine interactions in ESR or spin-spin interactions in NMR, ei << kT, the exponential terms 1, and Eint→ 0.

28. In a calculation of this type with the magnetic dipolar interactions involved in the hyperfine interactions in ESR or spin-spin interactions in NMR, ei << kT, the exponential terms 1, and Eint→ 0. Bur returning to the hyperfine splittings that are observed experimentally for a nitroxide radical with the same 3 orientations:

29. 3.2

30. It is observed that the average interaction 0. The average interaction = (0.6 + 0.6 –3.2) = –2 mT.

31. It is observed that the average interaction 0. The average interaction = (0.6 + 0.6 –3.2) = –2 mT, And the average splitting = 1/3(0.6+0.6+3.2) = 1.47 mT The latter value represents the isotropic or Fermi-contact contribution, which appears as the 3 sharp lines observed for a molecule tumbling rapidly in solution.

32. It is observed that the average interaction 0. The average interaction = (0.6 + 0.6 –3.2) = –2 mT, And the average splitting = 1/3(0.6+0.6+3.2) = 1.47 mT The latter value represents the isotropic or Fermi-contact contribution, which appears as the 3 sharp lines observed for a molecule tumbling rapidly in solution. The experimental spectra observed for the oriented radicals could be generated in the following manner:

33. z-z geometry x-x, y-y geometry aiso=1.47 mT aiso=1.47 mT +ad-d= +0.87 mT axx= ayy =0.6mT azz= 3.2 mT

34. z-z geometry x-x, y-y geometry aiso=1.47 mT aiso=1.47 mT -2ad-d= -1.73 mT +ad-d= +0.87 mT axx= ayy =0.6mT azz= 3.2 mT

35. z-z geometry x-x, y-y geometry aiso=1.47 mT aiso=1.47 mT -2ad-d= -1.73 mT +ad-d= +0.87 mT axx= ayy =0.6mT azz= 3.2 mT

37. If a spin label were able to ”jump” or rotate rapidly enough from the zz-orientation to the xx-orientation the ESR would display a sharp spectrum with a transition with a hyperfine splitting that was an average of the two.

38. If a spin label were able to ”jump” or rotate rapidly enough from the zz-orientation to the xx-orientation the ESR would display a sharp spectrum with a transition with a hyperfine splitting that was an average of the two. To determine how rapidly the exchange between the 2 orientations would have to be is determined by the Dn between the 2 hyperfine splittings. The rate is given by: hDn = gbDB

39. If a spin label were able to ”jump” or rotate rapidly enough from the zz-orientation to the xx-orientation the ESR would display a sharp spectrum with a transition with a hyperfine splitting that was an average of the two. To determine how rapidly the exchange between the 2 orientations would have to be is determined by the Dn between the 2 hyperfine splittings. The rate is given: hDn = gbDB

40. It can be noted in the nitroxide oriented spectra that the centers of the spectra, and therefore the g-values, do not coincide:

41. This reflects the anisotropy of the g-values. The diamagnetic shielding due to the electron density is a function of direction in the molecule. The anisotropy of the g-values is small in the nitroxide. Due to the small frequency differences involved, the anisotropy averages first as molecules begin to tumble in viscous solutions. In many molecules with unpaired spins, the g-value anisotropy can be large, dividing the overall spectrum in two. This appears in transition-metal complexes.

42. Differences in the rotational mobility of a nitroxide “spin label” attached at different points down the fatty-acid chain of a phospholipid is shown below:

43. The spectra clearly indicate that the mobility of the fatty acid chains at the ends or in the center of the bilayer is higher than near the phospholipid headgroup. The motions can also be shown to be isotropic.