Solid-state 2 H NMR Spectroscopy for the Undergraduate Physics Laboratory

1. Solid-state 2H NMR Spectroscopy for the Undergraduate Physics Laboratory Jacob J. Kinnun, Avi Leftin, Michael F. Brown University of Arizona, Tucson, AZ

2. Project Introduction Why is Solid-state NMR important? • Quantifies structure and dynamics of molecular systems • Growing applications to Biophysics in areas such as proteins and cellular membranes The Problem • Lack of undergraduate education on the subject The Goal • Provide a feasible and meaningful experiment for undergraduate research

3. Experiment Outline • Use powder deuterated hexamethylbenzene sample • Use a more available commercial solution NMR spectrometer • Use a quadrupolar echo pulse sequence • Interpret data using rotational symmetries

4. What is NMR? NMR in General • NMR stands for Nuclear Magnetic Resonance • Measures the spins of nuclei and their environmental properties Solid-state NMR • Uses samples in solid form (unlike solution NMR) • Often requires expensive and custom equipment 2H NMR • Measures the quadrupole effects of the deuterium nucleus

5. Basic NMR Theory • Zeeman Effect (static magnetic field) • Time dependent solution from Schrödinger equation • Spins precess around the static magnetic field and can be observed when “pulsed” to the x axis at the Larmor frequency

6. Quadrupolar Coupling • Quadrupolar Hamiltonian • Axially symmetric energy eigenvalues and frequency splitting

7. Euler Angles • Powder ensemble average and Wigner rotation element • Decomposition for parallel and perpendicular • Decomposition for internal symmetries • Final Result

8. Spectral Narrowing • Static coupling • Methyl group symmetry • Axial symmetry

9. NMR Spectrometer

10. Quadrupolar Echo Pulse Sequence • 1st pulse causes a free induction decay (FID) • 2nd pulse refocuses the FID • Solid-state spectrometers achieve 3-5 µs 90o pulse lengths

11. Solid-state Spectrometer Results • Bruker 500 Spectrometer

12. Solution Spectrometer Results • Bruker DRX-500 Spectrometer ~ 4 hours

13. Conclusions • Experiment feasible on solid-state and solution NMR spectrometers • Theoretical involvement is flexible for undergraduate physics students • Opens a doorway to biophysics theory and research

14. Future Work • Variable field NMR • “Hydration forces” on cellular membranes • Extend project to cover relaxation

15. Acknowledgements • Avi Leftin • Dr. Michael F. Brown • University of Arizona – Yay Matlab! • TCB Group at UI – Visual Molecular Dynamics

16. Solution Spectrometer Results • Varian 300 Spectrometer ~ 10 minutes

17. Free Induction Decay

18. Solid-state Spectrometers