1. Solid-state 2 H 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 2 H 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. Static coupling Methyl group symmetry Axial symmetry Spectral Narrowing

9. NMR Spectrometer

10. Quadrupolar Echo Pulse Sequence 1 st pulse causes a free induction decay (FID) 2 nd pulse refocuses the FID Solid-state spectrometers achieve 3-5 µs 90 o 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 Extend project to cover relaxation Variable field NMR “Hydration forces” on cellular membranes

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