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Pulsed Epr Primer PULSED EPR PRIMER Dr. Ralph T. Weber Bruker Instruments, Inc. Billerica, MA USA Pulsed EPR Primer Copyright © 2000 Bruker Instruments, Inc. The text, figures, and programs have been worked out with the utmost care. However, we cannot accept either legal responsibility or any liability for any incorrect statements which may remain, and their consequences. The following publication is protected by copyright. All rights reserved. No part of this publication may be reproduced in any form by photocopy, microfilm or other proce- dures or transmitted in a usable language for machines, in particular data processing systems with- out our written authorization. The rights of reproduction through lectures, radio and television are also reserved. The software and hardware descriptions referred in this manual are in many cases registered trademarks and as such are subject to legal requirements. Preface I gratefully acknowledge the many useful comments and discus- sions with Professor Gareth Eaton of the University of Denver and Dr. Peter Hoefer of Bruker Analytik. This document is best viewed with Adobe AcrobatTM 4.0. If you are using a PC running Microsoft WindowsTM, you can also view the several animations that are interspersed throughout the text. Simply click the movie poster with the blue frame and the movie will play in a floating window. To close the floating win- dow, place your cursor in the frame and press the <Esc> key. A Movie Poster iv Table of Contents 1 Pulse EPR Theory..................................................................3 1.1 The Rotating Frame..................................................................................... 3 Magnetization in the Lab Frame ................................................................... 4 Magnetization in the Rotating Frame ........................................................... 6 Viewing the Magnetization from Both Frames: The FID ........................... 10 Off-Resonance Effects ................................................................................ 11 1.2 Relaxation Times....................................................................................... 15 Spin Lattice Relaxation Time ..................................................................... 15 Transverse Relaxation Time ....................................................................... 19 1.3 A Few Fourier Facts .................................................................................. 21 The Fourier Transform ................................................................................ 24 Fourier Transform Pairs .............................................................................. 24 Fourier Transform Properties ...................................................................... 26 The Convolution Theorem .......................................................................... 28 A Practical Example ................................................................................... 29 1.4 Field Sweeps vs. Frequency Spectra ......................................................... 33 1.5 Multiple Pulses = Echoes .......................................................................... 34 How Echoes Occur ..................................................................................... 34 ESEEM ....................................................................................................... 37 Stimulated Echoes ....................................................................................... 38 Pulse Lengths and Bandwidths ................................................................... 39 2 Pulse EPR Practice..............................................................41 2.1 The Pulse EPR Bridge............................................................................... 42 Excitation .................................................................................................... 43 Detection .................................................................................................... 44 2.2 The Pulse Programmer...............................................................................48 2.3 Data Acquisition ........................................................................................50 Point Digitizers ............................................................................................51 Integrators ....................................................................................................52 Transient Recorders .....................................................................................55 Aliasing .......................................................................................................56 Dynamic Range ...........................................................................................58 Signal Averaging .........................................................................................59 2.4 Resonators..................................................................................................61 2.5 Phase Cycling.............................................................................................63 4 Step Phase Cycle ......................................................................................63 Unwanted Echoes & FIDs ...........................................................................66 3 Bibliography......................................................................... 67 3.1 NMR ..........................................................................................................67 3.2 EPR ............................................................................................................68 3.3 Pulsed ENDOR ..........................................................................................71 vi Pulsed EPR Primer This primer is an introduction to the basic theory and practice of Pulse EPR spectroscopy. It gives you sufficient background to understand the basic concepts. In addition, we strongly encour- age the new user to explore some of the texts and articles at the end of this primer. You can then fully benefit from your particu- lar pulse EPR application or think of new ones. A common analogy for describing CW (Continuous Wave) and FT (Fourier Transform) techniques is in terms of tuning a bell. We are assigned the task of measuring the frequency spectrum of the bell. In one scheme for tuning the bell, we use a frequency generator and amplifier to drive the bell at one specific fre- quency. In order to obtain a frequency spectrum of the bell, we slowly sweep the frequency in order to detect any acoustic reso- nances in the bell. We essentially perform a similar experiment in CW EPR: the field is slowly swept and we detect any reso- nances in the sample. This does not seem like the best means for tuning because we know from everyday experience that if we strike a bell with a hammer, it will ring (i.e. resonate acoustically at multiple frequencies). So an alternative approach is to strike the bell, digitize the resultant sound, and Fourier transform the digitized signal to obtain a frequency spectrum. Only one short experiment is required to obtain the frequency spectrum of the bell. This fact is often called the multiplex advantage. In FT-EPR, we apply a short but very intense microwave pulse (analogous to a hammer strike) and digitize the signals coming from the sample. After Fourier transformation, we obtain our EPR spectrum in the frequency domain. EPR has traditionally been a CW (Continuous Wave) spectros- copy. The NMR spectroscopist enjoyed substantial gains in sen- sitivity with a correspondingly drastic reduction in measurement time by moving to a pulse FT technique because they have a large number of very narrow lines spread over a wide (compared to the linewidth) frequency range. In most cases, the EPR spec- troscopist is unable to enjoy these sensitivity improvements because EPR spectra are usually broad and not as numerous. Why would EPR spectroscopists wish to switch to a pulse meth- odology without the promise of increased sensitivity? NMR spectroscopists soon discovered by measuring in the time domain and using multi-dimensional techniques, they were able to extract much more information than they ever could possibly imagine. We can enjoy these same advantages in EPR as well. Perhaps one of the most common pulse EPR applications is ESEEM (Electron Spin Echo Envelope Modulation) in which you obtain information regarding interactions of the electron spin with the surrounding nuclei. Interpretation of the data yields important structural information, particularly for large metallo- proteins for which no single crystals are available for X-ray dif- fraction and the molecules are too large to perform high resolution NMR experiments. Pulse experiments measure relaxation times more directly than CW techniques such as saturation. The relaxation time measure- ments offer you dynamical as well as distance information for the samples you are studying. As interest in measuring longer distances between paramagnetic centers increases, the techniques of 2 plus 1, DEER (Double Electron Electron Resonance), and ELDOR (ELectron DOuble Resonance) are invaluable in measuring particularly long dis- tances in very large molecules. Quite often there are events that take place on time-scales that do not influence the relaxation times and hence the lineshapes. EXSY (EXchange SpectroscopY) measures rates for slow inter- and intra-molecular chemical exchange, homogeneous electron transfer, and molecular motions.
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