Pulsed Nuclear Magnetic Resonance
Contents
1. 3 15V Oo 3 ad le ei black c4 E gt c on u white lamp Y ew 2 green Sola module 12V 1 5A E 12V Last printed 3 10 08 3 41 PM 38 Det neue ut T 9q0 0 HAN oe pepiejus eiqnop mojiaA 109 BWN kumi sapolg NUSWUELJL eqn ejduues esn4 pue Sepoig IusueJ1 mm Alum YOO WINN ZITA 09 w208 ZHINOS 9 v Y Ajayewixosddy gp Op xoudde xeu MOL yojeasaH Jeljudurv soyydwy COPA pue Jalla SSed 0 indui PINOA e 040250119250 OL oy uorsinboe jeubis 18 ndujo 01 1 QVZ Sun mum axy 20199189 OAINISUBS OStUd sopydury au sayydwe JH 9 1028t sopoip a l ne days p U01 90 01g Een epee J9 1920H ZHN 09 x49 UP AY OPIS wey JOXIW dH H 1 x J0X W dH 9SO IRIX ZHW 09 NN adinos X ne dors 19 Sue 1 20186 wt o1e6 ue6 es nd woy uoB esnd uio 39 Last printed 3 10 08 3 41 PM2. i Tre 2 diameter parallel to z axis are spaced by d so they see fields differing by Gd and their precession frequencies in Hertz differ by y 21 Gd Thus f fj Af o 2z yAH 2n YGAZ 2n yGd 2n The spectrum should be analyzed to find Af as in Figure 8 Of course you want to use the field shift knob so all the spins are above or below 60 0 MHz to avoid the spectrum folding over on itself Please refer to section III K on NMR imaging To measure the tube s inner diameter go to the shop and find the largest drill bit that can enter the tube then use calipers to Last printed 3 10 08 3 41 PM 30 measure the drill bit Wipe off all foreign material like steel particles before touching drill bit to sample tube You should measure G at 2 settings of the z shim knob and measure D for each value of G Writing down the knob setting will allow you to first measure both G values and then later do both echo measurements to determine D Last printed 3 10 08 3 41 PM 31 APPENDIX I Circuit Diagrams NMR PULSE GENERATOR Repetition Rate Generator Pulse One 15V in from power supply o to all 5V pins 100 ufd 0 22 B REP RATE GENERATOR PULSE ONE Pulse Width O 5V 5V Q 1K P 7 4 1 10 ps 680pf 2 0K 50K 047 I d man FRONT PANEL WH i Da 9 d 7400 2 E 3 Hal E e e W e e 7 T2 fo b PULSE 1 3 CH e w c 10uf 150uf 0 1 1s Last printed 3 10 0
3. 1 35 50 60 125 139 185 197 and 297 312 i High Resolution Nuclear Magnetic Resonance by J A Pople W G Schneider and H J Bernstein Specific attention should be given to Chapter 1 pages 3 11 Chapter 3 pages 22 49 and pages 50 73 and 82 86 of Chapter 4 Chapter 5 presents a fairly light introduction to the high resolution spectra used in chemical analysis il Concepts in Magnetic Resonance John Wiley amp Sons Inc Vol 12 5 257 268 2000 This article describes the apparatus and experiments of this laboratory exercise iV There is a good NMR text on the web by U Hornak at http www cis rit edu htbooks nmr Hornak has a companion text on MR Last printed 3 10 08 3 41 PM 1 imaging at the same address but htbooks mri The NMR text is available at the Physics 322 website II PULSED NMR APPARATUS HARDWARE DESCRIPTION The pulsed nuclear magnetic resonance apparatus used in this experiment 1s simple but exhibits state of the art performance Its principal components include a 14 092 gauss permanent magnet an NMR probe an RF receiver an RF transmitter and a pulse generator data analysis and spectra acquisition 1s performed using a PC For reference a block diagram of the complete system along with circuit drawings of the probe RF receiver RF transmitter pulse generator and power supply may be found in Appendix I The block diagram is must reading it 1s the last page of this write up A PERMANENT MAGNET
4. Measure the amplitude M of the spin echo as a function of t for a wide range of delays T Fit the data M with the equation below M A exp 21 T2 y G DT2 3 Last printed 3 10 08 3 41 PM 29 which combines the expected amplitude decreases due to T2 relaxation and diffusion The constant A 1s just the amplitude extrapolated to zero t you can treat it as a fitting parameter For T5 just use T2 T use T for water that you measured earlier this should be about 2 seconds this reduces the number of fitting parameters The horizontal axis of your plot is t The value of y for H nuclei is 27 times 4257 7 s per Gauss One way is to remove the T attenuation from your data according to M M exp 21 T gt A exp Y DC Thus taking the natural log of the corrected signal M gives In M In A yY G D2 3 7 which is slope intercept form In a plot of In M versus t the slope is CG D2 3 all the factors are known except D so D can be found from the experimentally determined slope We have glossed over one issue the value of G You can find G by measuring the spectrum of a known size sample in that z gradient With water a single resonance line in a tube of inner diameter d see Figure 8 two points at opposite ends of the Figure 8 Spectrum of round tube of diameter d of water in gradient G The object is pictured as having d many slices normal to z so the spectrum is the projection onto the z axis K Af
5. The permanent magnet used in this experiment is manufactured by Hitachi Having a field strength of 14 092 gauss the magnet also obtains very high field homogeneity 1 e field uniformity In order to maintain field stability the temperature of the magnet must remain at 35 degrees Celsius An inner proportional oven and an outer guard on off controller provide this regulation The electronics for temperature control are at one end of the magnet The power consumption for the magnet 1s well under 100 watts The field strength determines the frequency of spin precession which is here for H nuclei at 14 092 Gauss 60 00 MHz Note The Hitachi unit has no on off switch Leave it plugged in at all times including the days and months of semester breaks to keep the magnet at a stable temperature To improve the field homogeneity a set of electrical gradient coils termed shims are provided The shim coils are attached to the NMR probe and thus are not within viewing range These coils do allow for gradients to be generated A set of 9 controls on the front panel of the magnet frame permits for adjustment of field homogeneity The most recent resonance settings have been logged in a red notebook labeled NMR Experiment kept with the apparatus Fine tuning of these settings will cancel most imperfections in the permanent magnet thereby producing an extremely homogenous field to a few parts in 10 i As the labeling of some
6. oscilloscope and counter timer The rest of the apparatus should remain on 2 Depth Gauges i Two depth gauges are provided with the wooden sample tube holder made of Plexiglas these gauges allow you to insert the NMR tube and adjust the height of the air turbine wheel ii In the longer depth gauge the distance from tube bottom to the bottom of the air turbine is 103 mm This setting will be used in spinning the sample tubes At this setting the glass tube spins with its weight supported by a little Teflon disk bearing at the bottom of the probe The turbine wheel stands free so it can spin the tube il The shorter gauge is set for 89 mm and is used for holding the bottom of the NMR tube near the center of the RF coil This setting 1s handy for putting small amounts of sample into the RF coil Note the weight of the tube rests on the turbine so it will not spin this way leave the spinning air off IIl PROTON NMR EXPERIMENTS Last printed 3 10 08 3 41 PM 8 A SETTING UP FINDING A FIRST NMR SIGNAL Insert a sample of water into the probe and set the receiver attenuator to 16 dB towards the in direction of attenuation and the transmitter attenuator to 13 dB Use the 103 mm depth gauge so that this long sample extends both above and below the RF coil The oscilloscope should be on a 5 ms cm time base and a 20 mV cm vertical setting Ensure that the vertical input of the oscilloscope 1s connected to the unamplified outpu
7. 20 mV cm setting As previously mentioned handle the sample tubes with caution Once the sample tubes are in the hole at the top of the probe let the tubes gently fall into place When removing the tube gently lift straight up B MOTIONAL AVERAGING In general the diffusive motions of the molecules in a liquid average away the dipole dipole interactions between the spins This averaging 1s absent however in a solid As a result the free induction decay FID has a much more rapid decay time a smaller T5 in solids than in liquids The phenomenon arises because in a solid the presence of magnetic fields from neighboring nuclear spins causes a distribution of fields AH this 1s the dipole dipole interaction And since yH this field distribution also corresponds to a frequency distribution By the Fourier relationship uncertainty principle AoAt 1 this range of frequencies implies a more narrow time distribution and hence a Last printed 3 10 08 3 41 PM 10 shorter T2 Let s say it differently assume a set of spins or oscillators with frequencies distributed over a range Ao At t 0 they are all in phase It takes a time T5 for them to get appreciately out of phase maybe 1 or 2 radians with T5 1 Ao Use a single pulse of 2 usec width repeating every 2 seconds You do not need to spin these samples Compare the free induction decays of the following i Water il Adamantane an organic solid where the mo
8. a single phase detector with its output representing the spin magnetization along a particular axis in the rotating frame The software supports two phase detectors called in phase and quadrature I and Q along perpendicular axes in the rotating frame Before acquiring signal make sure that the data directory is set to c FIDo data Once signal has been acquired be sure to save the data in the data filename slot All filenames should end with the file extension dat The upper limit lower limit control adjusts the maximum and minimum voltage levels displayed on the graphs Note that the digitizer saturates at a 5 Volts regardless of the value of these controls To ensure that the signal 1s not clipped by exceeding the digitizer s input range the receiver attenuation should be set such the FID fits within 2 5 Volts on the display The trigger level value controls the voltage required to trigger the digitizer The trigger signal is TTL transistor transistor logic thus you should use the default value of 1 6 Volts The trigger slope function determines whether the digitizer will trigger on the rising positive edge of the signal or the falling negative edge This should remain in its default position of triggering on the negative falling edge FIDoLite also allows the user to set the dwell time the amount of time between successive time points the number of points how many points will be sampled each Note that Dr C
9. of the controls suggests each control adjusts a coefficient in a three dimensional Taylor expansion of the field strength Ha yz Ho axX ayy t azz where ax is controlled by the knob labeled x a is controlled by the knob labeled y and az is controlled by the knob labeled z Last printed 3 10 08 3 41 PM ii In addition there is a very FINE Y control which as the name suggests allows for fine tuning on Y A FIELD SHIFT knob at the left allows the field to be changed by 0 to 0 7 gauss approximately a 3000 Hz range up or down depending on the switch selection ii The power supply below the shim control panel is used to power both the shims and the temperature controller board It has 120 VAC at a few points so keep your hands out of it B NMR PROBE The NMR probe contains the RF coil that surrounds the NMR sample used for both transmitting 1 e flipping the spins and receiving De detecting the precessing spins This 1s accomplished by conversion of the precessing spin magnetization into a radio frequency voltage For greater efficiency the coil 1s tuned by appropriate capacitors to 60 MHz The impedance of the coil 1s transformed to be 50 ohm resistive the industry standard value for radio frequency equipment The NMR probe may be thought of as a transducer converting between the realm of RF voltages and currents and the realm of RF magnetic fields Loosely interpreted then the NMR probe may be con
10. separate intensity controls for store and non store Throughout most of this experiment the scope should remain in the stored display You ll really Last printed 3 10 08 3 41 PM 5 appreciate the storage feature it s a lot easier to look at In the event the scope is not set up for storage hit the ACQ button in the SETUP box Hit the 4K 1K button and turn the cursor knob until Trig Pos 4K 1K appears Now hit ACQ to exit the scope should be set to store Note that the Tektronix 2221A is a lot more oscilloscope than will be needed in this experiment Once set up though its extra capabilities do not get in the way G COUNTER The Hewlett Packard 5314A is a 100M Hz 100ns Universal Counter It features a seven digit seven segment LED display with overflow indication seven function performance and full input signal conditioning The seven functions of the counter include Frequency single Shot Period Period Average Time Interval Totalize Ratio and Self Check These functions are accomplished by a single LSI integrated circuit The input signal is AC coupled and can be conditioned by slope selection trigger level or attenuation Throughout this experiment the counter will be used to achieve enhanced accuracy in setting the pulse width and measuring pulse delays Only the four buttons to the right of the counter should be adjusted In adjusting the counter settings the objective 1s to trigger to start the timer on th
11. the RF coil has about a 5 5 mm diameter and is about 2mm long a very short solenoid This is why the field H is so inhomogeneous even across small volume samples Last printed 3 10 08 3 41 PM 3 the 32 dB gain amplifier is at the Larmor spin frequency the frequency at which the nuclear spins precess about their axis or nearly 60 MHz The amplified signal is then frequency shifted heterodyned to near zero frequency by mixing it with the 60 000 MHz crystal oscillator s output This oscillator is also the source of the RF transmitter Note that the output of the mixer the phase sensitive detector has components at both the sum and difference frequencies It 1s only the difference frequency that passes through the low pass filter Thus the NMR signal at 60 MHz A where A is small since the spins are quite near 60 MHz appears at frequency A This signal is of a much lower frequency than 60 MHz See section III L for more on phase sensitive detection In brief the receiver amplifies the weak signals from the precessing spins and the mixer shifts their frequencies to low values This frequency shifting makes the signal easier to see on the oscilloscope and easier to digitize for recording in the computer D RADIO FREQUENCY TRANSMITTER As seen in the system block diagram the 60 000 MHz crystal oscillator 1s the RF source The oscillator s output 1s split with one output going to the receiver s mixer and the other output gated by
12. the one with the wooden dowel inside Put it in the NMR probe with the tubes spaced along z from pole face to pole face or along the longest direction of the magnet assembly Use a single 90 degree pulse every 6 seconds To produce a large gradient turn the z control to one extreme or another 1 e if it s normal setting is 865 turn it to 000 if normally below 500 turn it to 999 Use a FIELD SHIFT of about 700 or 800 7 or 8 turns from zero beat As seen in figure 6 a signal reminiscent of Young s double slit should be observed Indeed there is a physical and mathematical connection between imaging and diffraction The FID envelope shows a beating or interference of the signals at the two frequencies m UI l 77 ii mE e Figure 6 Beat pattern Te A hy T Iv Bai m expected from the two NMR po E ey ee EN ay tubes in slightly different ORTU C Weg magnetic fields caused by the field gradient d e Send this signal to the computer and perform a Fourier analysis As depicted Figure 7 Frequency spectrum of the sample of two capillaries in a z gradient Frequency in figure 7 the projection of the phantom onto the z azis will be observed Now turn the phantom 90 so that the two capillaries have the same z coordinate The two peaks will merge Compare the image of the two capillaries with the image of the 5mm outer diameter tube of water about 4 2 mm inner diameter Do the dim
13. the spin sees H t rG cos wt The spin s precessional phase obeys yH dd dt Thus o Tan 0 So we have Wa wG P yrG Jeostar dt sin ot sin ex sin 9 A W W Clearly 1f t corresponds to an integer number of revolutions the periodic nature of the sine function will cause 0 The spins get back in phase every integer number of revolutions These re phasings have been termed spun echoes Get it For really large z gradients the spins will quickly de phase after each spun echo The FID will appear as a series of narrow pulses across the screen send the FID to the computer and examine the FT For small modulation you ll see the original resonance center band flanked by two spinning sidebands The sidebands are separated by the sample tube s rotation frequency typically 30 Hz These sidebands are just like those of AM radio For the case of a large z gradient producing sharp well separated echoes there are several sidebands on each side They are also each separated by the spinning frequency I THE MATHEMATICS OF SIDEBANDS To understand sidebands it is useful to understand the math relevant to AM radio Consider a signal t cos t 1 acos mnt Here 1s the carrier frequency and 1s the much smaller modulation frequency The term in parentheses is the modulation Expanding t cos ot a COSMot COSWmnt Recall that If you want you co
14. vectors into the xz plane During time T the transverse magnetization decays while M stays constant no precession since it 1s parallel to the field At time t T q the third 7 2 pulse transfers the z magnetization pattern again to transverse magnetization which forms an echo at time t T 2 along the y axis Roughly speaking the 7 2 1 1 2 T n 2 t echo sequence is a 90 1 180 t echo where the 180 1s broken into two 90 pieces spaced by T During this time out the spin magnetization component parallel to z does not precess so that the interval T does not affect the echo formation Try varying the delay intervals and see if you Last printed 3 10 08 3 41 PM 13 can identify all the FIDs and echoes you see We recommend the three pulses be 45 45 and 90 degrees to best see all the echoes Try turning off one or more of the RF pulses toggle switches on the pulse generator to check yourself the 1 3 echo FID following pulse 1 refocused by pulse 3 will not disappear when pulse 2 1s switched off though the 1 3 echo may change amplitude When pulse 1 is off you will see an echo of the FID following pulse 2 refocused by pulse 3 It may help to keep these echoes apart from each other in time We recommend using a first delay of 5 ms and a second delay of 15 ms You may need to reduce the field uniformity z shim knob so the FIDs and echoes are short and do not run into each other E MEASURE RELAXATION TIME T This exercise
15. you how to FT properly First choose a dwell time DW time per point which is short enough that you properly sample the highest frequency component of the signal look at FID on scope The Nyquist criterion 1s that the highest frequency sine or cosine needs at least 2 samples in each cycle Typically the dwell might be 100 us to 1 ms Next choose the number of acquired points N so that the total time duration T of the acquired data set 1s long enough to fully capture the signal the signal should decay fully in the first 30 of the time T determines the digital frequency resolution with the frequency domain points 1 e after Fourier transformation spaced by 1 T Let s say you want 0 25 Hz spacing in frequency so your time domain data set must be T 4 seconds long At a dwell DW 1 ms this 1s N 4000 points FIDo knows 2 so it will make this N 4096 a manageable data set But if you chose DW 10 Last printed 3 10 08 3 41 PM 18 us you d need 100 times as many points and you d quickly run out of disk space As a guide you will never need N to be greater than 16K 16 384 After acquiring the data usually the signal to noise is great so one acquisition or average 1s plenty go to the ANALYZE feature of FIDo Under TRANSLATION CONTROLS put in the baseline window for removing any dc additive offset from the data Use the last 25 of the data points so for N 4096 go from 3000 to 4000 Hit the button Baseline to do
16. 5 seconds Now use the computer to take the freq spectrum 1 e acquire the FID with the computer FT it and display the spectrum You ll see a single sharp resonance You may notice small periodic modulation in the FID envelope adjust the FIELD SHIFT away from zero beat so the envelope is easily seen This modulation 1s from the spinning Record the optimum setting of the Z shim Now change Z to make the modulation more evident Notice that the modulation is small for the correct Z setting and the modulation grows deeper the envelope decays closer to Zero as Z 1s changed away from the optimum setting Here s the physics in a Z gradient the spins will de phase more rapidly But when you rotate the sample about the y axis any spin sees exactly zero time average field from the Z gradient after an integer number of revolutions That 1s a spin may be in a region of extra large H field for a while and later an extra small H field After 360 of revolution all the field from the Z gradient averages to zero So the spins are all back in phase after 1 2 3 n revolutions of the sample tube Last printed 3 10 08 3 41 PM 2 The math for a z gradient of strength G gauss per cm H Gz Here we omit the constant magnetic field we are doing this in the appropriate rotating frame For a spin at radius r from the center line and initially at angle about the axis z r cos t Here ois the angular frequency of the tube rotation Thus
17. 60 0 MHz oscillator Try turning the shim controls to see how an inhomogeneous field leads to a more rapid decay shorter time duration T5 of the signal s envelope This free induction decay may be visualized in the following way Last printed 3 10 08 3 41 PM 9 Figure I The FID both as visualized in the x y rotating frame and as seen on the oscilloscope Note that the net magnetization vector precesses around the z axis eventually decaying to zero amplitude It 1s the projection of this circular motion onto one axis that produces the decaying sinusoid T5 can thus be measured by the time it takes the FID envelope to decay by l e Now remove the sample from the probe for 10 seconds a time much greater than Ti allowing the spins to demagnetize With 1 usec pulse width and a 0 4 sec repetition time let the sample back into the probe The signal amplitude will be observed to grow over a period of about 2 seconds the T relaxation time of water Note that it takes time T to bring the spins back into a state of equilibrium Here you used small angle RF pulses so as to perturb the relaxing spin magnetization as little as possible Avoid overloading the receiver Keep the output level at the unamplified output of the low pass filter below 0 1 Volts peak to peak 2 5 Volts peak to peak at amplified port Use the step attenuator to accomplish this This limit of 0 1 Volts peak to peak 1s 5 cm peak to peak vertically on the scope
18. 8 3 41 PM 32 0068uf e S 4 10 1004 NMR PULSE GENERATOR Delay Generator One Pulse Two DELAY GENERATOR ONE PULSE TWO pulse O 45V AEN c width 680pf 1 10 us gt PULSE TWO i FRONT PANEL Oluf da e ct e 1 10s 0001 001 Last printed 3 10 08 3 41 PM 33 10 100 ps o 0068uf NMR PULSE GENERATOR Delay Generator Two Pulse Three DELAY GENERATOR TWO PULSE THREE pulse O 5V AE a width 680pf 1 10 Us E 1 PULSE THREE OUT FRONT PANEL Oluf Uu ei e 0001 001 Last printed 3 10 08 3 41 PM 34 10 100 hs o 0068uf CIRCUIT TO DRIVE MIKER GATES Q 5V by 3428 0 Zn OCH oi UC 8v LVNI 5 en EN or 5V 5V co AS uid SJo up ejeb puno4j6 zuid OOPZ JO P E Q co Joan allo e eo O2vZ10 Sit I 5 gt o e CN C D I que Tv T Oo T b cc EXE S9U9 IMS 10 99 8S S d H TANVd LNOWS 35 Last printed 3 10 08 3 41 PM LOW PASS FILTER CIRCUIT Input from mixer o 270 001 J 0033 b A 01 001 I 022 Un N H o H pe l 2 047 o E 8 SS H E u 0 1 D NC 0 18 0 47 Ww Ww x um 9 unamplified output Last printed 3 10 08 3 41 PM 36 VIDEO AMPLIFIER CIRCUIT 15V in 470 150pf 2 0K 12Vin 047 5uf Ld Last printed 3 10 08 3 41 PM 37 limit to 2 5V pk pk Amplified Output POWER SUPPLY CIRCUIT toggle 1A fuse switch
19. Hewlett Packard gates By using two gates any leakage of RF pulses while the transmitter 1s in the off position 1s suppressed if the first gate doesn t kill the leakage the second gate will The gating signals for these gates come from the pulse generator as described below To control the strength of the RF field H presented to the spins the output of the gates passes through a step attenuator The attenuator output feeds a 10 Watt maximum RF power amplifier the gain control on this amplifier should remain fully clockwise The output of the RF power amplifier 1s directed to the probe through a network of diodes These diodes collectively form the automatic Transmit Receive T R switch Recall the V I characteristics of ordinary silicon diodes in the forward direction the current I remains nearly zero until V approaches 0 5 0 7 Volts this 1s termed the forward knee As a result a pair of diodes in parallel with reverse polarity will act as a high impedance for small signals like the 10 100 microvolts generated by the precessing spins and as a ow impedance for large signals like the many volts from the RF power amplifier during RF pulses Put otherwise for voltages greater than 0 5 to 0 7 Volts the diode in the forward direction conducts while for voltages more negative than 0 5 to 0 7 Volts the reverse diode will conduct In doing so the diodes essentially act as shorted wires or zero impedance on switch Howe
20. Physics 322 Physical Measurements Laboratory Pulsed Nuclear Magnetic Resonance version February 2008 I INTRODUCTION A GENERAL COMMENTS Nuclear Magnetic Resonance NMR spectroscopy is perhaps one of the most important scientific developments of the twentieth century Since its discovery in the mid 1940 s NMR has found applications ranging from solid state physics and materials science to chemical analysis and biophysics This experiment will serve as an introduction to many of the chemical and physical principles underlying such studies While many phenomena can be explored with this apparatus time may not allow for the completion of every exercise In performing the lab then be sure to choose a wide assortment of measurements B REFERENCES Before proceeding it is essential to become familiar with the theory and concepts governing NMR Particular emphasis should be given to understanding Boltzmann equilibrium the Larmor frequency rotating reference frames free precession nutation by radio frequency RF pulses spin echoes T T2 and chemical shifts Note that without a prior comprehension of these concepts the lab will not be understood at all The material in this write up does not substitute for reading the references The following publications are excellent references for this experiment 1 Experimental Pulse NMR A Nuts and Bolts Approach by E Fukushima and S B W Roeder A must read for the basics especially pp
21. air It s desirable to have the tube spin at a rate of about 30Hz which is faster than the human eye can follow On this valve about 1 4 turn will be fully open and will provide fast spinning The H20 FID will be much longer so you ll need to go to a longer oscilloscope time base Touch up the Y control or FINE Y to improve things a bit more You should Last printed 3 10 08 3 41 PM 19 be able to make a T5 of order 0 2 sec corresponding to a 2 Hz line width 1 30 ppm Put the ethyl alcohol back in and get it to spin Use the computer to take the spectrum You ll see each of the lines is split by spin spin or J couplings as in Figure 4 2 E3951 l CH CH OH freq gency gt Figure 4 2 Ethanol with added acid The frequency of the CH protons depends slightly on whether the CH protons are both up one up and one down twice as likely or both down Hence the CH3 resonance is split into a 1 2 1 pattern with a J splitting of about 5 Hz Likewise the CH protons have a frequency which depends on the states of the CH protons Thus the CH protons show they are interacting with 3 protons by the 1 3 3 1 pattern In other words the 3 H s can be all up two up and one down 3 ways two down and one up 3 ways or all down Under many conditions the OH protons exchange rapidly between different alcohol molecules Thus the OH proton shows neither J couplings nor gives rise to J couplings of the other protons This 1s anoth
22. ample of glycerol which has a very short convenient Ti of about 0 1 sec The amount of glycerol in the sample tube is fairly small allowing all the spins to more nearly see the same H Using the air turbine suspend the sample tube so that the sample is close to the center of the probe s RF coil from the bottom of the turbine to the bottom of the test tube should be 89 mm the 89 mm depth gauge should be used to obtain this distance Use a single pulse repeating every 1 0 sec gt gt T Record the initial amplitude of the spin signal versus t of the pulse Pulse width should be measured using either the oscilloscope or a second oscilloscope or the counter timer To measure the signal amplitude be sure to get off resonance enough to provide a convenient beat note whose amplitude is easily determined Use the field shift knob to get an FID similar to that of Figure 1 Note that by looking at the initial phase of the signal it is possible to distinguish between and amplitudes This is easier if you are closer to resonance since here there are fewer beats in the FID It is advisable to determine Hj for 3 settings of the transmitter attenuator Keep the results handy so you can set 90 and 180 pulses for many of the later exercises D SPIN ECHOES AND T MEASUREMENT Spin echoes are an interesting phenomenon demonstrating that spectroscopic techniques can modify the system Hamiltonian In the spin echo the 180 degree pulse positio
23. artment has approximately 4 NMR machines for analysis of reaction products This translates into a 2 million dollar investment Nationwide the monetary total of all NMR instruments is perhaps 1 billion dollars This exercise will lead you through the basics of chemical NMR spectroscopy So how does chemical NMR spectroscopy work Consider for example a simple and perhaps all too familiar molecule CH3CH2OH ethanol This compound has three types of hydrogen nuclei including CH methyl CH2 methylene and OH hydroxyl For each of these the resonance frequency is proportional to the field H at the nucleus f y 21 H And the field at the nucleus H 1s made up of the external field Ho from the magnet and a weak field from the nearby electrons f y 2n Ho AH Now AH is due to weak currents in the electronic cloud induced by the external field similar to eddy currents So AH is proportional to Ho AH o Ho Note that the negative sign 1s incorporated into the definition by convention Thus f YH 1 0 2n Here o is called the chemical shift for protons the range of chemical shifts 1s about 0 10 parts per million These shifts are smal NMR was around for a few years before the shifts were observed Basically the early magnets were not uniform in field so the NMR lines were too broad However and here s the good part even though o 1s small o is different for each type of hydrogen nuclei Thus in
24. ater Last printed 3 10 08 3 41 PM 24 If a gradient field 1s applied from head to toes the y direction each horizontal plane in the body will have a different resonance frequency Thus spins y coordinates have been labeled by their NMR frequencies If our physiology were one dimensional NMR imaging would be no more complex than acquiring the spectrum in the presence of the gradient and converting the NMR frequency back to the y coordinate using f y 2n H y 2n Ho Gy However since we are 3 dimensional real imagers use gradients along X Y and Z all three switching them on and off within each pulse sequence The method employed is called spin warp imaging and was involved in R R Ernst s Nobel Prize in chemistry in 1992 It is interesting to note that an ordinary x ray is a projection of a 3 dimensional body into two dimensions there is thus no way to distinguish objects in front of or behind each other This is true of any shadowgram And yet these simple pictures are of considerable diagnostic value Since static magnetic fields and RF pulses have been found not to injure living organisms MR imaging is competing with x ray tomography as a main diagnostic tool in medicine To illustrate the fundamentals of MR imaging we ll content ourselves with 1 D images of some simple phantoms test samples The wood sample tube holder should contain two NMR tubes that have glued inside two small water capillary tubes Use
25. ds out a triggering pulse every 0 1 100 seconds as selected by front panel knobs This triggers pulse 1 followed by a first delay then pulse 2 followed by a second delay and then pulse 3 The entire sequence repeats with the next triggering pulse as demanded by the repetition rate generator Note that the pulse widths can be independently adjusted from 1 100 usec and the delays can be set independently from 0 1 msec to 10 seconds Each pulse 1 2 and 3 has a separate front panel output BNC port for triggering either the counter timer the oscilloscope or the computer at the desired point in the pulse sequence The output to the transmitter gates 1s toggle switch selected to include pulse 1 off on pulse 2 off on and pulse 3 off on Turning a pulse off at the toggle switch does not change the internal workings of the pulse generator rather the deselected pulse simply 1s not sent to the transmitter gates So for example one could still trigger on pulse 2 even if only pulses and 3 are sent to the transmitter gates F OSCILLOSCOPE The Tektronix 2221A oscilloscope is a storage device allowing for real time acquisition and analysis of NMR signals To begin select non storage and use it as an ordinary scope Start with a liquid sample 2 ms cm time base 20 mV cm vertical base and external triggering one trace per pulse will be generated For a non blinking stored display hit the storage button Note that the scope has
26. e dots represent sampling instants Even though a high frequency signal is involved the digital oscilloscope will show a low frequency the difference between the signal and sampling frequencies This is called aliasing Thus it 1s imperative that the Nyquist criterion not be exceeded when sampling The Nyquist criterion dictates that the signal frequency cannot exceed half the sampling rate If the field 1s shifted too far signals will appear at alias frequencies One way to avoid aliasing then 1s to keep the NMR frequencies close to the 60 0 MHz reference frequency But then you risk not knowing which side above or below the spin frequencies are A second way is brute force using a very high sampling rate 1 sample every 5 us say so the dwell time DW is 5 us But then you will have a huge data set and you ll eat up the computer s disk space For example to record with 4 second acquisition duration 0 25 Hz per point after Fourier transforming would require 8 x 10 data points K NMR IMAGING MRI Perhaps one of the most influential applications of Nuclear Magnetic Resonance is MR imaging which relies upon the large water content of the body The concept is simple Since human constitution is nearly 70 percent water in a uniform field the body will show a single resonance line Note that the more interesting organic biological compounds in our system do have non trivial spectra but their concentrations are much lower than that of w
27. e front edge of the pulse and stop the timer on the back edge The slope switch controls whether the event occurs when the input voltage goes up or down through the selected level The level control 1s responsible for generating an event when the input signal passes the dialed in level DC voltage in the direction given by the slope There are 2 events one to start the counter and the other to stop You can choose to start and stop on the same voltage source or 2 different sources a setting marked SEP for separate inputs or COMMON for a single input On SEP you could choose to measure the time interval between the rising edge of a voltage input into the A BNC connector and stop on the edge of the voltage hooked to the B BNC connector or conversely you could choose to measure the interval starting on the edge of the A input and stopping on the edge of the B input On COMMON you can time the interval from one edge to the other of the same voltage input to A no choice it must be A So to measure the length of say pulse 1 hook the output 1 of the pulse generator to the timer s A input The slope settings should be and left right and you should select COMMON To measure the delay between pulses 1 and 2 hook output 1 to the timer s A input and output 2 to B input Select SEP for separate The delays are generally much longer As adopted from the HP 5314A Univ
28. ensions make sense compared with the NMR images Note that the glass tubes and the water have small but non negligible magnetic susceptibilities Thus each tube provides a gradient across the other tube To minimize this we are using the largest possible external gradient that the magnet can provide Nevertheless you will still notice that one peak 1s less tall and broader than the other Now let s consider NMR imaging if one images humans in terms of number of protons per cubic millimeter there is not much contrast Most body tissues and organs are all fairly similar as Lao Szu notes to an NMR machine our bodies are like big bags of dirty water However modern MRI uses pulse sequences that distinguish different tissues in terms of their T and T2 Let s examine how this is achieved The other phantom with 2 capillary tubes should be used Examining it straight up from the bottom it is seen that one capillary is blue it has CuSO dissolved into the H20 reducing the T of the water in this capillary The other capillary has pure H5O so its T is about 2 seconds First form an image with one 90 pulse repeating approximately every 6 seconds Both tubes should appear with equal intensity area in frequency domain Then increase the repetition rate to one pulse per 0 5 seconds The CuSO tube will recover fully since its T is short However the pure H2O will be partly saturated as the nuclear magnetization does not have suffic
29. er kind of motion averaging The ethanol sample with a bit of added acid has rapid exchange of OH hydrogens on the molecules This is the simplest case The sample of dry alcohol no water nor acid to catalyze hydroxyl exchange shows J couplings by the OH of the CH signal and J coupling of the OH signal by the CH hydrogens Another simple spectrum is ethylbenzene H3C CHo5 C6Hs The CeHs has the benzene ring structure The resonance spectrum shows J couplings between the CH2 and CH protons The ring protons are shifted up frequency because of currents induced in the ring The ring protons there are 5 do not show J couplings to the CH or CH they are too many bonds away Take a look at another sample tetramethylsilane TMS CH3 4S1 This compound shows a single line There are J couplings between the protons but a famous theorem states that J couplings cannot be observed between equivalent nuclei This theorem also explains the absence of J couplings in the spectrum of H20 Last printed 3 10 08 3 41 PM 20 Another sample is 2 2 2 trifluoroethanol F CCH2OH Here there are separate lines for the CH and OH resonances The CH resonance will be split by the three TE spins S 1 2 Thus one expects a 1 3 3 1 pattern for the CH protons It is a simple proof that the F nucleus has spin one half If F were spin zero there would be no splitting of the CH resonance Work out the patterns if F were spin 1 or spin 3 2 A re
30. ersal Counter Operating and Service Manual For additional information please refer to this manual located on the table next to the magnet The manual is also available from the 322 class web site Last printed 3 10 08 3 41 PM 6 than the pulses themselves so it matters little whether you trigger on pulse 1 s rising or falling edge same with pulse 2 Use the N 1 setting no averaging and select time interval A to B TL A B The shift key black blue should be on blue The timer counts in microseconds Leave the two level knobs pointing to the symbol this 1s in the middle of the TTL voltage range of 0 to 3 volts H COMPUTER The computer can be used to digitize signal average and or store any signal viewed by the oscilloscope The Pentium 4 PC supports a Windows XP operating system It has a processing speed of 1 6GHz and a memory of 128MB RAM FIDoLite software developed by Caleb Browning and Sam Gross of Mark Conradi s research group allows one to acquire and save signal data and launch the signal analysis FIDoLite may be accessed either from the Desktop or from the shortcut in the Start Menu Once the program has opened two displays can be seen on the screen If a sample is in the probe hit Acquire The top display will output the signal seen on the oscilloscope while the bottom display will be zeroed out This bottom graph is a remnant from the full FIDo program and is not used in this experiment Your hardware has
31. frequency the difference between the spin frequency and the 60 MHz oscillator The time varying amplitude a is present in the output Overall the mixer shifts the spin signal from 60 MHz A to simply A M MEASURING DIFFUSION BY NMR This 1s an advanced topic extending the study of spin echoes Here you will measure the diffusion coefficient or diffusivity D of water A good introduction to diffusion and random walks is the book by H C Berg Random Walks in Biology Also see Chapter 1 of F Reif s text on statistical physics Consider a random walker drunk starting at a lamppost who takes a unit length step every second randomly forward or backward After 5 steps his displacement x5 might be 1 1 1 141 1 Note that x x 1 Taking an ensemble average Xn Xn 0 since the average of 1 is zero By inductive reasoning we see x 0 xy 0 we are not surprised because each step is as likely plus as minus Squaring Xn 1 Xn 1 yields 2 Bp Kasi x4 125 2x Taking the ensemble average Kari Xn 1 0 Thus the mean squared displacement builds linearly in time Again using inductive reasoning n 0 n 1 n 2 etc we see x n Note this is very unlike constant velocity where the displacement itself not squared is linear in time Molecules in a gas or liquid move in such a fashion being propelled randomly by their own thermal motion and their neighbors This diffusive motion is three dimensio
32. ient time to relax between pulses Now in the image one peak will be decreased in area Rotation of the phantom by 180 in the probe should interchange the 2 peaks Thus not only can you tell there are 2 tubes and how big each is and how far 1s the spacing but you can tell that they are filled with different fluids different Tiet You have made a Ti weighted image Too bad your leg won t fit into this thing L PHASE SENSITIVE DETECTION The mixer also known as phase sensitive detector 1s a 3 port two inputs and one output analog passive device The output X 1s approximately the product of the L and R inputs The L input is from the 60 MHz 02m oscillator The R input is the amplified spin signal Thus L t cos Wot R t a t cos a t Last printed 3 10 08 3 41 PM 26 Here aq is the time varying amplitude think of an FID or echo o is the spin frequency yH and is a phase shift there are long cables in the apparatus long compared to the wavelength so 1s not known in advance The output X 1s Xt LR aw cos tt d cos Wol Using the trigonometric identity cos X cos y 2 cos x y cos x y Xa ay 2 Cos Wo t d COS W Wo t d We pass the output through a low pass filter so we take the average over the high frequency two nearly 2x times 120 MHz the cosine averages to zero Thus the time average of X is lt X gt a t 2 cos t The output is at the difference
33. it here Baseline is an imperative verb Get out of this screen use the OK button at the bottom and hit the Fourier Transform button The spectrum will show lines mirrored about zero frequency just pay attention to the positive frequency side If you have baselined correctly there should not be a spike at zero frequency For water there should be just one resonance line except for the mirror image Phasing Go to Phase Adjust and adjust the constant phase correction leaving the linear correction at zero Adjust until the upper display looks like in Figure 4 1 bad good bad Figure 4 1 Phasing of lineshape The idea is that the curve should not have negative regions Now put in ethyl alcohol The FID is much more complicated because there are 3 lines more than 3 if one considers the J couplings Capture the FID in the computer FT the signal and display You ll see 3 lines or 3 groups of lines like Figure 3 Because of the frequency ambiguity you ll want to use the FIELD SHIFT knob Hitachi shim panel so that all 3 lines are either all above or all below 0 this means the 3 sets of spins are above or below the 60 000 MHz source that drives the receiver s mixer Once all 3 lines are on the same side of 60 000 MHz the spacing between them will be independent of the field shift But there s more to be seen If you have not already shimmed on spinning water do itnow Put the H2O back in and turn on the spinning
34. lated sample is 2 10do 1 1 1 trifluoroethane IH2CCF Here the CH protons are the only protons on the molecule You ll see a 1 3 3 1 pattern from J coupling between the CH protons and the three F spins There is however no J coupling between the CH protons and the iodine I s 5 2 even though they are only two bonds separated I C H The reason is the I have a large electric quadrupole moment resulting in a very fast I T Thus the I are rapidly jumping between the levels m 5 2 3 2 1 2 1 2 3 2 5 2 This averages the J splittings to zero yet another example of motional narrowing But here it is the spin coordinate which is moving not a spatial coordinate Reviewing we have seen motional averaging to reduce the line width in liquids less than 1 Hz from the huge width 40 KHz in the solid state averaging of J couplings by OH groups hopping from one ethanol molecule to the next averaging of J couplings to I nuclei by the fast Ti of this spin and averaging of an inhomogeneous non uniform magnetic field by spinning of the sample H SPINNING SIDEBANDS Put the H20 sample in the probe and shim the magnet for longest T2 non spinning Use 1 short pulse 1 usec every 1 0 seconds Keep the signal below 100 mV peak to peak unamplified port of low pass filter Now turn on the spinning air and T5 will get much longer Adjust Y or FINE Y to optimize You will want to slow the repetitions to one every
35. lecules rotate freely but do not translate CioH16 a tetrahedral shaped molecule i Plexiglas a very rigid solid with essentially no motions poly methylmethacrylate iv Rubber which according to NMR seems more like a liquid than a solid v Grease also liquid like a swollen gel vi You could also study the curing of a 2 part epoxy Just mix the two parts together and place a small amount in the bottom of a 5mm NMR tube make sure none gets on the outside of your tube Use the air turbine to hold the end of the tube near the RF coil The 89mm depth gauge will help to achieve this end As the epoxy cures T2 should get shorter the material becomes increasingly solid like Use 5 minute epoxy and work fast so you don t waste a whole day doing this In each case it is the length of the decay T2 in which we are interested Note that the T of the above solids is on the order of 10 100 usec while the T5 of water is limited by the magnet s homogeneity and is approximately 20 msec here This factor of 1000 1s big When looking at the rapidly decaying signals of solids be sure to use a short filter time constant 1 or 2 psec To guarantee that you are seeing NMR and not just the tuned circuit ringing of the probe try removing the sample to see the difference Since the Hitachi built probe has some hydrogen bearing solids near the coil there is a signal with a short T2 even without a sample inserted but i
36. might mean 1 pulse every 3 seconds Patience 1s suggested Make sure to record your settings in the log book to help keep track of changes it helps the next group of students And if you turn the wrong knob you ll be glad to have recorded the optimum settings so your error is easily corrected Figure 4 This figure depicts the full width at half maximum FWHM of a resonance line You can now use the FIDoLite software to capture the FID and perform a FFT on the FID outputting the Real and Imaginary parts each as a function of frequency Be sure to save the FID and the final Real and Imaginary FFT files with the extension dat To view and print the files you can access the data arrays from EXCEL First from EXCEL open the directory the data is saved in should be c FIDo data Then choose file type as delimited hit next and set delimiters as tab The worksheet will display all numerical values associated with the signal and spectrum To graph the data simply create a new chart in the EXCEL worksheet Acquire one FID no averaging needed these are big signals and Fourier transform FT it you ll see a single line because H5O has all equivalent hydrogens Your FT software package cannot distinguish and frequencies so the spectrum will have mirror symmetry about the origin And there may be an even bigger line at zero frequency if you did not correct the baseline of the data How to FT Now isa good time to teach
37. nal but Last printed 3 10 08 3 41 PM IT like the random walk one expects Ax to be proportional to time This motion is what the botanist Brown saw and was labeled by others Brownian motion The definition of D is Ax 2Dt expressing the mean squared displacement during time interval t The units of D are 2 cm sec Diffusivity D decreases with increasing gas or liquid density In a denser fluid the diffusing molecule changes its direction more rapidly roughly one change for each collision So the D of water is about 2 x 10 cm sec at 25 C while D of helium atoms in helium gas at 1 atmosphere is about 2 cm sec The value for helium is large because of the low number density the small mass and correspondingly high thermal velocity with 4 mv KT and the small size of the He atom making collisions less frequent Long mean free paths translate into large values of D NMR Consider the response of spins to a 90 1 180 c echo pulse sequence when there 1s a uniform field gradient applied to the sample Between the two pulses the spins de phase the 180 pulse flips the spins in such a way that they will come back into phase at time 2t and generate a spin echo provided they run at the same frequency during the de phasing and re phasing parts of the experiment But if the spins can diffuse each spin will have a different average location and see a different average field and precess at a different average freque
38. ncy in the two halves between 90 and 180 versus between 180 and echo So the spins will not all be back in phase leading to a reduction in the echo amplitude Mathematically we approximate that a spin has average location x during the first half and x2 during the second half Clearly this is oversimplified the spin does not jump from x to x at the instant of the 180 pulse Anyway recall there is a field gradient along the x axis so a spin at x sees H Gx as always we are in a rotating frame so we can drop the uniform field from our equations and precesses at o yH yGx During the first half of duration t it accumulates precessional phase about the magnetic field of P ot yGzx In the second half the spin is taken to be at x2 so it accumulates phase P yGtx The total phase accumulated from the first 90 pulse where the spins all start in phase to the time of the echo is bo 2 P The crucial negative sign reminds you that the 180 pulse inverts the phase of the spins or makes it seem the spins all precessed backwards during the first half Thus Do yGt xo xi If there were no diffusion x2 x would be zero for every spin and every spin would have DP 0 All the spins would be back in phase at the echo time and the echo would be full amplitude But if there 1s diffusion then the spins will have a distribution of phases Po The spins will not all be in phase so the vector sum will not be as large the Las
39. ns the spins as though they ran backwards between the two pulses A spin echo is formed using a two pulse sequence consisting of a 90 pulse followed by a delay 1 and then a 180 pulse If the net magnetization vector is assumed to be initially oriented along the z axis the 7 2 pulse along x will rotate the magnetization by 90 degrees to the y axis During time T between the first and second pulse the different spin packets will freely evolve or dephase in the x y plane because they see slightly different static fields H and precess at slightly different frequencies o yH The z pulse then rotates each magnetization vector Last printed 3 10 08 3 41 PM 12 180 about the x axis of the rotating frame leaving the vectors again in the x y plane After a further time t the magnetization vectors are back in phase along the y axis and an echo 1s observed see Experimental Pulse NMR A Nuts and Bolts Approach for a good discussion complete with figures In this exercise the behavior of the spin echo will be used to determine T of glycerol Use the depth gauge and put the short sample of glycerol in the probe at the correct height 89 mm Select two pulses set to 90 pulse 1 and 180 pulse 2 Space the pulses by t 5 msec say to start Un adjust the shim controls to make a rapid decay short T5 easily achieved by mis adjusting the z shim by a couple of turns on the knob Don t forget to record the correct setting so you can return
40. onradi s group plans to maintain FIDoLite for its research Last printed 3 10 08 3 41 PM 7 acguisition and the number of acguisitions The phase which determines what angle in degrees the incoming data will be phase shifted can also be adjusted This value should remain at its default position of zero degrees Note that Fourier analysis is easily and quickly performed by depressing the analyze button Once in the analyze screen hit Fourier Transform to acquire the FFT spectrum Please see section III F for more details For additional information regarding the FIDoLite program a FIDoLite User s Manual is included on the Desktop In the event of program failure a backup floppy disc is available A copy of the backup disc may be obtained either from the teaching team or from Conradi s group IMPORTANT CONSIDERATIONS 1 Hardware Do s and Don ts i Always leave the Hitachi unit plugged in ii Do not break a sample tube in the probe Insert and remove sample tubes with the greatest caution If you do break one don t make it worse get help iii Do not let foreign objects fall into the magnet s opening Be sure to keep the opening covered by the Plexiglas fitting at all times iv Besides the shim controls do not adjust the magnet Receive help if it doesn t seem to be working v Always turn on the RF power amplifier LAST Turn this unit off first In fact we recommend turning on and off only the power amplifier
41. s t can be regarded as infinite M A so M Mj AB exp UT Taking the natural log of both sides Ln Mee M yJ In AB I T t Last printed 3 10 08 3 41 PM l4 We recognize this as slope intercept form y b mx where y In M Ma land x t and slope m 1 T Notice that it is important to measure M for a long delay time to get Moo You may recall that for t 5T exp t T 1s less than 1 You might also be impressed that our analysis in terms of the slope makes the value of B unimportant That is the first pulse need not be exactly 90 Inversion recovery uses a 180 t 90 inspect sequence to determine relaxation time The first pulse inverts Mz M then recovers towards equilibrium during the interval t The second 90 pulse tips whatever magnetization 1s along the z axis into the x y plane The resulting signal just after the 90 pulse 1s proportional to the z magnetization just prior to the pulse Therefore the signal amplitude will vary again as A 1 Be with B 2 for ideal 180 pulse See Figure 2 By plotting Moo M t on a log scale one again obtains a straight line with slope 1 Ti When using the 180 t 90 sequence be sure to wait at least 5T between repetitions of the experiment Otherwise the magnetization coming into the sequence will be less than the equilibrium value Moo That is you want your 180 pulse to work on the full 100 recovered magnetization So you let the spins reco
42. s the oscilloscope screen to the right longer T2 means better field uniformity as it takes longer to de phase when the spins all run at more nearly the same frequency Start with the settings 1n the logbook or the settings from the last group of students assuming they were successful Initial adjustment is done on x y and z with the sample tube not spinning Go over these in a loop 3 times Now turn on the spinner drive air and make sure the sample is indeed spinning With the sample of water spinning smoothly in truth the spinner turbine and bearing are the least robust parts of the apparatus be forgiving and having already set x y and z on the non spinning sample the important controls are y or fine y and curvature with the uninformative label B Maximize the duration of the FID using fine y then try a new setting of B by 10 or 20 points 1 e 0 1 or 0 2 turns on the knob again optimizing fine y With y or fine y and B adjustments you should be able to make the water FID last 0 5 seconds or so with a 1 e decay time of perhaps 0 2 seconds corresponding to a frequency width see below of about 2 Hz 2 Hz out of 60 MHz means the field is uniform to about 3 parts in 105 which is remarkable Last printed 3 10 08 3 41 PM 17 Note as you make the field more uniform and the FID grows longer in duration you will want to increase the repetition time so that one FID is fully decayed before you hit the next rf pulse This
43. sidered as an antenna note however that none of the energy is actually radiated For experiments requiring an extremely homogeneous field the sample tube can be rapidly rotated such that each spin will more nearly feel the same time averaged field strength That 1s each spin will spend time in regions of higher and lower field strength so an averaging occurs For this purpose an air Jet and air turbine wheel are used While Hitachi originally used a small compressor to generate the air for the jet this approach was abandoned in the Physical Measurements Lab Rather house air 1s used instead a regulator in the Lab is permanently set to 3 psig equivalently 0 2 atm positive pressure This air is connected via hoses to the barb fitting of a valve located on the front left side of the magnet s frame The amount of air flow into the probe may be controlled by this valve The spinner can be temperamental Hitachi chose their design to avoid the competitor s superior patented design C RADIO FREQUENCY RECEIVER As seen in the system block diagram the spin signal from the NMR probe is directed by the diode boxes to the Hitachi amplifier 51 dB gain 6021 MHz The input amplifier is low noise as is appropriate for 10 100 microvolt signals The signal is passed to an additional 32 dB gain amplifier through a step attenuator 0 31 dB in 1 dB step increments which allows the overall gain to be reduced for large signals The output of Note that
44. st the carrier and first sidebands When a 1s big you need to keep all the terms in the expansion so there are SE qu sidebands The correct math for this 1s the Bessel functions J A NOTE ON FOURIER TRANSFORMATIONS The receiver provided here has a single phase sensitive detector mixer Its output signal 1s essentially proportional to a component x or y or in between of the precessing magnetization in the x y plane Because the mixer reports the difference Last printed 3 10 08 3 41 PM 23 freguency between the spins and the 60 000 MHz reference the voltage gives the magnetization component in the rotating frame Consider a vector rotating in the x y plane Any one component x y or other simply oscillates With only one component one cannot tell which sense of rotation clockwise or counter clockwise the vector has In terms of NMR one cannot tell whether one is above or below the 60 MHz reference Thus one wants to adjust the field shift so that all the NMR lines are on the same side of 60 MHz removing the ambiguity But if you shift the field too far you are asking the computer to digitize a high frequency signal Please be aware that the computer and all digital storage oscilloscopes digitize the signal at evenly spaced times Thus if the input signal exceeds the sampling rate the situation below can occur Figure 5 Sine wave input to the digitizer where the input frequency is greater than the sampling rate Th
45. t of the low pass filter box The oscilloscope should remain on 20 mV cm If the signal 1s too large or too small change the receiver attenuator accordingly Note if the attenuator switch 1s IN this means the decibels dB of attenuation are in the signal path so attenuating If the switch is OUT the attenuator is out of the path so no attenuation The total attenuation in dB is the sum of all the IN sections Decibels The number of dB 10 log 5 So 10 dB is a power ratio of 0 1 and POUT voltage ratio of 1 410 because power 1s proportional to voltage squared dB P ratio V ratio 0 l l 3 2 1 414 6 4 2 10 10 3 16 20 100 10 30 1000 31 6 46 40000 200 Set the pulse generator for a repetition rate of one pulse per second input a single pulse make it pulse 1 of about 2 usec width Note the knobs on the pulse generator have scales for approximate reading The oscilloscope should trigger externally external trigger source on pulse 1 You should see an NMR signal To acclimate yourself with the electronics you may want to spend some time flying the controls Vary the receiver attenuation Make the pulse width shorter and longer Adjust the field shift control on the Hitachi shim panel you should be able to make the displayed signal pass through zero frequency zero beat Recall the oscilloscope sees the phase detector output which is the difference frequency between the spins and the
46. t printed 3 10 08 3 41 PM 28 echo will have less amplitude This decrease in echo amplitude 1s how we can measure D using NMR Squaring the above equation and taking its ensemble average there are lots of molecules in our sample A 2 Op GT x X Recall Ax 2Dt and assume the motion from X1 to X occurs in a time interval of about T yGt 2Dt So the mean squared de phasing grows as t How does this affect the signal amplitude For a random variable Po with probability distribution P o cos Pioo cos By d o And cos PDP is just the projection in the NMR experiment of the spins onto the x axis in the rotating frame Provided P is a Gaussian normal distribution centered about zero like we have here P o Ke SS Some integration yields cosP exp 6 2 So our echo amplitude M is M cos p exp y G D Now had we done no approximation but instead treated the position x of the spin as changing continuously we would have obtained the correct answer M cos ekp y G Dt 2 3 which 1s almost the same Please take the time to check the dimensions of the argument of the exponential You will find the argument 1s properly dimensionless You can find the dimensions of y from o yH Experiment Put the tube of H20 into the magnet with the spinning air off Create a gradient by mis adjusting by 4 turns or 9 turns the Z shim knob record the setting for later measurement of G
47. t will be smaller than the signal of the plexiglass You can convince yourself that you are seeing the plexiglass NMR signal by watching on the oscilloscope for the displayed signal to increase when you drop in the plexiglass sample tube C NUTATIONS The experimental objective in studying nutations is to examine the effect of an RF pulse upon the spins A single pulse is applied to the sample with a repetition time much greater than T In this way the spins are allowed to return to equilibrium before another pulse of magnitude H is applied for a time t the width of the pulse The spins are expected to nutate or Last printed 3 10 08 3 41 PM ll precess about H through an angle 9 of lte Since the spin s magnetization M starts along the z axis the projection of M in the x y plane will be Mosin 0 M sin yHi t From the variation of amplitude with t one can determine both the nutation frequency yHi 27 where y 2m 4 2577 x 10 Hz gauss for protons and the pulse widths that correspond to 90 and 180 degree pulses You will recognize a 90 degree pulse as the pulse giving maximum FID amplitude the 180 degree pulse produces a minimum amplitude FID following it Note that a plot of M versus t will produce a damped sinusoidal oscillation Plot this for yourself The damping is due to the variation of H over the sample volume Recall the RF coil is quite small so its field H is not very uniform For this experiment use the s
48. the same external field H the CH3 CH2 and OH protons hydrogen nuclei have three slightly different frequencies The Fourier spectrum should look like Last printed 3 10 08 3 41 PM 16 Figure 3 From left to right the peaks with increasing freguency are CH CH and OH with the intensity ratio 3 2 1 ratio of areas in the spectrum arising from the relative numbers of each kind of proton CH3 Frequency SCH Note that for ethanol the overall width of the spectrum 1s about 4 parts per million Ata 60 MHz frequency this implies that the spectrum is only approximately 240 Hz wide If the field H 1s not extremely homogeneous ppm or better then each line will be so broad that it merges with the next This 1s why it is of utmost importance to have a uniform field Let s get started To shim 1 e improve the homogeneity of the magnet use a single pulse of about 1usec every 0 5 seconds Use a transmitter attenuation of 13dB Such settings correspond to a small tip angle so that the experiment can be repeated faster than once per Ti More formally the small pulse barely perturbs the magnetization because the cosine of a small angle is nearly 1 Use the water sample suspended in the probe a distance of 103 mm use the depth gauge As will be seen the water sample has only a single resonance line all the H nuclei are equivalent G SHIMMING By adjusting the shim controls you can make the water FID extend further acros
49. to it Tune onto resonance use field shift knob so a rapidly decaying FID is seen after pulse 1 and you will see a similar but inverted spin echo at time c after the second pulse Use 1 0 sec repetition time and trigger on the first pulse You should see an FID after pulse 1 possibly a weak FID after pulse 2 and a spin echo at 27 after the first pulse Try varying the spacing tto see that the echo really does occur at time 2t measuring from the first pulse For fixed T vary the first and second pulse widths to obtain maximum echo amplitudes These pulse widths should correspond to 90 and 180 nutations as found in part C Plot the echo amplitude M on a log scale as a function of 21 A nearly exponential decay obeying Ae will be observed Determine T of glycerol You can use linear graph paper to plot log M as a function of 21 If M is the echo amplitude and M A exp 24 T5 then Ln M In A 21 This is of slope intercept form y b mx where y In M x 21and the slope m 1 T Likewise the three pulse sequence 7 2 1 7 2 T 7 2 t echo with T gt T creates a stimulated echo at time T after the third 7 2 pulse Again it 1s assumed that the net magnetization vector 1s initially oriented along the z axis This equilibrium z magnetization is transferred to transverse magnetization by the first 7 2 pulse During free evolution of length t the magnetization dephases The second 7 2 pulse rotates the magnetization
50. uld put a black dot or stripe on the turbine wheel and measure its frequency with a strobe light The Physics 117 118 technical assistant has a strobe Last printed 3 10 08 3 41 PM 22 cos x cos y 1 2 cos xt y 1 2 cos x y So the expression for f t becomes f t cOSMot a 2 COS Wo Mm t a 2 COS Wo Wm t Hence the signal f is composed of 3 pieces the carrier at frequency 0 the lower sideband at m and the upper sideband at m The amplitude of the sidebands is proportional to the depth of modulation a In AM broadcast radio the maximum allowed modulation frequency is 5 KHz leading to a 10 KHz bandwidth The channels are thus separated by 10 KHz FM sidebands are almost as easy A typical FM signal is f t cos p t acoS mt The acosogt is a phase shift of the carrier The phase of the oscillating signal is varied a time change of phase is a frequency shift Complex notation makes the math easier So we look at g t ENEE Looking at the last term the argument acosWmt is bounded by ta So if a is small we can Taylor expand e ixt x 2 which makes g t g t eg 1 iacos mt a 2 cos Wmt Using the definition cosot Alen da and recalling that COS Omt 1 2 1 C0820mt 1 2 1 4 e v e m we find 2 EE mm These terms are the carrier the first sidebands n 1 and the second side bands n 2 Note that for a small a a is negligible so the signal is essentially ju
51. ver at least 5 times T4 before doing the next 180 and 90 pulses By the way this tedious waiting is not required for Tj measurement by 90 t 90 After all any magnetization that recovers between the one 90 t 90 and the next is just slated for death M 0 by the next 90 pulse Figure 2 How the magnetization M varies just after the 90 pulse in the 180 t 90 inspect sequence solid curve and 90 t 90 dashed curve The plot also gives the amplitude of the FID following the second pulse The role of the second pulse is to convert M into observable NMR signal F CHEMICAL USES OF NUCLEAR MAGNETIC RESONANCE In recent years Nuclear Magnetic Resonance has become an indispensable analytical tool in chemistry The chemical applications of NMR range from analyzing the content and purity of a sample to determining its molecular structure NMR can quantitatively analyze mixtures containing known compounds For unknown compounds NMR can Last printed 3 10 08 3 41 PM 15 either be used to match against known spectral collections tabulated in books or on line or to infer the molecular structure directly Once the basic structure is known NMR can be used to determine molecular conformation in solution it can also be used to study physical properties at the molecular level including conformational exchange phase changes solubility and diffusion We note for example that the Washington University Chemistry Dep
52. ver if the voltage magnitude is below 0 5 Volts neither the forward nor the reverse diode can conduct rendering the diode assembly as off Using this model of on and off silicon switches it is possible to track the signal power flow to and from the NMR probe in transmit and receive modes Last printed 3 10 08 3 41 PM 4 In the event that a transmitter pulse of excessive amplitude and or duration is sent to the NMR probe the fuse should blow before the diodes and the NMR probe are damaged see block diagram Because the pulse generator can put out long pulses when it 1s turned on or off the RF power amplifier should always be turned on last and turned off first In this way no long pulses are sent to the probe In summary the RF transmitter generates RF pulses as commanded by the pulse generator to produce the RF magnetic field H in the NMR probe it is this time varying field that flips the spins A network of diodes performs automatic T R switching allowing the same probe to be used for both transmitting and receiving E PULSE GENERATOR The pulse generator controls both the length of the RF pulses and the spacing between them The output of the pulse generator drives the transmitter gates and triggers the oscilloscope and or computer used to display and or acquire the spin signal This is a simple pulse generator that runs a fixed sequence The sequence is initiated by the repetition rate generator which sen
53. will allow you to measure the spin relaxation time T 1 e the time it takes the system to return to equilibrium using two distinct methods Saturation Recovery and Inversion Recovery Measure T for any of the following samples i Glycerol il Rubber lil Grease iv Solid Adamantane v A solution of water with dilute cupric ion paramagnetic Note that the Tj of any substance is shortened by the large magnetic moment of paramagnetic ions Paramagnetic here means that the ion has a net unpaired electron spin In most substances all the election spins are paired anti parallel leading to cancellation Saturation uses a two pulse sequence consisting of a 90 pulse followed by a delay t and then another 90 pulse 90 t 90 The FID following the second inspection pulse is proportional to the z magnetization M just before the pulse Thus by measuring the amplitude of the FID following this pulse we inspect the Z magnetization just prior to the pulse In order for the FID to decay rapidly to prevent one FID from running into the next the z shim may be un adjusted Trigger the scope on the second 90 pulse so that the FID from pulse 2 1s observed Both pulse 1 and pulse 2 should be switched on at the pulse generator Vary the time t using the first delay s knobs watch the FID amplitude change as you do The FID signal amplitude M will vary as Ma A 1 B exp t T1 For a perfect first 90 pulse B 1 If t5 T thi
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