1 Nuclear Magnetic Resonance ANIMATED ILLUSTRATIONS MS Powerpoint Presentation Files Uses Animation Schemes as available in MS XP or MS 2003 versions A class room educational material PULSED FT NMR Video Conversion Using “WONDERSHARE PPT to WMV” Conversion Software Dr. S. ARAVAMUDHAN Automatic Timing: CLICK on “show” and wait and watch all the 13 slides which automatically transit one slide to the next.

2 A steady Uniform Magnetic Field of 9.34 Tesla is applied (find in Slide #3) Experimental sample is placed in the magnetic field (as in slide#3) Magnetization Builds up due to Relaxation process in Time T 1 (slide#3 & Slide#10) A rectangular pulse of 400 MHz RF frequency is applied to bring the magnetization to XY Plane (slide #3, 4, &5 and others) z x y Magnetization decay due to T 2 process. Free Induction Decay F.I.D. acquired (as in slides # 5, & 10) FID is digitized (slide#6) FID Fourier Transformed to obtain Spectrum (slide #6) Obtaining FT NMR Elaboration on the even more basic Single spin Magnetic moment situation in a steady applied Magnetic field and the Consequent Magnetization can be viewed at YOUTUBE.COM Uploaded files 1_NMR and 2_NMR

3 P -X π/2 At t =0, the end of pulse External Magnetic Field Chemical substance Spin ensemble Z X Y Magnetization Z X Y x,y-axes Rotating about Lab Z-axis; frequemcy same as the precession frequency Z X Y A rotating RF magnetic field results on application of RF at resonance frequency X Y The rotating magnetic field tilts the magentization away from z-axis by 90º for a π/2 pulse Viewed from within the rotating frame the RF field appears stationary Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame X Y Induced NMR signal at receiver (RF 300 MHz ) Phase Sensitive detector Reference in phase at NMR (400MHz) frequency Output (‘0’ freq) Reference in phase; offset from NMR frequency (400±0.004 MHz) Phase Sensitive detector Output at offset frequency (audio range) ~ 4KHz D.C. A depiction of the Induced RF signal Characteristics would appear……… After the pulse: at t>0 Transverse Relaxation and magnetization decay in XY plane is not depicted. No more CLICKs. This show has automatic timings from this stage. Free Induction NMR Signal NO F.I.D. yet! Right CLICK mouse And CLICK on option “PREVIOUS” OR…………. CLICK toTransit. Rotating x,y axes :rotation about Lab z-axis Apply the 90º, -X pulse now, P -X π/2 A BLUE line for z-Axis indicates the view from within the rotating coordinate system. X Y Rotating system viewed from within that system: STATIONARY X Y Z X Y Z Z Y

4 For a π/2 pulse the value of ‘ω 1 t ‘=90º; ω 1 =γH 1 The impulse on … x,y-axes Rotating about Lab Z-axis; frequency same as the precession frequency Z X Y X Y X Y Rotating system viewed from within that system: STATIONARY X Y Z A rotating RF magnetic field results on application of RF at resonance frequency Viewed from within the rotating frame the RF field appears stationary Z = unit vector along z-axis Rotation about z-axis= e -iφ Z Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed. Rotation about z-axis= e -i ω t Z An equation representing this rotation would be displayed In terms of Angular momenta, I z replaces ‘z’; for rotation about z-axis = e -iφ I z Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed. Rotation about z-axis= e -i ω t I z RF source/ transmitter Connected to coil. Linearly oscillating field along the coil axis (X-axis) The linearly oscillating field can be resolved into two counter rotating components Only one of the rotating component is effective in causing resonance 2 H 1 I -x cos(ωt) = H 1 e -iI -x ωt H 1 e +iI -x ωt A Pulse lasts only for a few μ Secs. For proton NMR a H 1 of ~25Gauss along ‘-x’, pulse widths are approximately 10-15μs + The impulse off… RF field is along –X in the XY plane, the effect caused would be rotation about X- axis, unlike the precession about z-axis To repeat the animated RF depictions “right click” and choose option: ‘previous’ Click to end this slide CLICK ! Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK!

5 Apply the 90º, -X pulse now, P -X π/2 X Y Z Viewed from within the rotating frame the RF field appears stationary Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. X Y After the pulse: at t>0 Rotating x,y axes :rotation about Lab z-axis A BLUE line for z-Axis indicates the view from within the rotating coordinate system. Z Y Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame X Y Z When the XY magnetization decays with transverse relaxation time T 2, immediately after the pulse…… When PSD reference is in phase off set from Resonance frequency; NMR signal at receiver (RF 400 MHz ) If No T 2 …….. Free Induction Decay Signal No More Clicks ! This show has automatic timings The F.I.D. When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 400 MHz ) Tilting of magnetization Described in rotating frame: Rotation about the X-axis I(t p ) = e -iI -x φ I z e +iI -x φ with φ=90º & t p is pulse duration At the end of pulse, time for F.I.D. begins with t=0 tptp t=0 Acquisition time ~5T 2 FID CLICK to Transit Induced NMR signal at receiver (RF 400 MHz )

6 PULSED NMRAcquire F.I.D. Free Induction Decay NMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation F.I.D. DIGITIZE Analogue to Digital Converter A.D.C. AddressContents Computer memory Time domain FFT from FID Computer input Frequency Domain Spectrum Computer output This one- dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum Acquisition is automatically in the digitized form Next Slide

7 dimension A(50),B(50),Y(50),X(50) K=32 open (unit=1, file="output") Print 10,K DO 11 N=1,K X(N)=(N-1)*3.5/K X(N)=EXP(-1.0*X(N)) Y(N)=X(N)*(COS(2*3.14*(N-1)*10.0/K)+ 1 COS(2*3.14*(N-1)*4.0/K)) 11 write (1,20) N,Y(N) DO 12 M=1,K A(M)=0 B(M)=0 DO 13 N=1,K-1 A(M)=A(M)+Y(N)*COS(2*3.14*(M-1)*(N-1)/K) 13 B(M)=B(M)+Y(N)*SIN(2*3.14*(M-1)*(N-1)/K) A(M)=A(M)/K B(M)=B(M)/K M2=M/2 12 write (1,30) M2,A(M2),B(M2) 10 FORMAT(1x,I2) 20 FORMAT(1x,I2,2x,F10.5) 30 FORMAT(1x,I2,2x,F10.5,2x,F10.5) close (unit=1) STOP END A program in Fortran for “Fast Fourier Transform” Digitized FID Signal Digital Computer FFT Program run OUTPUT

8 Time domain FID data: 32 points Real Imaginary 16 data 16data points points Frequency domain spectrum

9 COS Real Imaginary F.T Real Imaginary F.T SIN RealImaginary F.T Arbitrary Phase Provision is made in the data processing system, for routinely applying phase corrections t= Value between +1 & 0 f c cos(2πνt) + f s sin (2πνt) with f c 2 +f s 2 =1

10 No net magnetization CLICK ! Magnetization Sample: Ensemble of spins Magnetization Magnetization Builds up exponentially t Magnetization T1T1 I0I0 ItIt External Magnetic Field To repeat the above events: Right Click & Select option ‘previous” Z X Y Initially, before the external magnetization is applied, the spins are randomly oriented When the magnetic field is turned on, the spins align at the characteristic longitudinal relaxation time T 1 CLICK ! +1/2 -1/2 Magnetic field +1/2 -1/2 No radiations are present Not stimulated transitions: but spontaneous relaxation transitions Degeneracy removed/Energy levels split On the application of field….. Splitting is instantaneous & population redistribution requires more time called the relaxation time Thermal equilibrium Boltzmann distribution Net magnetization along Z-direction & ZERO XY component random (1-e -t/ ) T1T1 I0I0 = ItIt CLICK for…. CLICK ! ItIt CLICK for….... On-set of Longitudinal Relaxation

11 In XY plane precessing magnetization X Y Solenoidal sample coil axis Axis- Y Precessing magnetization induces rf voltage: NMR signal Pulse applied Z Z Y The above picture is for time scales small compared to relaxation time T 2 When relaxation process is effective, the relaxation leads to the decay of the transverse magnetization of XY plane This decay of magnetization due to the transverse relaxation time is because of the defocusing of the magnetization isochromats in XY plane

12 Randomization in XY plane: Magnetization Decays I h NET Magnetization Transverse T 2 Relaxation Longitudinal T 1 Relaxation Relaxation Longitudinal and transverse Magnetic field A π/2 pulse flips the z-magnetization to xy-plane CLICK ! Random… Alignment….. t

13 This Video Movie was made by Dr. S. Aravamudhan For the occasion of the WORKSHOP on FT NMR At S.A.I.F, North Eastern Hill University, Shillong The Sound Tracks ( playeable audio ) are from the album “ARZOO: Nirvana in six strings” and the Album “Elements: Water” of Shiv Kumar Sharma November 2009 Video Conversion Using “WONDERSHARE PPT to WMV” Conversion Software