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Nuclear Magnetic Resonance

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. http://ugc-inno-nehu.com/links_from_web.html. Video Conversion Using

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Nuclear Magnetic Resonance

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  1. Nuclear Magnetic Resonance ANIMATED ILLUSTRATIONS MS Powerpoint Presentation Files Uses Animation Schemesas available in MS XP or MS 2003 versions A class room educational material PULSED FT NMR http://ugc-inno-nehu.com/links_from_web.html 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. 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 http://www.youtube.com/aram1121944/ z y x Obtaining FT NMR 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) Uploaded files 1_NMR and2_NMR Magnetization Builds up due to Relaxation process in Time T1 (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) Magnetization decay due to T2 process. Free Induction DecayF.I.D.acquired (as in slides # 5, & 10) FID is digitized (slide#6) FID Fourier Transformed to obtain Spectrum (slide #6)

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

  4. Z Y X Y Y Y X X X In terms of Angular momenta, Izreplaces‘z’;forrotationabout z-axis= e-iφIz 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 tIz Viewed from within the rotating frame the RF field appears stationary Z= unit vector along z-axis Rotation about z-axis= e-iφZ 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 tZ RF field is along –X in the XY plane, the effect caused would be rotation about X-axis,unlike the precession about z-axis An equation representing this rotation would be displayed Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK! CLICK ! CLICK ! CLICK ! Z To repeatthe animated RF depictions “right click” and choose option:‘previous’ Click to end this slide A rotating RF magnetic field results on application of RF at resonance frequency x,y-axes Rotating about Lab Z-axis; frequency same as the precession frequency For a π/2 pulse the value of ‘ω1 t ‘=90º; ω1=γH1 The impulseoff… The impulseon… CLICK ! H1e-iI-xωt H1 e+iI-xωt A Pulse lasts only for a few μ Secs. For proton NMR a H1 of ~25Gauss along ‘-x’ , pulse widths are approximately 10-15μs + 2 H1I-x cos(ωt) = Only one of the rotating component is effective in causing resonance Rotating system viewed from within that system: STATIONARY 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 CLICK ! http://www.geocities.com/sankarampadi/eulexp.html

  5. Z Z Y Y X X Y X t=0 FID tp Acquisition time ~5T2 Rotating x,y axes :rotation about Lab z-axis A BLUE line for z-Axis indicates the view from within the rotating coordinate system. Viewed from within the rotating frame the RF field appears stationary Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. No More Clicks ! This show has automatic timings Z After the pulse: at t>0 Y If No T2…….. The F.I.D. Tilting of magnetization Apply the 90º, -X pulse now, P-Xπ/2 Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame At the end of pulse, time for F.I.D. begins with t=0 Described in rotating frame: Rotation about the X-axis I(tp) =e-iI-xφIz e+iI-xφwithφ=90º & tp is pulse duration When the XY magnetizationdecays with transverse relaxation time T2, immediately after the pulse…… When PSD reference is in phase off set from Resonance frequency; NMR signal at receiver (RF 400 MHz ) Induced NMR signal at receiver (RF 400 MHz ) CLICK to Transit When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 400 MHz ) FreeInductionDecay Signal

  6. Computer memory Time domain DIGITIZE 15 Analogue to Digital Converter A.D.C. 11 0 Computer output FFT from FID Next Slide Frequency Domain Spectrum Computer input PULSED NMR Acquire 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 Acquisition is automatically in the digitized form F.I.D. This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum

  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 data16datapoints points Frequency domainspectrum

  9. Value between +1 & 0 0 +1 F.T F.T COS Real SIN Imaginary Imaginary Real F.T Arbitrary Phase Real Imaginary t=0 Provision is made in the data processing system, for routinely applying phase corrections fc cos(2πνt) + fssin (2πνt) with fc2 +fs2 =1

  10. Z External Magnetic Field Y X T1 (1-e-t/ ) I0 T1 It = -1/2 Magnetization Magnetization Magnetization +1/2 random Sample: Ensemble of spins I0 It CLICK ! t It Magnetization Builds up exponentially To repeat the above events:Right Click & Select option ‘previous” 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 T1 On the application of field….. CLICK ! Splitting is instantaneous & population redistribution requires more time called the relaxation time -1/2 CLICK for….... On-set of Longitudinal Relaxation No radiations are present CLICK ! Not stimulated transitions: but spontaneous relaxation transitions No net magnetization CLICK for…. Magnetic field Net magnetization along Z-direction & ZERO XY component +1/2 Degeneracy removed/Energy levels split Thermal equilibrium Boltzmann distribution

  11. Z Pulse applied In XY plane precessing magnetization Y Solenoidal sample coil axis Axis- Y Y Precessing magnetization induces rf voltage: NMR signal X Z When relaxation process is effective, the relaxation leads to the decay of the transverse magnetization of XY plane The above picture is for time scales small compared to relaxation time T2 This decay of magnetization due to the transverse relaxation time is because of the defocusing of the magnetization isochromats in XY plane

  12. Relaxation Longitudinal and transverse Magnetic field I h NET Magnetization Alignment….. Random… CLICK ! Longitudinal T1 Relaxation Transverse T2 Relaxation Randomization in XY plane: Magnetization Decays t A π/2 pulse flips the z-magnetization to xy-plane

  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 November 2009 The Sound Tracks ( playeable audio ) are from the album “ARZOO: Nirvana in six strings” and the Album “Elements: Water” of Shiv Kumar Sharma Video Conversion Using “WONDERSHARE PPT to WMV” Conversion Software

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