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 File-12 1hr_lecture; PULSED NMR http://ugc-inno-nehu.com/links_from_web.html 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan

'PULSED NMR' by Dr.S.Aravamudhan External Magnetic Field Rotating x,y axes :rotation about Lab z-axis Z X Y Viewed from within the rotating frame the RF field appears stationary A BLUE line for z-Axis indicates the view from within the rotating coordinate system. Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. Magnetization X Y Z After the pulse: at t>0 Chemical substance Spin ensemble X Y Z Y Induced NMR signal at receiver (RF 300 MHz ) Apply the 90º, -X pulse now, P-Xπ/2 P-Xπ/2 At t =0, the end of pulse Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame Z No more CLICKs. This show has automatic timings from this stage. X Y X Y Z X Y A depiction of the Induced RF signal Characteristics would appear……… A rotating RF magnetic field results on application of RF at resonance frequency Phase Sensitive detector Reference in phase at NMR (300MHz) frequency Output (‘0’ freq) Free Induction NMR Signal x,y-axes Rotating about Lab Z-axis; frequemcy same as the precession frequency The rotating magnetic field tilts the magentization away from z-axis by 90º for a π/2 pulse X Y Z X Y D.C. Reference in phase; offset from NMR frequency (300±0.003 MHz) Phase Sensitive detector Output at offset frequency (audio range) ~3KHz Rotating system viewed from within that system: STATIONARY Transverse Relaxation and magnetization decay in XY plane is not depicted. CLICK toTransit. Right CLICK mouse And CLICK on option “PREVIOUS” OR…………. NO F.I.D. yet! 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan

'PULSED NMR' by Dr.S.Aravamudhan External Magnetic Field Sample: Ensemble of spins Magnetization Magnetization Magnetization I0 It T1 CLICK ! t It Magnetization Builds up exponentially (1-e-t/ ) T1 I0 = It Z X Y To repeat the above events: Right Click & Select option ‘previous” When the magnetic field is turned on, the spins align at the characteristic longitudinal relaxation time T1 Initially, before the external magnetization is applied, the spins are randomly oriented On the application of field….. CLICK ! Splitting is instantaneous & population redistribution requires more time called the relaxation time CLICK for….... On-set of Longitudinal Relaxation -1/2 No radiations are present CLICK ! -1/2 +1/2 Not stimulated transitions: but spontaneous relaxation transitions No net magnetization CLICK for…. random Magnetic field Net magnetization along Z-direction & ZERO XY component +1/2 Degeneracy removed/Energy levels split Thermal equilibrium Boltzmann distribution 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan

'PULSED NMR' by Dr.S.Aravamudhan In terms of Angular momenta, Iz replaces ‘z’; for rotation about z-axis= e-iφ Iz 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 Iz 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 Viewed from within the rotating frame the RF field appears stationary RF field is along –X in the XY plane, the effect caused would be rotation about X-axis, unlike the precession about z-axis X Y Z An equation representing this rotation would be displayed Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK! CLICK ! CLICK ! Z CLICK ! Click to end this slide To repeat the animated RF depictions “right click” and choose option: ‘previous’ X Y X Y 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 impulse on… The impulse off… CLICK ! X Y H1 e-iI-xωt 2 H1 I-x cos(ωt) = + 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 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 ! 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan http://www.geocities.com/sankarampadi/eulexp.html

The F.I.D. No More Clicks ! This show has automatic timings Viewed from within the rotating frame the RF field appears stationary A BLUE line for z-Axis indicates the view from within the rotating coordinate system. Rotating x,y axes :rotation about Lab z-axis No More Clicks ! This show has automatic timings Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. X Y Z X Y 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 At the end of pulse, time for F.I.D. begins with t=0 Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame Described in rotating frame: Rotation about the X-axis I(tp) =e-iI-xφ Iz e+iI-xφ with φ=90º & tp is pulse duration X Y Z When the XY magnetization decays 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 300 MHz ) Induced NMR signal at receiver (RF 300 MHz ) When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 300 MHz ) CLICK to Transit tp t=0 Acquisition time ~5T2 FID Free Induction Decay Signal 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan

'PULSED NMR' by Dr.S.Aravamudhan 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 5/4/2019 1:03:21 AM 'PULSED NMR' by Dr.S.Aravamudhan