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-1 FT NMR-1D http://ugc-inno-nehu.com/links_from_web.html 2/25/2019 1:22:42 AM Dr.Aravamudhan

A single pulse experiment for obtaining one dimension NMR spectrum is illustrated in the next slide. Signal acquisition following the pulse, and processing the acquired FID are illustrated schematically. pulse FID Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

Frequency Domain Spectrum This FID acquisition and the variations are considered in detail in the following slides 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 Computer memory Address Contents 1 0000 15 1111 2 0001 14 1110 3 0010 13 1101 4 0011 11 1011 5 0100 8 1000 6 0101 4 0100 7 0110 1 0001 0111 0000 --------- Next Slide Time domain 15 11 DIGITIZE Analogue to Digital Converter A.D.C. F.I.D. Frequency Domain Spectrum Computer output FFT from FID Computer input This one-dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

The FID can be described as a mathematical function of time The FID can be described as a mathematical function of time. This function can be obtained by multiplying a sinusoidal function with an exponential function. The sinusoidal (cosine/sine or a mixture of cos and sin) is characterized by a frequency and phase. The exponential function has a characteristic decay time constant. t Cosine form at angular frequency ω tc Exponentially decaying form with decay time constant = tc Further illustrations relevant for FID wave forms are described in the next slides. Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

t ω = 2 π ν Fourier Transform The time domain signal forms ω ω ω ω ω ω Real Part Imaginary part ω t ω Cosine form at angular frequency ω Corresponding Exponentially Decaying function ω ω The sine function ω ω ω = 2 π ν Click to transit ν is in cycles per second ω is in radians per second 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

Arbitrary Phase with sine and cosine PURE Cosine Arbitrary Phase with sine and cosine Mostly a negative of cosine Negative cosine and negative sine Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

t AUDIO SIGNAL (FID) FROM PSD IS ANALOGUE SIGNAL WHICH IS DIGITIZED +4 8 8 +4 16 6 24 +2 29 33 4 35 2 31 -2 27 20 -3 1 12 4 t 4 8 12 16 20 24 27 29 31 33 35 Each one of the time interval of duration specified within the line with double ended arrow is the digitizer time [per[point, i.e., the Dwell Time DW. 35 values are recorded in 35 DW For DW=5 μs with 36 data points (0,1…35) Acquisition time = 36x5= 180 μs Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

The FID2 is acquired after a delay one DW more compared to the FID1 Aquisition Time domain 15 12 14 13 11 10 8 Pulse This delay (after the first pulse/first scan) is called the receiver dead time. This is requirement due to response characteristics of the electronic system. This first FID acquisition can be repeated without any necessities of alterations in delay times. This is typically the single pulse experiment repeated for summing the FIDs to improve signal to noise ratio. FID 1 Receiver dead time/Acquisition delay The FID2 signal from probe is the same. But, the signal received is acquired after a larger delay than for FID1 Time domain 12 14 13 11 10 8 Aquisition FID 2 Pulse The delays of the type in FID2 are set by the experimenter to realize sequences of pulses for the case of multiple-pulse –sequence at the end of which the FID is ACQUIRED. These class of experiments dominate the advanced NMR techniques. The time interval between the dotted (digitized) points is the DWELL (DW) time of the digitizer. The FID2 is acquired after a delay one DW more compared to the FID1 Click to transit 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

Apply Pulse Acquisition of FID is started by sending a trigger pulse to the A to D converter/digitizer It is possible to increment the delay, and acquire the FID at different phases. Time domain 15 9 12 14 13 11 10 8 different phases Trigger to ADC cos Start acquisition after a delay D1 Time domain 9 12 11 10 8 Acquisition delay D1 Trigger to ADC -sin Trigger to ADC -cos Click to transit Note D2 > D1 How will be the Fourier transformed frequency domain spectrum of these three time domain signals with different phases? Start acquisition after a delay D2 Acquisition delay D2 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP

t=0 +1 COS SIN Click to transit Value between +1 & 0 Provision is made in the data processing system, for routinely applying phase corrections COS Real Imaginary F.T Real Imaginary F.T SIN Real Imaginary F.T Arbitrary Phase Click to transit fc cos(2πνt) + fs sin (2πνt) with fc2 +fs2 =1 12/31/2010 9:16:32 AM SAIF FT NMR WORKSHOP