NMR Basics. Lecture 2

Transcription

1 NMR Basics Lecture 2

2 Continuous wave (CW) vs. FT NMR There are two ways of tuning a piano: - key by key and recording each sound (or frequency). - or, kind of brutal, is to hit with a sledgehammer and record all sounds at once. CW Very old. Not used anymore FT Pulsed excitation

3 How to excite a range of frequencies with a single frequency pulse? A conbnuously oscillabng RF- field at frequency ν o i.e. a long pulse (>> 1s) will only excite nuclei with a narrow resonance frequency. A short pulse of radiofrequency (10 μs) covers a frequency range of about 100 khz. ν o

4 Fourier transform: ν o Short squared pulse FT The result is a signal centered at ν o which covers a wide range of frequencies in both directions. FT is a transformation of information in the time domain to the frequency domain (and vice versa). S(ω) = S(t) e - iωt dt -

5 cos(ω*t) FT -ω ω sin(ω*t) FT -ω ω Cosine give absorptive lines, while Sine give dispersive lines. Convert dispersive to absorptive by phasing the spectrum.

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7 Signal Detection An oscillating voltage is recorded as the magnetization vector precesses (rotates) Why is the oscillabon decaying? The Free Induction Decay (FID). Later..

8 How can we tell which frequency is going faster or slower relative to the carrier? The trick is to have 2 receiver coils (with a phase shift of 90 ) of each other. PH = 90 PH = 0 S F S ω (B1) F PH = 0 F S PH = 90 F S The phase of the Faster signals is opposite to that of the Slower signals, and the computer is then able to sort this out.

9 Free Induction Decay (FID) In the rotating frame, the frequency of this precession is ν - ν o. The relaxation of M o in the <xy> plane is exponential. Therefore, the receiver coil detects a decaying cosinusoidal signal (single spin type): ν = ν o M xy time ν - ν o > 0 M xy time

10 Having hundreds or thousands of spin systems, all with frequencies different than that of carrier frequency. Since all spins are excited at once, all of them are detected by the receiver coil at the same time t1 sec

11 Data processing: Window functions Next is digital filtering. As M xy decays, more and more noise is generated. Signal + noise Noise t1 sec Apply a line broadening (LB) factor

12 Sensitivity and resolution enhancement Apply a positive LB factor (e.g., 5 Hz) and see the effect after FT t1 sec LB FT t1 sec f ppm

13 Digital Resolution (DR) Number of Hz per point in the FID for a given spectral width: DR = SW / SI DR - digital resolution (Hz/point) SW - spectral width (Hz) SI - data size (points) For a SW of 5 KHz and an FID of 16K: digital resolution = Hz/point.

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15 Spin Relaxation There are two types of relaxation, and both are time-dependent exponential decay processes: Longitudinal or Spin-Lattice relaxation (T 1 ): - Restoration of magnetization along the z axis (M z ). - Loss of energy in the system to the surroundings (lattice) as heat. - Dipolar coupling to other spins, interaction with paramagnetic particles, etc... z M z y larce x T 1 is a time constant rather than a direct measure of time required for recovery Relaxation rate = 1/T 1

16 The time it takes a particular spin to fully restore the M o status after a 90 pulse ~ 5T 1.

17 How do we record a spectrum? 90 x FID

18 Accumulation of data and saturation saturation: α and β populations are equal and there is xy-magnetization only. No signal will be available after a second pulse. The longer T 1 the more pronounced saturation. 90 x 90 x 90 x FID1 FID2 FID3 Number of scans (ns): FIDs co-added to obtain stronger signal, i.e. better signalto-noise ratio (S/N). S/N = ns FID2, FID3 etc. weaker due to saturation (long T1) and too rapid pulsing.

19 How to cope with saturation: Introduce an extra delay (d1) in addition to the required acquisition time (aq) to allow for complete relaxation (return to equilibrium) before the next pulse. 90 x FID1 d1 ns

20 Transverse or Spin-Spin relaxation (T 2 ) Originates from mainly two sources: 1) Magnetic field inhomogeneity throughout the sample volume which is really an instrumental imperfection (minimized by what we call shimming) 2) From local magnetic fields arising from intermolecular and intramolecular interactions. z y x M xy M x = M y = M o exp( t)/t 2 ) T 1 T 2

21 Local field differences within the sample cause spins to precess with slightly differing frequencies, eventually leading to zero net M xy

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23 Phase detection A necessary transformation of the FID from radio-frequencies (700 MHz for 1 H) down to audio-frequencies that can be handled by the computer and its interfaces. A basic frequency ν o (= B1 s frequency) is subtracted from the nucleus resonance frequencies (ν A ). The new FID shows oscillations at a frequency (ν A ν o ) relative to the basic frequency.

24 Audio Amplifier The NMR-signal received from the resonant circuit in the probehead needs to be amplified to a certain level before it can be handled by the computer. This amplification can be controlled by the Receiver Gain parameter rg.

25 The 2 H field-frequency lock For the NMR nuclei of interest ( 1 H, 13 C etc.): Separating lines less than 0.7 Hz apart by NMR requires a a great fieldstability! This is quite unrealistic for a longer period of time. solution: We use a deuterated solvent and run 2 H NMR continuously in the background to correct the field while it tries to drift slowly away.

26 Field homogeneity, shimming Bad homogeneity affects 1 H, 13 C etc signals as well as the 2 H lock signal. To improve the homogeniety, we adjust the on-axis z, z2, z3, (z4) and off-axis shims: x, y, xy, x2 y2, (xz), (yz). Shimming is automated

27 NMR Instrumentation B o N S Magnet B 1 Frequency Generator Recorder Detector Magnet - Superconducting. Frequency generator - Continuous wave or pulsed. Amplifiers: Amplify the signals Detector - Subtracts the base frequency from the output frequency. It is lower frequency and much easier to deal with. Recorder Computer

28 Sample in Cryoprobe plasorm magnet console probe

29 NMR Magnet