NMR-Summary - Zusammenfassung Advanced Methods of NMR Spectroscopy\" (NMR-Spektroskopie in der Organischen Chemie) PDF

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Summary

Summary of Advanced Methods of NMR Spectroscopy

Winter Term 2019/20...

Description

NMR-Zusammenfassung

magnetic dipole moment

 Lamor frequency = frequency of precession:

intrinsic angular momentum

ω 0=γ ∙ B 0 (vgl. Spielzeugkreisel)

Pulse angle

Fourier transformation  converts time-dependent data into frequency dependent data

 dwell time Δt (time resolution) → spectral width

1 ∆t

 acquisition time nΔt (time interval) → digital resolution

1 n∆t

(n: number of points)

Nyquist theorem  NMR signal must be sampled at least twice per wavelength (max. frequency of signal) → falls within spectral width  higher frequencies are folded back → aliased / misidentified as lower frequency 

f s ≥ 2 f max

with f s=

1 dwell time

 Nyquist frequency = maximum resolvable frequency

Main Fourier pairs

Window function artificial periodization of signal within given time window to reduce backfolding, multiplication of signals and “blurs”  increase of intensity: short AQ, low resolution, enhancement of early part of FID → −t

exponential function S= A ∙ e T 2 ∙ e−at  increase of resolution: long AQ, a lot of noise, low intensity, enhancement of later part of FID → Lorentz to Gaussian transformation

−t −at

S= A ∙ e T 2 ∙ e

−b t2

∙e

Truncation  shortened acquisition before the FID is fully decayed, i.e. a partial rectangular function in time domain  causes wiggles in spectrum and shape of signal appears as sinc function

Zerofilling  retain experimental resolution in processed spectra since points are divided to real and imaginary part  no new information added  above experimental points only smoothening of spectra

Relaxation  spin-lattice relaxation (T1): longitudinal relaxation, energetic factor, return to Boltzmann equilibrium, inversion recovery experiment

 spin-spin relaxation (T2): transversal relaxation, entropic factor, loss of coherence going back to zero net transverse magnetization

 T2 determines line width of signal

Increasing S/N ratio of spectra  higher magnetic field

 lower temperature

 higher concentration

 number of scans

Macroscopic excess magnetization  two orientations for spin ½ possible: α and β → slight excess in α state (lower energy)  results in net magnetization along external magnetic field

Rotating frame  frame of reference is not fixed but rotating with its lamor frequency ω  z-axis is parallel to z-axis of laboratory frame and x- and y-axis rotate around z with ω  pulse with frequency ω generates a “static magnetic field” B1 for nucleus with frequency ω...