1. Determination of Spin-Lattice Relaxation Time using 13C NMR
CHEM 146_Experiment #4
Determination of Spin-Lattice Relaxation Time using 13C NMR
Yat Li
Department of Chemistry & Biochemistry
University of California, Santa Cruz

2. Objective In this laboratory experiment, we will learn:
The basic theory of Nuclear Magnetic Resonance (NMR) and pulse NMR spectroscopy
How to use inversion-recovery technique to determine relaxation time (T1) of carbon atoms in an aliphatic alcohol

3. Nuclear magnetic resonance (NMR)
Absorption spectroscopy: radio-frequency region 3 MHz to MHz
Transition between magnetic energy levels of the nuclei
Atomic nuclei possess spin (angular momentum, with half integer spin number)

4. Basic theory of NMR
Spinning nuclei behave like a tiny bar magnet with a magnetic moment m
In an external magnetic field (B0), the magnetic moment of nuclei may assume any one of the 2I + 1 orientations with respect to the direction of the B0

5. Basic theory of NMR
The energy difference DE has shown to be a function of the B0, and can be quantify by this equation
DE = hn = hgB0/2p
(g = 2pm/hI)
The precessional frequency of spinning nucleus is exactly equal to the frequency of EM radiation necessary to induce a transition from one nuclear spin state to another
n = gB0/2p

6. Basic theory of NMR
The population differences between these energy states, the differences at equilibrium being defined by the Boltzmann equation. Na Nb
= eDE/RT
Na & Nb : population of a and b spin states
Probability of observing absorption of energy is quite small
Larger B0 (large DE) and lower T lead to higher sensitivity

7. Chemical shift Circulating electron cloud:
d = （n – nref ）/ nref
d (ppm) =
chemical shift (Hz)
oscillator frequency (Hz)
x 106
Circulating electron cloud:
Shield or deshield applied field
Resonance at different frequencies
Differences in the chemical environment modify the electron density and distribution about nuclei

8. NMR spectrum Chemical shift: chemical environment
Coupling: how nuclei interact with each other
Intensity: number of nuclei

9. Pulse NMR_vector model
According to Boltzmann distribution there is a slightly excess of a-spin state, which results in a net magnetization vector M, along the +z axis (which is defined as being parallel to B0)
Apply a second magnetic field (B1) associated with the radiofrequency radiation of the transmitter pulse

10. Pulse NMR_data acquisition
A pulse which places M to exactly in the x-y plane. Any magnetization that is in the x-y plane will be rotating at its Larmor frequency and induce an oscillating voltage in the coil

11. Determination of spin-lattice relaxation (T1)
Design of pulse NMR experiment:
Pulse sequence: delay (D1) - 180° pulse - delay τ (D7) - 90° pulse - acquisition (FID).

12. Determination of spin-lattice relaxation (T1)
The evolution of the longitudinal (Z) component of nuclear magnetization towards equilibrium with the lattice is exponential in time with the time constant T1:
dMz dt =
-(Mz- M0) T1
Mz = M0 (1 - 2e-t /T1)
13C NMR T1 spectrum: