COURSE 146C Laboratory Experiment 4 Determination of Spin Lattice Relaxation Time using 13C NMR Please read the lab procedure before your experiment References 1 Yadav L D S Organic Spectrscopy Anamaya Publishers New Delhi 2005 2 Harwood L M and Claridge T D Introduction to Organic Spectroscopy Oxford Science Publications 1997 3 Gasyna Z L and Jurkiewicz A Determination of spin lattice relaxation time using 13 C NMR J Chem Educ 81 1038 1039 2004 4 Lorigan G A Minto R E and Zhang W Teaching the fundamentals of pulsed NMR spectroscopy in an undergraduate physical chemistry laboratory J Chem Educ 78 956 958 2001 1 Experiment 4 Determination of Spin Lattice Relaxation Time using 13C NMR I Introduction Nuclear magnetic resonance NMR spectroscopy is one the most powerful and versatile of all analytical techniques used routinely by organic chemists This technique provides very detailed information on the chemical environment of individual atoms within a molecule which is difficult for other spectroscopy techniques such as UV vis or Infrared spectroscopy In addition the power of modern pulse Fourier transform NMR makes available to us a variety of techniques to interpret the spectra in the subsequent determination of structures and allows the routine observation of nuclei other than protons In this experiment we will learn the basic theory of pulsed NMR spectroscopy and how to use inversion recovery technique to determine relaxation time of carbon atoms in an aliphatic alcohol II Physical Background of NMR The phenomenon of NMR occurs because the nuclei of certain atom posses spin The spin is characterized by the nuclei spin quantum number I which may take integer and halfinteger values depending on the mass number and atomic number of the atom as shown in Table 1 Nuclei with zero spin I 0 are not amenable to NMR observation From the chemist s point of view it is generally the nuclei that have I 1 2 that are of most interest e g 1H and 13C Table 1 Spin number of some isotopes 1 All nuclei have charge and therefore they have angular momentum when they spin The spinning charge nuclei posses a magnetic moment indeed the nuclei can be considered as a small bar magnet When these nuclei are placed in an external magnetic field B0 their magnetic moment may assume any one of the 2I 1 orientations with respect to the direction of the B0 Number of orientations for nuclei with I 1 2 they have two orientations which is aligned parallel spin state or anti parallel spin state to the B0 Figure 1 2 Figure 1 Orientation of nuclear magnetic dipoles in an external magnetic field B0 1 The energy difference E has shown to be a function of the B0 and can be quantify by this equation E h h B0 2 2 B0 hI B B If the axis of the nuclear magnet is not oriented exactly parallel or anti parallel to B0 they experience a torque which forces them into precession about the axis of the external field This motion is referred to as Larmor precession and it occurs at the Larmor frequency which is directly proportional to the strength of applied magnetic field The Larmor frequency is given by B0 2 B And it is exactly equal to the frequency of electromagnetic radiation necessary to induce a transition from one nuclear spin state to another The energy required for resonance depends on B0 and on the nuclei brought into resonance These frequencies are in the radio frequency region of the electromagnetic spectrum Most commonly the radiofrequency is kept constant and B0 is scanned Pulse Fourier Transform Approach It has been developed since early 1980s is the possibility of using more than one pulse prior to the data acquisition allowing one to control the behavior of nuclear spins and hence the information presented in the resulting spectra In this experiment we will use multi pulse experiment to study the longitudinal relaxation behavior of individual atoms in a sample A vector model of NMR will be used to explain the experiment According to Boltzmann distribution there is a slightly excess of spin state which results in a net magnetization vector M along the z axis which is defined as being parallel to B0 Consider we apply a second magnetic field B1 associated with the radiofrequency radiation of the transmitter pulse The B1 field is perpendicular to B0 static field Under the influence of the B1 field the longitudinal magnetization is rotated toward the x y plane by an amount dependent on the strength of the field and the duration of the pulse to produce transverse magnetization as shown in Figure 2 A pulse which places M to exactly in the x y plane is corresponding to equalizing the populations of the and spin states Any magnetization that is in the x y plane will be rotating at its Larmor frequency and induce an oscillating voltage in the coil Magnetization will not continue in the x y plane and return to the z axis by losing its excess energy relaxation Therefore the oscillating voltage will decay away with time producing the free induction decay Figure 3 that may be 3 Fourier transformed to produce the frequency spectrum For nuclei with half integer spin number the return of z magnetization follows a first order recovery characterized by the time constant T1 Transverse magnetization produced by a 90 degree pulse requires a period of approximately 5 T1 to relax back to its equilibrium state Figure 2 Magnetization is rotated through an angle which is dependent on the magnitude of B1 and the duration of the pulse Figure 3 Magnetization will precess in the x y plane but also return to the Z axis through relaxation and this process will induce a decaying oscillating voltage in the coil that is the FID In this experiment you will conduct pulse NMR studies on an aliphatic alcohol and analyze the spectra to determine the T1 for each carbon atoms in the alcohol The spin lattice relaxation can be expressed by Bloch equation in which it is assumed that the evolution of the longitudinal component of nuclear magnetization towards equilibrium with the lattice is exponential in time with the time constant T1 dMz d Mz M0 T1 where Mz is the Z component of magnetization at time and M0 is the Z component of the magnetization at thermal equilibrium Integration of the Bloch equation gives Mz M0 1 2e T1 A series of Mz values can be obtained by varying the delay time between the 180 and 90 pulses The recovery is observed as an exponential decay when Mz is plotted versus From the curve one can determine T1 4 Procedure 1 The sample for the NMR