NMR spectroscopy- Spin-lattice & spin-spin relaxation, signal splitting & signal multiplicity.

Spin-lattice & spin-spin relaxation, signal splitting & signal multiplicity concepts briefly explained relevant to Nuclear Magnetic Resonance Spectroscopy.

1. RELAXATION PROCESS: Spin-Lattice Relaxation, Spin-Spin Relaxation. SIGNAL SPLITTING: Spin-spin coupling and Signal Multiplicity. Presented By: Ayesha Nazeer, I MPharm (Dept. of Pharmacology) Srinivas College Of Pharmacy, Mangalore. NMR SPECTROSCOPY

2. Relaxation Process in NMR : Introduction Pg.No . 2-3 Spin-Lattice Relaxation. Pg.No . 4-6 Spin-Spin Relaxation. Pg.No . 7-9 Signal Splitting: Introduction Pg.No . 10-11 Origin of spin-spin Splitting: Spin-Spin Coupling. Pg.No . 12 Signal Multiplicity. Pg.No . 13-14 References Pg.No . 15 Page:1 CONTENTS

3. RELAXATION PROCESS in NMR The net absorption of radiofrequency by the nuclei present in sample only arises because there is an excess of nuclei in the lower energy state compared to the upper energy state at the thermal equilibrium. When suitable radiofrequency is absorbed the nuclei get excited to a upper energy spin state. Input of sufficient radiofrequency causes the populations of lower and upper energy states to be equal. Hence, there will be no further net absorption of energy. When this occurs, the spin system is said to be Saturated. Page:2

4. The Net absorption can only be restored if some of the nuclei in upper state relax back to the lower energy state. i.e., To avoid saturation, Rate of relaxation of excited nuclei to lower energy ≥ Rate of absorption of radiofrequency by lower energy. In NMR, Nonradiative Relaxation process is seen (i.e., no emission of radiation such as fluorescence) Optimal half-life of excited species range from 0.1 to 10 secs. TYPES OF RELAXATION PROCESS IN NMR SPECTROSCOPY Spin-lattice or Longitudinal Relaxation. Spin- Spin or Transverse Relaxation. Page: 3

5. The absorbing nuclei in an NMR experiment are part of the larger collection of atoms that constitute the sample. The entire collection is termed the Lattice , regardless of whether the sample is solid, liquid or gas. Particularly, in the latter two states the various other nuclei(atoms) comprising the lattice are in violent vibrational or rotational motions. Takes place in the z-direction.(longitudinal direction) Page:4 SPIN-LATTICE RELAXATION

6. THE PROCESS: The Brownian motion of these components gives rise to magnetic fields that have fluctuations whose frequency is equal to the precession frequency of the nuclei to be relaxed. This induces transitions in spin such that the nuclei lose magnetic energy as thermal energy to the lattice which produces a miniscule temperature rise in sample. Hence returning from high to low energy state. Spin lattice relaxation is a first order exponential decay . Where T1 is the Relaxation time, which is also a measure of average lifetime of nuclei in higher energy state. T1 is strongly influenced by the mobility of the lattice.  In crystalline solids or viscous liquids mobilities are low and T1 is large. Page:5

7. As mobility increases Vibrational & rotational frequency of neighbouring nuclei Increases Brownian motion interaction increases Probability of magnetic fluctuation to be of proper magnitude for a relaxation transition is enhanced T1 decreases. Page:6 In solids & viscous liquids relaxation time(T1) ranges in hours. In organic liquids & dilute solutions T1 ranges in 0.01- 100 sec.  At slower relaxation times (greater T1) signal is sharp  At faster relaxation time (lesser T1) spectral line broadening gives decreased resolution of spectral peaks.  Line width of NMR inversely proportional to relaxation time SIGNIFICANCE :

8. A nucleus in the higher energy state transfers its energy to the nucleus in the lower energy state.  Relaxation in x-y plane ( transverse direction) Randomization of spins takes place. (in different direction) THE PROCESS: When two neighbouring nuclei of same kind have identical precession rates, but are in different magnetic quantum states( i.e., Higher & lower energy states), The magnetic fields of each interact to cause an interchange of states. Therefore, a nucleus in the lower spin state is excited and the excited nucleus relaxes to the lower energy state. No net change in the relative spin-state population. Average lifetime of a particular excited nucleus is shortened. Page:7 SPIN-SPIN RELAXATION

9. SIGNIFICANCE As per Heisenberg’s Uncertainty Principle, If the lifetime of an energy state is very short then the uncertainty in its energy is very large. Uncertainties in the energy of the higher energy state in NMR Spectroscopy contribute to the linewidth of the peaks observed. If the uncertainty is large then the peaks will be broad. Hence by spin-spin relaxation line broadening of NMR Spectroscopy peak is the result. T2 is the spin-spin relaxation time. Values of T2 are generally small for crystalline solids or viscous liquids. ( as low as   Page:8

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11. The interaction between the spins of neighbouring nuclei in a molecule may cause the splitting of the signal lines in NMR spectrum. This is known as spin-spin coupling . The actual NMR spectra of most of the compounds are much more complicated than expected. Due to signal splitting led by spin-spin coupling. Page:10 SIGNAL SPLITTING

12. For example: consider 1,1,2-Tribromoethane. Similar phenomena is observed in case of other molecules. This means that the individual signal which we expect from a set of equivalent protons must be appearing not as a single peak but as a group of peaks. This is called splitting of NMR signals. Page:11

13. HOW DOES IT OCCUR? The magnetic field created by a spinning nucleus effect the distribution of electrons in its bonds to the other nuclei. This change in electron distribution produces changes in the magnetic field of adjacent nuclei and causes splitting of energy levels & hence multiple transitions. This magnetic coupling of nuclei transmitted by bonding electrons is often referred to as polarization interaction. Thus it is the spin-spin coupling of absorbing and neighbouring protons causing splitting of signals. Page:12 ORIGIN OF SPIN-SPIN SPLITTING: SPIN- SPIN COUPLING

14. The degree of splitting of the signal from any given nucleus is called Multiplicity. The multiplicity depends on the no. of other nuclei to which the given nucleus is coupled. Signal multiplicity pattern are, singlet, doublet, triplet, quartet, pentet , sextet, septet commonly called as multiplet . depicted by following figure , For a nuclei having a nuclear spin quantum number of 1/2 , the number of peaks ‘p’ observed is p=n+1 where n is the no. of equivalent hydrogen atom attached to an adjacent carbon atom. Page:13 SIGNAL MULTIPLICITY

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16. 1. J MENDHAM, R C DENNEY, J D BARNES, M J K THOMAS. VOGEL’S: Textbook of Quantitative Chemical Analysis, 6 th Edition(low price edition), Pearson Education. ( page no. 573) 2. J MENDHAM, R C DENNEY, J D BARNES, M THOMAS, B SIVASANKAR. VOGEL’S: Textbook of Quantitative Chemical Analysis, 6 th Edition, Pearson.(page no. 553-554) 3. SKOOG, HOLLER, CROUCH, Instrumental Analysis, India Edition, Clengage Learning. ( page no. 557,558,566) 4. GURDEEP R. CHATWAL, SHAM K. ANAND, Instrumental Methods of Chemical Analysis, Himalaya Publishing House. (page no.2.198) 5. WILLARD MERRITT, DEAN SETTLE. Instrumental Methods Of Analysis, 7 th Edition. (page no. 426, 427) 6. ROBERT D. BRAUN. Introduction to Instrumental Analysis, PharmaMed press. (Page no. 471, 482) Page:15 REFERENCES