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.

2. 1. Relaxation Process in NMR : Introduction Pg.No. 2-3
2. Spin-Lattice Relaxation. Pg.No. 4-6
3. Spin-Spin Relaxation. Pg.No. 7-9
4. Signal Splitting: Introduction Pg.No. 10-11
5. Origin of spin-spin Splitting: Spin-Spin Coupling. Pg.No. 12
6. Signal Multiplicity. Pg.No. 13-14
7. References Pg.No. 15
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3. 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.
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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
1. Spin-lattice or Longitudinal Relaxation.
2. Spin- Spin orTransverse Relaxation.
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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)
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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.
WhereT1 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.
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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.
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In solids & viscous liquids relaxation time(T1) ranges in hours.
In organic liquids & dilute solutionsT1 ranges in 0.01- 100 sec.
 At slower relaxation times (greaterT1) signal is sharp
At faster relaxation time (lesserT1) 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.
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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 10−4 𝑠𝑒𝑐𝑠)
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10. Page: 9

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.
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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.
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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.
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15. Page:14

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