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Encyclopedia of Physical Science and Technology EN010C-493 July 19, 2001 20:30

702 Nuclear Magnetic Resonance (NMR)

carcinogenic molecules. The manufacturer can use it to ments of their magnetic moments with respect to the static
study the morphology of polymer blends for constructing magnetic field [i.e., the nuclei develop discrete energies,
more durable battery casings. or states, the energy differences of which are in the radio-
frequency (millions of cycles per second, or megahertz)
I. INTRODUCTION region]. One may relate a frequency ν in cycles per sec-
ond, to an energy difference E by the relation E = hν,
Because some of the terms used to describe the phe- where h is Planck’s constant, h = 6.627 × 10 −27 erg sec.
nomenon of nuclear magnetic resonance are a bit unfa- When such nuclei are exposed to radio-frequency radia-
miliar, a more familiar physical example illustrating these tion at the appropriate resonant driving frequency match-
terms is presented. ing the energy differences of nuclear states in a magnetic
To illustrate the meaning of “resonance,” recall that a field, then in much the same manner that the suspen-
car driven at a certain speed, generally about 80 km/hr, will sion system of a car will efficiently absorb energy from a
sometimes begin to vibrate due to a wheel out of balance. vibrating wheel, the nuclei undergo resonant absorption of
This vibration is an example of the phenomenon of “res- the radio-frequency energy from a driving source, which is
onance.” In a “resonant energy exchange,” at a particular a resonant alternating current circuit of the type used in ra-
driving frequency (in this case the angular frequency of the dio broadcasting. Such excitation disturbs the nuclei from
wheel), a system with a “resonant state” matching the en- their initial equilibrium states in the static field. Changing
ergy of the driving frequency will begin to absorb energy the driving frequency or the external magnetic field will re-
from an external source in a very efficient manner. The move the resonant condition, and the nuclei will cease ab-
system with the resonant state in this case is the spring sorbing energy. Following, and during, a resonant absorp-
suspension system of the car. When the out-of-balance tion of energy, the nuclei can relax from their excited states
wheel, which is vibrating at all speeds, reaches a vibration back to states of energy intermediate between their initial
frequency matching a “resonant frequency” of the car’s states before resonant excitation and their excited states.
suspension system, then there is a “resonant exchange” Two common relaxation processes for nuclei are termed
between the wheel and the remainder of the car, and the “spin–lattice” or longitudinal relaxation, and “spin–spin”
entire car begins to vibrate as the energy in the vibrating or transverse relaxation. In longitudinal relaxation, the nu-
wheel becomes efficiently transferred to the remainder of clei lose their energy to the molecular framework in which
the car. The energy transferred in a resonant exchange can they reside, and relax to their initial state, which may be
be stored, and if not released quickly enough, can serve to thought of as alignment of their magnetic moments along
destroy the system. In a car, that might mean a tire blow- the static magnetic field. In transverse relaxation, the nu-
ing out from repeated resonant bouncing. In a molecule, clei relax to a state in which the net magnetic moment
it could mean thermal decomposition. Alternatively, the perpendicular to the static field is created by many nuclei
system might relax from its high energy state by releasing having their spins pointing “in phase” in the same direc-
energy back to the driving source in an oscillatory fashion, tion in the transverse plane, and the nuclei lose their phase
or by releasing energy to its surroundings in some mono- coherence, and thus their net nuclear magnetism perpen-
tonically decreasing manner, perhaps in an exponentially dicular to the static field. In the simplest cases (e.g., that
dampedfashion.Forexample,theout-of-balancewheelon of nuclei in molecules in many liquids), these relaxation
a car might simply exchange energy with the suspension processes are described by simple exponential forms. The
system of the car and oscillate indefinitely, if the speed of time constant for longitudinal relaxation is designated by
the car is maintained such that resonant exchange can take the symbol T 1 . After a resonant excitation, the recovery
place. Another possibility is that the spring suspension of the nuclear magnetization parallel to the static field is
system of the car, receiving the vibrations of the out-of- proportional to (1 − e −t/T 1 ). Note that this expression is
balance wheel, might eventually be shaken apart and fail. zero at time = t = 0 (i.e., immediately following the exci-
A driver of a car with a wheel badly out of balance might tation), and smoothly reaches unity at times longer than
automatically change the speed of the car to move away 5T 1 . Similarly, the time constant for relaxation of magne-
from the resonant situation, and thus allow the vibration tization transverse to the magnetic field is called T 2 , and
to damp away, or relax, by energy interchange between transverse relaxation is exponential in T 2 .
the suspension system of the car and the surroundings; The phenomenon of nuclei absorbing resonant radio-
the rapid vibration might have heated the springs, and the frequency energy in a static magnetic field is called nu-
heat could have been dissipated in the passing air. clear magnetic resonance (NMR), and this phenomenon is
Nuclei possessing a magnetic moment, and placed in a always accompanied by nuclear relaxation. The details of
static magnetic field of from 5 to 10 T (for comparison, resonant absorption of radio-frequency energy by nuclei
the earth’s field is about .00005 T, or one-half Gauss) may in a magnetic field leads to the “spectrum” of absorption
be thought of as developing discrete, or quantized align- lines, and the relaxation processes are responsible for line