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Keywords
(16)
Absorption Line
Degree of Freedom
Direct Method
Finite Temperature
Local Field
Magnetic Field
Magnetic Moment
Magnetic Resonance
Nuclear Magnetic Resonance
radiofrequency
Relaxation Time
Spectrum
Spin System
Strong Magnetic Field
brownian motion
Low Frequency
Related Publications
(1)
Principles of Nuclear Magnetism
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Relaxation Effects in Nuclear Magnetic Resonance Absorption
Relaxation Effects in Nuclear Magnetic Resonance Absorption,10.1103/PhysRev.73.679,Physical Review,Nicolaas Bloembergen,E. M. Purcell,R. V. Pound
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Relaxation Effects in Nuclear Magnetic Resonance Absorption
(
Citations: 504
)
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Nicolaas Bloembergen
,
E. M. Purcell
,
R. V. Pound
The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the "lattice") of the substance containing the magnetic nuclei, serves to bring the
spin system
into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied
radiofrequency
field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this "saturation" effect, and in some cases by a more direct method, the spinlattice
relaxation time
T1 can be measured. The interaction among the magnetic nuclei, with which a characteristic time T2' is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen.
Magnetic resonance
absorption is observed by means of a
radiofrequency
bridge; the
magnetic field
at the sample is modulated at a low frequency. A detailed analysis of the method by which T1 is derived from saturation experiments is given. Relaxation times observed range from 104 to 102 seconds. In liquids T1 ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spinspin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton
relaxation time
and line width has been investigated. The
relaxation time
and line width in ice have been measured at various temperatures. The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spinspin interaction. The local
magnetic field
produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a
spectrum
extending to frequencies of the order of 1tauc, where tauc is a correlation time associated with the local
Brownian motion
and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency omega is much less than 1tauc, the perturbations caused by the
local field
nearly average out, T1 is inversely proportional to tauc, and the width of the resonance line, in frequency, is about 1T1. A similar situation is found in hydrogen gas where tauc is the time between collisions. In very viscous liquids and in some solids where omegatauc>1, a quite different behavior is predicted, and observed. Values of tauc for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data. Formulas useful in estimating the detectability of
magnetic resonance
absorption in various cases are derived in the appendix.
Journal:
Physical Review  PHYS REV X
, vol. 73, no. 7, pp. 679712, 1948
DOI:
10.1103/PhysRev.73.679
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Citation Context
(40)
...The relaxation rate contribution due to these reorientations is given by the wellknown BPP expression
21
, which depends on a correlation time
τ
_{R}
and a prefactor
A
_{R}
...
M. Rajeswari
,
et al.
Slow molecular processes in a nematic liquid crystal confined to rando...
...Data are in qualitative agreement with literature (when available) taking into account that they are B0 dependent [
7
,8]...
A. Galante
,
et al.
Mobile NMR for surface analysis
...According to the BPP (Bloembergen, Purcell, and Pound) theory, the relationship between
T
_{1}
and
τ
_{c}
is described as where
γ
_{C}
is the magnetogyric ratio of
^{13}
C,
γ
_{H}
is the magnetogyric ratio of
^{1}
H,
ω
_{C}
is the resonance frequency of
^{13}
C,
ω
_{H}
is the resonance frequency of
^{1}
H,
r
is the
^{1}
H
^{13}
C bond distance,
τ
_{c}
is the correlation time of motion, and
h
is the Planck constant [
15
,
29
,
30
]...
KenIchiro Komiya
,
et al.
Molecular Dynamics in Smectic and Crystalline Phases Studied by CNMR ...
...With allowance for Eq. (2), within the framework of the standard Bloembergen–Pursell–Pound (BPP) model [
28
], the graph of the dependence of on T –1 must be linear in the limits of both slow and fast motion, and its slope must be equal to –E a /k B and +Ea/kB , respectively...
...where R1d(Ea) is the value of the dipole contribution obtained from the standard BPP formulas [
28
] and Eq. (2) at a fixed value of E a . For the parametrization of experimental data, we assume that both peaks in (3) are Gaussian functions...
A. V. Soloninin
,
et al.
Effect of mechanical milling on the mobility of hydrogen in the ZrTi 2...
...The need to determine experimentally the relaxation times stems from the fact that no theory can satisfactorily predict, from a quantitative point of view, the values of tissues’ water proton relaxation times, despite the fact that, in pure liquids, successful relaxation theories were developed decades ago[8,
9
]...
Yuhua Peng
,
et al.
Noninvasive Temperature Measurement Using MRI Based on T2 Relaxation T...
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M. Rajeswari
,
S. Dhara
,
K. Venu
,
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Journal:
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Joseph D. Fenstermacher
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James R. Ewing
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, vol. 54, pp. S176S179, 2011
Mobile NMR for surface analysis
A. Galante
,
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O. Losito
,
M. Alecci
,
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,
P. De Maio
,
A. Incampo
,
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,
A. Sotgiu
Conference:
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, 2011
Fast measurements of average flow velocity by LowField 1H NMR
T. M. Osán
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,
M. Carpinella
,
L. M. C. Cerioni
,
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,
M. Appel
,
J. Freeman
,
I. Espejo
Journal:
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, vol. 209, no. 2, pp. 116122, 2011
Association of − 762C/T P2X7 receptor gene polymorphism with susceptibility to tuberculosis in Zahedan, southeast Iran
Gholamreza Bahari
,
Abdolkarim MoazeniRoodi
,
Mohammad Naderi
,
Mohammad Hashemi
Journal:
Clinical Biochemistry  CLIN BIOCHEM
, vol. 44, no. 13, pp. S306S306, 2011